1. ANTI-STOKES STIMULATED RAMAN SCATTERING IN PHOTONIC CRYSTALS Nikolay S. Makarov, SPbSU ITMO/MSU, MT Victor G. Bespalov, S.I. Vavilov State Optical Institute

2. Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru 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 [6- 10]. 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. Introduction

3. Principles of quasi-phase matching Raman-active medium Nonlinearity  (2) Nonlinearity  (3) H2H2 H2H2 H2H2 H2H2  (3)  0  (3) =0 z I 2w LкLк d 31 c-axis LкLк Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

4. Model 11 22 11 22 l1l1 l1l1 l2l2 l2l2 pump Stokes anti-Stokes pump Stokes We consider one-dimension photonic crystals wits the lengths of layers l 1 and l 2 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. Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

5. Dispersion of photonic crystal At first approximation it is possible to consider photonic crystal as a continuous medium with effective dispersion, given by [14]: where k eff is an effective wave vector of radiation with wavelength, propagating through photonic crystal. k 1 ( );n 1 ( ) k 2 ( );n 2 ( ) At first approximation as continuous medium k effective ( );n effective ( ) Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

6. Steady-state SRS coupled differential equations system  – wave mismatching, g – steady-state Raman gain coefficient,  j – frequencies of interacting waves, E j – complex amplitudes of waves Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

7.  1 =1;  2 =13; l 1 =175.0000 nm; l 2 =287.8774;  =0.263 rad/cm; the efficiency of Stokes and anti-Stokes generation are about ~33.3% and ~30.1% correspondingly The interacting of waves in photonic crystal in conditions of quasi-phase matching Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

8. 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., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

9. Effective pump wave vector (  1 =1,  2 =2, l 2 =723.83 nm) Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

10. Effective Stokes wave vector (  1 =1,  2 =2, l 2 =723.83 nm) Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

11. Effective anti-Stokes wave vector (  1 =1,  2 =2, l 2 =723.83 nm) Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

12. Effective wave mismatching (  1 =1,  2 =2, l 2 =723.83 nm) Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

13. 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 l 1 =174.9986 nm. Moreover, the appropriate wave mismatching is possible between l 1 =440 nm and l 1 =441 nm, while in the range of l 1 =970 nm – l 1 =1035 nm photonic crystal at given wavelengths is equivalent to a simple media with constant refractive index l 1 =174.9986 nm; l 2 =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., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

14. Comparison with layered hydrogen and barium nitrate: periodicity of layers Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru The main difference between these two cases: using photonic crystals allows us to make Raman- active 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.

15. Comparison with layered hydrogen and barium nitrate: pump input parameters Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru 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.

16. Comparison with layered hydrogen and barium nitrate: Stokes input parameters Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru 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%.

17. Comparison with layered hydrogen and barium nitrate: wavelength sensitivity Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru 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%.

18. Conclusion We have proposed the method of increasing of efficiency of anti-Stokes SRS- generation 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., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

19. 1.Minck R.W., Terhune R.W., Rado W.G. Laser-stimulated Raman effect and resonant four-photon interactions in gaseous H 2, D 2 and CH 4 // Appl. Phys. Letts., 1963, V. 3,-№3, pp. 181-184. 2.Bloembergen N. Nonlinear Optics (NewYork:W. A. Benjamin, 1965). 3.Butilkin V.S., Kaplan A.E., Khronopulo I.G., Yakubovich E.M. Resonant nonlinear interactions of light with matter (Springer-Verlag, Berlin, 1989). 4.Shen Y.R. The principles of nonlinear optics (Wiley, New York, 1984). 5.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. 6.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. 7.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. 8.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. 9.Bespalov V.G., Makarov N.S. Combined Stokes-anti-Stokes Raman amplification in fiber // Proc. SPIE, 2001, V. 4605, p. 280-285. 10.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. 11.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. 12.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. 13.Perlin V.E., Winful H.G. Stimulated Raman scattering in nonlinear periodic structures // Phys. Rev. A, 2001, V. 64, p. 043804. 14.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. References Anti-Stokes stimulated Raman scattering in photonic crystals; San-Jose, 22 – 27 January 2005 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru