Simultaneously Stokes and anti-Stokes Raman amplification in silica fiber 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 The main goal Principle of quasi-phase matching System of SRS equations Properties of quasi-phase matching Numerical simulations results Conclusions References 2

EDFA-amplification 3 - It is necessary to provide amplification with an error no more than  5 dB in the whole spectral band of the amplifier.

SRS amplification in silica fiber 4 - With pump =1480 nm, due to the broadband of SRS- amplification stokes = nm.

- For opening of 1310 nm amplification window we offer to use simultaneously Stokes and anti-Stokes quasi-phase matching stimulated Raman scattering amplification Combined EDFA and Stokes SRS amplification 5 - Flattening of amplification curve is possible with combined using of EDFA and Stokes SRS amplifier.

Principle of quasi-phase matching Nonlinearity  (2) Nonlinearity  (3) 6 Raman active medium

Principle of quasi-phase matching at SRS - Generalized phase  =2  p -  a -  s -(k a +k s -2k p )r, where k i – is the wave vector of interacting wave, that describes the direction of energy conversion “pump – Stokes – anti-Stokes”, on passive layers input (  0,  2 ) and active layers input (  1,  3 ) do not practically change, that in a final result provides a realization of quasi- phase matching conditions.  (3)  0  (3) =0 7

System of steady-state SRS equations In this system the waves mismatching and Raman gain are the functions of coordinate for nonlinear (  (3)  0) and linear (  (3) =0) layers.  – wave mismatching, g – steady-state Raman gain coefficient,  i – frequencies of interacting waves, A j – complex wave amplitudes. 8

Optimum ratio of input Stokes/pump intensities 9 - There is an optimum value of input Stokes/pump waves intensities ratio. - This dependence can be approximated as I s /I p,opt =0,1359g -2,6146.

Comparison of quasi-phase and phase matching Hydrogen  = 3.84 rad/cm g = 3.0 cm/GW 1 - quasi-phase matching 2 - without (quasi-) phase matching 3 - phase matching. - Conversion efficiency at quasi-phase matching is lower than at phase matching and higher than at simple focusing in Raman media. 10

Critical pump wave intensity 11 - There is a critical value of pump intensity. - This dependence can be approximated as I cr.p =0.4Δ/g.

SRS in silica fiber 12 - For amplification in both windows it is possible to use simultaneously amplification of Stokes and anti- Stokes radiation at condition of quasi- phase matching. - The structure is quasi-periodic.

Simultaneously Stokes and anti-Stokes amplification 13 - Stokes and anti-Stokes amplification provides amplification peaks at wavelengths of 1389 and 1583 nm with pump 1480 nm.

Analytical model of quasi-phase matching SRS 14

Analytical model of quasi-phase matching SRS 15 Improvement of calculation rate with constant calculation accuracy is ~120 times

attenuation zone, 2 - amplification zone - With losses about 0.3 dB/km (characteristic value for today optical fiber) the amplification occurs practically in whole medium. Calculating losses in silica fiber

Conclusion Stokes-Anti-Stokes SRS amplification is useful for improvement of EDFA amplification curve and creating of amplified channel in 1310 nm transparency window. Layers lengths do not depend on input waves intensities if the ratio between pump/Stokes/anti-Stokes waves intensities does not change. The analytical model of quasi-phase matched stimulated Raman scattering in silica fiber is formulated and the recurrent formulas for layers lengths and amplitudes of interacting waves are received. The analytical model allow significant improvement of calculation rate with same accuracy. The obtained results are promising for the development of new effective optical amplifiers. 17

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