ANTI-STOKES STIMULATED
RAMAN SCATTERING IN
PHOTONIC CRYSTALS
Nikolay S. Makarov,
SPbSU ITMO/MSU, MT
Victor G. Bespalov,
S.I. Vavilov State Optical Institute
Introduction
Stimulated Raman scattering (SRS) is widely used for discrete frequency conversion of pulsed and
continuous-wave lasers [1-5]. It is especially interesting to use anti-Stokes SRS-radiation, however, its
efficiency in usual conditions is small enough, that is why some methods of its increasing were proposed [610]. For example, in papers [8-10] we have proposed to use quasi-phase matching conditions for efficient
anti-Stokes SRS generation in media with alternating of the third-order nonlinearity ((3)) along propagation
direction. By numerical simulations we showed that for each Raman-active medium there is an optimal value
of the input Stokes seed intensity at which the maximal efficiency of generation (up to 35%) is reached. This
value is much more than at simple focusing in Raman-active media and reaches to the efficiency of phase
matched conversion (50%).
In papers [11-12] authors have proposed to use photonic crystals for realization of quasi-phase matching
conditions at various harmonic generation. It was shown that using photonic crystals allows greatly
decreasing of active medium length and increasing of harmonic intensities. Today there are only a few studies
of SRS in photonic crystals, for example, [13], where the authors have studied the generation of Stokes SRS
component in Bragg gratings. By considering of propagation of pump and first-order forward and backward
Stokes waves, the authors have studied shaping of slow and practically stationary solitons due to interacting
of SRS, Kerr nonlinearity, grating dispersion and light reflection at its layers boundaries.
Since the fully correct modeling of SRS in photonic crystals is complicated enough, we try to evaluate the
possibility of efficient anti-Stokes generation in one-dimension photonic crystals.
Also, we present some comparison of results for quasi-phase matching SRS in hydrogen and barium nitrate
with results for photonic crystals and discuss the enhancement of anti-Stokes generation in photonic crystals.
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Principles of quasi-phase matching
Nonlinearity (3)
Nonlinearity (2)
(3)0
L
к
I2w
Lк
H2
c-axis

E
(3)=0
H2
H2
H2
Raman-active medium
d31
z
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Model
We consider one-dimension photonic crystals wits the lengths of layers l1 and l2 with
permittivities 1 and 2 correspondingly. Crystal layers are considered with the same
Raman transition frequency, while the pump and Stokes seed initial waves are
perpendicular to layers of photonic crystal. By varying of layers lengths and
permittivities it is possible to chouse the conditions at which the effective wave
mismatching of interacting waves is near to zero.
pump
1
l2
l2
2
2
1
pump
Stokes
Stokes
anti-Stokes
l1
l1
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Dispersion of photonic crystal
At first approximation it is possible to consider photonic crystal as a continuous
medium with effective dispersion, given by [14]:
 2 1l1   2  2 l2  1   2
 2 1l1   2  2 l2 
 cos


 

cos keff l1  l2   cos
sin
 
 2 
   sin 




1 2

 


 



where keff is an effective wave vector of radiation with wavelength , propagating
through photonic crystal.
k1
();n1()
At first
approximation
as continuous
medium
k2();n2()
keffective();neffective()
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Steady-state SRS coupled differential
equations system


2
2
 dE0 g 0
 dz  2  E1  E1 E0
1

 dE1 g
*
iz 
*


E
E
e

E

1 0
0 E1 E0
2
 dz
 dE1 g 1
*
* iz 
 dz  2   E1E0  E0 E1e E0
1





 – wave
mismatching, g –
steady-state
Raman gain
coefficient, j –
frequencies of
interacting waves,
Ej – complex
amplitudes of
waves
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
The interacting of waves in photonic crystal
in conditions of quasi-phase matching
1=1; 2=13; l1=175.0000 nm;
l2=287.8774; =0.263 rad/cm; the
efficiency of Stokes and anti-Stokes
generation are about ~33.3% and
~30.1% correspondingly
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
The required layers length accuracy
(the difference between maximal and minimal effective wave mismatching in photonic crystal at optimal conditions while
changing the length of one layers by 0.01 nm as a function on contrast in layers refractive indices)
Modeling shows
that the
appropriate wave
mismatching is
possible only at
very accurate
determining of
lengths of crystal
layers (~0.001
nm)
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Effective pump wave vector (1=1, 2=2,
l2=723.83 nm)
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Effective Stokes wave vector (1=1, 2=2,
l2=723.83 nm)
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Effective anti-Stokes wave vector (1=1, 2=2,
l2=723.83 nm)
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Effective wave mismatching (1=1, 2=2,
l2=723.83 nm)
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
The optimization of photonic crystal
parameters
Our simulations have shown that the optimal wave mismatching is equal
to 0.008 rad/cm is possible at l1=174.9986 nm. Moreover, the appropriate
wave mismatching is possible between l1=440 nm and l1=441 nm, while
in the range of l1=970 nm – l1=1035 nm photonic crystal at given
wavelengths is equivalent to a simple media with constant refractive
index
l1=174.9986 nm; l2=723.83 nm; 1=1; 2=2  =0.008 rad/cm
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Comparison with layered hydrogen and
barium nitrate: periodicity of layers
Active layer length, cm
Forward and backward SRS
0,8
0,7
0,6
0,5
0,4
0,3
0
10
20
layer number
30
40
Forward SRS
Passive layer length, cm
Forward SRS
0,9
Forward and backward SRS
1,3
1,25
1,2
1,15
1,1
1,05
1
0,95
0,9
0
10
20
layer number
30
40
The main difference between these two cases: using photonic crystals allows us to make Ramanactive medium significantly shorter and get some gain of its periodicity, however to achieve this
effect we need to use a lot of thin layers. The simulations show that the maximum efficiency of
anti-Stokes SRS generation is practically the same for both cases (about 30%) and is restricted by
energy transformation from pump into Stokes and anti-Stokes waves.
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
25
25
20
20
15
15
Eff_a, %
Eff_a, %
Comparison with layered hydrogen and
barium nitrate: pump input parameters
10
10
5
5
Ip, GW/cm^2
0
0
0
0,2
0,4
0,6
0,8
1
0
2
4
Tp, ns 6
8
10
For both photonic crystals and conventional layered structures the effective generation occurs
within a wide enough set of input pump parameters, that allows realization of the tuned source of
anti-Stokes SRS generation.
0.15 GW / cm  I 0  0.6 GW / cm
T0  1 ns
2
2
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
5 ns  T1  20 ns
25
25
20
20
Eff_a, %
Eff_a, %
Comparison with layered hydrogen and
barium nitrate: Stokes input parameters
15
10
15
10
5
5
0
0
0
0
5
10 Ts, ns 15
20
25
30
0,005
0,01
0,015
0,02
0,025
Is, GW/cm^2
For both photonic crystals and conventional layered structures the effective generation occurs
within a wide enough set of Stokes seed pulse parameters, at which the efficiency exceeds 20%.
0.001 GW / cm  I S  0.025 GW / cm
5 ns  TS  20 ns
2
2
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Comparison with layered hydrogen and
barium nitrate: wavelength sensitivity
25
Eff_a, %
20
15
10
5
0
510
515
520
525
530
535
540
545
550
pump wavelength, nm
All considered layered structures are very sensitive to the wavelength variations. This leads to
sufficient decreasing of the anti-Stokes generation efficiency even at small wavelength variations
about 0.75%.
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
Conclusion
• We have proposed the method of increasing of efficiency of anti-Stokes SRSgeneration in one-dimension photonic crystals in conditions of quasi-phase
matching
• We have simulated photonic crystals with different contrast in layers
refraction indices
• Modeling has shown that using of photonic crystals allows to increase the
efficiency on anti-Stokes SRS generation up to 30% and to design white-light
coherent sources
• However, it is required to provide high accuracy in layers lengths at
manufacturing of photonic crystal, and requirements to this accuracy increase
wits increasing of contrast in layers refraction indices
• It is shown that the realization of quasi-phase matching conditions is possible
in wide enough range of contrast in layers refraction indices (from 2/1=1.5 up
to 2/1=13)
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Minck R.W., Terhune R.W., Rado W.G. Laser-stimulated Raman effect and resonant four-photon interactions in gaseous H2, D2 and CH4 //
Appl. Phys. Letts., 1963, V. 3,-№3, pp. 181-184.
Bloembergen N. Nonlinear Optics (NewYork:W. A. Benjamin, 1965).
Butilkin V.S., Kaplan A.E., Khronopulo I.G., Yakubovich E.M. Resonant nonlinear interactions of light with matter (Springer-Verlag, Berlin,
1989).
Shen Y.R. The principles of nonlinear optics (Wiley, New York, 1984).
Bespalov V.G., Krylov V.N., Mikhailov V.N., Parfenov V.A., Staselko D.I. Generation of tunable radiation with high spectral brightness on
the basis of oscillatory and rotary SRS in gases // Opt&spectr., 1991, V. 70 №2, pp. 332-336.
Ottusch J.J., Mangir M.S., Rockwell D.A. Efficient anti-Stokes Raman conversion by four-wave mixing in gases // J. Opt. Soc. Am. B, Vol.
8 (1991) p. 68-77.
Sogomonian S., Niggl L., Maier M. Nonplanar phase-matching of stimulated anti-Stokes Raman scattering pumped by a Bessel beam // Opt.
Comm., 1999, V. 162, p. 261-266.
Makarov N.S., Bespalov V.G. SRS generation of anti-Stokes radiation under phase quasi-matching conditions // Opt. & Spectr., vol. 90, №
6, 2001, pp. 938-941.
Bespalov V.G., Makarov N.S. Combined Stokes-anti-Stokes Raman amplification in fiber // Proc. SPIE, 2001, V. 4605, p. 280-285.
Makarov N.S., Bespalov V.G. Quasi-phase matching generation of blue coherent radiation at stimulated Raman scattering // Opt. Comm.,
2002, V. 203 (3-6), p. 413-420.
Centini M., Sibilia C., Scalora M., Rugolo V., Bertolotti M., Bloemer M.J., Bowden C.M. On the phase matching conditions in applications
of one-dimensional photonic band gap structures for nonlinear frequency conversion // J. Opt. A: Pure Appl. Opt., 2000, V. 2, p. 327-331.
Dolgova T.V., Maidykovski A.I., Martemyanov M.G., Fedyanin A.A., Aktsipetrov O.A., Marowsky G., Yakovlev V.A., Mattei G., Ohta N.,
Nakabayashi S. Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic
crystals // J. Opt. Soc. Am. B, 2002, V. 19, № 9, p. 2129-2140.
Perlin V.E., Winful H.G. Stimulated Raman scattering in nonlinear periodic structures // Phys. Rev. A, 2001, V. 64, p. 043804.
Nefedov I.S., Tretyakov S.A. Photonic band gap structure containing metamaterial with negative permittivity and permeability // Phys. Rev.
E, 2002, V. 66, p. 036611.
Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005
Makarov N.S., [email protected]
Bespalov V.G., [email protected]