Quasi-phase matching transient SRS generation

Victor G. BespalovRussian Research Center

"S. I. Vavilov State Optical Institute"

Nikolai S. MakarovSaint-Petersburg State

Institute of Fine Mechanics and Optics (Technical

University)

Principle of quasi-phase matching

Nonlinearity (2) Nonlinearity (3)

2

Raman active medium

System of transient SRS equations

– wave mismatching, g –

steady-state Raman gain coefficient, i –

frequencies of interacting waves, T2 – dephasing time, q –

phonon wave, Aj – complex wave

amplitudes, z=z’+t’/c, t=t’.

*

2qA

gz

Ap

s

qAizg

z

Ap

s

aa )exp(2

))exp((2

* qAizqAg

z

Asa

s

pp

2

** )exp(

T

izAAAAq

t

q pasp

3

Principleof quasi-phase matching at SRS

- Generalized phase=2p-a-s-(ka+ks-2kp)r,

where ki – is the wave vector of interacting wave, that describes

the direction of energy conversion “pump – Stokes –

anti-Stokes”, on passive layers input (0, 2) and active layers input (1, 3) do not practically

change, that in a final result provides a realization of quasi-

phase matching conditions.(3)0 (3)=04

- It is possible to create conditions, at which anti-Stokes conversion coefficient reaches ~25% and the anti-Stokes wave

intensity is practically compared to Stokes wave intensity

Quasi steady-state SRSpulse25Т2 (Т2=0.203 ns,pulse=10 ns).

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Highly transient SRSpulse<<25Т2 (Т2=0.203 ns,pulse=25 ps).

6

- The efficiency of anti-Stokes SRS conversion much depends on a ratio of dephasing time T2 to pulse duration

Optimum ratio ofinput Stokes/pump intensities

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- There is an optimum value of input Stokes/pump waves

intensities ratio.

- This dependence can be

approximated as Is/Ip,opt=0,1359g-2,6146

Critical pump wave intensity

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- There is a critical value

of pump intensity.

- This dependence

can be approximated as Icr.p=0.4Δ/g

Conclusions

• The conversion efficiency can reached more than 25%

• The efficiency of anti-Stokes SRS conversion much decreased with increasing of a ratio of

dephasing time T2 to pulse duration

• For each medium there is an optimal ratio Is/Ip, at which conversion efficiency is maximal

• For each medium there is a critical value of pump intensity 9

References

• J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric” Phys. Rev., 127, pp. 1918-1939, 1962.• R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, V. A. Serebryakov, “About parametrical effects at SRS generation of higher components in gases”, Quantum Electronics, 9(1), pp. 56-60, 1982.•A. P. Hickman, W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit”, Physical review A, 37(7), pp 2516-2523, 1988.• J. J. Ottusch, M. S. Mangir, D. A. Rockwell, “Efficient anti-Stokes Raman conversion by four-wave mixing in gases” J. Opt. Soc. Am., B 8, pp. 68-77, 1991.• Makarov N. S. (Scientist supervisor – Bespalov V. G.) “Generation of anti-Stokes SRS radiation in conditions of quasi-phase matching”, in book “Problems of coherent and nonlinear optics”, pp. 180-190, 2000.• Bespalov V. G., Makarov N. S., “Quasi-phase matching anti-Stokes SRS generation”, Opt. & Spectr., vol. 90, No. 6, pp. 1034-1037, 2001.

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