Sequence-frequency three-wave mixing emissions in a birefringent optical fiber

K Kitayama,M Ohashi,T Gustafson

doi:10.1109/jqe.1985.1072550

Abstract

Efficient parametric stimulated and parametric mixing processes involving waves with many optical frequencies can occur in a highly birefringent single-mode optical fiber due to the third-order nonlinear susceptibility <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\chi^{(3)}</tex> . Three types of multiple-order sequence-frequency emissions, two associated with the LP <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> mode, with fundamental frequency-shifts <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta \bar{\nu}</tex> of approximately 1500 cm -1 and 150 cm -1 , and one associated with the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LP<_{11}</tex> mode, with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta \bar{\nu} \simeq 1000</tex> cm -1 , have been observed. Emissions are seen to be due to both degenerate stimulated four-photon mixing, which provides simultaneous amplification proportional to the square of the pump intensity for Stokes and anti-Stokes generation from noise, and parametric three-wave mixing in which already generated Stokes and anti-Stokes fields are mixed with a strong pump field to produce the newly generated field. Both the 1500 cm -1 and the 150 cm -1 fundamental anti-Stokes shifts associated with the LP <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> mode sequence-frequency emissions originate from the off-diagonal component of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\chi^{(3)}</tex> . The value of the shifts are such as to have compensation of the bulk material phase mismatch K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> of fused silica with the high birefringence of the mutually orthogonal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LP^{x}_{01}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LP^{y}_{01}</tex> modes. On the other hand. the 1000 cm -1 shift of the mixed-mode excitation of the LP <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> and LP <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> modes originates from the diagonal component of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\chi^{(3)}</tex> , and has a value such that the phase mismatch due to the mode dispersion K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</inf> cancels the material dispersion term K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> . The observed polarization directions of the generated waves are in good agreement with theoretical predictions, supporting the identification of the relevant waves. This is the first report of three-wave mixing due to the off-diagonal component of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\chi^{(3)}</tex> . Three-wave mixing due to the diagonal component has been seen previously, as has stimulated four-photon mixing due to both the diagonal and off-diagonal components.

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