Quasi-phase matching anti-Stokes SRS generation

Victor G. BespalovAll Russian Research Center "S. I. Vavilov State Optical

Institute"

Nikolai S. MakarovSaint-Petersburg State

Institute of Fine Mechanics and Optics (Technical

University)

Outline

• Principals of quasi-phase matching• Systems of SRS equations

• Numerical simulations results• Conclusions• References

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Principals of quasi-phase matching

(2) (3)

3

Raman active medium

System of transient SRS equations

– waves mismatching, g –

steady-state Raman gain coefficient, i –

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

phonon wave, Aj – complex wave

amplitudes.

*

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

4

System of steady-state SRS equations

In this system the waves mismatching and Raman gain are the functions of coordinate for nonlinear ((3)0) and

linear ((3)=0) layers.

– waves mismatching, g – steady-state Raman gain

coefficient, i – frequencies of

interacting waves, Aj –

complex wave amplitudes.

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Efficiency of anti-StokesSRS generation in Raman-active media

Hydrogen = 3.84 rad/cmg = 3.0 cm/GW.

- There is an optimal ratio Is/Ip, for maximal conversion efficiency.

- The ratio depended from waves mismatching and steady-state Raman gain coefficient.

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Energy conversion atquasi-phase matching

Hydrogen = 3.84 rad/cmg = 3.0 cm/GWIs(0) = 0.0023

GW/cm2

efficiency 30%

- At optimum ratio Is/Ip, conversion efficiency reached more than 30%, but Stokes intensity is higher then anti-Stokes

intensity. 7

Comparison ofquasi-phase and phase matching

Hydrogen = 3.84 rad/cmg = 3.0 cm/GW1 - quasi-phase

matching2 - without (quasi-)

phase matching3 - phase matching

- Conversion efficiency at quasi-phase matching is lower than at phase matching and higher than at simple focusing in

Raman media.8

Lengths of active and passive zones

0,2

0,4

0,6

0,8

1

1,2

1,4

0 10 20 30 40 50 60

zone, ed

L, cm

Lact Lpass

H2

- Structure of layers is not periodical.

- Similar plot can be achieved for barium

nitrate.

- It is essentially different from quasi-phase matching in (2)

media.

- Lengths of active/passive layers are monotonously decreased/ increased.

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Characteristic zone lengths

-2

-1,5

-1

-0,5

0

0,5

1

0 50 100 150

delta, rad/cm

log L, log cm

ln act ln pass

- It is possible to approximate

this dependence asLa = 2.6/ and

Lp = 3.9/.

- With increasing of waves mismatching structure become more periodical. 10

Critical pump wave intensity

- There is a critical value

of pump intensity.

- This dependence

can be approximated as Icr.p=0.4Δ/g

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Conclusions

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

- The Conversion efficiency can reached more than 30%

- Structure of layers is not periodical. Lengths of active layers are monotonously decreased and lengths of passive layers are

monotonously increased.

- With increasing of waves mismatching structure become more periodical.

- For each medium there is a critical value of pump intensity.12

Acknowledgment

I would like to thank:• SPIE - The International Society for

Optical Engineering for registration fee.• CRDF - US Civilian Research &

Development Foundation for support of my participation.

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References

•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.•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.•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.•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.•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.•Bespalov V. G., Makarov N. S., “Quasi-phase matching anti-Stokes SRS generation”, Opt. & Spectr., vol. , No. 5, 2001 (accepted for publication)

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