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Super-Resolution Far-Field Infrared Imaging by Photothermal Heterodyne Imaging Zhongming Li, Kyle Aleshire, Masaru Kuno, and Gregory V. Hartland* Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States
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S Supporting Information *
ABSTRACT: Infrared (IR) imaging provides chemical-specific information without the need for exogenous labels. Conventional far-field IR imaging techniques are diffraction limited, which means an effective spatial resolution of >5 μm with currently available optics. In this article, we present a novel far-field IR imaging technique based on photothermal heterodyne imaging (IR-PHI). In our version of IR-PHI, an IR pump laser excites the sample, causing a small temperature rise that is detected by a counterpropagating visible probe beam. Images and spectra of several different types of soft matter systems (polystyrene beads, thin polymer films, and single Escherichia coli bacterial cells) are presented to demonstrate the sensitivity and versatility of the technique. Importantly, the spatial resolution in the IR-PHI measurements is determined by the visible probe beam: a spatial resolution of 0.3 μm was achieved with a 0.53 μm probe wavelength and a high numerical aperture focusing objective. This is the highest spatial resolution reported to date for far-field IR imaging. Analysis of the experiments shows that for polymer beads in a dry environment, the magnitude of the IR-PHI signal is determined by the scattering cross section of the nano-object at the probe wavelength. This is in contrast to conventional PHI experiments in a heat-transfer medium, where the signal scales as the absorption cross section. This different scaling can be understood through the optical theorem. Our analysis also shows that both thermal expansion and changes in the refractive index of the material are important and that these two effects, in general, counteract each other.
1. INTRODUCTION Imaging for chemical-specific information is important for many different types of assays in chemistry and biology. Techniques for this purpose include vibrational spectroscopy measurements,1−5 fluorescence imaging,6−8 and laser ablation mass spectrometry.9−11 Among these, vibrational measurements stand out as nondestructive and labelfree. Common methods for vibrational measurements are infrared (IR) and Raman spectroscopy. In comparing these two techniques, the optical cross sections are much larger for IR absorption than Raman scattering. However, Raman scattering is backgroundfree and uses visible laser sources.1−3 Thus, Raman microscopes typically have superior spatial resolution and signal-to-noise level compared to conventional IR microscopes. The spatial resolution of an optical microscope can be defined by the Abbe diffraction limit of λ/2NA, where λ is the wavelength of the light and NA is the numerical aperture of the focusing objective.12,13 Conventional IR imaging is inferior to Raman imaging in both these factors. First, the wavelength of mid-infrared (mid-IR) light (3−10 μm) is an order-ofmagnitude larger than that for the visible light (0.4−0.8 μm) that is typically used in Raman microscopes. Second, reflective Cassegrain objectives are typically used to focus IR light, and the NAs of these objectives are lower than those for regular © 2017 American Chemical Society
refractive objectives (maximum NAs of 0.8 for Cassegrains compared to 1.4 for oil-immersion refractive objectives). As a result, the spatial resolution for a state-of-the-art IR microscope is approximately 5 μm, whereas it is around 0.5 μm for a regular Raman microscope.4 To overcome the spatial resolution challenge, several nearfield IR imaging techniques have been developed.14−19 One of the most widely used techniques is the combination of an atomic force microscope (AFM) with an infrared laser source (AFM-IR).20−24 In AFM-IR, absorption of IR radiation by the sample is detected by the deflection of an AFM cantilever due to thermal expansion. AFM-IR produces high quality spectra, comparable to traditional Fourier Transform Infrared (FT-IR) spectra of bulk samples,20 and has been used to examine soft matter systems and semiconductor structures at a spatial resolution of ∼20 nm.21−24 However, a major drawback of scanning-probe techniques like AFM-IR is the limited field of view as well as the instrumental complexity. In this article, we describe a novel implementation of infrared photothermal heterodyne imaging (IR-PHI),25−30 a far-field IR imaging Received: June 20, 2017 Revised: July 12, 2017 Published: July 25, 2017 8838
DOI: 10.1021/acs.jpcb.7b06065 J. Phys. Chem. B 2017, 121, 8838−8846
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Figure 1. (a) Schematic diagram of the IR-PHI experiment. The mid-IR pump and 0.53 μm probe beams are focused at the sample with separate objectives. The change in reflectivity of the probe is monitored by an APD with a lock-in amplifier. RC = reflective Cassegrain, FO = focusing objective, B/S = beam splitter, and TL = tube lens. (b) IR-PHI image of a 0.1 μm diameter polystyrene bead recorded with a step size of 0.05 μm. The pump and probe powers at the sample were 60 and 50 mW, respectively. (c) Line profile extracted from the image in panel (b) showing a full width at half-maximum (fwhm) of 0.3 μm.
technique that is capable of recording images with 0.3 μm spatial resolution over a wide field of view. In IR-PHI, an IR pump laser is focused at the sample at the same point as a nonresonant probe laser.25−30 Absorption of IR photons causes a local temperature change of the sample, which changes the reflected or transmitted intensity of the probe.31 IR-PHI experiments were performed by Erramilli and coworkers using a reflective Cassegrain objective to focus both the pump and probe beams.26,27 Recently, Cheng and co-workers used this scheme to study cells and organisms in vivo.29 The spatial resolution in these measurements is limited by the Cassegrain objective, and the best reported resolution that has been achieved to date is 0.6 μm.29,30 In our IR-PHI experiments, a tunable mid-IR optical parametric oscillator is focused at the sample using a Cassegrain objective, and a counterpropagating probe beam is focused at the same spot with a regular refractive objective. This arrangement has the advantage that a high NA objective can be used to focus the probe beam, which means we can obtain a spatial resolution of a few hundred nanometers, the diffraction limit for visible light. Here, we present images and spectra of several different types of soft matter systems (polystyrene beads, patterned polymer thin films, and single Escherichia coli cells) that demonstrate the sensitivity and spatial resolution of our IR-PHI system. Conventional visible wavelength PHI experiments are typically performed with a heat-transfer medium, which is usually, but not always, a liquid.31−38 Heat dissipation in the medium creates a refractive index gradient that acts as a lens and changes the transmission or reflection of the probe beam.39,40 This “thermal lens” amplifies the PHI signal to the extent that single-molecule detection has been demonstrated.41 However, the common liquids used for PHI measurements have strong IR absorbances, which means they are not suitable for IR-PHI experiments. Recent measurements have demonstrated that supercritical xenon can be used as the heat-transfer medium for PHI,38 but this is not practical for routine
measurements. Thus, the experiments described below were performed on dry samples. In this case, the PHI signal arises from thermal expansion and/or changes in the refractive index of the sample or the glass substrate. To understand the origin of the signal, thin-film reflectivity calculations and finite element (FE) simulations were used to model the IR-PHI experiments. The goal of the simulations is to elucidate the important factors that determine the magnitude of the IR-PHI signal in soft matter systems and to understand how the signal scales with the dimensions of the system.
2. METHODS 2.1. Experimental Section. Figure 1a shows a diagram of the experimental scheme. A tunable mid-IR optical parametric oscillator (M Squared Firefly-IR, 2.5−3.7 μm, 150 kHz repetition rate; or M Squared Firefly-IR Long Wavelength, 5.6−8.5 μm, 20 kHz repetition rate) was focused by a reflective Cassegrain objective (Edmund Optics 0.65 NA, or Pike Technologies 0.8 NA) onto the samples. A counterpropagating continuous wave probe laser (0.53 μm Spectral Physics Millenia Vs, or 1.06 μm iPG Photonics YLR-5-1064-LP) was focused at the same spot on the sample by a high NA refractive objective (Olympus RMS100X-PFO). The powers of the lasers at the sample were between 2 and 60 mW for the pump, and 10 and 50 mW for the probe. In all the experiments described below, the laser powers were kept below the damage threshold of the sample, which was confirmed by recording repeated images of the same sample area. In general, higher powers were used for the experiments on the smaller polymer beads. This was done both to increase the signal-to-noise level and because these samples have faster heat dissipation times and thus are more resistant to laser heating. To ensure the overlap of the two focal spots, we carefully optimized the beam paths until the transmitted probe beam was completely collinear with the incident mid-IR laser. The reflected probe was collected using a 50:50 beam splitter and sent to an avalanche photodiode (APD, 8839
DOI: 10.1021/acs.jpcb.7b06065 J. Phys. Chem. B 2017, 121, 8838−8846
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Figure 2. (a) IR-PHI image of two 0.46 μm polystyrene beads recorded at 3030 cm−1 with a 0.53 μm wavelength probe beam. The pump and probe powers were 6 and 20 mW, respectively. (b) The IR-PHI spectrum from a single bead recorded in the 4000−2600 cm−1 region, and (c) the FT-IR spectrum of a collection of beads. (d) IR-PHI image of a single 0.46 μm polystyrene bead recorded at 1428 cm−1 with a 1.06 μm wavelength probe beam. The pump and probe powers were 6 and 50 mW, respectively. (e) The IR-PHI spectrum of a single bead recorded in the 1850−1050 cm−1 region, and (f) the corresponding FT-IR spectrum.
sphere. A 3030 cm−1 plane wave propagated from the air domain into the glass domain perpendicular to the interface. To account for reflection at the interface, the total electromagnetic field was solved with just the air and glass domains. The computed field was then used as the background field for a second calculation, with the particle included in the simulation. The total absorbed power was determined by integrating the electromagnetic power loss density (Qrh) over the volume of the particle. Absorption cross sections for particles in a homogeneous environment calculated using COMSOL (σabs = ∭ QrhdV/P0, where P0 is the incident power) are compared to Mie theory calculations in the Supporting Information. The excellent agreement between the two calculations proves the accuracy of the finite element simulations. In the second step, the heat-transfer-in-solids module was used in a time-dependent study to simulate the heat dissipation for the system. The governing equation in this study is
Thorlabs APD120A). The signal from the avalanche photodiode was recorded by a lock-in amplifier (Stanford Research, SR844) that was referenced to the repetition rate of the OPO. Ensemble IR spectra were recorded with a PerkinElmer Frontier FT-IR spectrometer. Samples of polystyrene beads (Sigma-Aldrich) or E. coli (nonpathogenic E. coli from BEI Resources) were prepared by spin-coating. Thin-patterned photoresist polymer films (SHIPLEY Microposit S1813; 1.5 μm in thickness) were prepared by the standard photoresist protocol. The samples were mounted on a piezo stage (Physik Instrumente, P-527.3Cl), which was raster-scanned through the focus of the laser beams to form an image. The lock-in time constant for imaging was 10 ms, with a 30 ms pixel dwell time, and the step size for the piezo stage was 0.1 μm unless otherwise noted. Thus, a 5 × 5 μm2 image takes approximately 1 min to acquire. Spectra were recorded with a lock-in time constant of 100 and a 300 ms dwell time. The midIR laser was stepped at 1 cm−1 intervals, giving a total collection time of approximately 20 min for a single spectrum. 2.2. Finite Element Simulations. Finite element simulations of the experiments were performed with COMSOL Multiphysics (ver. 5.2a). In our model, a large sphere surrounded by perfectly matched layers was created to simulate the physical domain. For simulations of particles on a glass surface the top hemisphere was assigned as the air domain, whereas the bottom part was the glass domain. A smaller polystyrene sphere was built to sit on the interface with a small contact area,42 which was defined to have a radius of 0.4× the radius of the particle. The dimensions of the computational domain were chosen so that further increases in size did not change the solution. A diagram of the mesh used in the model is presented in the Supporting Information. The simulations comprised of three fully coupled studies. In the first study, the electromagnetic waves module of COMSOL was used to determine the IR absorption of the polystyrene
Cpρ
∂T + ∇·( −k∇T ) = Q d(t ) ∂t
(1)
where T is the temperature, Cp, ρ, and k are the heat capacity, density, and thermal conductivity of the different materials in the system, respectively, and Qd(t) is a time-dependent heating term.43 Qd(t) extends over the particle, and its time dependence was modeled as a Gaussian pulse with the same duration as that of the IR laser (10 ns). The magnitude of Qd(t) was determined from the calculated absorption cross sections from the electromagnetic wave simulations in step one and the power density of the pump laser (which was calculated assuming an 8 μm spot size and 60 mW power). The different materials were assumed to have the same temperature at their interfaces (i.e., thermal interface conductance was neglected). A solid mechanics module was coupled to the heat-conduction-insolids module through the thermal expansion multiphysics node in COMSOL to determine the changes in the dimensions 8840
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Figure 3. (a) IR-PHI images of a single E. coli cell at 2968 cm−1. (b) IR-PHI spectrum of a single E. coli cell. (c) Ensemble FT-IR spectrum of the E. coli sample. (d, e) IR-PHI images of a patterned photoresist recorded over different fields of view. (f) The corresponding white light image for panels (d) and (e). The pump and probe powers were 2 and 10 mW, respectively, and the step sizes for the images were 0.1 μm for panel (a), 0.5 μm for panel (d) and 1 μm for panel (e).
scan through the bead. The fwhm is 0.3 μm. This is much smaller than the spot size of the IR pump laser, which was determined to be 8 μm by direct imaging of a 1.1 μm polystyrene bead (see the Supporting Information). The measured resolution is equal to the expected spatial resolution for the probe. Thus, these results demonstrate super-resolution IR imaging of submicron objects,12,29 at a signal-to-noise level of approximately 70:1. The spatial resolution is an improvement over previous copropagating IR-PHI schemes26,29 due to a combination of the superior performance of refractive objectives compared to that of Cassegrains for focusing and collecting the visible probe and the shorter probe wavelength. Examples of spectra recorded by scanning the wavelength of the IR pump are presented in Figure 2. Figure 2a shows an image of two 0.46 μm diameter polystyrene beads, and a spectrum recorded from a single bead is shown in Figure 2b. Also shown in Figure 2c is the spectrum from a large number of 0.46 μm polystyrene beads recorded by FT-IR. The peaks observed in the IR-PHI and FT-IR spectra in Figure 2b,c are assigned to the C−H stretches of polystyrene.45 Note that the polystyrene FT-IR spectrum was used to calibrate the IR OPO used for the IR-PHI measurements and that the background signal from the glass substrate has been subtracted in the IRPHI spectrum (see the Supporting Information). Figure 2d−f shows images and spectra recorded in the 5.4− 9.6 μm wavelength region, which lies within the so-called “IR fingerprint” region. In this wavelength region, conventional microscope coverslips strongly absorb IR radiation much more than in the 2.5−3.7 μm region for Figure 2a,b. Thus, these measurements were performed on ZnSe windows. Because ZnSe is not transparent in the green spectral region, a near-IR laser (1.06 μm) was used for the probe beam for these measurements. This slightly reduces the spatial resolution but does not affect the signal-to-noise level.
of the materials due to heating. In this calculation, the bottom surface of the glass substrate was fixed but all other surfaces were free to move. In the third step, a second frequency-domain electromagnetic waves study was performed. A plane wave at 0.53 μm was introduced from the glass side of the system. Similar to the first electromagnetic waves study, the background field was first obtained without the particle. The scattered field with the particle present was then solved for every time step from the heat-conduction study in step two. Because polystyrene and glass do not absorb at 0.53 μm, the only measurable optical effect is the change in the scattering or reflection of the probe light. As shown below, the properties of the glass substrate are only slightly affected by IR excitation; the main effects are changes in the size and refractive index of the particle. Thus, the IR-PHI signal is simply equated to changes in the scattering cross section σsc of the polystyrene bead. σsc was computed by integrating the outgoing electromagnetic energy flux over the particle surface (σsc = ∬ n̂ · S⃗ dA/P0, where S⃗ is the Poynting vector for the scattered field and n̂ is a unit vector normal to the surface). The values of σsc calculated through COMSOL for particles in a homogeneous environment are compared to Mie theory calculations in the Supporting Information. The two calculations are again in excellent agreement. The σ sc calculations were performed for thermal expansion only, changes in refractive index only, and for both effects.
3. RESULTS AND DISCUSSION Figure 1b shows an IR-PHI image of a single 0.1 μm polystyrene bead on a glass substrate. These measurements were performed with a pump wavelength of 3.3 μm (3030 cm−1), with a 0.53 μm wavelength probe beam. Polystyrene beads were chosen for these measurements because they can be produced with a narrow size-distribution and the IR absorption spectrum of polystyrene is well known.44 Figure 1c shows a line 8841
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Figure 4. (a) Temperature profile of the system at the peak temperature for a 0.1 μm polystyrene sphere on a glass surface in air. (b) Refractive index change and (c) associated solid displacement of the system corresponding to the temperature profile in panel (a). (d, e) Plots of σsc vs time for 0.1 and 0.8 μm diameter polystyrene beads. The total change in σsc is plotted along with the individual effects (refractive index and size changes). (f) IR-PHI signal vs diameter for different-sized polystyrene beads.
The high spatial resolutions demonstrated in Figures 1 and 2 show that IR-PHI has the potential to access biological information at the subcellular level. To demonstrate the utility of IR-PHI for biological samples, Figure 3a,b shows IR-PHI images and spectra recorded from a single E. coli cell. Note that the dimensions of these specific cells are in the order of a micron, which means it is not possible to resolve their internal structure. The spectrum has characteristic absorption features at 2962 and 2934 cm−1, which are assigned to C−H stretching vibrations from the alkane chains of the lipids in the cell.46 The signal-to-noise level for the E. coli sample is comparable to that for our model system (polystyrene), which is encouraging given that biological samples contain a wide range of different chemical species. The spectrum in the 3000 cm−1 region for the E. coli cell is very broad due to the contributions from water in the cells. This is consistent with the FT-IR spectrum of an ensemble of E. coli cells presented in Figure 3c. Note that in contrast to the spectra for the polystyrene beads, there are now significant differences between the single cell and ensemble IR spectra. This implies that IR-PHI measurements may be able to provide information about differences in the chemical makeup of different cells in a sample.47,48 The images presented in Figures 1 and 2 were recorded over a relatively small area, with a step size of either 0.05 or 0.10 μm. This is similar to the typical field of view in scanning probe measurements. However, images over much larger areas can be easily obtained; indeed, the image size is only limited by the scanning stage used in the measurements. Figure 3d,e shows images recorded from a polymer film that was patterned through photolithography. The pattern consists of a grid of 2 μm wide trenches. In these experiments, the pump laser was tuned to the C−H stretching vibrations of the polymer. The IR-PHI images show that the trenches are sharply contrasted with the polymer blocks and that thickness variations in the film from the spin-coating process can be identified. This
demonstrates that IR-PHI images can be recorded over large areas and that bulk material can be imaged, not just point-like objects. A scattered light image of the sample is shown in Figure 3f. The spectra and images presented above demonstrate that IR-PHI can sensitively characterize soft matter systems without using the heat-transfer liquid that is employed in traditional PHI experiments.31−34,39−41 This raises the question of the origin of the signal in these experiments. To address this issue, calculations were performed for the change in reflectivity of the probe laser due to IR heating. Specifically, for the polystyrene beads we calculated the change in scattering of the probe beam through FE simulations, and for the films, the change in reflectivity was calculated using the standard equations for thin films.49−52 One of the major goals of the simulations is to establish how the IR-PHI signal scales with the dimensions of the system being interrogated. This is important for developing IR-PHI as a quantitative imaging technique. We first examine thin films, as the calculations are more straightforward than those for the particles.49−52 The IR-PHI signal is equated to the difference in reflectivity for a heated film compared to that of an unheated film. The changes in reflectivity versus thickness for 0.53 and 1.06 μm probe wavelengths with ΔT = 50 °C (consistent with the calculations for the particles in Figure 4 described below) are shown in Figure S3 of the Supporting Information. Heating causes thermal expansion and also changes the refractive index of the film, and both these effects change the reflectivity coefficient. (The individual contributions from thermal expansion and changes in the refractive index are presented in Figure S3, along with the total change in reflectivity.) The calculations show that the effects from refractive index changes and thermal expansion oppose each other and that the overall signal is controlled by the refractive index changes for the range of film thicknesses considered (0−2 μm). The ΔR/R signal shows strong etalon 8842
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Figure 5. Scattered light and IR-PHI images for different-sized polystyrene beads. (a, b) 0.46 and 0.6 μm beads, 14 × 14 μm2 image size with 0.2 μm steps; (c, d) 0.6 and 1.1 μm beads, 15 × 15 μm2 image size with 0.3 μm steps. The scattered light images are on the left and the IR-PHI images are on the right. The different intensities in the scattered light images show that the beads have different sizes. Note the change in sign of the IR-PHI signal for the larger bead in panel (d).
change in refractive index were then determined using σabs and modeling the heating laser as a Gaussian pulse with a 10 ns full width at half-maximum. Figure 4a shows the maximum temperature in the system following IR excitation of a 0.1 μm polystyrene sphere on a glass substrate. There are significant temperature increases for the particle and the air surrounding the particle. The temperature change in the glass substrate is much smaller than that in air due to the larger effective heat capacity (ρCp) for glass compared to that of air. Plots of the corresponding changes in the refractive index (determined from the values of dn/dT for each material) and the thermal expansion are presented in Figure 4b,c, respectively. Videos of the timedependent changes in the temperature (Video S1), refractive index (Video S2), and thermal expansion (Video S3) are presented in the Supporting Information. The simulations show that there are significant changes in the temperature of the surroundings following IR excitation. However, the changes in
effects that are well known for thin films.52 A consequence of the etalon effects is that an increase in film thickness can cause an increase or decrease in the IR-PHI signal and even a change in sign, depending on the exact thickness of the film. Analysis of the IR-PHI signal for particles is more complicated because there are no closed form expressions for the absorption and scattering of particles on a substrate. Thus, finite element simulations were used to determine the IR absorption of the particles and the change in reflection of the probe beam due to heating. First, the IR absorption cross sections σabs of the polystyrene beads at 3030 cm−1 were calculated. The values obtained for different-sized particles are given in the Supporting Information. For a 0.1 μm diameter bead on a glass substrate, we find σabs ≈ 40 nm2. For the bead sizes considered in this article (0.1−1.0 μm), σabs is proportional to volume. This is expected as the size of the beads is much less than that of the IR wavelength, so their response is in the quasistatic limit.53,54 The time-dependent temperature change in the system and the associated thermal expansion and 8843
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Experiments to probe the size dependence of the IR-PHI signal were performed by imaging samples consisting of two different-sized beads. Figure 5 shows results from experiments with 0.46 and 0.6 μm beads (Figure 5a,b) and 0.6 and 1.1 μm beads (Figure 5c,d). Scattered light images are shown on the left and IR-PHI image on the right. The results are in qualitative agreement with the simulations. For small beads (Figure 5a,b), the IR-PHI signal is of the same sign for different sizes of beads. However, for the 0.6 and 1.1 μm beads (Figure 5c,d), there is a change in sign of the IR-PHI signal with size, consistent with the simulations in Figure 4f. Note that the finite element simulations predict that the sign change should occur at approximately 0.7 μm diameter, which we do not see in our experiments (the IR-PHI signal is of the same sign for measurements with 0.6 and 0.8 μm beads). However, Mie theory calculations of Δσsc show that the size where the signal changes sign is very sensitive to the effective refractive index of the environment. This suggests that small changes to the model used for the beads on the substrate (varying the contact surface, adding a wetting layer, etc.) could bring the finite element simulations into better agreement with the experiments. Note that the IR-PHI signal for the larger particle in Figure 5d has both positive and negative parts. This is because the spatial resolution of the system is good enough to resolve the internal structure of the scattering efficiency for the larger beads. This structure does not appear in the scattered light images because the PHI and scattered light images are recorded under slightly different focusing conditions.39,40 The data and analysis presented above shows that the magnitude and sign of the IR-PHI signal have a complicated dependence on the dimensions of the sample for both thin films and particles. This is actually an issue for all reflectivity measurements.49−52 It is especially a problem here because the dimensions of the samples are in the order of the probe wavelength and indicate that IR-PHI measurements in reflection mode are not well suited for quantitative imaging of the sample thickness. The demonstration that the IR-PHI signal for particles is proportional to Δσsc at the probe wavelength is a major conclusion of this article and is seemingly at odds with the results and analysis in refs 31−34 and 39−41. Previous PHI measurements were mostly performed for small nano-objects in a heat-transfer medium. In this case, the dimensions of the thermal lens are determined by the thermal diffusivity of the medium and the modulation frequency for the pump laser.34,39,40 Changing the size of the absorber changes the amount of heat deposited into the medium, which changes the magnitude of the thermal lens (the contrast between the heated and unheated regions of the sample) but not its dimensions. Thus, the PHI signal simply depends on the absorption cross section of the particle. In contrast, in IR-PHI measurements on dry samples the particle acts as the lens and the signal comes from the change in scattering caused by the refractive index change and thermal expansion of the particle following pump laser excitation. The temperature rise induced by the pump laser is the same for different-sized particles because the IR absorption cross section and the total heat capacity of the particle are both proportional to volume. Thus, for particles made from the same material, the signal follows Δσsc at the probe wavelength.
the physical properties of the system (refractive index and dimensions) are localized in the polystyrene bead. The final step in the simulations involves calculating the time-dependent change in the reflection of the 0.53 μm wavelength probe beam. Because the changes in dimensions and refractive index are much larger for the bead than those of the surroundings, we equate the IR-PHI signal to the change in the scattering cross section, σsc, of the bead at the probe wavelength. This approach is different from the conventional description of PHI experiments,39,40 and can be understood through the optical theorem.53,54 The optical theorem states that the extinction of the probe beam at the detector due a particle, ΔItot, arises from the interference between the light scattered by the particle and the reflected or transmitted probe beam.53,54 It is straightforward to show that ΔItot/I0 = −σex(λ)/ A, where σex(λ) is the extinction cross section of the particle at the probe wavelength and A is the area of the beam at the sample (see the Supporting Information for details). In PHI experiments, the detected signal is proportional to the change in probe intensity induced by the pump laser, which is Δ(ΔItot)/I0 = −Δσex(λ)/A. For our system, polystyrene beads with a visible probe laser, σex, is dominated by scattering. Thus, the PHI signal is proportional to the change in scattering cross section of the particle, Δσsc, at the probe wavelength. Figure 4d,e shows plots of the σsc versus time for 0.1 and 0.8 μm diameter polystyrene beads for only refractive index changes, only thermal expansion, and for both effects. There are several points to note from this figure: First, the changes in σsc from the refractive index changes and thermal expansion are both significant and have opposite signs. Second, the time dependence of Δσsc changes with the size of the particle. This means that the IR-PHI signal cannot be simply equated to the maximum value of Δσsc. To account for the different timescales for the signal, the Δσsc data was integrated over time. The integrated data (the “PHI signal”) is plotted in Figure 4f versus the particle diameter. Plots of the individual components (the contributions from thermal expansion and changes in the refractive index of the particle) for the different-sized particles are presented in the Supporting Information. Figure 4f shows that the IR-PHI signal is not simply proportional to the absorption cross section of the nanoobject being interrogated.31−34,39−41 Furthermore, the simulations predict that the signal should change sign for large beads compared with small beads. To understand this effect, we note that for small changes in σsc, which is the case for our experiments, Δσsc can be written as ⎛ ∂σ ⎞⎛ ∂n ⎞ ⎛ ∂σ ⎞⎛ ∂R ⎞ Δσsc ≈ ⎜ sc ⎟⎜ ⎟ΔT + ⎜ sc ⎟⎜ ⎟ΔT ⎝ ∂n ⎠⎝ ∂T ⎠ ⎝ ∂R ⎠⎝ ∂T ⎠
(2)
where ∂R/∂T > 0 and ∂n/∂T < 0 for polystyrene. For small particles σsc increases with both R and n, that is (∂σsc/∂R), (∂σsc/∂n) > 0. This means that refractive index changes and thermal expansion will have opposite effects on Δσsc, as noted above, and we would expect the signal to be determined by one or the other. However, at larger sizes, resonances occur in σsc,54 which means that (∂σsc/∂R) and (∂σsc/∂n) can be positive or negative. In this case, the signal has a complicated size dependence and can change sign, as seen in the simulations in Figure 4f. Mie theory calculations of Δσsc versus diameter are presented in the Supporting Information. These calculations show the same effects as those of the finite element simulations in Figure 4. 8844
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4. SUMMARY AND CONCLUSIONS IR-PHI provides improved spatial resolution and sensitivity compared with conventional far-field IR imaging techniques. In this article, a novel optical setup for IR-PHI based on counterpropagating pump and probe beams is presented. The advantage of this configuration is that a high NA refractive objective can be used to focus the probe rather than a lower NA reflective objective. Experiments with submicron-sized polystyrene beads show a spatial resolution of 0.3 μm, which is the highest spatial resolution reported to date for far-field IR imaging measurements. IR-PHI can also be used to record images over a wide field of view, which is an advantage compared to scanning-probe measurements, such as AFM-IR. Thus far, we have used IR-PHI to record high quality images and spectra (signal-to-noise level in the order of 100:1) of single E. coli cells and polystyrene beads with sizes as small as 0.1 μm. The 0.1 μm polystyrene beads have IR absorption cross section of approximately 40 nm2, which is equivalent to the absorption cross section of a 10 nm diameter Au nanoparticle at its plasmon resonance, and are the smallest objects that have been detected by IR-PHI to date. Analysis of the IR-PHI signal shows that pump laser-induced changes in the refractive index and thermal expansion are both important and that these two effects counteract each other. This leads to a complicated dependence of the signal on the dimensions of the sample in our reflection mode experiments, which means that this technique is not well suited for quantitative cross-sectional measurements.55 However, the high sensitivity and spatial and spectral resolutions of the technique make it attractive for characterizing the chemical composition of soft matter systems20 as well as for “stain-less staining” measurements of biopsy samples.56,57
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ACKNOWLEDGMENTS
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REFERENCES
G.V.H. and Z.L. were supported by the United States National Science Foundation (CHE-1502848) and the Office of Naval Research (Award No.: N00014-12-1-1030). M.K. acknowledges the National Science Foundation (CHE-1563528). The IR OPO system was purchased through the DURIP Award W911NF1410604.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b06065. Images and spectra of 1.1 μm polystyrene beads recorded by direct IR absorption; description of the optical theorem applied to PHI; comparison of absorption and scattering cross sections calculated through COMSOL and the Mie theory; time-dependent scattering cross sections for beads with different sizes; temperaturedependent reflectivity changes for thin polymer films (PDF) Mie theory calculations of the changes in scattering cross section from heating; and videos of the time-dependent changes in temperature, refractive index, and thermal expansion following IR excitation (ZIP)(ZIP)(ZIP)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: 574-631-9320. ORCID
Masaru Kuno: 0000-0003-4210-8514 Gregory V. Hartland: 0000-0002-8650-6891 Notes
The authors declare no competing financial interest. 8845
DOI: 10.1021/acs.jpcb.7b06065 J. Phys. Chem. B 2017, 121, 8838−8846
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