102 research outputs found

    The Complex Way to Laser Diode Spectra: Example of an External Cavity Laser With Strong Optical Feedback

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    An external cavity laser with strong grating-filtered feedback to an antireflection-coated facet is studied with a time-domain integral equation for the electric field, which reproduces the modes of the oscillation condition as steady-state solutions. For each mode, the stability and spectral behavior is determined by analysis of the location of side modes in the complex frequency plane. The complex frequency diagrams are shown to be a useful tool to determine the self-stabilization effect of mode coupling and its dependence on laser parameters and external cavity design. The model is used to simulate the large signal time evolution after start from unstable mode

    Frequency and Time Domain Analysis of an External Cavity Laser with Strong Filtered Optical Feedback

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    The stability properties of an external cavity laser with strong grating-filtered optical feedback to an anti-reflection coated facet are studied with a general frequency domain model. The model takes into account non-linear effects like four wave mixing and gain compression. A small-signal analysis in the frequency domain allows a calculation of the range of operation without mode hopping around the grating reflectivity peak. This region should be as large as possible for proper operation of the tunable laser source. The analysis shows this stabilizing effect of mode coupling and gain copression in the lasing mode. An integral equation for the electrical field is derived from the frequency domain model and used for time domain simulations of large-signal behavior

    Analysis of Self-Pulsating DBR Lasing Dynamics with a Novel Formulation

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    The self-pulsation lasing dynamic of a long cavity integrated BDR laser or of an equivalent external cavity laser (ECL) with strong grating-filtered feedback is studied with a novel time domain integral equation for the electric field. The complex frequency diagram obtained from mode stability analysis of the field and carrier equations are shown to be a useful tool to determine the condition of instable operation to be investigated with the large signal time domain formulation

    Bounds on the diagonal elements of a unitary matrix

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    AbstractIt was shown by A. Horn that the diagonal elements of a unitary n×n matrix satisfy a set of linear inequalities (Theorem I). We give a simple proof of this result, and we show that the diagonal elements satisfy additional linear inequalities (Theorem II) if the matrix is also symmetric
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