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                  <mods:namePart>Alieva Krasheninnikova, Tatiana</mods:namePart>
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                  <mods:namePart>Bastiaans, Martin J.</mods:namePart>
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               <mods:abstract>A Collins transformation maps an orthonormal set of Hermite-Gaussian modes into an orthonormal set of beams with a Gaussian envelope. Among these beams are Laguerre-Gaussian beams and the recently introduced Hermite-Laguerre-Gaussian beams. Compact expressions for the complex field amplitudes of these modes are derived. The results obtained are useful for description of the propagation of light through first-order optical systems, for the solution of the phase-retrieval problem by noninterferometric techniques, and for the design of mode converters and information processing systems.</mods:abstract>
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