backward and forward quasi-phase matched multiwave srs in nonlinear periodical structures

Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures

Victor G. Bespalov,Russian Research Center

"S. I. Vavilov State Optical Institute"

Nikolai S. Makarov,Saint-Petersburg State Institute of

Fine Mechanics and Optics (Technical University)

Outline

• Principle of quasi-phase matching• System of multiwave SRS equations

• Numerical simulations results• Conclusions• References

Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures;Saint-Petersburg, 30 June – 2 July 2003

Makarov N.S., [email protected] Bespalov V.G., [email protected]

Principle of quasi-phase matching

Raman active medium

Nonlinearity (2) Nonlinearity (3)

H2

H2 H2H2

(3)0 (3)=0

z

I2w Lк

d31

E

c-axis

L

к



Principle of quasi-phase matching at SRS

• Generalized phase on active layers input

do not practically change, that in a final

result provides a realization of quasi-

phase matching conditions

,

rad

(3)0 (3)=0

-4

-3

-2

-1

0

1

2

3

4

0 0,3 0,6 0,9 1,2 1,5 1,8z, cm



System of forward and backward multiwawe SRS equations

ji – wave

mismatching, gj±

– steady-state Raman gain

coefficient, j – frequencies of

interacting waves, Ej

± – complex wave

amplitudes

j

iz

jjj

iz

jj

j

iz

jjj

iz

jj

iz

j

iz

j

iz

j

iz

jjj

jj

j

iz

j

iz

j

iz

j

iz

jjj

jj

j

jj

jj

jjjj

jjjj

eEEeEEiT

eEEeEEiqiTt

q

qeEeqEqeEeqEi

g

Eyxk

i

tc

n

z

qeEeqEqeEeqEi

g

Eyxk

i

tc

n

z

32

41

231

441

321

111

*1

*1

2

*1

*1

2

1*

11*

11

2

2

2

2

1*

11*

11

2

2

2

2

1

1

2

2

)(

2

2

)(



Model verification: waves profiles at different input pump intensities (left – input pump and

right – output pump)

0

0,01

0,02

0,03

0,04

0,05

0,06

0 20 40 60 800

0,01

0,02

0,03

0,04

0,05

0 20 40 60 80t, ns t, ns

I, GW/cm2 I, GW/cm2



Model verification: waves profiles at different input pump intensities (left – output forward Stokes and right – output backward Stokes)

0

0,01

0,02

0,03

0,04

0,05

35 40 45 50 55

0

0,01

0,02

0,03

0,04

0,05

0,06

35 40 45 50 55t, ns t, ns

I, GW/cm2I, GW/cm2



1

,)1019.7(

10411757218.1

;;0

,)1019.7(

10411757218.1

219

16

110

219

16

21

21

i

g

gggi

g

i

i

ii

ii

1

,)109.81(

1021.04426066

;;0

,)109.81(

1021.04426066

218

15

110

218

15

21

21

i

g

gggi

g

i

i

ii

ii

Barium nitrateHydrogen

Raman gain dispersion



Influence of high SRS components on calculations precision

•For best calculation accuracy it is necessary to take into account at least the generation of 3 Stokes and 3

anti-Stokes SRS components

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10Number of SRS components

Med

ium

len

gth

, cm

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10Number of SRS components

An

ti-S

toke

s S

RS

co

nve

rsio

n e

ffic

ien

cy, %



The influence of backward SRS on QPM realization (active layers length)

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

0 10 20 30 40layer numberA

cti

ve

lay

ers

len

gth

, cm

Forward SRS only Forward and backward SRS



0,9

1

1,1

1,2

1,3

1,4

1,5

0 10 20 30 40Layer numberP

as

siv

e la

ye

rs le

ng

th, c

mForward SRS only Forward and backward SRS

The influence of backward SRS on QPM realization (passive layers length)



Conclusions• Our model of forward and backward multiwave SRS is quality and

quantity compared with experimental results• For best accuracy of QPM SRS simulations it is necessary to take into

account the dispersion of Raman gain coefficient• For studying of multiwave SRS influence on QPM structure realization it is necessary to take into account the generation at least of 3 Stokes and

3 anti-Stokes SRS components• The influence of backward SRS on QPM structure realization results in the small difference between layers length of optimal QPM structure and small decreasing of resulting anti-Stokes conversion efficiency (~25% at

backward and forward SRS, ~30% at forward SRS)• The oscillations of optimal layers length are partially connected with

backward SRS influence and with insufficient precision of layers length determination due to high computational complexity of this task



References•Armstrong J.A., Bloembergen N., Ducuing J., Pershan P.S. // Phys. Rev., 1962, 127, pp. 1918-1939.•Bespalov V.G., Makarov N.S. Quasi-phase matching generation of blue coherent radiation at stimulated Raman scattering // Optics Communications 2002, 203 (3-6), pp. 413-420.•Maier M., Kaiser W., Giordmaine J.A. Backward stimulated Raman scattering // Phys. Rev., 1969, V. 177, №2, pp. 580-599.•Raijun Chu, Morton Kanefsky, Joel Falk Numerical study of transient stimulated Brillouin scattering // J. Appl. Phys., 1992, V. 71, №10, pp. 4653-4658.•Zaporozhchenko R.G., Kilin S.Ya, Bespalov V.G., Stasel’ko D.I. Formation of the spectra of backward stimulated Raman scattering from the quantum noise of polarization of a scattering medium // Opt.&Spectr., 1999, V. 86, №4, pp. 632-639.•Bischel W.K., Dyer M.J. Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transmission in H2 // J. Opt. Soc. Am. B, 1985, V. 3, pp. 677-682.



backward and forward quasi-phase matched multiwave srs in nonlinear periodical structures

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