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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 11 — Nov. 1, 2013
  • pp: 2930–2939
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Measurement of the Raman gain coefficient via inverse Raman scattering

L. Schneebeli, K. Kieu, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian  »View Author Affiliations


JOSA B, Vol. 30, Issue 11, pp. 2930-2939 (2013)
http://dx.doi.org/10.1364/JOSAB.30.002930


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Abstract

We report a new characterization technique of Raman gain materials through inverse Raman scattering (IRS). The technique is applied to silica glass optical fiber and several liquids in liquid-core optical fiber (LCOF). We obtain good quantitative agreement with a conventional technique that estimates the gain coefficient from steady-state Raman scattering measurements. Our results demonstrate that IRS is a viable tool to characterize new materials for ultralow-power nonlinear optics and all-optical switching.

© 2013 Optical Society of America

1. INTRODUCTION

Raman gain materials have a multitude of applications in nonlinear optics [1

1. F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002). [CrossRef]

3

3. J. E. Sharping, Y. Okawachi, and A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092–6098 (2005). [CrossRef]

]. 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

4. J. G. Skinner and W. G. Nilsen, “Absolute Raman scattering cross-section measurement of 992  cm-1 line of Benzene,” J. Opt. Soc. Am. 58, 113–119 (1968). [CrossRef]

7

7. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1991).

], the threshold pump energy for first-order Stokes generation [8

8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

], and the Stokes generation for various input pulse widths [9

9. D. Mahgerefteh, D. L. Butler, J. Goldhar, B. Rosenberg, and G. L. Burdge, “Technique for measurement of the Raman gain coefficient in optical fibers,” Opt. Lett. 21, 2026–2028 (1996). [CrossRef]

].

Recently, inverse Raman scattering (IRS), first experimentally reported in Ref. [10

10. W. J. Jones and B. P. Stoicheff, “Inverse Raman spectra–induced absorption at optical frequencies,” Phys. Rev. Lett. 13, 657–659 (1964). [CrossRef]

], has been observed in silica glass optical fibers for the first time [11

11. K. Kieu, L. Schneebeli, J. M. Hales, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “Demonstration of Zeno switching through inverse Raman scattering in an optical fiber,” Opt. Express 19, 12532–12539 (2011). [CrossRef]

]. 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

11. K. Kieu, L. Schneebeli, J. M. Hales, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “Demonstration of Zeno switching through inverse Raman scattering in an optical fiber,” Opt. Express 19, 12532–12539 (2011). [CrossRef]

] 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

12. K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse Raman scattering in liquid-core optical fibers,” Opt. Lett. 37, 942–944 (2012). [CrossRef]

] using integrated liquid-core optical fibers (LCOFs). In this particular implementation, a large range of the Raman spectrum can be covered, from 200cm1, limited by the dichroic filter separating the pump and probe, up to 4000cm1, 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

10. W. J. Jones and B. P. Stoicheff, “Inverse Raman spectra–induced absorption at optical frequencies,” Phys. Rev. Lett. 13, 657–659 (1964). [CrossRef]

]. 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

13. K. Kieu, L. Schneebeli, R. A. Norwood, and N. Peyghambarian, “Integrated liquid-core optical fibers for ultra-efficient nonlinear liquid photonics,” Opt. Express 20, 8148–8154 (2012). [CrossRef]

], 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 CCl4 with 3% CS2 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 3ps pulse duration, is generated by a single mode-locked Er-doped fiber laser [14

14. K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a fiber taper embedded in carbon nanotube/polymer composite,” Opt. Lett. 32, 2242–2244 (2007). [CrossRef]

,15

15. K. Kieu, R. J. Jones, and N. Peyghambarian, “Generation of few-cycle pulses from an amplified carbon nanotube mode-locked fiber laser system,” IEEE Photon. Technol. Lett. 22, 1521–1523 (2010). [CrossRef]

]. 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 (1.5nmFWHM) 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 1nm 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.

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.

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

16. R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978). [CrossRef]

], cross-phase modulation [17

17. M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fibers by crossphase modulation,” Electron. Lett. 23, 961–963 (1987). [CrossRef]

], or four-wave mixing [18

18. L. Prigent and J. P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by 4-wave-mixing,” IEEE Photon. Technol. Lett. 5, 1092–1095 (1993). [CrossRef]

,19

19. A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n(2) in various types of telecommunication fiber at 1.55  μm,” Opt. Lett. 21, 1966–1968 (1996). [CrossRef]

]; 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 Aas(z,t) and pump Ap(z,t) are given by [8

8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

,20

20. C. Headley and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170–2177 (1996). [CrossRef]

]
Aasz=l=2il+1l!βl,aslAastlαas2Aas+iγas(1fR)(|Aas|2+2|Ap|2)Aas+iγasfRAasthR(tt)[|Aas(z,t)|2+|Ap(z,t)|2]dt+iγasfRApthR(tt)Aas(z,t)Ap(z,t)eiΩR(tt)dt,
(1)
Apz=dwoApt+l=2il+1l!βl,plAptlαp2Ap+iγp(1fR)(|Ap|2+2|Aas|2)Ap+iγpfRApthR(tt)[|Ap(z,t)|2+|Aas(z,t)|2]dt+iγpfRAasthR(tt)Ap(z,t)Aas(z,t)eiΩR(tt)dt.
(2)
The optically active medium is characterized through dispersion (βl,j), linear losses (αj), Kerr nonlinearities (γj), where j=as or p denotes the anti-Stokes or pump, and the Raman response function [21

21. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman-scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989). [CrossRef]

]
hR(t)=τ12+τ22τ1τ22etτ2sin(tτ1).
(3)
The simple formula [Eq. (3)] describes a single resonance and is used to analyze a particular mode observed in the IRS spectrum. The position and width can be controlled via τ1 and τ2, in particular, and τ1 determines the Raman shift (τ1=1/(2πcΔν), where Δν is the vibrational frequency), while τ2 describes the Raman response time and, hence, the linewidth of the vibrational resonance (τ2=1/(πcδν), where δν is the FWHM linewidth of the transition). fR is the fractional contribution of the Raman response to the generation of nonlinear polarization and ΩR=ωasωp is the difference between the anti-Stokes and pump carrier frequencies. The group-velocity mismatch between the anti-Stokes and pump determines the walk-off parameter dwo=1/vg,as1/vg,p=β1,asβ1,p.

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

22. Q. Lin, F. Yaman, and G. P. Agrawal, “Raman-induced polarization-dependent gain in parametric amplifiers pumped with orthogonally polarized lasers,” IEEE Photon. Technol. Lett. 18, 397–399 (2006). [CrossRef]

]
gR=2γasAefffRIm[h˜R(1/τ1)],
(4)
Im[h˜R(1/τ1)]=2τ1τ2(τ12+τ22)τ14+4τ12τ22,
(5)
where Aeff is the effective mode area and h˜R denotes the Fourier-transform of the Raman response function. To determine the Raman gain coefficient, we sweep the nonlinearities γ while keeping all other parameters fixed. The Gaussian pump pulse has a duration (FWHM) of 3 ps with central wavelength of 1560 nm, while the broad supercontinuum anti-Stokes pulse is a 10fs chirped pulse with a resulting duration of 3 ps (we have increased the duration of the probe pulse to 8 ps for some of the experiments, e.g., for beta-carotene and CS2). The linear losses are measured and dispersion is obtained via simple dispersion calculations based on measured Sellmeier coefficients. The Raman parameters τ1, τ2 are taken from the measured spectrum that yields the Raman shift and the linewidth. Since IRS yields a loss spectrum, we determine the Raman linewidth by taking the 3 dB value below the baseline of the anti-Stokes spectrum. The IRS spectrum is a convolution of the pump spectrum and the actual Raman response, such that the resolution of the IRS linewidth is limited by the pump bandwidth. For all materials that have a Raman linewidth larger than the pump bandwidth, IRS gives a good estimate for τ2. For materials with a very narrow Raman linewidth, such as CS2, we need to adjust τ2 according to literature values. The parameter fR typically requires a separate measurement of the polarizability [23

23. R. W. Hellwarth, A. Owyoung, and N. George, “Origin of nonlinear refractive index of liquid CCl4,” Phys. Rev. A 4, 2342–2347 (1971). [CrossRef]

]. However, the IRS methodology is independent of the exact knowledge of fR. This can be seen from the propagation equations (1) and (2) and the Raman gain coefficient [Eq. (4)], which all depend on products γfR in the absence of self-phase modulation, an approximation that is valid for all of the observed IRS spectra.

The relative standard deviation error associated with the extracted value of gR was estimated to be ±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%), Aeff (10%), fractional IRS loss (5%), and τ1 (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 gR. The error associated with τ2 was conservatively estimated to be 20%. While extracting τ2 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 (λL=1064nm). The system utilizes a 180° excitation geometry and scattered radiation of all polarization orientations was collected. Typical excitation powers were 500mW 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 0.5cm1 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 (ρ) 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 dσ/dΩ) from easily measured experimental observables in a steady-state SpRS measurement [4

4. J. G. Skinner and W. G. Nilsen, “Absolute Raman scattering cross-section measurement of 992  cm-1 line of Benzene,” J. Opt. Soc. Am. 58, 113–119 (1968). [CrossRef]

,5

5. M. J. Colles and J. E. Griffiths, “Relative and absolute Raman scattering cross-sections in liquids,” J. Chem. Phys. 56, 3384–3391 (1972). [CrossRef]

]
dσdΩsam=dσdΩref·PsamRPrefR·PrefLPsamL·NrefNsam·δzrefδzsam·nsam2nref2.
(6)
In the above equation, the subscripts “sam” and “ref” refer to the unknown sample under investigation and the reference standard, respectively. PR is the Raman scattered power determined from the integrated area of the line shape function used to fit the particular vibrational band in the instrument-corrected Raman spectrum, while PL is the laser power used to excite the sample. Nsam and δzsam are the number density and the path length of the sample, respectively, and accordingly for Nref and δzref. Correction for refractive index variation across samples is taken into consideration through the ratio nsam2/nref2. The relative standard deviation error for this referential measurement is estimated to be ±25% [via standard experimental error propagation using Eq. (6)] with its main contribution coming from the error in (dσ/dΩ)ref (see below).

Accordingly, the frequency-dispersion of the literature-based RSC values for the 992cm1 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 ωL=9.4kK). This value of 8.7·1035m2molecule1srad1 was then employed as (dσ/dΩ)ref in Eq. (6).

Fig. 3. Frequency dispersion of the Stokes RSC for the 992cm1 ring breathing mode in benzene. The excitation frequency is given in kiloKaisers (1kK=1000cm1), the fitting is performed using Eq. (7) with ωE=50kK (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 ±20%.

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 ωS replaced by ωas (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

6. Y. R. Shen, Principles of Nonlinear Optics (Wiley-Interscience, 1984).

,7

7. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1991).

]
gR=4πcN(dσ/dΩ)ωas3nasnLδν,
(8)
where nas and nL are the indices of refraction at the anti-Stokes and laser frequencies, respectively, N is the number density, and δν is the linewidth of the transition. The linewidth is determined by fitting the 3 dB value below the peak, which is the usual method for gain spectra. Again, the gR values determined from Eq. (8) for the solutions/solvents studied herein are given in Table 1.

Table 1. Compiled Experimental Parameters Acquired from SpRSh

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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 Coefficientsa,b

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A. Germanium-doped Silica Optical Fiber

We apply the IRS technique to extract the Raman gain coefficient of the GeO2-doped silica optical fiber that was used in Ref. [11

11. K. Kieu, L. Schneebeli, J. M. Hales, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “Demonstration of Zeno switching through inverse Raman scattering in an optical fiber,” Opt. Express 19, 12532–12539 (2011). [CrossRef]

]. 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 100nm 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

11. K. Kieu, L. Schneebeli, J. M. Hales, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “Demonstration of Zeno switching through inverse Raman scattering in an optical fiber,” Opt. Express 19, 12532–12539 (2011). [CrossRef]

], signatures of the doping material could be identified as a peak at around 220cm1, which is associated with a symmetric bending vibrational mode of trigonal GeO2 groups in the fiber [11

11. K. Kieu, L. Schneebeli, J. M. Hales, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “Demonstration of Zeno switching through inverse Raman scattering in an optical fiber,” Opt. Express 19, 12532–12539 (2011). [CrossRef]

].

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.

The same numerical parameters employed in Ref. [11

11. K. Kieu, L. Schneebeli, J. M. Hales, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “Demonstration of Zeno switching through inverse Raman scattering in an optical fiber,” Opt. Express 19, 12532–12539 (2011). [CrossRef]

] (see Appendix therein), are used to model the IRS spectra. Especially, the τ1 and τ2 values, see Table 2, are obtained from the measured Raman-response function of GeO2-doped fiber [11

11. K. Kieu, L. Schneebeli, J. M. Hales, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “Demonstration of Zeno switching through inverse Raman scattering in an optical fiber,” Opt. Express 19, 12532–12539 (2011). [CrossRef]

]. For the iteration process depicted in Fig. 2(b), we adjust the Kerr nonlinearity γas with γp=(ωp/ωas)γas [8

8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

], 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 gR=1.1·1013m/W [see the blue line in Fig. 4(b)]. For comparison, a measurement of pure silica glass was found to give gRfusedsilica=0.82·1013m/W at 1460 nm [35

35. M. E. Lines, “Raman-gain estimates for high-gain optical fibers,” J. Appl. Phys. 62, 4363–4370 (1987). [CrossRef]

]. The extracted value found here may be slightly higher than standard glass due to the influence of the germanium doping.

B. Carbon Tetrachloride (CCl4)

We observe strong attenuation in the anti-Stokes spectrum when CCl4 is introduced into a LCOF, as shown in Fig. 5(a) and reported in Ref. [12

12. K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse Raman scattering in liquid-core optical fibers,” Opt. Lett. 37, 942–944 (2012). [CrossRef]

]. In particular, the well-known vibrational frequencies of CCl4 [36

36. H. J. Marrinan and N. Sheppard, “Relative intensities of the Raman lines of carbon tetrachloride, chloroform, and methylene chloride,” J. Opt. Soc. Am. 44, 815–819 (1954). [CrossRef]

] at 460cm1, 314cm1, and 218cm1 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 (460cm1) for the highest pump power (32 mW). Thus, Fig. 5(a) shows that all Raman-active modes of CCl4 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

37. O. D. Herrera, L. Schneebeli, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Raman-induced frequency shift in CS2-filled integrated liquid-core optical fiber,” Submitted to Optics Letters.

]. Another important aspect is that the IRS technique is capable of covering the low frequency regime (down to 200cm1). 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 CCl4+3% CS2. (a) Measured IRS spectra. The average pump power is increased, resulting in clear attenuation in the anti-Stokes spectrum at the CCl4 vibronic modes at 460cm1, 314cm1, and 218cm1. 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 gR=1.5·1012m/W.
Fig. 6. IRS versus spontaneous Raman for CCl4. (a) IRS response spectra for increasing pump power. (b) Spontaneous Raman spectrum with logarithmic ordinate scale.

Fig. 7. Total dispersion of a step-index liquid-core fiber. The core is filled with CCl4 and 3% CS2, with a core diameter of 10 μm. The cladding is fused silica. (a) Dispersion D(=(2πc/λ2)β2). (b) Dispersion coefficient β2.

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 γas=0.44W1/(km). Using Eqs. (4) and (5), we extract a Raman gain coefficient of gR=1.5·1012m/W, which is remarkably similar to the extracted Raman gain coefficient obtained via the SpRS approach outlined in Section 4, i.e., gR=1.6·1012m/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 CCl4 and CS2. In particular, the core was filled with CCl4+5% CS2 and a chromophore concentration of 12·103Mol/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

12. K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse Raman scattering in liquid-core optical fibers,” Opt. Lett. 37, 942–944 (2012). [CrossRef]

]. We observe the main resonances of CCl4 (at 460cm1) and CS2 (at 655cm1), as well as the resonances associated with beta-carotene (1160cm1 and 1530cm1). 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 (>1000cm1). The resonance of beta-carotene at 1160cm1 shows an IRS loss of 5dB. 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 CCl4+5% CS2 and 12·103Mol/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 1160cm1 resonance (at 1321 nm) of beta-carotene. The blue curve matches the dip best and yields an extracted Raman gain coefficient of gR=6·1013m/W for the given beta-carotene concentration.
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 1160cm1 corresponds to zero time delay. (b) Spontaneous Raman spectrum with logarithmic ordinate scale.

D. Carbon Disulfide (CS2)

Figure 10(a) shows the measured IRS spectrum when the fiber was filled with neat liquid CS2. In order to accommodate the narrower linewidth expected for the vibrational resonance of CS2, the resolution of the optical spectrum analyzer was increased to 0.1 nm for these experiments. We observe an attenuation at 660cm1 of 18dB at a pump power of only 1.5mW. 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 (6cm1), 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 CS2 in air, we expect some water contamination.

Fig. 10. IRS spectra of liquid-core fiber filled with neat CS2. (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 gR=3·1011m/W.
Fig. 11. IRS versus spontaneous Raman for CS2. (a) IRS response spectra for increasing pump power. (b) Spontaneous Raman spectrum with logarithmic ordinate scale.

Since the Raman linewidth is much smaller than the pump bandwidth, the IRS propagation equations were solved with τ1=8.04fs and τ2=15ps, values which have been reported in the literature [43

43. W. R. L. Clements and B. P. Stoicheff, “Raman linewidths for stimulated threshold and gain calculations,” Appl. Phys. Lett. 12, 246–248 (1968). [CrossRef]

]. Figure 10(b) shows the experimentally determined fractional IRS loss spectrum (shaded) and the corresponding theoretical curves (solid). We obtain a best fit for gR=3·1011m/W, which is on the same order as measured values derived from steady-state Raman spectroscopy (gR=1.3·1011m/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., 1.2cm1 compared with 0.5cm1 [43

43. W. R. L. Clements and B. P. Stoicheff, “Raman linewidths for stimulated threshold and gain calculations,” Appl. Phys. Lett. 12, 246–248 (1968). [CrossRef]

]). 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.

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.

APPENDIX A: DISPERSION COEFFICIENTS

We explicitly give the computed dispersion coefficients for a core that is filled with CCl4 and 3% CS2. The core diameter is 10 micron and the cladding is fused silica. The dispersion coefficients up to the sixth-order at the anti-Stokes (1447 nm) and pump (1550 nm) wavelengths are β2,as=17.87ps2/(km), β2,p=12.16ps2/(km), β3,as=6.567·102ps3/(km), β3,p=7.661·102ps3/(km), β4,as=1.127·104ps4/(km), β4,p=1.620·104ps4/(km), β5,as=4.952·107ps5/(km), β5,p=7.488·107ps5/(km), β6,as=2.445·109ps6/(km), β6,p=3.955·109ps6/(km).

ACKNOWLEDGMENTS

For financial support we thank the DARPA ZOE program (Grant No. W31P4Q-09-1-0012) and the CIAN ERC (Grant No. EEC-0812072). We would like to acknowledge Matt Goodman at DARPA for helpful discussions.

REFERENCES

1.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002). [CrossRef]

2.

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004). [CrossRef]

3.

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092–6098 (2005). [CrossRef]

4.

J. G. Skinner and W. G. Nilsen, “Absolute Raman scattering cross-section measurement of 992  cm-1 line of Benzene,” J. Opt. Soc. Am. 58, 113–119 (1968). [CrossRef]

5.

M. J. Colles and J. E. Griffiths, “Relative and absolute Raman scattering cross-sections in liquids,” J. Chem. Phys. 56, 3384–3391 (1972). [CrossRef]

6.

Y. R. Shen, Principles of Nonlinear Optics (Wiley-Interscience, 1984).

7.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1991).

8.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

9.

D. Mahgerefteh, D. L. Butler, J. Goldhar, B. Rosenberg, and G. L. Burdge, “Technique for measurement of the Raman gain coefficient in optical fibers,” Opt. Lett. 21, 2026–2028 (1996). [CrossRef]

10.

W. J. Jones and B. P. Stoicheff, “Inverse Raman spectra–induced absorption at optical frequencies,” Phys. Rev. Lett. 13, 657–659 (1964). [CrossRef]

11.

K. Kieu, L. Schneebeli, J. M. Hales, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “Demonstration of Zeno switching through inverse Raman scattering in an optical fiber,” Opt. Express 19, 12532–12539 (2011). [CrossRef]

12.

K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse Raman scattering in liquid-core optical fibers,” Opt. Lett. 37, 942–944 (2012). [CrossRef]

13.

K. Kieu, L. Schneebeli, R. A. Norwood, and N. Peyghambarian, “Integrated liquid-core optical fibers for ultra-efficient nonlinear liquid photonics,” Opt. Express 20, 8148–8154 (2012). [CrossRef]

14.

K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a fiber taper embedded in carbon nanotube/polymer composite,” Opt. Lett. 32, 2242–2244 (2007). [CrossRef]

15.

K. Kieu, R. J. Jones, and N. Peyghambarian, “Generation of few-cycle pulses from an amplified carbon nanotube mode-locked fiber laser system,” IEEE Photon. Technol. Lett. 22, 1521–1523 (2010). [CrossRef]

16.

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978). [CrossRef]

17.

M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fibers by crossphase modulation,” Electron. Lett. 23, 961–963 (1987). [CrossRef]

18.

L. Prigent and J. P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by 4-wave-mixing,” IEEE Photon. Technol. Lett. 5, 1092–1095 (1993). [CrossRef]

19.

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n(2) in various types of telecommunication fiber at 1.55  μm,” Opt. Lett. 21, 1966–1968 (1996). [CrossRef]

20.

C. Headley and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170–2177 (1996). [CrossRef]

21.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman-scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989). [CrossRef]

22.

Q. Lin, F. Yaman, and G. P. Agrawal, “Raman-induced polarization-dependent gain in parametric amplifiers pumped with orthogonally polarized lasers,” IEEE Photon. Technol. Lett. 18, 397–399 (2006). [CrossRef]

23.

R. W. Hellwarth, A. Owyoung, and N. George, “Origin of nonlinear refractive index of liquid CCl4,” Phys. Rev. A 4, 2342–2347 (1971). [CrossRef]

24.

Y. Kato and H. Takuma, “Experimental study on wavelength dependence of Raman scattering cross sections,” J. Chem. Phys. 54, 5398–5402 (1971). [CrossRef]

25.

K. T. Schomacker, J. K. Delaney, and P. M. Champion, “Measurements of the absolute Raman cross-sections of Benzene,” J. Chem. Phys. 85, 4240–4247 (1986). [CrossRef]

26.

M. O. Trulson and R. A. Mathies, “Raman cross-section measurements in the visible and ultraviolet using an integrating cavity–application to benzene, cyclohexane, and cacodylate,” J. Chem. Phys. 84, 2068–2074 (1986). [CrossRef]

27.

N. Abe, M. Wakayama, and M. Ito, “Absolute Raman intensities of liquids,” J. Raman Spectrosc. 6, 38–41 (1977). [CrossRef]

28.

F. J. McClung and D. Weiner, “Measurement of Raman scattering cross sections for use in calculating stimulated Raman scattering effects,” J. Opt. Soc. Am. 54, 641–643 (1964). [CrossRef]

29.

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, “Intensity and gain measurements on stimulated Raman emission in liquid O2 and N2,” Phys. Rev. 180, 61–68 (1969). [CrossRef]

30.

T. C. Damen, R. C. C. Leite, and S. P. S. Potro, “Angular dependence of Raman scattering from benzene excited by He–Ne cw laser,” Phys. Rev. Lett. 14, 9–11 (1965). [CrossRef]

31.

A. C. Albrecht and M. C. Hutley, “Dependence of vibrational Raman intensity on wavelength of incident light,” J. Chem. Phys. 55, 4438–4443 (1971). [CrossRef]

32.

W. R. Hess, H. Hacker, H. W. Schrotte, and J. Brandmul, “On measurement of intensity and depolarization ratio of Raman lines with laser excitation,” Z. Angew. Phys. 27, 233–238 (1969).

33.

A. Hoffmann, S. Keller, B. Schrader, R. Ferwerda, and J. H. Vandermaas, “Polarization measurements in near-infrared Fourier-transform spectroscopy,” J. Raman Spectrosc. 22, 497–503 (1991). [CrossRef]

34.

W. Proffitt and S. P. S. Porto, “Depolarization ratio in Raman spectroscopy as a function of frequency,” J. Opt. Soc. Am. 63, 77–84 (1973). [CrossRef]

35.

M. E. Lines, “Raman-gain estimates for high-gain optical fibers,” J. Appl. Phys. 62, 4363–4370 (1987). [CrossRef]

36.

H. J. Marrinan and N. Sheppard, “Relative intensities of the Raman lines of carbon tetrachloride, chloroform, and methylene chloride,” J. Opt. Soc. Am. 44, 815–819 (1954). [CrossRef]

37.

O. D. Herrera, L. Schneebeli, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Raman-induced frequency shift in CS2-filled integrated liquid-core optical fiber,” Submitted to Optics Letters.

38.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

39.

B. E. Little, J. P. Laine, and H. A. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17, 704–715 (1999). [CrossRef]

40.

A. Samoc, “Dispersion of refractive properties of solvents: chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174 (2003). [CrossRef]

41.

H. H. Marvin, “The selective transmission and the dispersion of the liquid chlorides,” Phys. Rev. 34, 161–186 (1912).

42.

I. H. Malitson, “Interspecimen comparison of refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1208 (1965). [CrossRef]

43.

W. R. L. Clements and B. P. Stoicheff, “Raman linewidths for stimulated threshold and gain calculations,” Appl. Phys. Lett. 12, 246–248 (1968). [CrossRef]

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(160.4330) Materials : Nonlinear optical materials
(190.5650) Nonlinear optics : Raman effect
(300.6450) Spectroscopy : Spectroscopy, Raman

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 10, 2013
Revised Manuscript: September 10, 2013
Manuscript Accepted: September 26, 2013
Published: October 24, 2013

Virtual Issues
October 25, 2013 Spotlight on Optics

Citation
L. Schneebeli, K. Kieu, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, "Measurement of the Raman gain coefficient via inverse Raman scattering," J. Opt. Soc. Am. B 30, 2930-2939 (2013)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-11-2930


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References

  1. F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002). [CrossRef]
  2. O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004). [CrossRef]
  3. J. E. Sharping, Y. Okawachi, and A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092–6098 (2005). [CrossRef]
  4. J. G. Skinner and W. G. Nilsen, “Absolute Raman scattering cross-section measurement of 992  cm-1 line of Benzene,” J. Opt. Soc. Am. 58, 113–119 (1968). [CrossRef]
  5. M. J. Colles and J. E. Griffiths, “Relative and absolute Raman scattering cross-sections in liquids,” J. Chem. Phys. 56, 3384–3391 (1972). [CrossRef]
  6. Y. R. Shen, Principles of Nonlinear Optics (Wiley-Interscience, 1984).
  7. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1991).
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
  9. D. Mahgerefteh, D. L. Butler, J. Goldhar, B. Rosenberg, and G. L. Burdge, “Technique for measurement of the Raman gain coefficient in optical fibers,” Opt. Lett. 21, 2026–2028 (1996). [CrossRef]
  10. W. J. Jones and B. P. Stoicheff, “Inverse Raman spectra–induced absorption at optical frequencies,” Phys. Rev. Lett. 13, 657–659 (1964). [CrossRef]
  11. K. Kieu, L. Schneebeli, J. M. Hales, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “Demonstration of Zeno switching through inverse Raman scattering in an optical fiber,” Opt. Express 19, 12532–12539 (2011). [CrossRef]
  12. K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse Raman scattering in liquid-core optical fibers,” Opt. Lett. 37, 942–944 (2012). [CrossRef]
  13. K. Kieu, L. Schneebeli, R. A. Norwood, and N. Peyghambarian, “Integrated liquid-core optical fibers for ultra-efficient nonlinear liquid photonics,” Opt. Express 20, 8148–8154 (2012). [CrossRef]
  14. K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a fiber taper embedded in carbon nanotube/polymer composite,” Opt. Lett. 32, 2242–2244 (2007). [CrossRef]
  15. K. Kieu, R. J. Jones, and N. Peyghambarian, “Generation of few-cycle pulses from an amplified carbon nanotube mode-locked fiber laser system,” IEEE Photon. Technol. Lett. 22, 1521–1523 (2010). [CrossRef]
  16. R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978). [CrossRef]
  17. M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fibers by crossphase modulation,” Electron. Lett. 23, 961–963 (1987). [CrossRef]
  18. L. Prigent and J. P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by 4-wave-mixing,” IEEE Photon. Technol. Lett. 5, 1092–1095 (1993). [CrossRef]
  19. A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n(2) in various types of telecommunication fiber at 1.55  μm,” Opt. Lett. 21, 1966–1968 (1996). [CrossRef]
  20. C. Headley and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170–2177 (1996). [CrossRef]
  21. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman-scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989). [CrossRef]
  22. Q. Lin, F. Yaman, and G. P. Agrawal, “Raman-induced polarization-dependent gain in parametric amplifiers pumped with orthogonally polarized lasers,” IEEE Photon. Technol. Lett. 18, 397–399 (2006). [CrossRef]
  23. R. W. Hellwarth, A. Owyoung, and N. George, “Origin of nonlinear refractive index of liquid CCl4,” Phys. Rev. A 4, 2342–2347 (1971). [CrossRef]
  24. Y. Kato and H. Takuma, “Experimental study on wavelength dependence of Raman scattering cross sections,” J. Chem. Phys. 54, 5398–5402 (1971). [CrossRef]
  25. K. T. Schomacker, J. K. Delaney, and P. M. Champion, “Measurements of the absolute Raman cross-sections of Benzene,” J. Chem. Phys. 85, 4240–4247 (1986). [CrossRef]
  26. M. O. Trulson and R. A. Mathies, “Raman cross-section measurements in the visible and ultraviolet using an integrating cavity–application to benzene, cyclohexane, and cacodylate,” J. Chem. Phys. 84, 2068–2074 (1986). [CrossRef]
  27. N. Abe, M. Wakayama, and M. Ito, “Absolute Raman intensities of liquids,” J. Raman Spectrosc. 6, 38–41 (1977). [CrossRef]
  28. F. J. McClung and D. Weiner, “Measurement of Raman scattering cross sections for use in calculating stimulated Raman scattering effects,” J. Opt. Soc. Am. 54, 641–643 (1964). [CrossRef]
  29. J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, “Intensity and gain measurements on stimulated Raman emission in liquid O2 and N2,” Phys. Rev. 180, 61–68 (1969). [CrossRef]
  30. T. C. Damen, R. C. C. Leite, and S. P. S. Potro, “Angular dependence of Raman scattering from benzene excited by He–Ne cw laser,” Phys. Rev. Lett. 14, 9–11 (1965). [CrossRef]
  31. A. C. Albrecht and M. C. Hutley, “Dependence of vibrational Raman intensity on wavelength of incident light,” J. Chem. Phys. 55, 4438–4443 (1971). [CrossRef]
  32. W. R. Hess, H. Hacker, H. W. Schrotte, and J. Brandmul, “On measurement of intensity and depolarization ratio of Raman lines with laser excitation,” Z. Angew. Phys. 27, 233–238 (1969).
  33. A. Hoffmann, S. Keller, B. Schrader, R. Ferwerda, and J. H. Vandermaas, “Polarization measurements in near-infrared Fourier-transform spectroscopy,” J. Raman Spectrosc. 22, 497–503 (1991). [CrossRef]
  34. W. Proffitt and S. P. S. Porto, “Depolarization ratio in Raman spectroscopy as a function of frequency,” J. Opt. Soc. Am. 63, 77–84 (1973). [CrossRef]
  35. M. E. Lines, “Raman-gain estimates for high-gain optical fibers,” J. Appl. Phys. 62, 4363–4370 (1987). [CrossRef]
  36. H. J. Marrinan and N. Sheppard, “Relative intensities of the Raman lines of carbon tetrachloride, chloroform, and methylene chloride,” J. Opt. Soc. Am. 44, 815–819 (1954). [CrossRef]
  37. O. D. Herrera, L. Schneebeli, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Raman-induced frequency shift in CS2-filled integrated liquid-core optical fiber,” Opt. Commun. 318, 83-87 (2014).
  38. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  39. B. E. Little, J. P. Laine, and H. A. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17, 704–715 (1999). [CrossRef]
  40. A. Samoc, “Dispersion of refractive properties of solvents: chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174 (2003). [CrossRef]
  41. H. H. Marvin, “The selective transmission and the dispersion of the liquid chlorides,” Phys. Rev. 34, 161–186 (1912).
  42. I. H. Malitson, “Interspecimen comparison of refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1208 (1965). [CrossRef]
  43. W. R. L. Clements and B. P. Stoicheff, “Raman linewidths for stimulated threshold and gain calculations,” Appl. Phys. Lett. 12, 246–248 (1968). [CrossRef]

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