Vibrational phase imaging by stimulated Raman scattering via polarization-division interferometry

Stimulated Raman scattering (SRS) allows chemical identification of substances based on their third-order nonlinear vibrational susceptibility (3) ( ) χ ω . In its standard singlefrequency implementation, SRS can only access the imaginary part of (3) ( ) χ ω . Here we introduce interferometric SRS (iSRS), which has the capability to measure both the real and the imaginary parts of the nonlinear susceptibility. With respect to a standard SRS setup, iSRS simply requires the insertion of a few optical elements in the Stokes(pump) beam pathway to generate an intrinsically phase-coherent local oscillator. While preserving the acquisition speed and the simplicity of single-frequency SRS, iSRS considerably increases its information content by providing access to the vibrational phase, which allows one to distinguish overlapping species in congested spectra and is more robust with respect to noise. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Coherent Raman scattering (CRS) encompasses a class of nonlinear spectroscopy and microscopy techniques for label-free identification of molecules and solids based on their characteristic vibrational fingerprints, which find a growing range of applications in life and materials sciences [1,2]. By illuminating the system with synchronized pump (at frequency ω p ) and Stokes (at frequency S ω ) pulses, whose frequency difference matches a vibrational frequency Ω of the molecule, CRS sets up a vibrational coherence which drives a nonlinear signal many orders of magnitude stronger than in the case of spontaneous Raman. In coherent anti-Stokes Raman scattering (CARS) [3] the nonlinear signal is at the anti-Stokes frequency, aS p ω ω = +Ω, while in stimulated Raman scattering (SRS) [4] the signal is emitted at the Stokes/pump frequency, resulting in Stokes amplification and pump attenuation, called stimulated Raman gain (SRG) and stimulated Raman loss (SRL), respectively. The CRS signal depends on the third-order nonlinear vibrational susceptibility, which can be written as (3) (3) NR χ term, on the other hand, is the real vibrationally nonresonant susceptibility generated by the electronic contributions of the molecules under study and of the surrounding environment. Standard CRS techniques do not allow the retrieval of the full complex nonlinear susceptibility (3) ( ) χ ω . In CARS the nonlinear signal is given by where p E and S E are the pump and Stokes field amplitudes, respectively. The measured intensity is thus resulting in a complicated mixing of the real and imaginary components of the nonlinear susceptibility. SRS, on the other hand, measures the Stokes/pump intensity change, resulting in the signal (3) Im( ) [19,20], and i anti-Stokes f application du also been app for high-speed In this pa detection to s of measuring retrieving the

Experimental results
We experimentally tested the iSRS configuration using a previously described SRS setup driven by a compact fiber laser [29,30]. The system starts with a femtosecond Er:fiber oscillator seeding two synchronized Er:doped fiber amplifiers, each providing 80-fs pulses at ~1550 nm wavelength with ~350 mW average power. The output of the first branch is frequency doubled by a long periodically poled lithium niobate (PPLN) crystal, generating ~2-ps pump pulses at ~780 nm wavelength with 120-mW average power. The second branch feeds a highly nonlinear fiber generating a supercontinuum, the long-wavelength part of which is frequency doubled in a second PPLN crystal, with a fan-out geometry, generating ~1-ps Stokes pulses with 2-5 mW average power, continuously tunable in the 930-1060 nm range. In this way, it is possible to vary the pump-Stokes frequency detuning in the 2070-3400 cm −1 range, which comprises the entire CH molecular vibrational region (2800-3200 cm −1 ). The pump beam is modulated at 1 MHz by an acousto-optic modulator and the SRG is detected by a photodiode in combination with a high-frequency lock-in amplifier. A 6-mm thick birefringent YVO 4 plate is inserted in the Stokes beam to generate a LO which is anticipated by ~4ps [27]. After the sample, the delay between Stokes and LO is canceled with interferometric precision by a pair of YVO 4 wedges (apex angle 10°), whose insertion can be finely tuned via a mechanical motor [28,31]. The use of a wedge pair is crucial, as it would be very difficult to find two plates with precisely matched thickness. The QWP and the LP, which are inserted after the wedges, are also rotated through motorized mechanical stages. We note that, due to the common-path nature of the interferometer, phase stability between Stokes and LO fields is achieved effortlessly and with high fidelity. We first tested our birefringent interferometer by measuring the Stokes intensity 0 , ) (θ φ S I , in the absence of the pump beam. The experimental colormap, reported in Fig. 2(b), is in excellent agreement with the calculated one ( Fig. 2(a)). We then turned on the pump beam and measured ( , ) iSRS I θ φ on acetone at 2950 cm −1 detuning, for which the ratio of real and imaginary parts of χ (3) matches the value used in the calculations. The results, shown in Fig.  2(d), are again in excellent agreement with the computed intensities (Fig. 2(c)). As shown by Fig. 2, there are several working points of the interferometer that allow isolating the real and the imaginary part of the third-order nonlinear susceptibility. In the following, we chose ( , ) (61°, 151°) θ φ = , to measure (3) Im( ) χ and ( , ) (54°, 131°) θ φ = for (3) Re( ) χ (see spots "A" and "B" in Fig. 2(b-c)). These working points were selected to obtain the highest positive signals. Furthermore, we highlight the possibility of carrying out a complete measurement of the complex vibrational susceptibility in parallel, by simply duplicating the interferometric block of the setup composed by QWP and LP, after the wedge pair, and properly setting the working point of each of the two blocks. Having verified the working principle of the interferometer, we proceeded to its application. Solid lines in Fig. 3 report real and imaginary parts of the vibrational susceptibility measured for different solvents. Experimental data were fitted by Eq. (1) with two or three resonances, keeping fixed the resonance frequencies ( k Ω ) and the linewidths ( k Γ ) parameters for real and imaginary parts. The fits (dashed lines in Fig. 3) show a good agreement with the data. The offset present in the (3) Re( ) χ measurements is due to the nonresonant part of the vibrational susceptibility, which is constant with respect to the Raman Shift, and indicated with dashed orange line in Fig. 3.
Finally, to show the added information content provided by iSRS, we imaged a test sample consisting of a mixture of poly-methylmethacrylate (PMMA) and polystyrene (PS) beads with 6-and 3-µm diameters, respectively. Figure 4 shows in panels (a) and (b) iSRS images of the imaginary and the real part of the nonlinear susceptibility of the sample, respectively, at a frequency 2990 cm −1 , intermediate between the main Raman resonances of PMMA (2953 cm −1 ) and PS (3060 cm −1 ). Due to the different vibrational phases of the two materials at this frequency, one observes a contrast reversal between the two images, with the PMMA (PS) beads dominating in the imaginary (real) image. Having measured the full complex nonlinear susceptibility at this frequency, one can easily calculate amplitude and phase. The image of the vibrational phase of the sample, reported in Fig. 4 (c), shows an enhanced contrast between the two components, with very sharp boundaries even at the thin borders of the beads, demonstrating that iSRS provides a more robust discrimination criterion than the Raman amplitude of standard SRS setups, provided that, as explained in Ref [22], the two measurement of Real and Imaginary parts are performed with the same level of detected power. The selected working points (see. spots "A" and "B" in Fig. 2(b-c)) satisfy this condition being the measured intensities of 75 mV and 68 mV respectively. The corresponding noise variation will be therefore of the order of 5%, a difference that can be considered negligible. Finally, Fig. 4 (d) plots real and imaginary components of the signal against each other for every pixel of the image. The points are clustered in two well-defined clouds, each with its own vibrational phase, corresponding to the two chemical species composing the sample (PS along the red line with ≈20° phase, PMMA along the green line with ≈75° phase).

Summary
In conclusion, we have extended interferometric detection to single-frequency SRS, which is currently the mainstream CRS technique for high-speed label-free vibrational imaging. We use an in-line common-path interferometer to create an intrinsically phase-stable LO pulse which interferes with the Stokes pulse, allowing measurement of both real and imaginary components of the nonlinear Raman signal. Our approach involves minimal modifications of a standard SRS setup and in particular, if compared with iCARS, it does not require an LO pulse at a different color with respect to pump and Stokes. Access to the vibrational phase, which is more robust with respect to noise [22], significantly enhances the chemical selectivity of single-frequency SRS, since it enables one to distinguish between different overlapping vibrational resonances with comparable amplitudes but different phases.

Appendix: Interferometer working principle
The common-path interferometer that allows one to independently measure real and imaginary parts of the (3) χ vibrational susceptibility can be modeled via Jones algebra [26].
Here we report the calculations in detail. In the following, the delay between the two equally intense orthogonally polarized (along x and y directions) Stokes and LO after the sample is assumed to be already canceled out by the proper insertion of the birefringent wedges, so that only the effect of the QWP and the LP will be considered. In the absence of the pump pulse and neglecting linear absorption from the sample at the Stokes wavelength, as expected in SRS, the resulting light field of the two replicas entering the interferometer will be polarized at −45° with respect to the x direction, and it is represented by the Jones vector LP and QWP are the two Jones matrices representing the linear polarizer and the quarter wave plate, and are defined as 1 cos (2 ) sin (2 )  1  ) sin (2 ) 1 cos (2 ) The light intensity reaching the detector can therefore be written as where θ and φ are the angles formed by the transmission axis of the polarizer and by the optical axis of the wave plate with the x direction respectively, as shown in Fig. (5). Values of 0 ( , ) S I θ φ are reported in Figure 2(a). In presence of the SRG signal due to interaction with the pump pulse in the sample, the Stokes electric field entering the interferometer is modified as where δ is a complex quantity, responsible for SRG, that modifies the vertical replica. Due to the complex nature of δ , the new resulting field E is slightly rotated (shown by the yellow arrow) with respect to the its original direction (that of 0 E , along the red arrow) and acquires a small elliptical polarization, represented as the orange ellipse in Fig. 5. In analogy to Eq. Im( ) sin(2( )) 2 1 Re( ) 2 cos(2 ) cos(2( 2 )) sin(2 ) sin(2( 2 )) 4 1 2 cos(2 ) cos(2( 2 )) 1 , , ) sin(2( )) Re( ) 2 1 2 cos(2 ) cos(2( 2 )) sin(2 ) sin(2( 2 )) which can finally be rearranged as  Fig. 2 (c) and also in Fig. 3 (d). Finally, the iSRS signal is defined as reported in Eq. (8).