Vector-Field Nonlinear Microscopy of Nanostructures - ACS Photonics

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Review

Vector-field nonlinear microscopy of nanostructures Godofredo Bautista, and Martti Kauranen ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00052 • Publication Date (Web): 25 Jul 2016 Downloaded from http://pubs.acs.org on July 26, 2016

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Vector-field nonlinear microscopy of nanostructures Godofredo Bautista and Martti Kauranen Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland Keywords Nonlinear optics, microscopy, tight focusing, polarization, nanostructures Abstract Microscopic techniques based on nonlinear optical processes provide alternative ways to visualize natural and artificial nanoscopic systems with minimum disturbance. In such techniques, each nonlinear process provides its own contrast mechanism and thus sensitivity to different sample properties. Powered by the mutual developments in instrumentation and theoretical descriptions, the capabilities of nonlinear microscopy have significantly increased in the past two decades. In addition, the vectorial focusing properties of conventional (for example, linear and circular) and unconventional (for example, radial and azimuthal) light polarizations are providing new capabilities for nonlinear microscopy, while simultaneously requiring new approaches in the interpretation of the acquired data. In this review article, we discuss the principles of nonlinear microscopy with vector fields and how its unique properties have recently been put to use in the imaging and characterization of various types of nanostructures. Nonlinear microscopy embraces the art and science of all imaging techniques that rely on nonlinear optical effects as the primary source of contrast. Here, the high field strength at the focus of a laser beam is exploited to give rise to nonlinear effects such as two-photon-excited

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luminescence (TPEL)1 and fluorescence (TPEF),2 second-harmonic generation (SHG),3 thirdharmonic generation (THG),4,5 and coherent anti-Stokes Raman scattering (CARS).5 These processes can be associated with different contrast mechanisms, each of them thereby providing complementary information about the sample. From the conception of nonlinear signal detection and point-scanning instrumentation,6–8 nonlinear microscopy has thus matured into a powerful imaging technique for the characterization of individual subwavelength objects of varied properties. To date, these possibilities have been attested by the vast and continuously growing number of publications about nonlinear microscopy for basic and applied research. Due to the availability of commercial fluorophores (molecules that fluoresce),9–11 TPEF is the most widely used imaging contrast for nonlinear microscopy.12 This phenomenon is based on the theory of two-photon quantum transitions by Göppert-Mayer in 193113 but was experimentally observed only after the invention of the laser.2,14 Here, a fluorophore in the electronic ground state absorbs simultaneously two incident photons in order to access an electronic excited state. After vibrational relaxation, the fluorophore emits a single-photon with energy that is higher than either of the incident photons. Since the efficiency of absorption here depends quadratically on the excitation intensity, the fluorescence is always localized at the focus of the excitation beam providing images with high contrast. This intrinsic feature is the basis of the technique’s three-dimensional optical sectioning capability that can traditionally be achieved only with a confocal detection pinhole.15 Similarly, three-photon-excited fluorescence16 has been shown to be a powerful imaging contrast provided that there is a suitable laser source and satisfactory intensity at the focus of the microscope objective.17–22 It is therefore evident that, fluorescence microscopy has benefitted significantly from the use of nonlinear excitation.23–25 However, similar to single-photon fluorescence, these nonlinear


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fluorescence techniques have potential problems because they rely on molecular tagging. Aside from the issues of bleaching and toxicity, large-sized fluorophores and similar fluorescent agents disturb the natural state of small molecules inside living cells. To reduce the detrimental effects of labelling, techniques26–28 to control the delivery and detection of light in a fluorescence microscope and strategies29 to target small molecules are continuously being developed. These challenges have also been facilitated by the use of autofluorescent probes.30 Nevertheless, the development of other high-contrast microscopy techniques is crucial to characterize untreated non-fluorescent samples. In this context, the coherent nonlinear processes of SHG, THG, and CARS have become important. The nonlinear optical processes are described by the respective nonlinear susceptibility tensors. The tensors are determined by the structural properties of the sample and give rise to polarization-dependent nonlinear responses. A simple yet very effective strategy to enhance the capability of nonlinear microscopy is therefore to harness the vectorial properties of the focused excitation beams. It is now well-known that strong focusing of a linearly-polarized Gaussian beam gives rise to three-dimensional vector fields in the focal volume of the microscope objective.31 Such vector fields are expected to strongly influence the nonlinear signal generation from a variety of materials. Beyond the use of conventional linear and circular polarizations, beams with spatially varying, i.e., transversely non-uniform, or engineered states of polarization, are now being utilized in nonlinear microscopy. Such advances are expected to expand the capabilities and enhance the sensitivity of nonlinear microscopes as well as other optical systems, in general. In this Review, we discuss and highlight the emerging capabilities that are provided by vector fields in advancing nonlinear microscopy. We first examine the fundamentals of polarized


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beams under tight focusing conditions and discuss their implications for imaging. We first consider the focusing properties of conventional polarizations such as linear and circular. Next, we discuss the focusing properties of cylindrical vector beams (CVB) with radial and azimuthal polarization distributions. We then revisit the fundamentals of the most common nonlinear effects such as SHG, THG, CARS, TPEF and TPEL and their imaging properties for far-field detection. We then give examples of the emerging nonlinear microscopy techniques that utilize vector fields in addressing general and specific problems for a variety of applications. Finally, we close the Review by providing a discussion and outlook. For details, the reader is advised to follow the key references provided. Due to the broad scope of this Review, it is necessary to limit the number of topics covered. For example, we will not discuss the applications of vector fields in linear microscopic techniques.32–34 Also, we will not discuss in-depth near-field effects35–37 nor the nanofocusing of light using nanostructures.38–44 Even though optical vortices with phase singularities,45 wavefront shaping,46–48 femtosecond pulse shaping,49–54 stimulated Raman scattering (SRS)55–57 and their applications to imaging are somewhat related, these topics are also beyond the scope of this review. Finally, the discussions of nonlinear microscopy in the context of instrumentation and optimization are also excluded.24,25,58–63 For these and related topics, the reader is referred to the above references.

Tight focusing of vector beams In microscopy, the spatial resolution is critical because it determines the level of detail that can be achieved in sample characterization. To achieve high spatial resolution, microscope objectives with high numerical aperture (NA) are utilized. Under such tight focusing conditions, the light


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emerging from the objective contains wave-vector components that are highly tilted with respect to the original direction of propagation, as can be pictured by simple ray tracing. In such cases, scalar diffraction theory is not anymore sufficient to predict the light distribution at the beam focus even for the case of unpolarized light.64 This issue is significant in the interpretation of many fundamental light-matter interactions, which may depend on the detailed properties of the optical fields. Richards and Wolf were the first to take these issues into account by developing vectorial diffraction theory based on angular spectrum approach.31 This elegant theoretical description allowed the calculation of the three-dimensional distribution of vectorial electromagnetic fields at the focal region of lenses. Conventional polarizations It is quite common to perform microscopy by using a beam that exhibits either linear or circular polarization before focusing (Figure 1a). Such beams exhibit states of polarization that are spatially uniform across the beam and we will refer to such cases as conventional polarizations. Let us now revisit the case of a monochromatic linearly-polarized (along x) beam that propagates along the z-axis and is incident on an aplanatic (free from spherical aberration) lens with focal length f (Figure 1b).31,65 It is also assumed that the incident field is a fundamental Gaussian beam [more precisely, Hermite-Gaussian beam of order (0,0) (HG00)] with waist w0 before the lens and the environment is air. After the focusing lens, the distribution of wave vectors is characterized by angle θ, which has a maximum related to the NA of the lens given by NA = n sin θmax where n is the refractive index of the surrounding environment. The focal electric fields are then:31,65

 I 00 + I 02 cos2φ  ikf x E00 ( r ) = E0e−ikf  I 02 sin 2φ  , 2  −2iI 01 cos φ 

(1)


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where the superscript x refers to the incident linear polarization and the column vector represents the x, y, and z components of the electric field at the beam focus. Similarly, the forms of the focal electric fields for x-polarized higher-order HG01 and HG10 beams are:65

i ( I11 + 2 I12 ) sin φ + iI14 sin 3φ  ikf 2  − ikf  E (r ) = E0e  −iI12 cos φ − iI14 cos3φ  2w0   2 I13 sin 2φ

(2)

 iI11 cos φ + iI14 cos3φ  ikf 2 − ikf  E (r ) = E0e −iI12 sin φ + iI14 sin 3φ    2 w0  −2 I10 + 2 I13 cos 2φ 

(3)

x 01

x 10

In equations (1-3), E0 is the electric field amplitude of the incident beam, k is the magnitude of the wave-vector and φ is the azimuthal angle with respect to the axis of beam propagation. The spatial dependence on r is implicit in Imn’s, which are one-dimensional integrals over the aperture of the focusing lens, i.e., with respect to the polar angle θ, generally formulated as (Figure 1b):31,66

I mn = ∫

θmax

0

1

f w (θ )( cos θ ) 2 g mn (θ ) J l ( k ρ sin θ ) eikz cosθ sin θ dθ

(4)

where f w (θ ) is known as the apodization function of the aperture and ρ = ( x 2 + y 2 ) 2 . In 1

equation (4), the Jl’s, which are Bessel functions of the first kind with index l, and the relevant

gmn (θ ) functions with indices m and n have the following properties:66 if n ≤ m, l = n; if n > m, l = n – m; g0n = 1 + cos θ, sin θ, 1 – cos θ for n = 0, 1, and 2; and g1n = sin2 θ, sin θ (1 + 3cos θ), sin θ (1 – cos θ), sin2 θ, sin θ (1 – cos θ) for n = 0, 1, 2, 3, and 4. The existence of new field components that are orthogonal to the incident linear polarization provides clear evidence that the vector nature of light needs to be carefully treated in high NA microscopy.31,65,67,68 Here, the component of the electric field along the overall beam


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propagation direction z is referred to as “longitudinal”. The longitudinal components exhibit asymmetric spatial distributions at the focal plane, which cannot be predicted by scalar diffraction theory (see Figure 1c).31 Also, the axis connecting the two maxima of the longitudinal fields is parallel to the direction of the incident linear polarization.31 Although the strength of the longitudinal fields produced by linear polarization is in general not comparable to the strength of the dominant transverse field components, this issue could still be significant in nonlinear microscopy due to the tensorial nature of the nonlinear responses. The strength of the field components at the beam focus is influenced by several factors. These factors include the NA of the objective, the incident polarization, the apodization function, and the presence of interfaces at the focal plane. The case of circular polarization can be treated by combining the results for x and y linear polarization with the appropriate phase difference. Consequently, the resulting longitudinal fields are of similar strength as for linear polarization under similar focusing conditions.69 Due to symmetry, the longitudinal fields produced by circular polarization exhibit a doughnut-shaped spatial intensity distribution at the focal plane.69 In addition, the transverse fields at the focal plane maintain their polarization properties. Equation (4) shows that the apodization function f w (θ ) plays a crucial role in controlling which wave-vector components contribute to the balance between the longitudinal and transverse focal fields. The apodization function is usually implemented by placing an annular filter just before the objective lens. This has been shown to be useful in detecting the absorption dipole orientation of individual fluorescent molecules.70 The strength of the longitudinal fields can also be enhanced by interfaces, which has been shown to allow determination of orientational effects in microscopy.71 Yet another way to control longitudinal fields is by introducing a π-phaseshaping element just before the annulus.72 In this case, the longitudinal fields peak at the center


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of the focal volume.65 It should also be intuitively clear that similar techniques can be implemented in signal collection. For example, a π-phase step at the back focal plane of the collecting optics has permitted the measurement of the longitudinal component of an emitter’s dipole moment.73 The results of equations (1)-(4) show that when the vectorial properties of focal fields are properly treated, the spot can strongly deviate from the ideal predicted by simple geometrical optics. In particular, for linear incident polarization, the spot is not even azimuthally symmetric, which can greatly hamper the image formation. Thus, the development of vector beams that are better suited for tight focusing is an important research topic. Cylindrical vector beams The azimuthal symmetry of the optical fields at the focal plane of a microscope objective can be restored by using optical beams with tailored polarization properties. For example, certain types of beams with spatially varying polarization states offer optical fields that exhibit reduced asymmetry in the focal volume of a microscope. An established class of vector fields with transversely non-uniform polarization states across the beam cross section is represented by CVBs. They are the axially symmetric beam solutions to the full vector electromagnetic wave equation.32–34 CVBs have been discussed since the 1970’s in the context of both experiments74 and theory75 of laser modes and resonators. The interest in CVBs was later renewed due to advances in generating CVBs outside of the laser cavity.32–34,76–84 These techniques utilize passive optical elements that convert conventional linear or circular polarizations into CVBs. CVBs can be conveniently synthesized by superposing HG10 and HG01 modes with orthogonal linear polarizations.65,32–34 Two famous CVBs that are of current interest are illustrated in Figure 1a. A radially-polarized CVB exhibits linear polarizations that are locally


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aligned in the radial direction of the beam cross section. In contrast, an azimuthally-polarized CVB contains linear polarizations that are aligned in the azimuthal direction. Throughout the article, the radially (azimuthally) polarized CVB will be called RP (AP). Both RP and AP exhibit a dark region at the center of the beam because the field direction is undetermined there. Additional information about CVBs, such as their mathematical descriptions, synthesis, manipulation, and applications, can be found in excellent reviews.32–34 RP and AP exhibit very unique properties when tightly focused. The theory of RP and AP focusing is based on the angular spectrum method31 for transversely non-uniform beams.85–88 The focusing of RP has been further optimized by using a parabolic mirror focusing system,89 which permits chromatic aberration-free and even tighter focusing than refractive lenses. These predictions were coupled with key experiments77,78,86,87 that verified the new opportunities that can be achieved by focusing of RP, AP and generalized CVBs, which are superpositions of RP and AP.90 Let us now revisit the focal field distributions of RP and AP. Using similar conditions and notations as earlier, the electric field components at the beam focus of RP and AP are:65

i ( I11 − I12 ) cos φ  ikf 2  − ikf  ERP ( r ) = E0e  i ( I11 − I12 ) sin φ  2w0   −4 I10

(5)

 i ( I11 + 3I12 ) sin φ  ikf 2  − ikf  EAP ( r ) = E0e  −i ( I11 + 3I12 ) cos φ  2 w0   0

(6)

These results show immediately, that the focal fields have azimuthal symmetry. Furthermore, equation (5) indicates that RP generates significant transverse and longitudinal fields at the focal


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plane. The longitudinal fields for RP exhibit a spatial intensity distribution that is rotationally symmetric and maximum at the center of the focal plane as depicted in Figure 1c. In addition, the transverse fields for RP preserve the radial distribution of the local polarizations (Figure 1c), which exhibits a minimum at the center. In contrast to linear polarization, the longitudinal fields at the focus of RP are significantly stronger than the transverse fields.65 Equivalently, equation (6) shows that the field distribution of AP is strictly transverse at the beam focus, as also shown in Figure 1c. These remarkable characteristics of the focal-field distributions of RP and AP have found a lot of potential in optical microscopy. One aspect that was significantly influenced is spatial resolution. For example, the focusing of RP combined with an apodization annulus significantly decreased the achievable spot size and thus the energy distribution at the focal plane.77,85,86 In Reference 77, RP combined with an annulus was found to exhibit an experimental spot size significantly smaller (0.16λ2) than for linear polarization (0.26λ2). Later, Sheppard and Choudhury confirmed theoretically that, indeed, the best approach to significantly reduce the focal spot size is to combine RP and an annular excitation pupil, resulting in, e.g., transverse spot size of 112 nm for the excitation wavelength of 488 nm.91 Without the annulus, the spatial resolution of RP was found to be even inferior than for circular polarization.92 Interestingly, the optimum spot size using RP and an annulus can be well predicted by scalar diffraction theory.91,92 The longitudinal fields of focused RP can also be enhanced by dielectric interfaces at the focal volume, thereby allowing better lateral confinement.93 The determination of the spatial resolution in an optical microscope relies on interactions between the incident light and the material at the beam focus. Various types of objects have been used to evaluate the tight focus of a high NA objective. For example, the longitudinal fields


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produced by RP and conventional beams were characterized using techniques based on near-field optical microscopy.94,95 The local polarization in the focal region of CVBs can also be imprinted on transparent media at subwavelength spatial resolution using ablation.96 The strength of the longitudinal fields produced by RP has also been determined by absorption in photopolymers.97,98 Furthermore, the energy densities of the longitudinal and transverse electric fields produced by RP and AP have also been measured by exploiting the polarization-dependent responses of semiconductor structures.99 More recently, the light scattered from a gold nanoparticle was used to measure and reconstruct the amplitudes and relative phases of the focal field components of a tightly focused RP.100 Due to their unique longitudinal and transverse focal fields, RP and AP have found several applications in the characterization of anisotropic structures, such as oriented molecules and particles. In particular, they allow orientational imaging without doing several matched polarization measurements as in traditional methods. As an example, CVBs endow dark-field microscopy with sensitivity to the orientation of the sample edges.101 The orientation sensitivity was also demonstrated using fluorescence from single molecules102–106 and nanodiamonds,107 where a single confocal scanning microscopy image replaces multiple polarization measurements and reflects the three-dimensional orientation of the emitter. High detection efficiency for arbitrarily-oriented emitters has also been predicted for parabolic mirror microscopy.89 In the context of nanoparticles, interference scattering microscopy with RP and AP provides information on both the orientation and shape of anisotropic metal nanoparticles.108,109 In photoluminescence measurements, both RP and AP have been employed to determine the threedimensional dipole moment of gold nanorods,110 SiO2 nanoparticles111 and quantum dots112 as well as to efficiently excite a gold nanocone antenna.113


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The lack of longitudinal electric fields at the focus of AP is also becoming important [equation (6)]. Due to the complementary properties of AP and RP beams, the focus of AP actually contains a very strong longitudinal magnetic field component.65 This feature is expected to be useful in probing magnetic interactions where residual electric fields should not impede the measurements. Very recently, AP was used to excite a magnetic dipole transition in rare earth ions.114 Similarly, a magnetic response was observed in a single split-ring resonator using a linearly polarized TEM10 mode115 which also provided a longitudinal magnetic field component when focused. CVBs have recently been used to interrogate individual nanoplasmonic systems.116 For example, RP was recently employed to demonstrate the high directivity of position-dependent scattering or emission from an individual gold nanoparticle.117 Such capability is expected to be useful for optical field steering on the nanoscale, which is inaccessible using conventional excitation schemes. Furthermore, by tuning the excitation beam between RP and AP, multipole resonances in a high-refractive-index dielectric nanoparticle were selectively excited.118 In addition, RP and AP have been used to excite the collective response of a variety of plasmonic oligomers119–121 which cannot be done using conventional polarizations.

Sources of contrast in nonlinear microscopy We will now discuss the nonlinear contrast mechanisms that are provided by optical excitation. The polarization of the material P, which depends on the strength of the incident electric field E, can be often expanded in a power series of the applied field as:

P = ε0 χ ( ) E + ε0 χ ( ) E2 + ε0 χ ( ) E3 + ... 1

2

3

(7)


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where ε0 is the permittivity of free space and χ(n) is the nth-order susceptibility of the material.122 When the incident light intensities are relatively weak (e.g., sunlight or a lamp), only the first term in equation (7) is important. This linear optical response of the material is the basis of contrast used in the classical types of light microscopy based on, e.g., absorption, reflection, refraction or scattering. The higher-order polarization terms in equation (7) become significant only when sufficiently strong optical fields are applied on the material. In general, the nonlinear terms will become important for optical field strengths on the order of the characteristic atomic electric field strength (~1011 V/m).122 However, depending on the sample, the effects can become observable even at significantly lower field strengths. Nevertheless, in microscopy, the use of nonlinear contrast necessitates the use of pulsed laser sources for excitation. The higher-order terms give rise to radiation at new frequencies generated by the interaction of the incident field frequencies with the medium (Figure 2). In general, each of these new frequencies is associated with a unique contrast mechanism for nonlinear microscopy. For example, the second term describes interactions like SHG and sum-frequency generation (SFG). The third term, on the other hand, describes phenomena like THG and CARS. Since P and E are vector quantities, the susceptibilities are tensors. Importantly, the structure of the tensors, i.e., their non-vanishing components and interrelation between the components, are strongly affected by the structural properties of the material.122 For example, within the electric-dipole approximation of the light-matter interaction, the second- and evenorder nonlinear effects are forbidden in centrosymmetric materials, i.e., in materials that have an inversion center. In spite of this, second-order effects can occur also in centrosymmetric materials due magnetic and quadrupole effects.123 Such higher-multipole effects are associated


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with gradients in the field and material properties and can therefore play an important role in nanostructured materials. On the other hand, third-order interactions are more general and can occur in all materials even within the electric-dipole approximation. But most importantly, due to the tensorial character of the nonlinear interactions, they are expected to be influenced also by the three-dimensional optical fields provided by a high NA objective. Finally, when beam propagation effects become important, one also needs to consider phase matching.122 This refers to the fact that because the indices of refraction of materials depend on frequency, the incident and generated fields maintain their phase relation only over a distance known as the coherence length, which limits the growth of the nonlinear signal. Predicting the nonlinear signals generated by tightly-focused laser beams and relating the acquired information with the properties of a three-dimensional and usually heterogeneous sample is a crucial question in nonlinear microscopy. The nonlinear signal originates from a collection of nonlinear dipoles that oscillate at the signal frequency in the focal volume. For coherent nonlinear processes, the deconvolution techniques used for image analysis in fluorescence microscopy, where the spatial resolution is conveniently specified in terms of the point spread function, are not applicable anymore. As an example, the radiation pattern and total power of SHG can be strongly influenced by the spatial distribution of the scatterers within the focal volume.124,125 Similarly, the CARS signal can be significantly influenced by the size of the object and coherent buildup dynamics.126 Thus, the development of theoretical tools that account for high NA focusing in nonlinear microscopy has become a fundamental issue. The theoretical descriptions for the different contrast mechanisms of SHG,127,128 THG,129,130 and CARS131,132 were introduced in the early 2000’s and have since been further developed. Briefly, using the calculated focused fields at the incident wavelengths, the three-dimensional nonlinear


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polarizations and their distribution in the focal volume are computed. After this, the far-field radiation at the signal wavelength is described using the Green's function approach.131 For coherent (incoherent) detection schemes, the far-field radiation amplitude (intensity) is then integrated over the acceptance angle of the detector system. The emergence of these core modeling capabilities has significantly helped in understanding the experiments on nonlinear microscopy and in shaping its future. In the following, we give an overview of the most common nonlinear effects used in microscopy. Second-harmonic generation SHG is one of the simplest second-order interactions, which is very straightforward to implement experimentally.3 In fact, the pioneering demonstrations of non-scanning133,134 and scanning135,136 nonlinear microscopies were based on SHG. Here, two-photons at the fundamental frequency ω are combined into a single photon at the doubled frequency 2ω (Figure 2a). Due to such energy conservation, the process is parametric, i.e., the interacting fields do not deposit ideally any energy onto the material. This makes SHG very useful for nondestructive label-free imaging, especially for biological samples.62,137,138 Nevertheless, keeping the excitation power low is always beneficial as femtosecond laser irradiation may still be accompanied by high-order absorption.139–141 The second-order polarization for SHG is driven by two electric field components at the fundamental frequency ω and can be represented as:

Pi (

2)

( 2ω ; r ) = ε 0 ∑ χ ijk(2 ) (ω , ω ; r ) E j (ω , r ) E k (ω , r )

(8)

jk


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where ε0 is the permittivity of free space, E j (ω,r) and Ek (ω,r) are the polarization components of the field at the fundamental frequency, χ ijk( 2 ) is a third-rank tensor that has 27 components and the indices ijk are summed over the polarization directions x, y, and z. The susceptibility tensors are sample-specific. Note also that all quantities depend on the spatial location r, both due to focusing of the fields and due to variations in the sample properties. In addition, the tensor components are complex-valued whenever the material exhibits absorption at either the fundamental or second-harmonic frequency.122 Fortunately, the number of independent tensor components can be greatly reduced by symmetry considerations.122 As a rule of thumb, SHG is electric-dipole-allowed only in noncentrosymmetric materials. However, the symmetry is always broken at the surface of a centrosymmetric material or at the interface of two centrosymmetric materials. When illuminated by intense light fields, such surfaces or interfaces can therefore radiate second-harmonic light. Hence, SHG has found a lot of uses in studying surface properties and dynamics.142 For surfaces and interfaces of high symmetry, the nonlinearity has a significant out-of-plane character, i.e., it requires that at least one of the interacting fields has a field component along the surface normal. Under plane-wave excitation, the experiments must therefore be performed at oblique angles of incidence. However, as we have already seen, this need not be the case under strong focusing, where the longitudinal fields couple with the surface nonlinearity even at normal incidence. Another important symmetry property is chirality, i.e., the lack of mirror symmetry. Chirality necessarily breaks the centrosymmetry, and chiral materials always have a secondorder response, but not necessarily a second-harmonic response. The sum-frequency response of chiral isotropic materials is actually cumbersome to access in a reliable way.143–146 On the other hand, techniques to detect chirality of thin-film and surface samples were successfully developed


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in the 1990’s.147–152 Such techniques relied on plane-wave excitation and oblique angles of incidence and gave rise to different SHG responses for left- and right-hand circularly-polarized fundamental light. Such SHG circular-difference (CD) approach was later found to lead to problems for the case of samples with in-plane anisotropy, which can give rise to false chiral signatures in SHG.153 Coming back to nonlinear microscopy, the symmetry properties of SHG have made it a powerful imaging tool in the life62,137,138,154 and physical sciences.155–157 As the SHG signals reflect the degree of ordering in the sample, polarization modulation and analysis have been used to quantify and extract information about the properties of biomolecular systems,158–165 and nanomaterial systems.166–172 For more information, a comprehensive tutorial by S. Brasselet examined in detail the capability of SHG (and also other nonlinear effects) for molecular orientation imaging of biological structures.138 Third-harmonic generation While the second-order processes are constrained by the non-centrosymmetry requirement of the material, third-order processes are electric-dipole-allowed in all media. THG is a third-order process, which was first observed in a centrosymmetric calcite crystal.4 In this contrast mechanism, three photons at the fundamental frequency are combined in order to generate a single photon at the tripled frequency (Figure 2b). Similar to SHG, the interaction in THG is parametric. The third-order polarization can be expressed as:

Pi (

3)

( 3) ( 3ω ; r ) = ε 0 ∑ χ ijkl (ω , ω , ω ; r ) E j (ω , r ) E k (ω , r )El (ω , r )

(9)

jkl

( 3) where the quantities are otherwise the same as in equation (8) but χ ijkl is a fourth-rank tensor

with indices ijkl summed over the linear polarization directions x, y, and z.


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When light is tightly focused into a homogeneous nonlinear material, the phase matching of the THG signal is suppressed by the destructive interference arising from the Gouy phase shift.122,173 However, whenever there are inhomogeneities in the focal volume such as small inclusions or an interface between two materials, the suppression is incomplete and THG can occur. THG is highly localized in three dimensions so that it also provides inherent optical sectioning. These features were exploited in the development of the first THG microscopes.173– 176

Moreover, the THG signal also depends on the properties of the beam focus such as

polarization177 and on the sample geometry.178 In particular, THG is forbidden in isotropic materials for circularly-polarized incident light. Nevertheless, since all materials have nonvanishing third-order susceptibilities, THG microscopy has been used as a general probe of all kinds of materials but has found particularly important applications in biology158,177–181 and nanotechnology.182–187

Coherent anti-Stokes Raman scattering CARS is a four-wave mixing process5 which involves a pump photon at frequency ωp, a Stokes photon at frequency ωs, and a probe photon at frequency ωpr that combine in a sample in order to produce a signal (or anti-Stokes) photon at frequency ωas = ωp − ωs + ωpr. When the energy difference ωp − ωs is close to the characteristic vibrational frequency of a molecule Ω, the pump and Stokes beams generate a beat which drives the molecular vibration coherently. The driven molecular vibration then scatters the probe beam giving rise to a coherent anti-Stokes photon. In CARS, the incoming photons ωp and ωpr typically come from the same laser source so the signal will be emitted at ωas = 2ωp − ωs (Figure 2c), which was found to be more efficient than conventional Raman.188 The first CARS microscope189 was developed in 1982 but its usefulness was limited due to sensitivity issues. CARS microscopy was taken into wider use only after 1999


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when the technique was shown to be capable of imaging in three dimensions at high contrast.188 For example, this technique is now commonly used in life sciences.131,190,191 Recently, CARS microscopy has also been utilized in physical sciences, e.g., in the characterization of nanostructures.66,192,193 In CARS, the resonant response associated with the molecular vibrations is hampered by the non-resonant background,194 which exists even in the absence of a vibrational resonance. This non-resonant background was found to be detrimental to imaging, especially when the vibrationally resonant signal is very weak.190 The suppression of this non-resonant background in CARS spectroscopy and microscopy has been an active research area for decades, with each approach establishing different levels of success. One emerging nonlinear imaging technique that is free from the non-resonant background signal is based on SRS.55–57 In SRS, a molecular vibration is excited by a pump and a Stokes photon, which leads to a transfer of energy from the pump source to the Stokes source.195 The specific discussion of SRS,190,196,197 however, is beyond the scope of the present article.

Two-photon excited fluorescence and luminescence TPEF and TPEL are also important contrast mechanisms that use nonlinear excitation. From the viewpoint of optical fields, the difference between the two processes regards terminology. TPEF is used for molecular systems, where the excitation pathway proceeds through electronic molecular states. TPEL on the other hand, is often used for solid-state systems, such as metals and semiconductors, where the excitation pathways through the band structure can be more complex. Nevertheless, both TPEF and TPEL involve the absorption of two photons and subsequent energy transfer in the material (Figure 2d). Furthermore, these contrast mechanisms often use bright labelling agents such as fluorophores, semiconductors (e.g., quantum dots), or


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metal (e.g., gold) nanoparticles. Although these techniques are generally invasive, especially in the context of biological applications, they still provide useful information. For example, a comprehensive tutorial by S. Brasselet showed the use of TPEF for molecular orientation imaging.138 Since we have already discussed TPEF in the Introduction as an example of a nonlinear response, we will only give an overview of TPEL below. TPEL for gold is well-documented.1,198,199 Although luminescence due to multiphoton absorption was first observed by Chen et al.,200 TPEL of noble metals and their enhancement on roughened surfaces was first examined by Boyd et al.1 Furthermore, the intensity of the TPEL signal was found to exhibit a quadratic dependence on the excitation intensity,1 so in principle the technique can be used for three-dimensional imaging. TPEL is also often a sequential process, where the absorption of the two incident photons is separated by a small time delay.199 This is in contrast to TPEF, which involves essentially simultaneous absorption of the two incident photons. Single gold nanoparticles have been widely utilized in TPEL microscopy. In addition, the polarization dependence of TPEL from a single gold nanorod has been studied in detail.199 In particular, the TPEL intensity was found to be enhanced whenever the polarization of the incident light is aligned with the nanorod long axis.199 Due to ease of synthesis and simplicity of conjugation to biological systems, gold nanorods have been widely used as contrast agents in TPEL microscopy.201–203

Emerging trends in nonlinear microscopy with vector fields Under strong focusing, three-dimensional vector fields occur in the focal volume of microscope objectives. Depending on the input polarization and apodization, the focusing gives rise to


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distinct spatial intensity distributions of the electric (and magnetic) field components at the focus. On one hand, the longitudinal electric fields generated by focusing linear polarization are generally weak and exhibit asymmetric field distributions at the focal plane. On the other hand, the longitudinal electric fields produced by focusing RP, are strong and exhibit rotational symmetry at the focal plane. Such longitudinal fields have been shown to be important in probing and demonstrating a variety of novel phenomena that utilize linear microscopies. In nonlinear microscopy, the nonlinear susceptibility tensors govern the accessible types of image contrast. The three-dimensional vector fields can therefore lead to important new capabilities in nonlinear microscopy. However, before proceeding to combine concepts from focused vector fields and nonlinear processes, we need to give an overview of the basic design of nonlinear microscopes. In the past decade, thorough and extensive reviews on the instrumentation and optimization of parameters of nonlinear microscopes have been published.24,25,58–63 A generic nonlinear microscope consists of a pulsed laser (with single or tunable wavelengths in the nearinfrared), a high NA microscope objective, a photon detector and a point-scanner. Depending on the sample properties, the detection of the nonlinear signals can be done in the backward or forward direction. By placing appropriate optical components before the detector, spectral and polarization discrimination can be achieved. Similar to a confocal laser scanning microscope, the image here is built point-by-point, i.e., as a function of spatial coordinates. By adding polarization mode converters32–34,76–84 or programmable instruments103,204–208 in the illumination path, different vector-field nonlinear microscopy configurations are realizable. In the following, we will highlight some of the recent achievements that have been obtained using nonlinear microscopy with vector fields.


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SHG Microscopy In order to get a basic idea how focused vector fields can affect SHG microscopy, we first consider their use in the characterization of some relatively conventional types of samples starting from non-centrosymmetric crystals. Asatryan et al. considered SHG under focused linear polarization from a single BaTiO3 crystal, which has a significant second-order response.127 However, by developing vector field theory for SHG microscopy, the authors showed that the largest contribution to the SHG intensity actually originated from the smallest component of the second-order susceptibility tensor. This can only occur due to the peculiar polarization properties of the focal field, including the spatial distribution of the three-dimensional field vector. Similarly, the SHG (and also THG) efficiency in a nonlinear crystal has been predicted to be strongly affected by the longitudinal field component even when a linearly-polarized, weakly focused Gaussian beam is used.209 In general, these findings have clearly proven that the threedimensional fields at the beam focus should be accounted for even if the longitudinal fields are weak as in the case of linear incident polarization. RP and AP beams have also been studied in the context of nonlinear crystals. Depending on the structure of the second-order susceptibility tensor of the crystal, this can lead to very interesting polarization effects. For the case of barium borate (BBO), AP fundamental beam gives rise to RP SHG beam.210 Furthermore, the emitted RP has an annular distribution and nearly six-fold symmetry as determined by the crystal symmetry. SHG conversion has also been reported in ZnSe crystals using focused CVBs in theory211 and experiment.212 Another basic sample is an isotropic surface or thin film with full rotational symmetry about the surface normal. Recall that the SHG response of such samples has a strong out-ofplane character, which necessitates field components along the surface normal. Such components


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are provided by vectorial focusing even at normal incidence, which is sufficient to drive the weak electric-dipole-allowed surface SHG. This is particularly so for focused RP, which produces a strong and highly-confined longitudinal field at the beam focus. Indeed, Biss and Brown were able to demonstrate this added sensitivity by driving SHG at metal and semiconductor surfaces using focused RP, where the results were also compared to AP and linear and circular polarizations.213 Similarly, the enhanced longitudinal fields at the focus of RP have been used to enhance SHG from self-assembled monolayers on a gold substrate214 and from organic monolayers on a platinum substrate.215 In addition, the full tensorial character of the process in thin films can lead to highly asymmetric second-harmonic emission in the forward and backward directions, which is not possible without the longitudinal field components (Figure 3a).216 This result can be explained by applying a multipolar approach to the finite excitation volume in the thin film.216 SHG with focused vector fields from nanostructures can be used for several complementary purposes. First, such structures can provide confined and tailorable sources of SHG light. As an example, the excitation provided by an inhomogeneous longitudinal field distribution of focused linear polarization can be used to tailor second-harmonic scattering from a silicon sphere placed at varying distances from a dielectric substrate.217 The generation of confined sources is closely associated with the fact that certain types of nanostructures couple strongly to the longitudinal fields of focused vector beams. Metal cones with a sharp tip are prominent for this since they support plasmonics oscillations along the cone axis. Indeed, a highly confined SHG source provided by a tip dipole oscillating at the secondharmonic frequency has been theoretically formulated and experimentally demonstrated.218 In addition, mapping of the longitudinal fields has been demonstrated for the tight focus of linear


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polarization (Figure 3b) and a HG10 mode.218 Subsequently, SHG (and also THG) microscopy with RP has been used to efficiently excite a metal nanocone (Figure 4a).219,220 Later, an even more systematic study of metal nanocones (e.g., with different nanocone sizes, environment and illumination directions) was reported using SHG (and TPEL) imaging with CVBs, further establishing the connection of nanocones to polarization dependent point sources.221 Another obvious application of vector fields is in the characterization of nanostructures. SHG imaging with RP and AP has been shown to be extremely sensitive to the nanoscale features and symmetry of nanoparticles, which cannot be obtained by conventional polarizations or microscopies based on the linear optical response with CVBs.219 In another example, a nanoparticle with lowered symmetry of a winged nanocone was investigated using SHG imaging with RP and AP (Figure 4b).222 Such three-dimensional structures support plasmon oscillations that are best excited by a polarization that contains both longitudinal and transverse components. This can be achieved off-center of focused RP, which facilitated the transformation of far-field radiation to strong longitudinal fields near the tip of the cones.222 The combination of SHG with RP is not limited to subwavelength metal nanostructures, whose second-order response has predominantly surface origin. The longitudinal field of RP has also been used to drive SHG from vertically-standing semiconductor nanowires with bulk nonlinearity. The response was found to be very strong because the longitudinal field couples well with the dominant tensor component of the nanowires. This result is important, because this technique allows nanowires to be characterized in their native growth environment (Figure 4c), which is awkward using collimated beams.223 The development of microscopic techniques is also motivated by their applications in biomedical imaging. Vectorial focusing can provide new capabilities also in this context. In an


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early work, the effect of the longitudinal fields produced by tight focusing of linear polarization was found to drastically influence SHG from structures like collagen (Figure 5a).128 It was also suggested that by accounting for the electric field components and the nonlinear susceptibility tensor, it is possible to achieve polarization conversion, e.g., from linear to radial polarization, in the nanoscale at high efficiency.128 Furthermore, the modeling of these effects as modified by the excitation and detection properties of the SHG microscope has also been investigated.224,225 In subsequent work, SHG microscopy using focused RP has been found to be very sensitive to the three-dimensional orientation of collagen fibers derived from human (Figure 5b)226,227 and rat228 tendons. Although the three-dimensional orientation sensitivity of SHG imaging with CVBs was achieved qualitatively in these works, the results were difficult to analyze due to the complexity of biological samples. Nevertheless, SHG with RP and AP has also been numerically studied and experimentally demonstrated on porcine cornea, suggesting the enhanced sensitivity of the technique to determine molecular orientation in biological samples.229 With regard to biological samples, chirality is a particularly interesting symmetry property. In general, chirality leads to different optical responses for left- and right-hand circularly-polarized light. As already mentioned, chiral probes for thin films were developed in the 1990’s on the basis of SHG-CD effects,147–152 but they can lead to false chiral signatures if the sample has in-plane anisotropy.153 This problem is related to the handedness of the experimental setup that arises from the oblique angle of incidence needed for plane-wave excitation. It can be shown that, in principle, these problems can be completely avoided if the experimental setup has full azimuthal symmetry about the sample normal. Clearly, this requires excitation at normal incidence.


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Tightly-focused circular polarizations have all the required properties to provide ideal probes of surface chirality in SHG microscopy.230 They provide the longitudinal field components to drive the SHG response of samples with even very high symmetry. On the other hand, they possess the azimuthal symmetry to avoid any possibility of false chirality. These concepts have also been demonstrated experimentally.230 In line with this, vector beams that are handed superpositions of RP and AP were also proposed as new probes to investigate chirality of surfaces and thin films.231 CD effects in SHG232 and SFG233 microscopy have been investigated to probe the chirality of a variety molecules and nanostructures. Combined with spatial mapping, SHG-CD was reported as a new chirality probe for biological samples such as collagen234,235 and starch,236 providing new tools for biomedical applications. Equivalently, SHG microscopy was employed to

study

the

strong

coupling

of

circularly-polarized

light

to

individual

chiral

nanostructures.155,237–242 It should be noted however that there are still open questions as to when these techniques are truly sensitive only to the chirality of the sample. THG Microscopy THG is another nonlinear process that is simple to implement experimentally. In some sense, it is very similar to SHG, the only difference being the wavelength of the detected signal. In consequence, some of the concepts used for focused vector beams are very similar to those for SHG. This is especially so for the cases where the vector fields are used to control coupling of light to nanostructures and to create confined nonlinear sources of light. On the other hand, the body of work on combining vector fields with THG microscopy is at this time much more scattered than that on SHG.


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In spite of the similarities between SHG and THG, the symmetry properties of the two processes are different. In particular, THG is allowed in all materials but, as mentioned, is sensitive to sample inhomogeneities due to the Gouy phase shift. However, THG possesses some very unique polarization properties. In general, linear polarizations are used to probe anisotropic domains. On the other hand, THG always vanishes in isotropic materials for circular polarizations.177 Thus, any THG signal acquired with circular polarizations contains direct evidence about sample anisotropy. Both linear and circular polarizations have thus been used to address anisotropic structures. Linear polarizations have been applied to map molecular ordering in multilamellar lipid vesicles and in the multilamellar, intercorneocyte lipid matrix of the stratum corneum of human skin (Figure 6a).243 In addition, a recent THG microscopy study with linear and circular polarizations revealed different structures in intact human corneas at high contrast.244 In another recent work, THG microscopy with circular polarization was shown to be capable of differentiating both artificial and mammalian lipid droplets in cells that have different degrees of ordering (Figure 6b).245 THG microscopy is also expected to benefit from more advanced focal fields that can be obtained by tailoring the field distribution before focusing. For example, Masihzadeh et al. achieved a spatial resolution enhancement by manipulating the polarization structure of the incident beam using a spatial light modulator.246,247 By synthesizing a focal field that is linearly polarized at the center and switched to circularly polarized at the edges, up to a factor of two enhancement was obtained in spatial resolution (Figure 6c).247 In addition, THG microscopy with tightly focused RP combined with an annulus has also been numerically studied and found to be capable of increasing the spatial resolution even further.248 Another possibility is to utilize field


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enhancement effects, where THG imaging with RP was also able to increase the lateral spatial resolution as probed by a metal nanocone.220 With regard to orientational imaging, the use of beams with spatially-varying states of polarization in THG microscopy was found to be very sensitive to the three-dimensional orientation of the structure or interface that is enclosed by the focus.130

CARS Microscopy SHG and THG microscopies are easy to implement experimentally because they only require a single laser beam to drive the nonlinear response. CARS microscopy, on the other hand, requires incident light at two different wavelengths. Nevertheless, this technique provides the significant additional benefit of being chemically specific. It therefore offers more versatility in detecting microscopic structures with different chemical properties. The main applications of CARS microscopy are therefore in biomolecular structures. In spite of its evident potential, CARS microscopy is hampered by the non-resonant background signal.194 It turns out that vector beams can provide new approaches also to the suppression of this background. This possibility was demonstrated in a numerical study by Krishnamachari and Potma where they introduced phase jumps along the transverse directions in the focal volume of a CARS microscope, resulting in the suppression of the non-resonant background in the forward detected CARS signal.132 Instead of the traditional linearly-polarized HG00 Stokes beam, they used spatially phase-shaped beams such as HG10 and HG01 modes to detect one-dimensional lateral interfaces and a Laguerre-Gauss mode of order (0,1) (LG01) to detect two-dimensional lateral interfaces.132 In another numerical study by the same authors, an optical bottle beam distribution was used as the Stokes beam to create phase jumps along the longitudinal direction, i.e., parallel to the axis of beam propagation.249 Such beams have zero on-


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axis intensity at the focus which is surrounded in all three dimensions by regions of higher intensity. The resulting focal distribution was shown to be capable of detecting vibrationally resonant interfaces that are perpendicular to the direction of beam propagation and suppressing also the non-resonant background in the forward detected CARS signal.249 The benefits of CARS microscopy with focus-engineered Stokes beams were also confirmed experimentally by the same team (Figure 7a).250,251 RP and AP have also been combined with CARS microscopes to suppress the non-resonant background. For example, an annular aperture detection scheme in a CARS microscope with RP has been shown to suppress the non-resonant background from water, yielding over 50-fold improvement for the backward CARS detection and 110-fold for the forward CARS detection.252 The spatial resolution of a CARS microscope can be also enhanced using focused vector fields. For example, the reduction of the CARS interaction volume using focus-engineered beams has been numerically studied.253 Related to this, resolution enhancement in CARS microscopy based on focus-engineered Stokes beams has recently been experimentally demonstrated (Figure 7b).254 RP can also be used to improve the spatial resolution in CARS microscopy. This possibility has been demonstrated in numerical simulations, where the near field CARS radiation due to tightly focused RP was found to be strongly influenced by the size of the scatterers in the medium.255 This result has strong implications for the imaging of very fine structures that utilize enhanced longitudinal fields for CARS. Finally, RP can also be utilized in tip-enhanced CARS microscopy, where the improved coupling of RP to the tip amplified the CARS signal by a factor of six as compared to linear polarization.256 Another application of RP in CARS microscopy is in orientational imaging. This was demonstrated for the detection of oriented molecules in a leaf vascular bundle, where the


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sensitivity increased by a factor of three when RP was used instead of linear polarization (Figure 7c).257 In addition, both RP and AP have been used in CARS microscopy to dynamically monitor the molecular orientation of 8CB liquid crystal samples.258 TPEF and TPEL microscopies SHG, THG, and CARS are coherent nonlinear optical processes. They are therefore very sensitive to the phase of the optical fields, including their polarization components. TPEF and TPEL, on the other hand, are incoherent processes, which mainly depend on the intensity of the fields. They benefit therefore from vector fields primarily through the capabilities that arise from controlling the focusing properties of the fields and their coupling to the sample structure. For this purpose, HG10 beams and CVBs provide many more new opportunities than the more conventional linear and circular polarizations. For the case of TPEF, vector field focusing has been used to advantage in improving the resolution and sensitivity of microscopy. Resolution enhancement can be achieved by minimizing the excitation volume in TPEF, which has the additional benefit that it reduces the invasiveness of the method arising from the excitation of the fluorophores. This has been achieved through the enhancement of the longitudinal fields of RP at dielectric-air interfaces, which resulted in the reduction of the spot size at the focal plane of a TPEF microscope by a factor of 1.7 (Figure 8a).259 In another study, by taking the difference of the TPEF images that were acquired by a bright (linear polarization) and a dark (AP) beam, the spatial resolution was shown to improve by a factor of two (Figure 8b).260 In a separate application, AP was used as a robust depletion beam in a fiber-optical TPEF stimulated emission depletion (STED) endoscope.261 Finally, RP has been used to further enhance the sensitivity of total-internalreflection TPEF correlation spectroscopy for single-molecule studies.262


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RP can also be utilized in the context of scanning-probe microscopy based on tipenhanced TPEF. This has been applied to quenching-free detection of quantum dots in combination with a scanning silicon tip, resulting in significantly enhanced TPEF by a factor of 3–5 depending on the quantum dots.263 RP has also been employed to excite surface plasmons on a metal surface to create a “virtual” scanning probe for exciting and detecting nonlinear effects, including TPEF, from biological samples that are near interfaces.264 Note that such sample locations are not accessible in traditional scanning-tip microscopes. TPEL microscopy is usually used to address nanocrystals and plasmonic nanostructures. As in other nonlinear microscopy techniques, the vector fields can be used to control the coupling of incident light to anisotropic nanoparticles and thereby to enhance the TPEL signal. This has been demonstrated by using RP and AP to achieve three-dimensional orientation imaging in the context of TPEL. For example, tip-enhanced TPEL (or TPEF) with AP and RP was used to determine the orientation and precise position of quantum dots.263,265 Similar to SHG, the efficiency of TPEL in gold nanocones was found to be significantly influenced by the focal fields of RP and AP.221 Recently, RP and AP were also implemented in a multifocal TPEL microscopy scheme to enable fast and large-scale orientation imaging of gold nanorods.266 Another example is that, due to the highly symmetric focal fields provided by RP, TPEL imaging of randomly oriented gold nanorods inside a cancer cell was found to be more efficient than using linear polarization.267 Another interesting achievement is the recent demonstration of arbitrary control of threedimensional focal polarization using a single vector beam for TPEL imaging of gold nanorods (Figure 8c).268 Here, the desired vector beam was achieved by the superposition of RP and AP and customized amplitude apodizers.268 The authors further demonstrated the applicability of the


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technique by encoding five pre-configured polarization orientations that could have potential in multidimensional encryption.268 TPEL microscopy can also be used to probe and characterize optical antennas that consist of two metal bars and an air gap.269–271 Applying a linearly polarized electric field across the gap results in surface charge distribution that is responsible for enhanced local fields within the gap. However, the overall near-field response and the far field TPEF signal of the antenna were found to be significantly altered when the bars forming the antenna were driven out of phase using a HG10 mode.272

Discussion and outlook In this review, we have presented and discussed the emerging opportunities that are now becoming possible through a new family of nonlinear microscopy techniques that rely on vectorial focusing effects. Since the electromagnetic field distribution in the focal volume of a high NA objective is inherently three-dimensional, the vectorial effects need to be considered very carefully. Such three-dimensional vector fields are particularly important for nonlinear microscopy techniques, where the sources of contrasts arise from the tensorial character of the nonlinear susceptibilities. The key effect that arises from vectorial focusing is the occurrence of the longitudinal field component and the capability to manipulate the relative strength of the transverse and longitudinal components. The vectorial focusing effects play a role even when conventional polarization states are focused. Even though the longitudinal fields produced by linear polarization are weak even under tight focusing, previous demonstrations have clearly shown that they are very important and should not be neglected, as is often done. This is particularly important for SHG, which is


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governed by strict symmetry rules. Additional capabilities arise from the focusing properties of unconventional polarizations such as radial and azimuthal, where the former can give rise to very strong longitudinal component. By exploring such techniques, we have witnessed a rapid increase in the sensitivity and capabilities of nonlinear microscopy particularly, in orientation imaging of molecules, interfaces and nanostructures, which is difficult to achieve using traditional approaches. The recent experimental and theoretical demonstrations of such capabilities, however, have not yet been widely implemented. Nevertheless, it is evident that such techniques will blossom in the coming years to meet the requirements and challenges regarding unexplored sample types and situations. Although the topics reviewed here are still young, an important task in the future is to find ways to assess the strengths and limitations of nonlinear microscopy with vector fields. This needs to be done by investigating a wide range of sample types that can be used to unambiguously probe the vector fields and their influence on each distinct nonlinear contrast mechanism. We expect that anisotropic nanostructures will play an important role as probes of the vector fields because such structures can be made sensitive to a particular field component. Once reliable ways to characterize and manipulate vectorial focal fields have been properly established, the techniques based on vectorial focusing are expected to lead to completely new capabilities in a number of applications. An obvious example is in tailoring the efficiency of low- and high-order138,273 nonlinear light-matter interactions on the nanoscale. This will rely on matching the focal fields to the electromagnetic eigenmodes and associated localfield distributions of nanoparticles. Another important application will be in biomedical sciences, where new ways to address, for instance, hallmarks of imbalances and diseases will be crucial. New devices,


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instrumentation and computational models in this field are expected to play important roles in formally establishing nonlinear microscopy as a general tool for the quantitative analysis of disease. For example, advanced SHG microscopy will have the capability to accurately probe changes in the second-order susceptibility tensors of biologically-relevant structures such as collagen or membranes. Advanced THG and CARS microscopies, on the other hand, will be able to detect the onset of structure-related disorders or chemical imbalances at the level of the substructures of an organelle. Such developments will push these nonlinear techniques to the limits of label-free imaging of biological samples. Thus, it is expected that novel metrics acquired from nonlinear techniques will be able to provide new knowledge about early stage diseases, their progression and treatment. Such metrics are also expected to provide complementary information to current and traditional methods in histology. Another important goal would be to achieve super-resolution techniques that do not rely on fluorophores or absorption effects. It is clear that any nonlinear microscopy contrast will benefit from an even sharper focal spot and some inroads are now being made in this direction. Taking advantage of vector field effects at the focal plane, the focus of high-order RP was found to be smaller than that for lowest-order radial polarization.274 Introducing these beams to scanning microscopy has already resulted in reduced lateral resolution.275 Similarly, new routes to super-resolution imaging via SHG are now being taken through sample labeling with nanocrystals276 and more recently, with spatial frequency modulation.277 It is important to note that vector field nonlinear microscopy also has significant challenges. For example, there are not yet ways to generate completely arbitrary threedimensional vector fields in the focal volume even in free space. In addition, even when this is achieved, full vector field control inside different types of samples will continue to be very


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difficult. This is a particular challenge for thick inhomogeneous materials, e.g., biological tissues, where the incident wave is necessarily modified in propagation. Adaptive wavefront correction46–48 is presently being employed to optimize the focus of light inside such complex media. Although polarization control has been recently attempted in this context using schemes that employ spatial light modulators,278,279 the techniques are still very limited and not yet applicable to nonlinear imaging. In spite of these challenges, vectorial focal fields with increasing level of control are continuously being proposed and synthesized.268,280–286 Equipped with fully programmable optical fields and the curiosity of the increasing number of nonlinear microscopy enthusiasts, completely new capabilities for nonlinear microscopy are certain to emerge, benefiting both fundamental and applied sciences. These key scientific advances are within grasp, and only time can tell how the vector fields will fortify the ongoing revolution in nonlinear microscopy.


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Figures

Figure 1. (a) Examples of polarizations used in microscopy, (b) typical tight focusing configuration and (c) focal field intensity distributions as a result of tight focusing. (a) Linear and circular polarizations are considered conventional because these beams exhibit uniform states of polarization across the beam cross section. Radial and azimuthal polarizations are considered unconventional because these beams display states of polarization that vary across the beam cross section. The arrows indicate the instantaneous electric field vector. (b) Simple schematic of the tight focusing configuration used in vectorial diffraction theory for a linearly polarized (along x) beam that is travelling in the z-direction and incident on a lens. The lens has a focal length f and is considered aplanatic. The emerging rays from the lens are directed to the


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focal point at an angle θ with respect to the direction of beam propagation. φ is the azimuthal angle with respect to the axis of beam propagation. (c) Calculated intensity distributions of the electric field components at the focus of a uniformly-filled microscope objective (NA = 0.8). Corresponding spatial intensity distributions of the transverse (Ex) and longitudinal (Ez) electric field components of input linear (along x), radial and azimuthal polarizations are depicted. The wavelength of the input beam is 1060 nm. Each column is separately normalized and the relative strengths are shown (bottom-right). In all panels, the coordinate axes are indicated.


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Figure 2. Photon diagrams of nonlinear processes commonly used in microscopy. (a) SHG, (b) THG, (c) CARS and (d) TPEF and TPEL. The electronic and vibrational (virtual) states of the material are shown as solid (dashed) lines. The input (generated) fields are shown as solid (dashed) arrows. In CARS, the vibrational energy Ω corresponds to ωp − ωs. The processes of SHG, THG and CARS are parametric.


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Figure 3. Examples of SHG microscopy that use linear polarizations. (a) Measured and calculated microscopic SHG responses from a 50 nm-thick SiN film as a function of a rotating quarter-wave plate (QWP). Asymmetry is observed between the transmitted (black curve) and reflected (red curve) emissions and agrees well with the calculations (dotted curves). Adapted with permission from ref 216. Copyright 2012 Institute of Physics Publishing. (b) Experimental SHG image of the focal fields of a tightly focused HG00 beam that is probed by a metal tip. The experimental SHG image agrees well with the calculated intensity distribution of the longitudinal field components of a tightly focused HG00 beam (inset). The two lobes are oriented in the direction of the incident polarization (along the vertical). Scale bars = 250 nm. Adapted with permission from ref 218. Copyright 2003 American Physical Society.


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Figure 4. Examples of SHG microscopy that use radial and azimuthal polarizations for the characterization of nanostructures. (a) Experimental SHG images of a gold nanocone using AP (left) and RP (right). The nanocone axis is perpendicular to the plane of this page. Note that the longitudinal field of RP can be used to excite the nanocone efficiently. The relative signal strengths are also shown. Adapted with permission from ref 219. Copyright 2012 American Chemical Society. (b) Schematic of the winged nanocone optical antenna that was investigated using SHG microscopy with RP and AP in ref 222. This three-dimensional structure permits the


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coupling of planar optical fields with wave vector k and polarization E0 to a localized hot spot at the sharp tip of the nanocone. Adapted with permission from ref 222. Copyright 2014 Optical Society of America. (c) Experimental SHG images of vertically-aligned semiconductor nanowires (diameter = 40 nm, length = 10 µm) using RP (left) and AP (right) under the same experimental settings. Note that the strongest signals are obtained only with RP and from nanowires oriented perpendicular to the plane of this page. Adapted with permission from ref 223. Copyright 2015 American Chemical Society.

Figure 5. Examples of SHG microscopy that use linear and radial polarizations for biological applications. (a) Far-field SHG radiation pattern from a collagen fiber that is made up of subunits which are extended along the z-direction. The length of the collagen subunits corresponds to a dipole (left), -2.5 to 2.5 (middle) and -5 to 5 (right). The axis of symmetry of the collagen is along the z axis. The x, y and z axes are expressed in arbitrary units. Adapted with permission from ref 128. Copyright 2006 Optical Society of America. (b) SHG images of a sliced portion of an Achilles tendon that has collagen fibers aligned perpendicular to the slice plane.


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The SHG images were taken with linear polarization along the vertical direction (left) and RP (right). Adapted with permission from ref 226. Copyright 2005 The Japan Society of Applied Physics.


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Figure 6. Examples of THG microscopy that use vector fields. (a) THG images of a human skin biopsy acquired using two different linear polarizations as shown by the double-headed arrows. Scale bar = 50 µm. Adapted with permission from ref 243. Copyright 2013 American Physical Society. (b) THG images of cholesteryl ester-enriched lipid droplets in macrophages using opposite-handed circular polarizations. Scale bar = 5 µm. Adapted with permission from ref 245. Copyright 2014 by Elsevier. (c) An unconventional focal field with states of polarization that switches from linear in the center to circular at some radius rs. This vector beam suppresses the THG signal at the edges, giving rise to an enhanced spatial resolution. Adapted with permission from ref 247. Copyright 2009 Optical Society of America.


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Figure 7. Examples of CARS microscopy that use focus-engineered beams. (a) Chemical interface detection in CARS microscopy with a HG00 (top-left) and HG10 (top-right) Stokes beam. The horizontal line cuts are shown below. The interface is between the dodecane:paraffin mixture on the left side and the deuterated dimethyl sulphoxide (d-DMSO) on the right side. Images are 30 µm × 30 µm. CARS signal was taken at 2941 cm-1. Adapted from ref 250. Copyright 2008 by John Wiley and Sons. (b) CARS images of 300 nm-diameter polystyrene beads using conventional HG00 (left) and Toraldo-phase-filter-shaped (right) Stokes beams. Adapted with permission from ref 254. Copyright 2012 Optical Society of America. (c) CARS images of cottonwood leaf vascular bundles that were sectioned perpendicularly to the vein fibers. The CARS images were taken with RP (left) and linear polarization (right). Adapted with permission from ref 257. Copyright 2009 Optical Society of America.


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Figure 8. Examples of TPEF and TPEL microscopy that use CVBs. (a) Experimental TPEF images of a fluorescent bead that is immersed in the mounting medium (top) and deposited at the glass-air interface (bottom). Both images were taken with RP. Scale bar = 500 nm. Adapted with permission from ref 259. Copyright 2009 Optical Society of America. (b) Demonstration of resolution enhancement that is achieved by subtracting the TPEF images of fluorescent beads acquired with bright (Gaussian, top-left) and dark (AP, top-right) beams. Corresponding line cuts are shown (bottom). Scale bar = 500 nm. Adapted with permission from ref 260. Copyright 2013 Optical Society of America. (c) Scheme of the TPEL microscopy setup for arbitrary threedimensional polarization orientation and examples of arbitrary linear polarizations. Adapted with permission from ref 268. Copyright 2012 Nature Publishing Group.


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Author Information Corresponding Authors *Email: [email protected], [email protected] Notes The authors declare no competing financial interest. Acknowledgement This work was supported by grants of the Academy of Finland (Nos. 267847, 287651 and 134973) and Tampere University of Technology (Strategy funding for Optics and Photonics). This work was performed in the context of the European COST Action MP1302 Nanospectroscopy.


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For Table of Contents (TOC) Use Only

Vector-field nonlinear microscopy of nanostructures Godofredo Bautista and Martti Kauranen

This TOC Graphic represents the emerging importance of nonlinear microscopy with vector fiels for the characterization and imaging of various types of nanostructures.


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ACS Photonics

Figure 1. (a) Examples of polarizations used in microscopy, (b) typical tight focusing configuration and (c) focal field intensity distributions as a result of tight focusing. (a) Linear and circular polarizations are considered conventional because these beams exhibit uniform states of polarization across the beam cross section. Radial and azimuthal polarizations are considered unconventional because these beams display states of polarization that vary across the beam cross section. The arrows indicate the instantaneous electric field vector. (b) Simple schematic of the tight focusing configuration used in vectorial diffraction theory for a linearly polarized (along x) beam that is travelling in the z-direction and incident on a lens. The lens has a focal length f and is considered aplanatic. The emerging rays from the lens are directed to the focal point at an angle θ with respect to the direction of beam propagation. Φ is the azimuthal angle with respect to the axis of beam propagation. (c) Calculated intensity distributions of the electric field components at the focus of a uniformly-filled microscope objective (NA = 0.8). Corresponding spatial intensity distributions of the transverse (Ex) and longitudinal (Ez) electric field components of input linear (along x), radial and azimuthal polarizations are depicted. The wavelength of the input beam is 1060 nm. Each column is separately normalized and the relative strengths are shown (bottom-right). In all panels, the coordinate axes are indicated. 177x125mm (300 x 300 DPI)


ACS Photonics

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Figure 2. Photon diagrams of nonlinear processes commonly used in microscopy. (a) SHG, (b) THG, (c) CARS and (d) TPEF and TPEL. The electronic and vibrational (virtual) states of the material are shown as solid (dashed) lines. The input (generated) fields are shown as solid (dashed) arrows. In CARS, the vibrational energy Ω corresponds to ωp - ωs. The processes of SHG, THG and CARS are parametric. 177x67mm (300 x 300 DPI)


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ACS Photonics

Figure 3. Examples of SHG microscopy that use linear polarizations. (a) Measured and calculated microscopic SHG responses from a 50 nm-thick SiN film as a function of a rotating quarter-wave plate (QWP). Asymmetry is observed between the transmitted (black curve) and reflected (red curve) emissions and agrees well with the calculations (dotted curves). Adapted with permission from ref 216. Copyright 2012 Institute of Physics Publishing. (b) Experimental SHG image of the focal fields of a tightly focused HG00 beam that is probed by a metal tip. The experimental SHG image agrees well with the calculated intensity distribution of the longitudinal field components of a tightly focused HG00 beam (inset). The two lobes are oriented in the direction of the incident polarization (along the vertical). Scale bars = 250 nm. Adapted with permission from ref 218. Copyright 2003 American Physical Society. 84x126mm (300 x 300 DPI)


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Figure 4. Examples of SHG microscopy that use radial and azimuthal polarizations for the characterization of nanostructures. (a) Experimental SHG images of a gold nanocone using AP (left) and RP (right). The nanocone axis is perpendicular to the plane of this page. Note that the longitudinal field of RP can be used to excite the nanocone efficiently. The relative signal strengths are also shown. Adapted with permission from ref 219. Copyright 2012 American Chemical Society. (b) Schematic of the winged nanocone optical antenna that was investigated using SHG microscopy with RP and AP in ref 222. This three-dimensional structure permits the coupling of planar optical fields with wave vector k and polarization E0 to a localized hot spot at the sharp tip of the nanocone. Adapted with permission from ref 222. Copyright 2014 Optical Society of America. (c) Experimental SHG images of vertically-aligned semiconductor nanowires (diameter = 40 nm, length = 10 µm) using RP (left) and AP (right) under the same experimental settings. Note that the strongest signals are obtained only with RP and from nanowires oriented perpendicular to the plane of this page. Adapted with permission from ref 223. Copyright 2015 American Chemical Society. 84x136mm (300 x 300 DPI)


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ACS Photonics

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ACS Photonics

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Figure 5. Examples of SHG microscopy that use linear and radial polarizations for biological applications. (a) Far-field SHG radiation pattern from a collagen fiber that is made up of subunits which are extended along the z-direction. The length of the collagen subunits corresponds to a dipole (left), -2.5 to 2.5 (middle) and 5 to 5 (right). The axis of symmetry of the collagen is along the z axis. The x, y and z axes are expressed in arbitrary units. Adapted with permission from ref 128. Copyright 2006 Optical Society of America. (b) SHG images of a sliced portion of an Achilles tendon that has collagen fibers aligned perpendicular to the slice plane. The SHG images were taken with linear polarization along the vertical direction (left) and RP (right). Adapted with permission from ref 226. Copyright 2005 The Japan Society of Applied Physics. 84x71mm (300 x 300 DPI)


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Figure 6. Examples of THG microscopy that use vector fields. (a) THG images of a human skin biopsy acquired using two different linear polarizations as shown by the double-headed arrows. Scale bar = 50 µm. Adapted with permission from ref 243. Copyright 2013 American Physical Society. (b) THG images of cholesteryl ester-enriched lipid droplets in macrophages using opposite-handed circular polarizations. Scale bar = 5 µm. Adapted with permission from ref 245. Copyright 2014 by Elsevier. (c) An unconventional focal field with states of polarization that switches from linear in the center to circular at some radius rs. This vector beam suppresses the THG signal at the edges, giving rise to an enhanced spatial resolution. Adapted with permission from ref 247. Copyright 2009 Optical Society of America. 177x97mm (300 x 300 DPI)


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Figure 7. Examples of CARS microscopy that use focus-engineered beams. (a) Chemical interface detection in CARS microscopy with a HG00 (top-left) and HG10 (top-right) Stokes beam. The horizontal line cuts are shown below. The interface is between the dodecane:paraffin mixture on the left side and the deuterated dimethyl sulphoxide (d-DMSO) on the right side. Images are 30 µm × 30 µm. CARS signal was taken at 2941 cm-1. Adapted from ref 250. Copyright 2008 by John Wiley and Sons. (b) CARS images of 300 nmdiameter polystyrene beads using conventional HG00 (left) and Toraldo-phase-filter-shaped (right) Stokes beams. Adapted with permission from ref 254. Copyright 2012 Optical Society of America. (c) CARS images of cottonwood leaf vascular bundles that were sectioned perpendicularly to the vein fibers. The CARS images were taken with RP (left) and linear polarization (right). Adapted with permission from ref 257. Copyright 2009 Optical Society of America. 177x97mm (300 x 300 DPI)


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ACS Photonics

Figure 8. Examples of TPEF and TPEL microscopy that use CVBs. (a) Experimental TPEF images of a fluorescent bead that is immersed in the mounting medium (top) and deposited at the glass-air interface (bottom). Both images were taken with RP. Scale bar = 500 nm. Adapted with permission from ref 259. Copyright 2009 Optical Society of America. (b) Demonstration of resolution enhancement that is achieved by subtracting the TPEF images of fluorescent beads acquired with bright (Gaussian, top-left) and dark (AP, top-right) beams. Corresponding line cuts are shown (bottom). Scale bar = 500 nm. Adapted with permission from ref 260. Copyright 2013 Optical Society of America. (c) Scheme of the TPEL microscopy setup for arbitrary three-dimensional polarization orientation and examples of arbitrary linear polarizations. Adapted with permission from ref 268. Copyright 2012 Nature Publishing Group. 177x69mm (300 x 300 DPI)


ACS Photonics

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TOC Graphic 60x39mm (300 x 300 DPI)


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Vector-Field Nonlinear Microscopy of Nanostructures - ACS Photonics

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