Bandwidth, compact support, apertures and the linear canonical transform in ABCD systems

John J. Healy; John T. Sheridan

doi:10.1117/12.780313

Abstract

In the paraxial limit, optical systems can be well described as ABCD systems, which are linear, lossless systems and can be well modeled using the Linear Canonical Transform (LCT). In theory, their effects are perfectly reversible. In practice, finite component sizes mean that a system designer must be aware that a waveform passing through a practical implementation of such a system may lose information due to walk-off and apertures, and make allowances accordingly. Such limitations also place restrictions on the bandwidth of a waveform which may be propagated through a system. These considerations are also very important from the point of view of attempting to simulate such systems for design or analysis. We consider the parameters of a system which result in low loss due to this factor, demonstrating the parameters which result in lossless systems for particular types of signal. We offer mathematical proof that certain classes of two-parameter LCTs preserve bandwidth or compact support, or transform one into the other. We propose a matrix-based methodology for minimizing aperture effects in ABCD systems.

Citation Download Citation

John J. Healy, John J. Healy, John T. Sheridan, John T. Sheridan, } "Bandwidth, compact support, apertures and the linear canonical transform in ABCD systems", Proc. SPIE 6994, Photon Management III, 69940W (25 April 2008); doi: 10.1117/12.780313; https://doi.org/10.1117/12.780313

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