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Coupled-Mode Theory


Coupled semiconductor laser arrays are of particular interest for applications that require high-power, narrow divergence laser light or electrically tunable beam-steering. For these applications, the coupled elements of the array must be highly coherent, having a mutual degree of coherence at or near unity. The second-order correlation functions of the fields emitted by the array elements describe the coherence of the array. In order to understand and design highly-coherent laser arrays, the development and analysis of these correlation functions is especially illuminating.

Semiconductor laser arrays can be modeled as coupled oscillators or coupled waveguides. Both approaches can be formulated as derivatives of coupled-mode theory. However, traditional coupled-mode theory is entirely deterministic and predicts all fields to be fully coherent. By introducing random sources or boundary conditions and looking at the second-order correlations, we have demonstrated that partial coherence is expected under certain conditions. This result has been verified experimentally.


This work has been done in collaboration with Prof. Kent Choquette's group at the University of Illinois.


  • Coherence of Photonic Crystal Vertical Cavity Surface Emitting Laser Arrays
    A.C. Lehman, J.J. Raftery, P.S. Carney and K.D. Choquette
    Journal of Quantum Electronics,  Vol. 4325-30  (2006 PDF
  • Partial coherence in coupled photonic crystal vertical cavity laser arrays
    A.C. Lehman Harren, K.D. Choquette, and P.S. Carney
    Optics Letters,  Vol. 34905-907  (2009 PDF

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