Vol. 3, No. 10/October 1986/J. Opt. Soc. Am. B 1461
Phase correlation in a Raman amplifier
Gabriel G. Lombardi* and Hagop InjeyanAdvanced Technology Division, TRW, One Space Park Drive, Redondo Beach, California 90278
Received March 5, 1986; accepted May 15, 1986
The effects of pump-beam temporal structure in a Raman amplifier were studied by using a frequency-doubledNd:YAG laser. The experiment demonstrated that the Stokes wave becomes correlated with the pump as it isamplified. This leads to the result that, in general, the amplified Stokes wave is not coherent with the incidentStokes wave. The implications of this result for multiple-beam Raman amplifiers are discussed.
1. INTRODUCTION
Stimulated forward Raman scattering has been suggestedfor a variety of applications including wavelength conver-sion, beam cleanup, and, more recently, the combination ofthe energy from several pump beams into a coherent Stokesbeam. The superfluorescent seed-generator-amplifier con-figuration' has been used in these applications to providehigh first-Stokes efficiency and beam-quality control by us-ing a diffraction-limited Stokes seed in a relatively low-gainamplifier. Although the dependence of the behavior of Ra-man amplifiers on parameters such as gain and intensityuniformity is well known, other more subtle Raman effectssuch as gain enhancement and phase locking in finite-band-width amplifiers have been recently discovered.
Several previous publications have touched on the subjectof phase correlation in broadband Raman amplifiers andlaid the foundation for this work. Raymer et al.2 predictedphase locking in Raman amplifiers, whereby uncorrelatedpump and Stokes waves become correlated, after which theStokes wave experiences monochromatic gain. The lattereffect (gain enhancement) was also predicted by Egglestonand Byer 3 and was experimentally observed by Stappaerts etal.
4 Finally, two recent papers on independent theoreticalwork by Ackerhalt and Kurnit5 and Druhl6 further explorephase-locking and coherence effects in Raman amplifiers.
A significant aspect of the theoretical predictions is that aRaman amplifier changes the temporal-coherence proper-ties of the Stokes wave such that the amplified wave may notbe coherent with the Stokes seed. To our knowledge, ex-perimental verification of this effect has not been publishedhitherto. This prediction is particularly significant in Ra-man beam combination because a change in the temporalproperties of a pump beam affects the spatial coherence ofthe amplified Stokes wave. In what follows, we will showthat the spatial coherence of the Stokes output in a high-gain Raman amplifier depends on the mutual coherence ofthe pump beams. This was demonstrated experimentallyby the data presented in Section 3. Analysis leading to theinterpretation of the data is presented in Section 2. Theimplications for Raman beam combination and a brief dis-cussion of related effects in off-axis pumping are presentedin Section 4.
2. THEORY
Consider pump, and Stokes fields in a Raman amplifier ex-pressed in the form
'/2Ep(z, t)exp[i(wpt - Pt)] + c.c.
and
/2E(z, t)exp[i(Ct - ksz)] + c.c.
These fields may be expanded into a sum over laser modesEp(z, t) = Y,, E,, exp(inwt) and E,(z, t) = En E5 n exp(incot),where w is the mode spacing of the laser. This is the startingpoint of the work of Eggleston and Byer, who solve theequations of motion of the pump and Stokes amplitudesunder the assumption that >> r, where is the Ramanlinewidth. They define a parameter that characterizes thecorrelation of pump and Stokes waves in a Raman amplifier:
|Z EpnE s 2
= n
n
From its definition, it follows that < 1, with / = 1, if theratio En/Epn is the same for all n. This is equivalent to thestatement that the pump and Stokes waves are correlated.The quantity /3 also represents a fraction of the monochro-matic gain go experienced by the Stokes wave. The equationthat describes the evolution of as the Stokes and pumpwaves propagate in the amplifier shows that a weak Stokesseed becomes correlated with the pump wave ( - 1):
Oz 2 ~~2- 1P\ - 2I21U,1 VO(ZIEn1-P~ ~J E,n co' ~n
(2)
This was verified experimentally by measuring interfero-metrically (cf. Section 3).
Consider the interference of two waves E(z, t) and E2 (z,t), each consisting of modes spaced by co, centered at 0.The visibility of the fringes formed is given by
1462 J. Opt. Soc. Am. B/Vol. 3, No. 10/October 1986
DICHROICMIRROR
MACH ZEHNDERINTERFEROMETER
__ ---- I
SUPER-FLUORESCENTCELL CAMERA
BEAM' -- ;SPLITTER
SPATIALFILTER
OPTICALDELAY
Fig. 1. Raman beam-combination schematic.
n (3)
1(~n2 + E 1I2)~1IE2,J2
The visibility is defined by
Imax -min (4)
,max + min
where Imax and mill are the maximum and minimum intensi-ties of the fringe pattern. For correlated beams,
V = 2 , ~r I-2 (5)
where I, = 1/2 ZlE11112 and I2 = 1/2 E E2n are the intensitiesof the two interfering waves. The observed fringe visibility,normalized to V,, is a measure of the correlation of the twointerfering waves
ElnE 2n3V2 n (6)
Vc2 4IlI2
Comparison with Eq. (1) shows that V2/V, 2 is equal to theparameter d for waves of the same frequency. Since theportion of the pump was used to generate the input Stokeswave in a superfluorescent Raman oscillator, it is assumedthat the two are well correlated. Under these conditions,
El,, = c Epn = Esn, and E2n1 = Esn, which implies that d = V2/
v2.
By varying the relative optical delay of the pump andinput Stokes waves, the degree of correlation between themcould be changed, thus reducing the initial value of / in theamplifier. The effect on / of an optical delay z is illustratedby considering a laser with N modes and coherence length I= 27rc/Nw. If all modes are of equal intensity, the correla-
tion is
sin2 (7rz/l)
N2
sin2(7rz/lN)
Compensating changes in the relative optical path lengths ofthe interferometer arms were used to demonstrate that increased as the Stokes wave was amplified.
3. EXPERIMENTS
The experiments were performed by using a Q-switched,doubled Nd:YAG laser as the pump. Figure 1 shows a sche-matic diagram of the apparatus used. A superfluorescentRaman seed generator and a Raman amplifier with 7-8 ama-gats of hydrogen were used in tandem. High-order Stokesgeneration was controlled by using a bandpass filter follow-ing the superfluorescent cell that prevented all but first-Stokes wavelengths from reaching the amplifier. Fast pho-todiodes were used to record the temporal profiles of thepump and depleted pump beams, and the conversion effi-ciency was calculated by measuring the amount of pumpdepletion. The laser bandwidth (coherence length) could bechanged from 25 to 10 GHz by introducing an intracavity
2
Fig. 2. Beam splitting apparatus. 1, Prism motion in this direc-tion varies the optical delay between the two beams; 2, prism motionin this direction varies the separation between the two beams; 3,mirror rotation changes the angle between the two beams.
G. G. Lombardi and H. Injeyan
Vol. 3, No. 10/October 1986/J. Opt. Soc. Am. B 1463
6talon; the longitudinal mode spacing was approximately200 MHz (approximately half the Raman linewidth at 8amagats). A pair of mirrors and a prism were used to splitthe pump beam into two and to introduce a variable opticaldelay between them (Fig. 2); by using this technique, themutual coherence of the two beams could be varied. AMach-Zehnder interferometer was formed by splitting off afraction of the seed beam before amplification and combin-ing it with the amplified Stokes beam; this allowed the phaserelationship between the amplified Stokes and the seed to berecorded and studied. The length of the reference arm ofthe interferometer could be varied by placing fused-silicawindows in the beam path, and Polaroid film was used torecord the interferograms.
Two sets of experiments were performed. The first setconsisted of characterizing the Raman amplifier and study-ing the correlation properties of the amplified Stokes beamby using a single pump. The second set consisted of lookingat the spatial coherence of the Stokes beam generated byusing two parallel pump beams with varying levels of mutualcoherence.
The amplifier gain was adjusted to be high enough (gIL =8-10) to allow phase locking and efficient conversion, re-gardless of the correlation between the pump and the seed.This was confirmed by introducing delays between thepump and the seed of up to several centimeters. A delay of 1cm represents approximately one coherence length at thenominal laser bandwidth of 25-30 GHz. Figure 3 showstemporal profiles of the pump and the depleted pump at the
REFERENCE ARM
OPTICl/ DELAY
Hf 11 -< _INTERFEROGRAM
STOKES I 8 t \ J SEED
OPTICALLYDELAYED RAMANPUMP AMPLIFIER
f the amplifier, indicating significant depletion with1 efficiencies near 50%. Figure 4 shows three seed-iied-Stokes interferograms. The first interferogrambtained when the pump was correlated with the seedLe interferometer arms were path matched, the seconda 2.5-cm delay was introduced in the reference arm,he third when a compensating delay was introducedhe pump upstream of the interferometer. Fringesbtained only if the seed and the pump were correlatedlengths matched within a coherence length), regard-F the path lengths of the two interferometer arms.learly indicates that the amplified Stokes acquires thecharacteristics of the pump.observation seems innocent enough for a single beam
is a profound effect on Raman beam combination.the amplified Stokes acquires the phase characteris-the pump, it now becomes essential for the pumpin a Raman beam combiner to be mutually coherent;
vise, the amplified Stokes beam would consist of mu-incoherent subapertures. This hypothesis was veri-.perimentally. Beam-combination experiments weremed by using two adjacent parallel beams with variousits of delays (1-10 cm) introduced between the two
Figure 5a shows the interference pattern obtainedlying one pump beam such that the path mismatch is
than the coherence length. The interferogramthat fringes appear only on one side of the amplified, which indicates two mutually incoherent subaper-ven though the injected seed was coherent across theaperture. Figure 5b, on the other hand, shows theituation when the pump beam is narrowed such thatth mismatch is less than the coherence length, andious fringes are observed on both halves of the beam,ting coherence across the entire aperture.
SCUSSION
sults shown above indicate that Raman beam combi-using multiple parallel pump beams can be achievedthe individual pump beams are mutually coherent.)nclusion is evident because beam combination as-coherence across the entire aperture that determines
Path lengths matched
2.5 cm optical delayin reference arm
2.5 cm optical delay inreference arm andcompensating delay inpump beam
AW 25 GHz2vr
Fig. 4. Single-beam Mach-Zehnder interferograms.
G G Lombardi and H. lnjeyan
Al
1464 J. Opt. Soc. Am. B/Vol. 3, No. 10/October 1986
PUMP AND SEEDARE CORRELATED -
PUMP AND SEEDVr ARE UNCORRELATED
a
Fig. 5. Raman combination of parallel pump beams. a, Interferogram of Stokes seed with amplified Stokes generated by mutually incoherentpump beams; b, interferogram of Stokes seed with amplified Stokes generated by mutually coherent pump beams resulting in continuousfringes.
d
INPUT PUMP
d tan af2
STOKESSEED
AMPLIFIEDSTOKES
DEPLETEDPUMP
Fig. 6. Off-axis-pumped Raman amplifier. Pump beam must be coherent across the Stokes-beam wave front to preserve Stokes-beam spatialcoherence.
the far-field spot size. For a practical system using severallarge laser heads, this means that all units must be driven orinjection locked by a common master oscillator. In addi-tion, the path lengths of each laser to the Raman amplifiermust be matched within a coherence length.
A problem closely related to this effect is that of off-axispumping. Figure 6 shows a typical configuration for off-axispumping in a Raman amplifier. In this case, although thereis only one pump beam, a careful look at the geometry showsthat the seed wave front samples the pump beam over adistance X. It can be easily shown that the distance x is thepath difference between the pump and the seed beams and isgiven by
x = d tan a/2,
where d is the seed aperture size and a is the angle betweenthe pump and the seed. Thus, in a manner very similar tothat demonstrated for multiple parallel beams, coherenceacross the seed aperture requires that the pump-beam co-herence length be larger than x. In essence, what happensduring off-axis pumping is that the temporal-coherencecharacteristics of the pump over the distance x are trans-ferred into spatial coherence on the Stokes wave front. Forsmall apertures (a few centimeters) and pump angles (a few
degrees), x is typically very small and well below reasonablecoherence lengths (a few centimeters) for most lasers. Thusthe coherence issue is of concern only for large-apertureamplifiers (tens of centimeters) and large pump angles (>10deg). This argument can be extended for multiple off-axispump beams in which now simultaneous requirements formutual coherence and coherence over the distance x corre-sponding to the specific amplifier geometry must be satis-fied.
In conclusion, we have shown experimentally that theStokes beam in a large-gain Raman amplifier acquires thetemporal-phase characteristics of the pump and becomescorrelated with the pump beam. We have also shown thatbecause of this phenomenon, Raman combination of multi-ple pump beams can be achieved only if the pump beams aremutually coherent. Finally, it was deduced that, for off-axispumping, this effect results in the transfer of temporal(in)coherence of the pump into spatial (in)coherence on theStokes beam.
ACKNOWLEDGMENTS
The authors are grateful to H. Komine, E. A. Stappaerts, M.Valley, and S. Pfeifer for their helpful comments and in-
G. G. Lombardi and H. Injeyan
G. G. Lombardi and H. Injeyan
sights as well as to R. Johnson for his able technical assis-tance.
* Present address, Northrop Research and TechnologyCenter, 1 Research Park, Palos Verdes Peninsula, California92074.
REFERENCES
1. H. Komine and E. A. Stappaerts, "Efficient higher-Stokes-orderRaman conversion in molecular gases," Opt. Lett. 4, 358 (1979).
Vol. 3, No. 10/October 1986/J. Opt. Soc. Am. B 1465
2. M. G. Raymer, J. Mostowski, and J. L. Carlsten, "Theory ofstimulated Raman scattering with broadband lasers," Phys. Rev.A 19, 2304 (1979).
3. J. Eggleston and R. L. Byer, "Steady-state stimulated Ramanscattering by a multimode laser," IEEE J. Quantum Electron.QE-16, 850 (1980).
4. E. A. Stappaerts, W. H. Long, Jr., and H. Komine, "Gain en-hancement in Raman amplifiers with broadband pumping," Opt.Lett. 5, 4 (1980).
5. J. R. Ackerhalt and N. A. Kurnit, "Phase pulling effects in Ra-man amplifiers," J. Opt. Soc. Am. A 2(13), P13 (1985).
6. K. J. Druhl, "Limitations on Stokes beam coherence for broad-band pumping," J. Opt. Soc. Am. A 2(13), P14 (1985).
