Makarov N.S. , [email protected]

Quasi-phase matched anti-Stokes stimulated Raman scattering; Saint-Petersburg, 6 – 9 June 2003

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

Raman active medium

H2

H2 H2H2

(3)0 (3)=0

Method principle 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

)(

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

0 0,5 1 1,5l, cm

An

ti-S

toke

s ef

ficie

ncy

, %

4,852

4,854

4,856

4,858

4,86

4,862

4,864

0,558 0,758 0,958 1,158 1,358 1,558l, cm

An

ti-S

toke

s ef

ficie

ncy

, %

La(opt)

Lp(opt)

Zoom

Layer lengths selection

In simulations we used various Raman-active media, like hydrogen, barium nitrate, silica fiber, photonic crystals. The efficiency of anti-Stokes generation reached about

30% and practically compared to Stokes generation efficiency. The efficiency of high-order components was negligible.

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



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





Backward SRS vs. QPM realization

0,3

0,4

0,5

0,6

0,7

0,8

0,9

0 10 20 30 40

layer number

Ac

tiv

e la

ye

r le

ng

th, c

m

Forward SRS Forward and backward SRS

0,9

0,95

1

1,05

1,1

1,15

1,2

1,25

1,3

0 10 20 30 40

layer number

Pa

ss

ive

lay

er

len

gth

, cm

Forward SRS Forward and backward SRS

High SRS components vs. calc. precision

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Number 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, %



Influence of input waves parameters on anti-Stokes generation efficiency

0

5

10

15

20

25

0 0,005 0,01 0,015 0,02 0,025

Is, GW/cm^2

Eff

_a, %

0

5

10

15

20

25

0 5 10 15 20 25 30Ts, ns

Eff

_a, %

0

5

10

15

20

25

0 2 4 6 8 10Tp, ns

Eff

_a, %

0

5

10

15

20

25

0 0,2 0,4 0,6 0,8 1

Ip, GW/cm^2

Eff

_a, %



The influence of pump wavelength on anti-Stokes generation efficiency

0

5

10

15

20

25

510 515 520 525 530 535 540 545 550

pump wavelength, nm

Eff

_a, %



221121

21

221121

2sin

2sin

2

2cos

2coscos

ll

llllkeff

Effective wave vector in one-dimension photonic crystal

The effective generation of anti-

stokes radiation in one dimensional photonic

crystals1=1, 2=13, l1=175.0000 nm, l2=287.8774 nm

=0.263 rad/cm; eff_a=30.1%1=1, 2=13, l1=175.037 nm, l2=287.870 nm

=0.004 rad/cm; eff_a=29.8%

Conclusions• Our model of forward and backward multiwave SRS is the extension of

multiwave SRS model and it may be reduced to well-known systems of forward multiwave SRS and backward SRS

• For best accuracy of QPM SRS simulations it is necessary to take into account the dispersion of Raman gain coefficient

• 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), however it is still high enough

• 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 effective anti-Stokes SRS generation occurs in a wide range of input

radiation parameters• It is possible to use one-dimension photonic crystals for high effective (up to

30%) anti-Stokes SRS generation



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.•Nefedov I.S., Tretyakov S.A. Photonic band gap structure containing metamaterial with negative permittivity and permeability // Phys. Rev. E, 66, 2002, p. 036611.



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Makarov N.S. , [email protected]