Evolution of first-order sidebands from multiple FWM processes in HiBi optical fibers

Abstract The generation of two idler waves inside a high birefringent (HiBi) optical fiber through three four-wave mixing (FWM) processes is studied theoretically. The coupled-equations for the field amplitudes are derived and analytically solved, in the co-polarized and orthogonal polarization schemes. The obtained solutions take into account the delayed Raman response of the medium. The polarization sensitivity of the generation of the idler waves is analyzed. Results show that the stimulated Raman scattering does not change the efficiency of the idler wave generation in the co-polarized scheme, whereas in the orthogonal polarization scheme that nonlinear process decreases the efficiency of the four-wave mixing processes. Results also show that this set of multiple four-wave mixing processes is physically quite different from the typical single or dual pump four-wave mixing configurations. Findings show that the power transfer from the pumps to the idler fields can lead to a monotonous growth, or a periodic evolution of the sidebands along the fiber. Results show that the process efficiency varies greatly with the angle between the two pump polarizations.

[1]  James W. Beletic,et al.  Dynamical evolution of multiple four-wave-mixing processes in an optical fiber , 1998 .

[2]  G. Millot.  Multiple four-wave mixing-induced modulational instability in highly birefringent fibers. , 2001, Optics letters.

[3]  Chongxiu Yu,et al.  Applications of Nonlinear Effects in Highly Nonlinear Photonic Crystal Fiber to Optical Communications , 2005 .

[4]  R. Stolen,et al.  Phase matching in birefringent fibers. , 1981, Optics letters.

[5]  Peter A. Andrekson,et al.  16 Gbit/s all-optical demultiplexing using four-wave mixing , 1991 .

[6]  A Yariv,et al.  Compensation for channel dispersion by nonlinear optical phase conjugation. , 1979, Optics letters.

[7]  Fatih Yaman,et al.  Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization , 2007 .

[8]  X. Liu,et al.  Multiple four-wave mixing self-stability in optical fibers (9 pages) , 2005 .

[9]  M. Karlsson,et al.  Polarization dependence and efficiency in a fiber four-wave mixing phase conjugator with orthogonal pump waves , 1996, IEEE Photonics Technology Letters.

[10]  R. Leonhardt,et al.  Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers , 2002 .

[11]  R. Stolen,et al.  Parametric amplification and frequency conversion in optical fibers , 1982 .

[12]  A. Hasegawa,et al.  Generation of a train of soliton pulses by induced modulational instability in optical fibers. , 1984, Optics letters.

[13]  K. Inoue,et al.  Wavelength conversion experiment using fiber four-wave mixing , 1992, IEEE Photonics Technology Letters.

[14]  P. A. Andersen,et al.  A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber , 2003, IEEE Photonics Technology Letters.

[15]  N. Bloembergen,et al.  Coupling Between Vibrations and Light Waves in Raman Laser Media , 1964 .

[16]  Kenneth O. Hill,et al.  cw three-wave mixing in single-mode optical fibers , 1978 .

[17]  S. Kishida,et al.  Efficient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fibre , 1980 .

[18]  N. Silva,et al.  Effective Nonlinear Parameter Measurement Using FWM in Optical Fibers in a Low Power Regime , 2010, IEEE Journal of Quantum Electronics.

[19]  Federica Poli,et al.  Photonic crystal fibers : properties and applications , 2007 .

[20]  C. Xie,et al.  Phase conjugation driven by orthogonal pum pwaves in birefringent fibers , 2003 .

[21]  N. Silva,et al.  Influence of the Stimulated Raman Scattering on the Four-Wave Mixing Process in Birefringent Fibers , 2009, Journal of Lightwave Technology.

[22]  Roy,et al.  Statistical fluctuations in multiple four-wave mixing in a single-mode optical fiber. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[23]  W A Reed,et al.  Phase matching in the minimum-chromatic-dispersion region of single-mode fibers for stimulated four-photon mixing. , 1981, Optics letters.

[24]  R. W. Hellwarth,et al.  Third-order optical susceptibilities of liquids and solids , 1977 .

[25]  Kennedy,et al.  Nonlinear dynamics of dual-frequency-pumped multiwave mixing in optical fibers. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[26]  P. Andrekson,et al.  Broad-band continuous-wave-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency , 2001, IEEE Photonics Technology Letters.

[27]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[28]  A. Martínez-Ríos,et al.  Influence of the symmetry rules for Raman susceptibility on the accuracy of nonlinear index measurements in optical fibers , 2001 .

[29]  P. Petropoulos,et al.  Four-wave mixing based 10-Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold , 2003, IEEE Photonics Technology Letters.

[30]  N. Silva,et al.  Evolution of the degree of co-polarization in high-birefringence fibers , 2010 .

[31]  X. M. Liu,et al.  Theory and experiments for multiple four-wave-mixing processes with multifrequency pumps in optical fibers , 2008 .

[32]  Peter A. Andrekson,et al.  Demonstration of fibre four-wave mixing optical demultiplexing with 19 dB parametric amplification , 1996 .

[33]  Armando N. Pinto,et al.  Low‐cost Raman amplifier for CWDM systems , 2008 .

[34]  G. Agrawal,et al.  Raman response function for silica fibers. , 2006, Optics letters.

[35]  S V Chernikov,et al.  Ultrashort-pulse propagation in optical fibers. , 1990, Optics letters.

[36]  J R Thompson,et al.  Multiple four-wave mixing process in an optical fiber. , 1991, Optics letters.

[37]  Andrew G. Glen,et al.  APPL , 2001 .

[38]  Roy,et al.  Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[39]  S. Wabnitz,et al.  Parametric and Raman amplification in birefringent fibers , 1992 .

[40]  D J Richardson,et al.  2R-regenerative all-optical switch based on a highly nonlinear holey fiber. , 2001, Optics letters.

[41]  John E. Bjorkholm,et al.  Phase‐matched three‐wave mixing in silica fiber optical waveguides , 1974 .

[42]  Keith J. Blow,et al.  Theoretical description of transient stimulated Raman scattering in optical fibers , 1989 .

[43]  Nori Shibata,et al.  Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber , 1987 .