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Beams and pulses

A rigorous solution of Maxwell's equations, which reduces to a conventional Gaussian beam for small angles of divergence is described. The resonance conditions for a resonator can be derived. Various different polarizations can also be considered, including plane polarized, transverse electric and transverse magnetic modes. Free-space propagation of ultra-short pulses is also investigated. General conditions for the formation of pulse beams are presented. Space-time couplings are reduced for these beams. The special cases of collapsing pulses, Gaussian pulses and Bessel pulse beams are described.