The influence of backward Stokes on quasi-phase matched multiwave SRS in nonlinear periodical structures Victor G. Bespalov, Russian Research Center "S

The influence of backward Stokes on 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)

AbstractIn 1962 N. Bloembergen proposed the quasi-phase matched interaction in media with periodic variations in the second order nonlinearity ((2)) along longitudinal coordinate for efficient second harmonic generation [1] and then it was experimentally demonstrated. We offer to use the similar approach for anti-Stokes radiation generation in the medium with variable parameters of the third order Raman nonlinearity along longitudinal coordinate [2].In previous publications we showed that our proposal provides the increasing of anti-Stokes SRS conversion efficiency. For each set of medium parameters we determined the optimum ratio between input pump and Stokes waves intensities at which the efficiency of energy conversion in anti-Stokes wave is maximal. We also describe the analytical model of four-wave quasi-phase matched SRS in silica fiber, where the efficiency of high-order Stokes and anti-Stokes components generation is very low.In this paper we analyze the influence of backward SRS on realization of quasi-phase matched conditions at multiwave SRS. We received a system of differential equations described multiwave backward and forward SRS, where E j

are complex amplitudes of interacting waves ((+) corresponds forward components and (-) corresponds backward components), gj

are Raman gain coefficients, q are complex amplitudes of phonon wave, j=0+j, 0 is the frequency of pump wave, is the Raman shift frequency, j

i are the wave mismatchings and T2 are the dephasing times.

By numerical simulation we analyzed the influence of backward SRS on realization of quasi-phase matched conditions at multiwave SRS in hydrogen and barium nitrate. In our calculations we used systems up to 42 equations (pump, 10 Stokes and 10 anti-Stokes, all backward and forward). Our calculations have showed that for high precision it is required to take into account at least the generation of 3 Stokes and 3 anti-Stokes backward and forward components. We determined that at backward SRS the optimal ratio between input Stokes and pump waves intensities is changed. It is connected with changing of phase-matching conditions for interacting waves on layers input and output due to existence of backward waves. We discovered that taking into account the process of backward SRS results on slightly increasing of medium length.The obtained results of numerical simulations are promising for development and optimization of new effective nonlinear frequency up-converter devices.

The influence of backward Stokes on quasi-phase matched multiwave SRS in nonlinear periodical structures; Munich, 22 – 27 June 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

Lк



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

amplitudesThe influence of backward Stokes on quasi-phase matched multiwave SRS in nonlinear periodical

structures; Munich, 22 – 27 June 2003


j

izjj

j

izjj

j

izjj

j

izjj

izj

izj

izj

izj

jj

jj

j

izj

izj

izj

izj

jj

jj

j

jj

jj

jjjj

jjjj

eEEeEEiT

eEEeEEiqiTt

q

qeEeqEqeEeqEi

g

Eyxk

itc

nz

qeEeqEqeEeqEi

g

Eyxk

itc

nz

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 50 550

0,01

0,02

0,03

0,04

0,05

0,06

35 40 45 50 55t, ns t, ns

I, GW/cm2 I, GW/cm2

1

,)1019.7(

10411757218.1

;;0

,)1019.7(

10411757218.1

219

16110

219

16

21

21

i

g

gggi

g

i

i

ii

ii

1

,)109.81(

1021.04426066

;;0

,)109.81(

1021.04426066

218

15110

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

leng

th, c

m

0

5

10

15

20

25

30

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

Anti-

Stok

es S

RS

conv

ersi

on e

ffici

ency

, %



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



0,2

0,30,4

0,50,6

0,70,8

0,9

0 10 20 30 40layer numberAc

tive

laye

rs le

ngth

, 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 numberPass

ive

laye

rs le

ngth

, cm

Forward 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.



Documents

The influence of backward Stokes on quasi-phase matched multiwave SRS in nonlinear periodical structures Victor G. Bespalov, Russian Research Center "S