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Time-frequency optical filtering: efficiency vs. temporal-mode discrimination in incoherent and coherent

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    This study introduces a general formalism for designing optical time-frequency (TF) filters to improve signal transmission and reject noise in classical and quantum communications. It analyzes the trade-off between efficiency and temporal mode discrimination for incoherent TF filtering.

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    Area of Science:

    • Optical communications
    • Quantum optics
    • Signal processing

    Background:

    • Time-frequency (TF) filtering is crucial for radio-frequency (RF) and optical communications.
    • Designing optical TF filters to pass target temporal modes (TMs) while rejecting background noise is essential.
    • Coherent TF filtering uses a quantum pulse gate, while conventional methods use incoherent spectral filtering and temporal gating.

    Purpose of the Study:

    • To derive a general formalism for two-stage incoherent optical time-frequency filtering.
    • To compare incoherent filtering with coherent methods for optical communications.
    • To analyze the trade-off between signal transmission efficiency and temporal mode discrimination ability.

    Main Methods:

    • Derivation of a general formalism for two-stage incoherent TF filtering.
    • Calculation of expressions for signal pulse transmission efficiency and TM discrimination.
    • Application of the formalism to rectangular and Gaussian filters.
    • Analysis of insertion loss and SNR for incoherent filters followed by direct detection.

    Main Results:

    • A general formalism for incoherent TF filtering was derived.
    • Expressions for signal transmission efficiency and TM discrimination were obtained.
    • A concise relation was found between efficiency, discrimination, and the time-bandwidth product.
    • The analysis highlights the impact of incoherent filters on insertion loss and SNR in direct detection scenarios.

    Conclusions:

    • The derived formalism provides a method to optimize incoherent optical TF filters for classical and quantum communications.
    • Incoherent filtering offers a viable alternative to coherent methods in optical domains where direct detection is optimal.
    • The findings have implications for improving performance in applications like quantum key distribution.