Combined Stokes-anti-Stokes Raman amplification in fiber Victor G. Bespalov All Russian Research Center "S. I. Vavilov State Optical Institute" Nikolai S. Makarov Saint-Petersburg State Institute of Fine Mechanics and Optics (Technical University)

Outline Main goals Principle of quasi-phase matching System of SRS equations Properties of quasi-phase matched SRS Numerical simulations results for fibers Conclusions References

EDFA-amplification - 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 - With pump =1480 nm, due to the broadband of SRS- amplification stokes = nm.

Combined EDFA and Stokes SRS amplification - Flattening of amplification curve is possible with combined using of EDFA and Stokes SRS amplifier. - For improvement of amplification curve and creating of a new channel in 1310 nm we propose to use simultaneous Stokes and anti-Stokes SRS amplification at QPM.

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

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

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.  – waves mismatching, g – steady-state Raman gain coefficient,  i – frequencies of interacting waves, A j – complex wave amplitudes. 5

Efficiency of anti-Stokes SRS generation in Raman-active media Hydrogen  = 3.84 rad/cm g = 3.0 cm/GW. - There is an optimal ratio I s /I p, for maximal conversion efficiency. - The ratio depended from waves mismatching and steady- state Raman gain coefficient. 6

Energy conversion at quasi-phase matching Hydrogen  = 3.84 rad/cm g = 3.0 cm/GW I s (0) = GW/cm 2 efficiency  30% - At optimum ratio I s /I p, conversion efficiency reached more than 30%, but Stokes intensity is higher then anti-Stokes intensity. 7

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. 8

Lengths of active and passive zones H2H2 - Structure of layers is not periodical. - Similar plot can be achieved for barium nitrate. - It is essentially different from quasi-phase matching in  (2) media. - Lengths of active/passive layers are monotonously decreased/ increased. 9

Characteristic zone lengths - It is possible to approximate this dependence as La = 2.6/  and Lp = 3.9/ . - With increasing of waves mismatching structure become more periodical. 10

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

SRS in silica fiber - 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 - Stokes and anti-Stokes amplification provides amplification peaks at wavelengths of 1389 and 1583 nm with pump 1480 nm.

EDFA and anti-Stokes SRS amplification - Combined EDFA and simultaneously Stokes and anti- Stokes amplification provides the amplification in both windows.

Conclusions Stokes-Anti-Stokes SRS amplification is useful for improvement of EDFA amplification curve and creating of amplified channel in 1310 nm transparency window. Quasi-phase matching structure in silica fibers is quasi- periodic. Layers lengths do not depend on input waves intensities if the ratio between pump/Stokes/anti-Stokes waves intensities does not change. For more effective flattening of the amplification curve and broadening of amplified channel in 1310 nm transparency window we can use pump at several wavelengths.

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