Parametric instabilities driven by orthogonal pump waves in birefringent fibers

Abstract

The four-sideband model of parametric instabilities driven by orthogonal pump waves in birefringent fibers is developed and validated by numerical simulations. A polynomial eigenvalue equation is derived and used to determine how the spatial growth rates and frequency bandwidths of various instabilities depend on the system parameters. The maximal growth rate is associated with a group-speed matched four-sideband process (coupled modulation instability), whereas broad-bandwidth gain is associated primarily with a two-sideband process (phase conjugation). This four-sideband model facilitates the design of parametric amplifiers driven by two pump waves with different frequencies and polarizations.

Quantum noise properties of parametric amplifiers driven by two pump waves

“…For co-polarized waves β 1 = β 2 and ε = 2 [3]. For cross-polarized waves in fibers with constant birefringence β 1 = β x , β 2 = β y and ε = 2/3 [4], whereas for cross-polarized waves in fibers with random birefringence β 1 = β 2 , the self-nonlinearity coefficient is reduced by the factor 9/8 and ε = 1 [5].…”

“…where B 1± and B 2± are the sideband amplitudes. By substituting ansätze (5) and (6) in the NS equations, linearizing the equations that result and collecting terms of like frequency, one obtains the FS equations [3,4,5]…”

“…Then the modulation interaction (MI) in which 2γ 1 → γ 1− + γ 1+ produces an idler with frequency ω 1+ = ω 1 + ω, the Bragg-scattering (BS) process in which γ 1− + γ 2 → γ 1 + γ 2− produces an idler with frequency ω 2− = ω 2 − ω and the PC process in which γ 1 + γ 2 → γ 1− + γ 2+ produces an idler with frequency ω 2+ = ω 2 + ω. The classical theory of PA driven by two pump waves was reviewed by McKinstrie [3,4,5].…”

Parametric amplification and processing in optical fibers

“…In practical terms, the two-pump architecture can be used to circumvent the onset of stimulated Brillouin scattering [28][29][30] and achieve a polarization-diverse parametric response [24,31,32] or scalable signal multicasting [20,21].…”

Parametric amplification and processing of optical signals

“…By tuning the pump frequencies judiciously, relative to the zero-dispersion frequency (ZDF) of the fiber, one can control whether MI, PC and BS occur separately or simultaneously, as a four-sideband (FS) interaction. The properties of MI and PC are well understood [4][5][6][7][8][9][10][11][12][13] and have been demonstrated experimentally [14][15][16][17][18][19][20][21][22][23]. In this review, we only discuss PC explicitly, because MI behaves like PC with degenerate pumps.…”