[Paper Review] Frequency dependence of mode coupling gain in Yb doped fiber amplifiers due to stimulated thermal Rayleigh scattering

Arlee V. Smith, J. Joshua Smith|arXiv (Cornell University)|Jan 18, 2013

Photonic Crystal and Fiber Optics9 citations

TL;DR

This paper presents a detailed numerical model of mode coupling gain in Yb-doped fiber amplifiers due to stimulated thermal Rayleigh scattering (STRS), showing that the frequency of peak gain (FM) depends strongly on core size, doping profile, population inversion, thermal lensing, fiber coiling, pumping direction, and photodarkening. The model predicts FM scales inversely with effective area (1/A_eff), and hole burning reduces FM below the thermal diffusion estimate, with good qualitative agreement to measured values when input noise spectra are accounted for.

ABSTRACT

Using a numerical model we study the frequency dependence of mode coupling gain due to stimulated thermal Rayleigh scattering in step index, Yb doped, fiber amplifiers. The frequency at the gain peak is shown to vary with core size, doping size, population saturation, thermal lensing, fiber coiling, direction of pumping, photodarkening, and pump noise spectra. The predicted frequencies are compared with measured values whenever possible.

Motivation & Objective

• To model the frequency dependence of mode coupling gain in Yb-doped fiber amplifiers due to stimulated thermal Rayleigh scattering (STRS).
• To investigate how FM—the frequency of peak gain—varies with fiber design and operating conditions such as core size, doping, pumping direction, and thermal lensing.
• To compare model predictions with measured FM values to validate the model and diagnose performance anomalies like low instability thresholds.
• To identify the influence of transverse hole burning, photodarkening, and pump/signal noise spectra on FM.
• To improve upon simplified models by incorporating dynamic changes in population inversion and heat deposition profiles along the fiber.

Proposed method

• A detailed numerical model simulates STRS-driven mode coupling in step-index Yb-doped fibers, solving coupled heat and mode propagation equations.
• The model accounts for spatially varying population inversion (transverse hole burning), which alters the oscillating heat source profile.
• Gain is computed as a function of frequency offset between LP01 and LP11/LP02 modes using a steady-periodic approach.
• Thermal diffusion time across the effective core radius is used as a baseline estimate for FM, given by FM ≈ 1/(4πD r_eff²), where D is thermal diffusivity.
• Fiber coiling, asymmetric cooling, and mode profile changes due to thermal lensing are included as perturbations to the heat and mode profiles.
• Input signal and pump noise spectra are modeled as frequency-shifted components to simulate real-world modulation effects.

Experimental results

Research questions

• RQ1 How does the frequency of peak mode coupling gain (FM) scale with effective mode area (A_eff) in Yb-doped fiber amplifiers?
• RQ2 To what extent does transverse hole burning in the population inversion reduce FM below the thermal diffusion estimate?
• RQ3 How do fiber coiling and asymmetric cooling affect the position of the gain peak frequency?
• RQ4 How do pumping configuration (co- vs. counter-pumping), photodarkening, and thermal lensing influence FM?
• RQ5 Why do measured FM values in experiments sometimes differ from model predictions, and what role do pump or seed noise spectra play?

Key findings

• The frequency of peak mode coupling gain (FM) scales approximately as 1/A_eff, consistent with thermal diffusion across the effective core radius.
• Transverse hole burning shifts the oscillating heat source away from the core center, reducing FM below the simple thermal diffusion estimate.
• Coiling the fiber or asymmetric cooling compresses the mode profile toward the outer bend, increasing FM by reducing effective mode area.
• For a co-pumped fiber with A_eff = 4536 μm², the model predicts FM = 325 Hz, while the measured value was 220 Hz, suggesting additional effects like photodarkening or 1/f noise may be present.
• In a counter-pumped fiber with A_eff = 3595 μm², the model predicts FM = 490 Hz, while the measured peak was 350 Hz, indicating possible input modulation or spectral structure in the pump or seed.
• For a 39.5 μm core fiber, the model predicts FM ≈ 2420 Hz, and measured FM was 2000 Hz, with good agreement after accounting for hole burning effects.