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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. - PowerPoint PPT Presentation
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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
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 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
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]
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
)(
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]
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
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]
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
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]
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 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]
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, %
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]
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
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]
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)
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]
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
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]
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;Saint-Petersburg, 30 June – 2 July 2003
Makarov N.S., [email protected] Bespalov V.G., [email protected]