Two-beam coupling, attributed to Raman gain, is observed in dielectrics using chirped femtosecond pulses. A time resolved pump-probe geometry is used to vary the frequency difference between pulses in the terahertz frequency band. Stimulated Raman scattering couples the pulses transferring energy from the higher to the lower frequency beam, resulting in a dispersion shaped curve as a function of the temporal delay, dependent on the product of the pump and probe irradiances. The observed signal gives the Raman gain in SiO2 and PbF2 for detunings up to 10 THz (approximately 300 cm(-1)) using mm-thick samples. This method may also be sensitive to the electronic motion responsible for bound-electronic nonlinear refractive index, which could yield the optical response time of bound electrons

Dogar, Arthur

Hagan, David J.

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University of Central Florida STARS Faculty Bibliography 1990s Faculty Bibliography 1-1-1997 Low frequency Raman gain measurements using chirped pulses Arthur Dogar University of Central Florida David J. Hagan University of Central Florida Find similar works at: https://stars.library.ucf.edu/facultybib1990 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 1990s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation Dogar, Arthur and Hagan, David J., "Low frequency Raman gain measurements using chirped pulses" (1997). Faculty Bibliography 1990s. 1889. https://stars.library.ucf.edu/facultybib1990/1889 Low frequency Raman gain measurements usingchirped pulsesArthur Dogariu† and David J. HaganCenter for Research and Education in Optics and Lasers (CREOL)University of Central Florida, P.O. Box 162700, Orlando, FL 32816-2700.hagan@creol.ucf.eduAbstract:  Two-beam coupling, attributed to Raman gain, is observed indielectrics using chirped femtosecond pulses.  A time resolved pump-probegeometry is used to vary the frequency difference between pulses in theterahertz frequency band.  Stimulated Raman scattering couples the pulsestransferring energy from the higher to the lower frequency beam, resultingin a dispersion shaped curve as a function of the temporal delay, dependenton the product of the pump and probe irradiances.  The observed signalgives the Raman gain in SiO2 and PbF2 for detunings up to 10 THz(approximately 300 cm-1) using mm-thick samples. This method may alsobe sensitive to the electronic motion responsible for bound-electronicnonlinear refractive index, which could yield the optical response time ofbound electrons.1997 Optical Society of AmericaOCIS codes: (060.7140) Ultrafast processes in fibers; (190.7070) Two-wave mixing;(320.7110) Ultrafast nonlinear optics; (190.5650) Raman effect; (190.5890) Scattering,stimulated† Present Address: Institute for Polymers and Organic Solids, University of California, Santa Barbara, CA.___________________________________________________________________________References and Links1. N. Bloembergen, “The stimulated Raman effect,” Am. J. Phys. 35, 989 (1967).2. W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin and Raman spectroscopy,” in Laser Handbook,Vol. 2 edited by F. T. Arecchi and E. O. Schulz-DuBois, North-Holland, p. 1077, 1972.3. M. J. Weber, Handbook of Laser Science and Technology, Vol. 3, Optical Materials: Part 1, CRC PressInc., p. 287-292(1986).4. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659(1986)5. D. J. Dougherty, F. X. Kartner, H. A. Haus, and E. P. Ippen, “Measurement of the Raman gain spectrum ofoptical fibers,” Opt. Lett. 20, 31 (1995).6. A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland and N. Bloembergen, “Purely refractivetransient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B, 14, 796 (1997).7. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662 (1986).8. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-corefibers,” J. Opt. Soc. Am. B, 6, 1159 (1989).___________________________________________________________________________The properties of stimulated Raman scattering (SRS)[1,2] and measurements of the Ramangain have been made in many materials and at various detunings.[3]  Effects commonlyobserved in pulse propagation in optical fibers, such as the soliton self-frequency shift,[4]have their origin in low-frequency SRS making the low-frequency Raman gain spectrum ofconsiderable interest.  The limit in measuring the Raman gain at small frequency detunings isdetermined by the requirement that the DC pump beam must be removed from the detectionsystem.  Low-frequency Raman gain measurements have been reported down to 6 cm-1 inglass fibers with interaction lengths of several hundred meters. [5]  Obviously this method is(C) 1997 OSA 4 August 1997 / Vol. 1, No. 3 / OPTICS EXPRESS 73#2183 - $10.00 US Received July 3, 1997; Revised July 28, 1997not applicable to other materials.  Here we propose a novel method for measuring the Ramangain at low frequency with much shorter interaction lengths based on two-beam coupling ofchirped pulses.  This method relates the frequency difference between the pump and probebeams in a pump-probe experiment to the time-delay between the pulses.The experiment essentially consists of a non-collinear pump-probe system.[6]  Thetwo-beam coupling between the pump and probe beams is due to a frequency differencebetween the beams.  Because the pulses are identically chirped, this frequency differenceoccurs when the pulses are displaced in time with respect to each other.  For a linearly chirpedpulse, this frequency difference is constant in time at any given delay between the pulses. Byvarying the delay between the pulses, we vary the detuning between the pump and probebeams.A noncollinear pump-probe geometry is used with pump and probe derived from thesame source.  Monitoring the probe beam energy, the gain of the SRS can be directlymeasured as a function of time-delay.  Dogariu et. al.[6] recently reported a similarexperiment for measuring stimulated Rayleigh-wing scattering in liquids using picosecondpulses.  In that case, the signals are relatively large, with gains of several percent.  However,Raman gains in thin dielectric samples of similar dimensions are several orders of magnitudesmaller.  Despite this, we demonstrate here that by using signal retrieval techniques, we canmeasure the Raman gain in dielectrics with interaction lengths of only a millimeter or so.To measure very small changes in probe transmittance, we use a dual frequencymodulation technique consisting of 1 MHz mechanical modulation of the pump beam, and100 Hz modulation of the probe.  The signal is detected by cascading high frequency andlow-frequency lock-in amplifiers, resulting in a sensitivity to normalized changes in probeenergy as low as a few times 10-6.  In measuring small Raman gain signals we have toeliminate competing signals such as three-photon absorption, scattering due to impurities, etc.We used a mode-locked Ti:Sapphire laser source providing purposely-chirped 100 fs(FWHM) pulses at 840 nm.  We estimate the chirp by measuring pulse temporal and spectralwidths.  For linearly chirped pulses we can measure the linear chirp coefficient C, where, forGaussian pulses, the input electric field is defined as:( ) ( ) 22202 10),( ptiCwrtrki eeeEtrE τω +−−−⋅=&&&, (1)with τp the pulse width (HW1/eM).  For a given time-delay, τ, we can calculate the frequencydifference between the pump and probe beam, Ω.  For linearly chirped pulses,2pprobepumpCττωω =−=Ω. (2)We can immediately see the linear relationship between the time-delay and thedetuning. The irradiance, I, of the probe beam (subscript p) sees the Raman gain, g, inducedby the excitation beam (subscript e):pep IgIdzdI= . (3)Integrating Eq. (3) over the pulse width τp and beam waists w0p,e, we obtain thenormalized change in the weak probe transmittance:(C) 1997 OSA 4 August 1997 / Vol. 1, No. 3 / OPTICS EXPRESS 74#2183 - $10.00 US Received July 3, 1997; Revised July 28, 1997)(21exp121)(202020ττττ gLIwwTTpeepp−+= ∆ , (4)where I0e is the peak pump irradiance and L is the sample length.Fig.1 Two-beam coupling data (circles) (a) in PbF2 and (b) in SiO2 with theoretical fits (solid lines)assuming a Raman gain linearly dependent on time-delay. The pulses are linearly chirped with C = 1.3.Here C is measured to be 1.3± 0.1.Figure 1 represents the measured normalized changes in transmittance (circles) forPbF2 (a) and SiO2 (b) as functions of the time-delay τ.  The solid lines are fits using Eq. 4,which give a Raman gain, g(τ) that is linearly dependent on τ.  We obtain g(τ) = 5.5⋅10-14 τfor PbF2 and g(τ) = 4.8⋅10-15 τ   for SiO2, where g is in cm/W and τ is in fs.For linear chirp we can use Eq. 2 to express the time-delay dependence in terms offrequency ν=Ω/2pi. In this case we can directly extract the linear frequency dependence of thegain from Eq. 4 by removing the time-correlation term, exp{-½(τ/τp)2}, from the data shownin Fig. 1.  By fitting the so-transformed data shown in Fig. 2 for PbF2 (squares) and SiO2(circles) we obtain g(ν).The lines fitting the data in Fig. 2 give the following frequency dependence for theRaman gain:νν 1310)9.16.9()(2−⋅±=PbFg (5.a)νν 1410)7.14.8()(2−⋅±=SiOg , (5.b)where g is in cm/W and ν in THz.Equation 5.b is in good agreement with the previously reported measured Ramangain spectra of silica glass in fibers,[5,7] if we account for the fact that our measurements areperformed with 100 fs pulses, within the 400 fs turn-on of the vibrational Raman effect.[8]However, those methods are limited to glass since long fibers are required to achievedetectable stimulated Raman gain.  Using our method, any sample can be used as long as thelaser frequency is chosen to lie in a region of very low nonlinear absorption.-0 .0 0 0 4-0 .0 0 0 200 .0 0 0 20 .0 0 0 4-3 0 0 -1 5 0 0 1 5 0 3 0 0(a )D e la y  ( fs )(∆T/T)p-4 x1 0 -5-2 x1 0 -502 x1 0 -54 x1 0 -5-3 0 0 -1 5 0 0 1 5 0 3 0 0(b )D e la y  ( fs )(∆ T/T) p(C) 1997 OSA 4 August 1997 / Vol. 1, No. 3 / OPTICS EXPRESS 75#2183 - $10.00 US Received July 3, 1997; Revised July 28, 1997-1.0x10-11-0.5x10-1100.5x10-111.0x10-11-10 -5 0 5 10SiO2PbF2ν (THz)g (cm/W) Fig. 2. Low frequency Raman spectra for PbF2 (squares) and SiO2 (circles) obtained using thechirped-two-beam coupling method, along with linear fits.So far, the chirped pulse two-beam coupling technique has been used to measure theeffects of molecular rotation (stimulated Rayleigh-wing scattering),[6] and of nuclearvibration (stimulated Raman scattering).  However, this method may also be sensitive to theelectronic motion responsible for bound-electronic nonlinear refractive index, n2.  Typicallythis response time is predicted to be ~1 fs or less.  A simple calculation assuming 0.1 ~ 1 fsDebye relaxation times for the bound electrons reveals that signals similar in magnitude to theRaman signals should be measurable.  The challenge that remains here is to findcombinations of materials and detunings for which the nuclear signals would not dominatethe electronic signals.AcknowledgementsWe would like to thank Eric Van Stryland, Hermann A. Haus and Boris Ya.Zel’dovich for very useful discussions.(C) 1997 OSA 4 August 1997 / Vol. 1, No. 3 / OPTICS EXPRESS 76#2183 - $10.00 US Received July 3, 1997; Revised July 28, 1997

Low frequency Raman gain measurements using chirped pulses

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Low frequency Raman gain measurements using chirped pulses

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