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A fractional diffusion random laser.

Yuyao Chen1, Alfredo Fiorentino2,3, Luca Dal Negro4,5,6

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This study introduces non-resonant fractional random lasers by extending photon diffusion models with fractional calculus. This approach enables lasers with smaller footprints and reduced amplification volumes in disordered media.

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Area of Science:

  • Photonics and Laser Physics
  • Nonlinear Optics
  • Complex Systems

Background:

  • Classical photon diffusion models (Letokhov model) describe laser dynamics in disordered media.
  • Anomalous sub-diffusion phenomena, memory effects, and long-range correlations are observed in non-uniform scattering media.
  • Limitations exist in traditional models for complex disordered systems.

Purpose of the Study:

  • To introduce the concept of a non-resonant fractional random laser.
  • To extend the classical Letokhov model using fractional differential operators.
  • To investigate anomalous photon sub-diffusion in disordered gain media.

Main Methods:

  • Extension of the classical Letokhov model to fractional differential operators in space and time.
  • Formulation and analytical solution of fractional transport equations in one-dimensional slab geometry.
  • Application to fractional-order (FO) and distributed-order (DO) space-time fractional reaction-diffusion equations.

Main Results:

  • Derivation of simple closed-form expressions for critical amplification volumes.
  • Demonstration of anomalous sub-diffusive photon transport benefits in correlated disordered media.
  • Identification of reduced footprint and amplification volumes for novel random lasers.

Conclusions:

  • Fractional calculus provides an effective framework for modeling photon transport in complex disordered media.
  • Non-resonant fractional random lasers offer advantages over conventional designs.
  • This work stimulates the engineering of advanced random lasers with enhanced performance characteristics.