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    Area of Science:

    • Nonlinear optics
    • Waveguide optics
    • Quantum optics

    Background:

    • Optical rogue waves (RWs) are extreme events in nonlinear systems.
    • Previous studies primarily focused on RWs on a plane wave background.
    • Nonlinear graded-index waveguides with variable coefficients present unique optical phenomena.

    Purpose of the Study:

    • To investigate optical rogue waves (RWs) in a nonlinear graded-index waveguide with variable coefficients.
    • To present an exact RW solution on a Gaussian background beam.
    • To analyze the characteristics of RWs on a Gaussian background.

    Main Methods:

    • Theoretical analysis of nonlinear wave propagation.
    • Derivation of an exact analytical solution for RWs.
    • Numerical simulations to verify the solution and analyze RW characteristics.

    Main Results:

    • An exact solution for optical rogue waves (RWs) on a Gaussian background beam was derived.
    • The fundamental characteristics of RWs are maintained on a Gaussian background.
    • The spatial scale of the rogue wave is comparable to or smaller than the background beam width.

    Conclusions:

    • The study demonstrates the existence and characteristics of RWs on a Gaussian background in a specific waveguide.
    • These findings open avenues for experimental realization of RWs in controlled optical environments.
    • Potential applications in nonlinear optics and optical communications may be explored.