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arXiv:0705.1261 · Physical Review A

Theory of spatial mode competition in a fiber amplifier

Anatoly P. Napartovich, Dmitry V. Vysotsky

Published Dec 5, 2007• 11 citations
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Abstract

A theory is developed of monochromatic wave field amplification in a waveguide array based on expansion of the wave field in terms of guided array modes. The equations for the expansion coefficients include cross-modal gain, which completely changes the behavior of the amplified wave field. Analysis of the two-mode amplification reveals unusual features in its characteristics. Instead of unlimited growth of both modes for incoherent fields, one of the modes grows with no limit and suppresses the lower-power mode. Effects associated with the cross-modal gain are illustrated analytically on a system of two thin parallel planar waveguides. Conditions are found where the mode with lower gain can become the dominant one at the output of the amplifier.

DOI
10.1103/physreva.76.063801

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A theory is developed of monochromatic wave field amplification in a waveguide array based on expansion of the wave field in terms of guided array modes. The equations for the expansion coefficients include cross-modal gain, which completely changes the behavior of the amplified wave field. Analysis of the two-mode amplification reveals unusual features in its characteristics. Instead of unlimited growth of both modes for incoherent fields, one of the modes grows with no limit and suppresses the lower-power mode. Effects associated with the cross-modal gain are illustrated analytically on a system of two thin parallel planar waveguides. Conditions are found where the mode with lower gain can become the dominant one at the output of the amplifier.
The non-Hermitian character of a gain-guided amplifier leads naturally to a description of the amplified field in terms of a nonorthogonal mode basis. We present a theoretical analysis, based on a nonorthogonal mode expansion, for the output of an amplifier with focused gain. The theory predicts that the gain-guided nature of the amplification process can lead to excess noise in the output of the amplifier. We then report the results of two experiments in which the output from a focused-gain Raman amplifier was measured. The experimental results are found to be in reasonable agreement with the nonorthogonal mode theory.
Amplification of a light signal propagating in a single-mode fiber of passive core and active cladding (dye solution) is investigated. The active cladding region is excited by the evanescent field of a pump mode. Calculations are based on exact field expressions (weakly guiding case) and rate equations for the dye under steady-state conditions. Assuming the 'slow growth approximation' to be valid, two coupled nonlinear differential equations are derived for the powers in pump and signal modes, respectively. The influence of various fiber and dye parameters on the gain is studied. It is concluded that CW single-pass amplification by factors of up to five seem realistically achievable.
Measurements of the output of a Raman amplifier when there is no input Stokes seed are presented.It is shown that a fully quantum mechanical scaled planewave theory describes the growth from spontaneous emission well in the high gain limit.However, in the low gain regime there is a significant increase in the amount of Stokes output which is not predicted by the plane wave theory.To account for the deviation from planewave growth observed at low gain, a fully quantum mechanical theory of amplification in a focused gain geometry is presented.The theory is based on a non-orthogonal mode expansion of the amplified field and incorporates the effects of both gain-guiding and diffraction.In addition to accounting for the observed Stokes output at low gain the non-orthogonal mode theory predicts that the Stokes field cart experience enhanced gain as well as have excess noise.Results from an experiment are presented which verify the existence of enhanced gain in a multipass Raman amplifier.Though the experiment does not give a direct measure of the excess noise factor the results
We develop a theoretical model describing the mutual amplification of two counter-propagating monochromatic waves in a rare-earth-doped fiber amplifier. It is shown that the interference between the waves forms a dynamic population inversion grating within the active fiber core, which, in turn, mediates a nonlinear coupling between the waves. This coupling enables energy transfer from one optical wave to the other, leading to preferential amplification of one of them at the expense of the opposite-propagating field. The phenomenon occurs in both pumped and unpumped active fibers provided there exists a nonzero difference in the polarizabilities of the dopant ions in their ground and excited states. Such dynamical interactions can substantially modify the local gain profile and open a pathway to novel optical amplification regimes.
Introduction In this chapter we will present the theory of spectral gain in optical amplifiers and the related optical power distribution. The concepts are general, as they apply to every optical amplifier configuration, independent of the specific architecture and implementation technology. We will configure the optical amplifying medium as a traveling-wave device, where the optical field undergoes optical amplification as it propagates from the input to the output sections. Generally speaking, optical amplification is achieved by a net stimulated emission process. Referring to a generic section z of infinitesimal thickness dz , optical gain is determined by the imbalance between net stimulated emission and cavity losses, including extrinsic absorption, reflection and radiated fields. As we know from the theory of light amplification in the three-level atomic system presented in Chapter 5, stimulated absorption of photons is governed by the same transition rate as stimulated emission, and is included in the net stimulated emission process. With this in mind, we note the identity between stimulated emission and the stimulated absorption rates, Γ 12 = Γ 21 , and the net stimulated photon term Γ[ j 2 ( t ) – j 1 ( t )] p ( t ) in the rate equation. In order to develop the traveling-wave model, the photon density becomes a function of the longitudinal position 0 ≤ z ≤ L along the amplifier medium. Accordingly, we will set p ( t , z ) as the relative density of stimulated photons per unit volume (0 ≤ p ( t , z ) ≤ 1) at time t and section z . When photons with appropriate energy proceed along the amplifying medium, they are amplified by means of net stimulated emission. At some section z = z 0 , the steady-state photon density P ( z ) can approach the saturation density P sat ( z ).