1. INTRODUCTION

Raman gain materials have a multitude of applications in nonlinear optics [1–3]. Consequently, materials with large Raman gain coefficients are of interest because they can induce a significant nonlinear response at relatively low pump powers. Several methods have been proposed and tested in the literature to determine the Raman gain coefficient, such as measurements on Raman scattering cross sections [4–7], the threshold pump energy for first-order Stokes generation [8], and the Stokes generation for various input pulse widths [9].

Recently, inverse Raman scattering (IRS), first experimentally reported in Ref. [10], has been observed in silica glass optical fibers for the first time [11]. In IRS, optical loss at the anti-Stokes frequency can be observed when a strong pump field is present. Energy is transferred from the shorter wavelength to the longer wavelength, as in stimulated-Raman scattering (SRS); however, IRS results in loss for the weaker field (the anti-Stokes field), as opposed to amplification in SRS. IRS was used in Ref. [11] to extract the Raman response spectrum and to demonstrate all-optical switching with high contrast and broad optical bandwidth. Narrow-band all-optical switching via IRS in liquids was recently reported in Ref. [12] using integrated liquid-core optical fibers (LCOFs). In this particular implementation, a large range of the Raman spectrum can be covered, from $200{\mathrm{cm}}^{-1}$, limited by the dichroic filter separating the pump and probe, up to $4000{\mathrm{cm}}^{-1}$, due to the bandwidth of the probe used in the current experiment. In addition to broadband spectral coverage, IRS is capable of resolving narrow-band vibrational resonances, limited mainly by the pump pulse width. This technique should be capable of extracting the relevant spectroscopic signatures of any number of different materials, including neat (i.e., the absence of any additives) glasses, neat liquids, and doped glasses or solutions of organic chromophores.

As a characterization tool, IRS in integrated LCOF allows for experimenting with extremely long path lengths of liquids and solutions of chromophores, equivalent to several meter-length liquid cells, without typical problems, such as diffraction. It also provides large optical intensities over a longer interaction path length, a necessary condition for efficient nonlinear optics in transparent media. Consequently, IRS can resolve very low Raman gain coefficients, providing us with higher sensitivity compared to conventional techniques, such as SRS. This increased sensitivity is partly due to the fact that IRS does not have to overcome linear losses in a material in order to present itself; that is, a threshold condition does not exist as it does for amplification in SRS [10]. While losses can serve to attenuate either the pump or probe beams, shorter path length fibers can be used to accommodate such lossy materials.

In this paper, the IRS technique is applied to germanium-doped silica glass, liquid carbon tetrachloride, carbon disulfide, and a solution of beta-carotene. We have studied each of these examples in order to highlight certain attributes of the technique. The extracted Raman gain coefficients are compared with estimations from steady-state Raman scattering measurements and good agreement is found with the proposed IRS methodology. Interestingly, this aforementioned correlation suggests that this technique can be used to extract microscopic quantities from materials, such as the spontaneous Raman cross section.

The structure of the paper is as follows. In Section 2, the experimental details of IRS are discussed. Section 4 presents the procedure for estimating the gain coefficient from spontaneous Raman spectroscopy (SpRS) and Section 3 contains the modeling of IRS. Section 5 highlights the technique through its application to different materials.

2. EXPERIMENT ON INVERSE RAMAN SCATTERING

We use LCOF and a special splicing technique, as reported in Ref. [13], to work with liquids integrated into a waveguide platform. The core is filled with a liquid with the appropriate refractive index to achieve waveguiding of the light as well as providing a numerical aperture that appropriately matches the solid core optical fiber on either end. In order to achieve this waveguide condition, the refractive index of the liquid must be higher than that of fused silica. In the event that the neat liquid does not have a sufficiently large index, it can be “doped” with a small fraction of a larger index liquid. As an example, this was achieved by doping ${\mathrm{CCl}}_4$ with 3% ${\mathrm{CS}}_2$ by volume, to achieve waveguiding in the core of the fiber.

A schematic of the experimental IRS setup is shown in Fig. 1. A narrow-band pump at 1550 nm with 50 MHz repetition rate and a broad supercontinuum anti-Stokes probe, both having $\sim 3\mathrm{ps}$ pulse duration, is generated by a single mode-locked Er-doped fiber laser [14,15]. The pump bandwidth (FWHM) is determined to be 1.4 nm. An Er-doped fiber amplifier (EDFA) was used to amplify the output of the oscillator. 80% of the power after the amplifier was used to generate the broad supercontinuum anti-Stokes probe in a short piece (60 cm) of highly nonlinear fiber (HNLF). The remaining 20% of the power after the amplifier passed through a narrow ($\sim 1.5\mathrm{nm}\mathrm{FWHM}$) bandpass filter (working around 1560 nm) and presents the narrow-band pump. A delay line was used to adjust the temporal delay between the pump and the anti-Stokes probe. Polarization controllers were used to independently optimize the polarization state of pump and probe. A fiber pigtailed WDM thin-film coupler combined the pump and the probe. which were launched into a fiber with either a solid-core fiber or a LCOF. The IRS-modified probe spectrum was sampled (following rejection of the residual pump light with a band-pass filter) using an optical spectrum analyzer with $\sim 1\mathrm{nm}$ resolution, unless otherwise noted.

 

Fig. 1. Schematic of experimental IRS setup. ML laser, mode-locked fiber laser with carbon nanotube saturable absorber; PC, polarization controller; WDM, wavelength division multiplexer; and OSA, optical spectrum analyzer.

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3. INVERSE RAMAN SCATTERING MODEL

A diagram detailing the methodology for extracting Raman gain coefficients from IRS spectra is shown in Fig. 2. Induced optical absorption of the anti-Stokes probe is observed when the pump and probe are overlapped in time. As a result, we observe a loss in the spectrum of the anti-Stokes signal [Fig. 2(a), gray shaded area]. The measured spectrum serves as input to an IRS model that simulates the propagation equations and determines the output spectrum. For a given set of model parameters, an intermediate result for the output spectrum is obtained and is schematically shown by the red dashed line in Fig. 2(b). To improve the result, the model parameters are iterated until sufficient agreement between model and experiment is achieved. The resulting theoretical description is finally used to extract Raman spectroscopic data [Fig. 2(c)].

 

Fig. 2. General method to extract Raman spectroscopic data from measured IRS spectra. (a) Schematic of measured IRS spectrum. (b) IRS modeling. (c) Extraction of Raman properties via IRS modeling results.

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In practice, we solve the nonlinear Schrödinger equation and fit the measured spectra by varying the nonlinearity. When extracting the Raman gain coefficients, we are mainly interested in matching the dip depth at the anti-Stokes central wavelength. For simplicity, we have gradually increased the nonlinearities until the dip depths agreed. The resulting Kerr nonlinearity is then used to compute the Raman gain coefficient. Similar approaches exist to extract the instantaneous Kerr nonlinearity in fibers including self-phase modulation [16], cross-phase modulation [17], or four-wave mixing [18,19]; however, the determination of the Raman gain coefficient of silica fiber and liquids in integrated LCOFs through IRS is reported here for the first time, to the best of our knowledge.

The underlying model depicted in Fig. 2(b) to compute the IRS spectra is briefly described in the following. We use the coupled nonlinear Schrödinger equations in the slowly varying envelope approximation to solve the simultaneous propagation of the pump and anti-Stokes fields along the fiber. The propagation equations for the space–time dependent anti-Stokes $A_{\mathrm{as}}(z,t)$ and pump $A_p(z,t)$ are given by [8,20]

The Raman gain coefficient is obtained by applying the formula [22]

The relative standard deviation error associated with the extracted value of $g_R$ was estimated to be $\pm 21\%$. This value was determined by taking into account experimental uncertainties in the various optical and material parameters used in the numerical fitting. These include errors in the pump power (5%), $A_{\mathrm{eff}}$ (10%), fractional IRS loss (5%), and ${\tau }_1$ (10%). Experimental errors associated with the fiber length, dispersion parameters, and walk-off parameter were found to have relatively small impacts on the resulting value of $g_R$. The error associated with ${\tau }_2$ was conservatively estimated to be 20%. While extracting ${\tau }_2$ for materials with large Raman linewidths gives lower errors, samples with small Raman linewidths require usage of literature values (as discussed above) and this could increase the error in this term.

4. DETERMINATION OF GAIN/LOSS COEFFICIENT FROM STEADY-STATE RAMAN SPECTROSCOPY

In order to assess the accuracy of the aforementioned technique for extracting the Raman gain/loss coefficients from LCOF measurements, we used the well-established technique of SpRS to determine these coefficients for comparison purposes. Steady-state Stokes–Raman emission was acquired using a Fourier-transform Raman spectrometer (Bruker Optics, MultiRAM), with polarized laser excitation (${\lambda }_L=1064\mathrm{nm}$). The system utilizes a 180° excitation geometry and scattered radiation of all polarization orientations was collected. Typical excitation powers were $\sim 500\mathrm{mW}$ and no photo-induced decomposition was observed in the samples either during or after the measurements. The solution/solvent samples were housed in 5 mm path length quartz cuvettes with mirrored back surfaces, repeatedly placed in identical positions for subsequent measurements. All spectra were acquired with $\sim 0.5{\mathrm{cm}}^{-1}$ resolution and were subsequently instrument—response corrected to account for the frequency response of the detector, filters, and interferometer optics. The corrected spectra were fitted for extraction of the RSCs (Raman scattering cross sections, see below) using sums of Lorentzian or Voigt line shape functions. To determine depolarization ($\rho$) values (i.e., ratios of the scattered emission perpendicular to the incident polarization to the scattered emission parallel to the incident polarization), grid polarizers in the appropriate orientation were inserted after the collection lens and prior to the detector. All chemicals (i.e., beta-carotene and spectrophotometric-grade solvents) were purchased from Sigma-Aldrich and used without further purification.

Utilizing a reference standard to calibrate the response of an unknown sample under the same excitation/collection geometries can eliminate the need to determine certain experimental parameters that can be difficult to quantify. For instance, it is well-known that using a referential method to determine the quantum yield of fluorescence obviates the need to accurately determine the solid angle of collection or the absolute emitted intensity. Similarly, we have chosen to utilize a referential method to determine the RSC (or, more specifically, the total differential Raman scattering cross section, depicted as $d\sigma /d\mathrm{\Omega }$) from easily measured experimental observables in a steady-state SpRS measurement [4,5]

This method is predicated on the availability of a trustworthy reference standard. A number of reliable literature sources report on the absolute measurements of the RSC of the $992{\mathrm{cm}}^{-1}$ ring breathing mode of benzene [4,24–30]. These studies all involved excitation with either UV or visible laser sources; consequently, the value of the RSC at 1064 nm, germane for the current studies, had to be extrapolated based on the frequency dependence of $d\sigma /d\mathrm{\Omega }$. In addition to the well-known ${\omega }_S^4$ (scattered Stokes frequency) dependence of the RSC, an additional frequency-dependent contribution exists which is related to the proximity of the excitation frequency (${\omega }_L$) to an electronic absorption resonance (${\omega }_E$). When only one electronic resonance needs to be considered, the RSC frequency dependence is given by [24,26,31]

Accordingly, the frequency-dispersion of the literature-based RSC values for the $992{\mathrm{cm}}^{-1}$ mode of benzene could be fit using Eq. (7) and the results are depicted graphically in Fig. 3. The fit with the literature data was quite good; therefore, the trend line was used to extrapolate to an RSC value for benzene at 1064 nm (or ${\omega }_L=9.4\mathrm{kK}$). This value of $8.7·{10}^{-35}{\mathrm{m}}^2{\mathrm{molecule}}^{-1}{\mathrm{srad}}^{-1}$ was then employed as ${(d\sigma /d\mathrm{\Omega })}_{\mathrm{ref}}$ in Eq. (6).

 

Fig. 3. Frequency dispersion of the Stokes RSC for the $992{\mathrm{cm}}^{-1}$ ring breathing mode in benzene. The excitation frequency is given in kiloKaisers ($1\mathrm{kK}=1000{\mathrm{cm}}^{-1}$), the fitting is performed using Eq. (7) with ${\omega }_E=50\mathrm{kK}$ (or 200 nm), and the extrapolated value at 9.4 kK (or 1064 nm) is displayed. The error associated with this extrapolated RSC is estimated to be $\pm 20\%$.

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Once the Stokes RSC of a particular vibrational mode at 1064 nm is determined using the referential technique, this value is dispersion-corrected to 1550 nm excitation for comparison with the LCOF-IRS experiments. This is accomplished using Eq. (7) with the appropriate electronic resonance frequency, and with ${\omega }_S$ replaced by ${\omega }_{\mathrm{as}}$ (or the scattered anti-Stokes frequency). The RSC values for the solutions/solvents studied herein are given in Table 1. Finally, the Raman gain/loss coefficient at 1550 nm was determined according to the following [6,7]

Table 1. Compiled Experimental Parameters Acquired from SpRS^h

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5. APPLICATION TO DIFFERENT MATERIALS

In this Section, we apply the IRS characterization technique to different materials. Specifically, we investigate a doped glass, neat liquids, and a solvent of organic chromophores. In each case, the characteristics of the proposed IRS technique are discussed. The material parameters are summarized in Table 2, along with Raman gain coefficients determined from IRS. For comparison, the SpRS-determined and literature values are also shown.

Table 2. Material Parameters Used for the IRS Methodology and Extracted Raman Gain Coefficients^a,b

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A. Germanium-doped Silica Optical Fiber

We apply the IRS technique to extract the Raman gain coefficient of the ${\mathrm{GeO}}_2$-doped silica optical fiber that was used in Ref. [11]. The measured IRS spectra for increasing pump average power are shown in Fig. 4(a). The left spectrum shows the broad supercontinuum of the chirped anti-Stokes pulse and the right spectrum shows the Gaussian pump pulse. The vertical line in between marks the position of the filter used in the experiment. We can clearly see strong attenuation of up to 20 dB in the anti-Stokes spectra at around 1460 nm. We stress that a broad optical bandwidth of $\sim 100\mathrm{nm}$ could be achieved here. By subtracting the anti-Stokes spectra at low pump power from the anti-Stokes spectra at high pump power, as shown in Fig. 4(a) in Ref. [11], signatures of the doping material could be identified as a peak at around $220{\mathrm{cm}}^{-1}$, which is associated with a symmetric bending vibrational mode of trigonal ${\mathrm{GeO}}_2$ groups in the fiber [11].

 

Fig. 4. Extraction of Raman gain coefficient for germanium-doped glass optical fiber. (a) Measured IRS spectra for increasing pump power, according to Ref. [11]. (b) IRS modeling spectra (solid lines) for increasing Raman gain coefficient and measured IRS spectrum (shaded) for 50 mW pump power.

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The same numerical parameters employed in Ref. [11] (see Appendix therein), are used to model the IRS spectra. Especially, the ${\tau }_1$ and ${\tau }_2$ values, see Table 2, are obtained from the measured Raman-response function of ${\mathrm{GeO}}_2$-doped fiber [11]. For the iteration process depicted in Fig. 2(b), we adjust the Kerr nonlinearity ${\gamma }_{\mathrm{as}}$ with ${\gamma }_p=({\omega }_p/{\omega }_{\mathrm{as}}){\gamma }_{\mathrm{as}}$ [8], until model spectra and measured spectra are approximately the same. The results presented in Fig. 4(b) show the simulated spectra (solid lines) and measured spectrum (shaded) for 50 mW pump power. The Raman gain coefficient is determined to be $g_R=1.1·{10}^{-13}\mathrm{m}/\mathrm{W}$ [see the blue line in Fig. 4(b)]. For comparison, a measurement of pure silica glass was found to give $g_R^{\mathrm{fused}\mathrm{silica}}=0.82·{10}^{-13}\mathrm{m}/\mathrm{W}$ at 1460 nm [35]. The extracted value found here may be slightly higher than standard glass due to the influence of the germanium doping.

B. Carbon Tetrachloride (${\mathrm{CCl}}_4$)

We observe strong attenuation in the anti-Stokes spectrum when ${\mathrm{CCl}}_4$ is introduced into a LCOF, as shown in Fig. 5(a) and reported in Ref. [12]. In particular, the well-known vibrational frequencies of ${\mathrm{CCl}}_4$ [36] at $460{\mathrm{cm}}^{-1}$, $314{\mathrm{cm}}^{-1}$, and $218{\mathrm{cm}}^{-1}$ are visible. When the pump power is increased, the dip in the anti-Stokes spectrum gets more pronounced, and a loss of up to 18.7 dB is observed at the strongest mode ($460{\mathrm{cm}}^{-1}$) for the highest pump power (32 mW). Thus, Fig. 5(a) shows that all Raman-active modes of ${\mathrm{CCl}}_4$ can be detected via IRS, allowing us to obtain spectroscopic signatures of the investigated liquid. The IRS response spectra and the spontaneous Raman spectrum were also acquired and are shown in Fig. 6. The spectral signatures in both methods agree qualitatively very well. We note that in some cases the frequency shifts of the IRS spectra are larger than those of the spontaneous Raman spectra. We ascribe these shifts to the Raman-induced frequency shift, and describe their analysis in a recently submitted manuscript [37]. Another important aspect is that the IRS technique is capable of covering the low frequency regime (down to $\sim 200{\mathrm{cm}}^{-1}$). We further note that the linewidths of these modes are significantly narrower than the gain bandwidth measured for the Ge-doped glass, highlighting this technique’s ability to resolve narrowband resonances.

 

Fig. 5. IRS spectra of liquid-core fiber filled with ${\mathrm{CCl}}_4+3\%$ ${\mathrm{CS}}_2$. (a) Measured IRS spectra. The average pump power is increased, resulting in clear attenuation in the anti-Stokes spectrum at the ${\mathrm{CCl}}_4$ vibronic modes at $460{\mathrm{cm}}^{-1}$, $314{\mathrm{cm}}^{-1}$, and $218{\mathrm{cm}}^{-1}$. According to Ref. [12]. (b) IRS modeling spectra (solid lines) for increasing Raman gain coefficient and measured fractional IRS loss spectrum (shaded) for 32 mW pump power. The blue curve matches the dip best and yields an extracted Raman gain coefficient of $g_R=1.5·{10}^{-12}\mathrm{m}/\mathrm{W}$.

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Fig. 6. IRS versus spontaneous Raman for ${\mathrm{CCl}}_4$. (a) IRS response spectra for increasing pump power. (b) Spontaneous Raman spectrum with logarithmic ordinate scale.

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We next extract the Raman gain coefficient of ${\mathrm{CCl}}_4$. Similar to the methodology detailed for the solid-core fiber, we vary the Kerr nonlinearity ${\gamma }_{\mathrm{as}}$, ${\gamma }_p=({\omega }_p/{\omega }_{\mathrm{as}}){\gamma }_{\mathrm{as}}$ and keep all other model parameters fixed. To compute the dispersion, we describe a liquid-core fiber via a simple step-index model [38,39]. The core is filled with ${\mathrm{CCl}}_4$ and 3% ${\mathrm{CS}}_2$ and the cladding is fused silica. The refractive indices are determined via the Sellmeier coefficients of ${\mathrm{CS}}_2$ [40], ${\mathrm{CCl}}_4$ [41], and fused silica [42]. Figure 7(a) shows the resulting total dispersion parameter $D$ and Fig. 7(b) shows the second-order dispersion coefficient ${\beta }_2$. Based on this calculation, we determine the dispersion coefficients up to the sixth-order at the anti-Stokes (1447 nm) and pump (1550 nm) wavelengths (see Appendix A). The dispersion coefficients, together with the walk-off parameter $d_{wo}=1.2\mathrm{ps}/\mathrm{m}$, enter the coupled Eqs. (1) and (2). The linear losses ${\alpha }_{\mathrm{as}}$ and ${\alpha }_p$ are set to zero because no appreciable absorption was measured at the working wavelengths. The Raman parameters are chosen to model the dominant resonance at $459{\mathrm{cm}}^{-1}$ Raman shift with a linewidth (FWHM) of $9.6{\mathrm{cm}}^{-1}$, approximately as seen in the measured IRS spectra.

 

Fig. 7. Total dispersion of a step-index liquid-core fiber. The core is filled with ${\mathrm{CCl}}_4$ and 3% ${\mathrm{CS}}_2$, with a core diameter of 10 μm. The cladding is fused silica. (a) Dispersion $D(=-(2\pi c/{\lambda }^2){\beta }_2)$. (b) Dispersion coefficient ${\beta }_2$.

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Figure 5(b) shows the resulting modeling results (solid lines) and measured IRS response spectrum (shaded) for the highest pump power in Fig. 5(a). These results represent the fractional loss induced by IRS, which is accomplished by dividing the probe spectra with the pump applied by the probe spectrum without the pump applied. We obtain a best fit for the blue curve, which corresponds to ${\gamma }_{\mathrm{as}}=0.44{\mathrm{W}}^{-1}/(\mathrm{km})$. Using Eqs. (4) and (5), we extract a Raman gain coefficient of $g_R=1.5·{10}^{-12}\mathrm{m}/\mathrm{W}$, which is remarkably similar to the extracted Raman gain coefficient obtained via the SpRS approach outlined in Section 4, i.e., $g_R=1.6·{10}^{-12}\mathrm{m}/\mathrm{W}$ (see Table 1). This strong correlation suggests that this IRS-based LCOF methodology may permit accurate determination of spontaneous RSCs using Eq. (7) in Section 4. Indeed, a comparison of the IRS loss spectrum and the SpRS spectrum (see Fig. 6) shows a strong correlation.

C. Beta-carotene

The IRS characterization technique in LCOFs also allows us to accommodate solutions doped with organic chromophores present at specific concentrations. We have used a low concentration of beta-carotene in a mixture of ${\mathrm{CCl}}_4$ and ${\mathrm{CS}}_2$. In particular, the core was filled with ${\mathrm{CCl}}_4+5\%$ ${\mathrm{CS}}_2$ and a chromophore concentration of $12·{10}^{-3}\mathrm{Mol}/\mathrm{L}$ was used. Figure 8(a) presents the measured IRS spectra for different time delays between the anti-Stokes probe and pump, as reported in Ref. [12]. We observe the main resonances of ${\mathrm{CCl}}_4$ (at $460{\mathrm{cm}}^{-1}$) and ${\mathrm{CS}}_2$ (at $\sim 655{\mathrm{cm}}^{-1}$), as well as the resonances associated with beta-carotene ($1160{\mathrm{cm}}^{-1}$ and $1530{\mathrm{cm}}^{-1}$). IRS response spectra and the spontaneous Raman spectrum are shown in Fig. 9 for direct qualitative comparison. These results show that IRS can accommodate Raman modes present in the high frequency regime ($>1000{\mathrm{cm}}^{-1}$). The resonance of beta-carotene at $1160{\mathrm{cm}}^{-1}$ shows an IRS loss of $\sim 5\mathrm{dB}$. We notice that the Raman linewidth of beta-carotene is much narrower than that of glass optical fiber and comparable to carbon tetrachloride.

 

Fig. 8. IRS spectra of liquid-core fiber filled with ${\mathrm{CCl}}_4+5\%$ ${\mathrm{CS}}_2$ and $12·{10}^{-3}\mathrm{Mol}/\mathrm{L}$ of beta-carotene. (a) Measured IRS spectra for various time delays between anti-Stokes probe and pump, according to Ref. [12]. (b) Measured fractional IRS loss spectrum at zero time delay (shaded) and IRS modeling spectra (solid lines) for the $1160{\mathrm{cm}}^{-1}$ resonance (at 1321 nm) of beta-carotene. The blue curve matches the dip best and yields an extracted Raman gain coefficient of $g_R=6·{10}^{-13}\mathrm{m}/\mathrm{W}$ for the given beta-carotene concentration.

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Fig. 9. IRS versus spontaneous Raman for beta-carotene. (a) IRS response spectra for various time delays between pump and probe. The step size of the temporal delay between pump and signal pulses is 0.8 ps. The magenta line showing maximum IRS loss at $1160{\mathrm{cm}}^{-1}$ corresponds to zero time delay. (b) Spontaneous Raman spectrum with logarithmic ordinate scale.

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The beta-carotene solution is analyzed via the IRS model. Similar to the previous analyses, we have fixed the dispersion and Raman parameters and extracted the Raman gain coefficient by changing the nonlinearities. The Raman response function Eq. (3) is chosen to describe the resonance at $1160{\mathrm{cm}}^{-1}$ of beta-carotene. Figure 8(b) shows the result of fitting the fractional IRS-induced loss for this mode. The shaded area is the measured fractional IRS loss spectrum at zero time delay while the solid lines are model results. For the given concentration of beta-carotene, we extract a Raman loss coefficient of $g_R=6·{10}^{-13}\mathrm{m}/\mathrm{W}$ [see the blue line in Fig. 8(b)]. The extracted Raman gain coefficient is consistent with Raman spectroscopy approach (and the full spectra are compared in Fig. 9), which predicts a value of $g_R=7.0·{10}^{-13}\mathrm{m}/\mathrm{W}$ for the $1160{\mathrm{cm}}^{-1}$ mode (see Table 1). It is interesting to note that this gain coefficient is similar to that of ${\mathrm{CCl}}_4$ despite the fact that the neat liquid has a concentration that is nearly 1000 times that of the beta-carotene solution. This can be easily rationalized through Eq. (8) in Section 4 that shows the gain coefficient depends on the product of the concentration and the spontaneous RSC; the RSC of beta-carotene is $\sim 1000$ times larger than ${\mathrm{CCl}}_4$.

D. Carbon Disulfide (${\mathrm{CS}}_2$)

Figure 10(a) shows the measured IRS spectrum when the fiber was filled with neat liquid ${\mathrm{CS}}_2$. In order to accommodate the narrower linewidth expected for the vibrational resonance of ${\mathrm{CS}}_2$, the resolution of the optical spectrum analyzer was increased to 0.1 nm for these experiments. We observe an attenuation at $660{\mathrm{cm}}^{-1}$ of $\sim 18\mathrm{dB}$ at a pump power of only $\sim 1.5\mathrm{mW}$. For qualitative comparison, we have also shown the IRS response spectra and the corresponding spontaneous Raman spectrum (see Fig. 11). In the IRS measurement, the Raman linewidth (FWHM) is determined to be 1.5 nm ($6{\mathrm{cm}}^{-1}$), which is much narrower than for the glass and even narrower than for carbon tetrachloride and beta-carotene. This also demonstrates that the IRS linewidth is pump–bandwidth limited because the pump bandwidth (FWHM) is 1.4 nm. We note that the sharp absorption resonances in Fig. 10(a) in the region of 1350–1420 nm are the well-known water absorption peaks. Since we have filled the fiber with ${\mathrm{CS}}_2$ in air, we expect some water contamination.

 

Fig. 10. IRS spectra of liquid-core fiber filled with neat ${\mathrm{CS}}_2$. (a) Measured IRS spectra for increasing pump power. (b) Measured fractional IRS loss spectrum at 1.5 mW pump power (shaded) and IRS modeling spectra (solid lines). The blue curve yields a Raman gain coefficient of $g_R=3·{10}^{-11}\mathrm{m}/\mathrm{W}$.

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Fig. 11. IRS versus spontaneous Raman for ${\mathrm{CS}}_2$. (a) IRS response spectra for increasing pump power. (b) Spontaneous Raman spectrum with logarithmic ordinate scale.

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Since the Raman linewidth is much smaller than the pump bandwidth, the IRS propagation equations were solved with ${\tau }_1=8.04\mathrm{fs}$ and ${\tau }_2=15\mathrm{ps}$, values which have been reported in the literature [43]. Figure 10(b) shows the experimentally determined fractional IRS loss spectrum (shaded) and the corresponding theoretical curves (solid). We obtain a best fit for $g_R=3·{10}^{-11}\mathrm{m}/\mathrm{W}$, which is on the same order as measured values derived from steady-state Raman spectroscopy ($g_R=1.3·{10}^{-11}\mathrm{m}/\mathrm{W}$, see Table 1). The discrepancy can likely be attributed to an overestimation in the Raman linewidth measured by SpRS compared to the value typically reported in the literature (i.e., $1.2{\mathrm{cm}}^{-1}$ compared with $0.5{\mathrm{cm}}^{-1}$ [43]). Since the steady-state gain coefficient [see Eq. (8)] is inversely proportional to the linewidth, the SpRS-predicted gain could be underestimated by more than two times.

Compared with the previous examples, carbon disulfide thus yields an enhanced Raman gain coefficient. This is also reflected in the reduced pump power that was required to observe an appreciable loss, particularly when compared with the solid-core glass fiber where 50 mW pump power was necessary to observe similar losses. Carbon disulfide provides the narrowest and strongest Raman response of all the materials measured. Along these lines, we emphasize that a gain coefficient of ${\mathrm{CS}}_2$ is measurable even at small concentrations in ${\mathrm{CCl}}_4$, as seen in Fig. 8(a), which shows IRS attributed to ${\mathrm{CS}}_2$ despite its low doping weight %.

6. CONCLUSIONS

We have demonstrated that the inverse Raman process can be utilized as a new characterization technique for Raman gain materials. We have analyzed the IRS response for a silica glass optical fiber and several liquids in a LCOF. Compared with traditional setups involving SRS, the IRS methodology yields many advantages. There is no threshold requirement for IRS unlike for SRS, which has to overcome linear losses in a material for observation. Moreover, the measured IRS spectrum typically shows some attenuation at the anti-Stokes signal at powers below those required to observe significant self-phase modulation broadening, the presence of which can lead to significant complications in modeling the Raman response in a system. IRS shows great versatility regarding the screening of potential Raman gain materials, as well as the spectroscopic characterization of such materials with good spectral resolution and broadband spectral coverage.

The technique has been applied to detect spectroscopic signatures and to extract the Raman gain coefficients of doped glass, neat liquids, as well as a solution of organic chromophores. Good agreement with both literature values and measurements based on spontaneous Raman scattering were obtained, the latter observation suggesting that this technique could be amenable for determination of molecular RSCs. We believe that IRS is a versatile tool for the characterization of new materials for ultralow-power nonlinear optics and all-optical switching.