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Super-Resolution Far-Field Infrared Imaging by Photothermal Heterodyne Imaging Zhongming Li, Kyle Aleshire, Masaru Kuno, and Gregory V Hartland J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b06065 • Publication Date (Web): 25 Jul 2017 Downloaded from http://pubs.acs.org on July 30, 2017

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The Journal of Physical Chemistry

Super-Resolution Far-Field Infrared Imaging by Photothermal Heterodyne Imaging

Zhongming Li, Kyle Aleshire, Masaru Kuno, Gregory V. Hartland*

Department of Chemistry and Biochemistry University of Notre Dame Notre Dame, IN 46556

*

Corresponding author: e-mail: [email protected]; tel.: 574-631-9320 1 ACS Paragon Plus Environment


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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 paper we present a novel far-field IR imaging technique based on photothermal heterodyne imaging (IRPHI). In our version of IR-PHI an IR pump laser excites the sample, causing a small temperature rise that is detected by a counter-propagating visible probe beam. Images and spectra of several different types of soft matter systems (polystyrene beads, thin polymer films and single E. 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.

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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 imaging6-8 and laser ablation mass spectrometry.9-11 Among these, vibrational measurements stand out as non-destructive and label-free. 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 background-free and uses visible laser sources.1-3 Thus, Raman microscopes typically have superior spatial resolution and signal-to-noise 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 light (3 - 10 µm) is an order-of-magnitude 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 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, while it is around 0.5 µm for a regular Raman microscope.4 In order to overcome the spatial resolution challenge, several near-field 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



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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 paper we describe a novel implementation of infrared photothermal heterodyne imaging (IR-PHI),25-30 a far-field IR imaging 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 non-resonant 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 co-workers 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 counter-propagating 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. In the following we present images and spectra of several different types of soft matter systems (polystyrene beads, patterned polymer thin films and single E. coli cells) that demonstrate the sensitivity and spatial resolution of our IR-PHI system.


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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 molecules 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 super-critical 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 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: Figure 1(a) 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 counter-propagating 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



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NA refractive objective (Olympus RMS100X-PFO). The powers of the lasers at the sample were between 2 – 60 mW for the pump and 10 – 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 and because these samples have faster heat dissipation times and, thus, are more resistant to laser heating. In order 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 (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 Perkin Elmer 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 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 5x5 µm2 image takes approximately one minute to acquire. Spectra were recorded with a lock-in time constant of 100 ms and a 300 ms dwell time. The mid-IR laser was stepped at 1 cm-1 intervals, giving a total collection time of approximately 20 minutes for a single spectrum.


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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 avalanche photodiode (APD) with a lock-in amplifier. RC = reflective Cassegrain; FO = focusing objective; B/S = beam splitter; 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 mW and 50 mW, respectively. (c) Line profile extracted from the image in panel (b) showing a FWHM of 0.3 µm.

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 (PMLs) was created to simulate the physical domain. For simulations of particles on a glass surface the top hemisphere was assigned as the air domain, while the bottom part was the glass domain. A smaller polystyrene sphere was built to sit on the interface with a small contact area,42



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which was defined to have a radius of 0.4x 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 for this paper. 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 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 (Q !" ) over the volume of the particle. Absorption cross-sections for particles in a homogeneous environment calculated using COMSOL (𝜎abs =

Q !" 𝑑𝑉 𝑃! , where 𝑃! 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 Conduction 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 !"

𝐶! 𝜌 !" + ∇ ∙ −𝑘∇𝑇 = 𝑄! (𝑡)

(2)

where T is the temperature, 𝐶! , 𝜌 and 𝑘 are the heat capacity, density and thermal conductivity of the different materials in the system, and 𝑄! (𝑡) is a time dependent heating term.43 𝑄! (𝑡) extends over the particle, and its time dependence was modeled as a Gaussian pulse with the same duration as the IR laser (10 ns).

The magnitude of 𝑄! (𝑡) was determined from the 8

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calculated absorption cross-sections from the Electromagnetic Waves simulations in step one, and the power density of the pump laser (which was calculated assuming a 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 in Solids Module through the Thermal Expansion Multiphysics node in COMSOL to determine the changes in the dimensions 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. Since 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 will be 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 𝜎!" of the polystyrene bead. 𝜎!" was computed by integrating the outgoing electromagnetic energy flux over the particle surface (𝜎sc =

𝒏 ∙ 𝑺𝑑𝐴 𝑃! where 𝑺 is the Poynting vector for the scattered

field and 𝒏 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!"



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calculations were performed for thermal expansion only, changes refractive index only, and for both effects.

3. Results and Discussion: Figure 1(b) 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 1(c) shows a line scan through the bead. The full-widthhalf-maximum (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 sub-micron objects,12, 29

at a signal-to-noise level of approximately 70:1. The spatial resolution is an improvement over

previous co-propagating IR-PHI schemes,26, 29 due to a combination of the superior performance of refractive objectives compared to 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 2(a) shows an image of two 0.46 µm diameter polystyrene beads, and a spectrum recorded from a single bead is shown in Figure 2(b). Also shown in Figure 2(c) 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 Figures 2(b) and 2(c) are assigned to the C-H stretches of polystyrene.45 Note that the polystyrene FT-IR spectrum was used to calibrate the IR


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OPO used for the IR-PHI measurements, and that the background signal from the glass substrate has been subtracted in the IR-PHI spectrum (see the Supporting Information).

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 mW and 20 mW, respectively. (b) IR-PHI spectrum from a single bead recorded in the 4000 – 2600 cm-1 region, and (c) FT-IR spectrum of a collection of beads. (d) IR-PHI image of a single 0.46 µm polystyrene beads recorded at 1428 cm-1 with a 1.06 µm wavelength probe beam. The pump and probe powers were 6 mW and 50 mW, respectively. (e) IR-PHI spectrum of a single bead recorded in the 1850 – 1050 cm-1 region, and (f) corresponding FT-IR spectrum. Figures 2(d) - 2(f) show 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 Figs. 2(a) and 2(b). Thus, these measurements where performed on ZnSe windows. Because ZnSe is not transparent in the visible, a near-IR laser (1.06 µm) was used for



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the probe beam for these measurements. This slightly reduces the spatial resolution, but does not affect the signal-to-noise. The high spatial resolution demonstrated in Figures 1 and 2 shows that IR-PHI has the potential to access biological information at the sub-cellular level. To demonstrate the utility of IR-PHI for biological samples, Figures 3(a) and 3(b) show IR-PHI images and spectra recorded from a single E. coli cell. Note that the dimensions of these specific cells are on the order of a micron, which means it is not possible to resolve their internal structure. The spectrum has characteristic absorption features at 2962 cm-1 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 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 3(c). 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 make up 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 µm 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. Figures 3(d) and 3(e) show images recorded from a polymer film, which was patterned through photolithography. The pattern consists of a grid of 2 µm wide trenches. In these experiments the pump laser was


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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 3(f).

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) and (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 mW 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). 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



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the probe laser due to IR heating. Specifically, for the polystyrene beads we calculated the change in scattering of the probe beam through Finite Element (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 an unheated film. The changes in reflectivity versus thickness for 0.53 µm and 1.06 µm probe wavelengths with ∆𝑇 = 50°C (consistent with the calculations for the particles in Figure 4 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, as well as 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 ∆𝑅 𝑅 signal shows strong etalon 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 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


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reflection of the probe beam due to heating. First, the IR absorption cross-sections 𝜎!"# 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 𝜎!"# ≈ 40 nm2.

For the bead sizes considered in this paper (0.1 to 1.0 µm), 𝜎!"# is

proportional to volume. This is expected as the size of the beads is much less than the IR wavelength, so their response is in the quasi-static limit.53-54 The time-dependent temperature change in the system, and the associated thermal expansion and change in refractive index were then determined using 𝜎!"# and modeling the heating laser as a Gaussian pulse with a 10 ns fullwidth-at-half-maximum. Figure 4(a) 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 air due to the larger effective heat capacity (𝜌𝐶! ) for glass compared to 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 Figures 4(b) and 4(c), respectively. Videos of the time-dependent changes in the temperature (Video S1), refractive index (Video S2) and thermal expansion (Video S3) are presented in the Supporting Information for this paper. The simulations show that there are significant changes in the temperature of the surroundings following IR excitation.

However, the changes in the physical properties of the system

(refractive index and dimensions) are localized in the polystyrene bead.



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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) and (e) Plots of 𝜎!" versus time for 0.1 and 0.8 µm diameter polystyrene beads. The total change in 𝜎!" is plotted, along with the individual effects (refractive index and size changes). (f) IR-PHI signal versus diameter for different sized polystyrene beads.

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 the surroundings, we equate the IR-PHI signal to the change in the scattering cross-section 𝜎!" 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, Δ𝐼!"! , arises from the interference between the light


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scattered by the particle and the reflected or transmitted probe beam.53-54 It is straightforward to show that Δ𝐼!"! 𝐼! = − 𝜎!" (𝜆) 𝐴 where 𝜎!" (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 Δ𝐼!"!

𝐼! = − Δ𝜎!" (𝜆) 𝐴.

For our

system — polystyrene beads with a visible probe laser — 𝜎!" is dominated by scattering. Thus, the PHI signal is proportional to the change in scattering cross-section of the particle Δ𝜎!" at the probe wavelength. Figures 4(d) and 4(e) show plots of the 𝜎!" 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 these figures: First, the changes in 𝜎!" from the refractive index changes and thermal expansion are both significant and have opposite signs. Second, the time dependence of Δ𝜎!" changes with the size of the particle. This means that the IR-PHI signal cannot be simply equated to the maximum value of Δ𝜎!" . To account for the different timescales for the signal, the ∆𝜎!" data was integrated over time. The integrated data (the “PHI signal”) is plotted in Figure 4(f) versus 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 4(f) shows that the IR-PHI signal is not simply proportional to the absorption cross-section of the nano-object being interrogated.31-34,

39-41

Furthermore, the simulations

predict that the signal should change sign for large beads compared to small beads. To understand this effect, we note that for small changes in 𝜎!" , which is the case for our experiments, Δ𝜎!" can be written as:



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∆𝜎!" ≈

𝜕!!"

𝜕𝑅

𝜕𝑅

𝜕𝑇

∆𝑇 +

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𝜕!!"

𝜕𝑛

𝜕𝑛

𝜕𝑇

∆𝑇

(1)

where 𝜕𝑅 𝜕𝑇 > 0 and 𝜕𝑛 𝜕𝑇 < 0 for polystyrene. For small particles 𝜎!" increases with both R and n, that is 𝜕𝜎!" 𝜕𝑅 , 𝜕𝜎!" 𝜕𝑛 > 0. This means that refractive index changes and thermal expansion will have opposite effects on ∆𝜎!" , as noted above, and we would expect the signal to be determine by one or the other. However, at larger sizes resonances occur in 𝜎!" ,54 which means that 𝜕𝜎!" 𝜕𝑅 and 𝜕𝜎!" 𝜕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 4(f). Mie theory calculations of ∆𝜎!" versus diameter are presented in the Supporting Information. These calculations show the same effects as the Finite Element simulations in Figure 4. 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 (Figs. 5(a) and (b)), and 0.6 and 1.1 µm beads (Figs. 5(c) and (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 (Figs. 5(a) and (b)) the IRPHI signal is the same sign for different sizes beads. However, for the 0.6 and 1.1 µm beads (Figs. 5(c) and (d)) there is a change in sign of the IR-PHI signal with size, consistent with the simulations in Figure 4(f). 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 IRPHI signal is the same sign for measurements with 0.6 and 0.8 µm beads). However, Mie theory calculations of ∆𝜎!" 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


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the IR-PHI signal for the larger particle in Figure 5(d) has both positive and negative parts. This is because the spatial resolution of the system is good enough to resolve 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

Figure 5. Scattered light and IR-PHI images for different sized polystyrene beads. (a) and (b) 0.46 and 0.6 µm beads, 14x14 um image size with 0.2 um steps; (c) and (d) 0.6 and 1.1 µm beads, 15x15 um image size with 0.3 um 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).



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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 on the order of the probe wavelength, and indicates that IR-PHI is not well suited for quantitative imaging of the sample thickness. The demonstration that the IR-PHI signal for particles is proportional to ∆𝜎!" at the probe wavelength is a major conclusion of this paper, and is seemingly at odds with the results and analysis in Refs. [31-34, 39-41]. Previous PHI measurements were mostly performed in a heattransfer 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 crosssection 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 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 ∆𝜎!" at the probe wavelength.

4. Summary and Conclusions: IR-PHI provides improved spatial resolution and sensitivity compared to conventional far-field IR imaging techniques. In this paper a novel optical set-up for IR-PHI based on counterpropagating pump and probe beams is presented. The advantage of this configuration is that a


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high NA refractive objective can be used to focus the probe, rather than a lower NA reflective objective. Experiments with sub-micron 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 on 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 has 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, which means that this technique is not well-suited for quantitative cross-section measurements.55 However, the high sensitivity, and spatial and spectral resolution of the technique make it attractive for characterizing the chemical composition of soft matter systems,20 as well as for “stain-less staining” measurements of biopsy samples.56-57

Acknowledgements: GH and ZL were supported by the United States National Science Foundation (CHE-1502848), and the Office of Naval Research (Award No.: N00014-12-1-1030). MK acknowledges the National Science Foundation (CHE-1563528). The IR OPO system was purchased through the DURIP Award W911NF1410604.

Supplemental Information: The Supplemental Information for this paper includes images and



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spectra of 1.1 µm polystyrene beads recorded by direct IR absorption; a description of the optical theorem applied to PHI; comparison of absorption and scattering cross-sections calculated through COMSOL and Mie theory; time-dependent scattering cross-sections for beads with different sizes; temperature dependent reflectivity changes for thin polymer films; Mie theory calculations of the changes in scattering cross-section from heating; and videos of the timedependent changes in the temperature, refractive index and thermal expansion following IR excitation. This information is available free of charge via the Internet at http://pubs.acs.org


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