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We present a general framework capable of describing the nonlinear propagation of pulsed optical beams of arbitrary shapes and phase fronts inside a graded-index (GRIN) fiber. The main assumption made is that the spatial self-imaging features of the beam are not affected by the temporal evolution of optical pulses. A propagation kernel known from the work done in the 1970s is used to obtain a distance-dependent nonlinear coefficient that captures all spatial effects within an effective nonlinear Schrödinger equation. We consider three specific beam shapes (Gaussian, circular, and square) to study the impact of the shape, position, and curvature of optical beams on the complex spatiotemporal dynamics specific to GRIN fibers. In particular, we focus on the impact of an input beam’s shape on the modulation-instability sidebands and the generation of multiple dispersive waves when higher-order solitons form inside a GRIN fiber. The results of our numerical analysis indicate that for beam widths chosen to yield the same value of the effective mode area at the input end of the fiber, the nonlinear effects are pronounced considerably when a Gaussian beam is launched into the fiber. We also found that even though the self-imaging period is doubled when an off-centered Gaussian beam is launched into a GRIN fiber, it does not affect the nonlinear evolution because the effective beam area still maintains the same periodicity, as long as the shift in the beam’s center is not so large that it does not remain confined to the fiber’s core.
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Spatial beam narrowing in multimode graded-index fiber amplifiers: an analytic approach
Doped and optically pumped graded-index (GRIN) fibers can be used to amplify an optical beam such that its spatial quality is improved at the output end of the fiber compared with that of the unamplified beam. We develop a simple model of the amplification process in such GRIN fiber amplifiers and show that the resulting equations can be solved analytically with suitable approximations. The solution shows that the width of the amplifying beam oscillates but also becomes narrower because of the radial dependence of the optical gain. The main advantage of our simplified approach is that it provides an analytic expression for the damping distance of beam-width oscillations that shows clearly the role played by various physical parameters.
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- Award ID(s):
- 1933328
- PAR ID:
- 10389199
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Letters
- Volume:
- 48
- Issue:
- 2
- ISSN:
- 0146-9592; OPLEDP
- Format(s):
- Medium: X Size: Article No. 259
- Size(s):
- Article No. 259
- Sponsoring Org:
- National Science Foundation
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