ABCD matrices for dispersive pulse propagation

The use of the ABCD matrices for the calculation of pulse propagation in second-order dispersive media is developed rigorously. Their usefulness is demonstrated by obtaining the results for the propagation of a Gaussian pulse with an arbitrary linear chirp. By analogy with ray optics, the concept of a time ray is introduced to give further insight. The analogy with paraxial optics is carried further by extending the matrix method to a complete Hermite-Gaussian basis and thus to arbitrarily shaped and nonlinearly chirped pulses. Some practical applications of the matrix method are discussed.<
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