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
Quasi-phase matched anti-Stokes stimulated Raman scattering; Saint-Petersburg, 6 – 9 June 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
Quasi-phase matched anti-Stokes stimulated Raman scattering; Saint-Petersburg, 6 – 9 June 2003
Makarov N.S., [email protected] Bespalov V.G., [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]
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, %
Quasi-phase matched anti-Stokes stimulated Raman scattering; Saint-Petersburg, 6 – 9 June 2003
Makarov N.S., [email protected] Bespalov V.G., [email protected]
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, %
Quasi-phase matched anti-Stokes stimulated Raman scattering; Saint-Petersburg, 6 – 9 June 2003
Makarov N.S., [email protected] Bespalov V.G., [email protected]
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, %
Quasi-phase matched anti-Stokes stimulated Raman scattering; Saint-Petersburg, 6 – 9 June 2003
Makarov N.S., [email protected] Bespalov V.G., [email protected]
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
Quasi-phase matched anti-Stokes stimulated Raman scattering; Saint-Petersburg, 6 – 9 June 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.•Nefedov I.S., Tretyakov S.A. Photonic band gap structure containing metamaterial with negative permittivity and permeability // Phys. Rev. E, 66, 2002, p. 036611.
Quasi-phase matched anti-Stokes stimulated Raman scattering; Saint-Petersburg, 6 – 9 June 2003
Makarov N.S., [email protected] Bespalov V.G., [email protected]