CO_2 laser beam shaping with computer generated holograms

Sweeney, Donald W.; Stevenson, W. H.; Campbell, D. K.; Shaffer, Garrett

doi:10.1364/ao.15.002959

Cited by 12 publications

(1 citation statement)

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“…To some extent f 1 and f 3 were applied as design parameters. Independent of Bryngdahl' s work Sweeney et al demonstrated the use of CGHs for laser beam shaping [21]. They used the 1st order of a CGH to obtain a desired intensity pattern jU out j 2 .…”

Section: Customary Beam Shaping Approachmentioning

confidence: 99%

Amplitude matching strategy for wave-optical design of monofunctional systems

Schimmel

Wyrowski

2000

Journal of Modern Optics

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The design of optical systems capable of transforming one given input ® eld into an output ® eld which maximizes one prescribed merit function is discussed in the functional embodiment of the system, that is by dealing with transmission functions instead of structured matter. Customary beam shaping techniques are identi® ed as a special case of a more general strategy which is called amplitude matching. This strategy makes use of the ® eld quantities amplitude and phase and therefore it is a wave-optical design approach. Thē exibility of the technique is demonstrated by various examples. Parameters like conversion eae ciency, signal-to-noise ratio, distances between transmission functions, and the number of transmission functions necessary for the implementation of wave transformations are discussed. IntroductionMost optical systems are designed to transport and transform a set of waves in a homogeneous dielectric input region into another set of waves in a homogeneous dielectric output region. The waves in the output region must satisfy prescribed quality criteria. In the following we apply some restrictions to this very general situation. (1) The refractive index in the input and output regions obeys nˆ1.(2) Monochromatic and coherent waves are assumed. (3) We consider only one scalar component U of the electromagnetic ® eld. The general vectorial case may be understood as a two channel generalization of the strategy described below, as long as the system response on both independent scalar components is decoupled, that is for instance a polarization conversion does not occur. (4) The monofunctional case is addressed, that is the system is designed to transform one speci® ed input wave into an output wave which satis® es one prescribed merit function. (5) The structure of the system is mathematically speci® ed by the refractive index of a linear, isotropic and inhomogeneous dielectric, that is n…x ; y ; z †, in a region z in µ z µ z out . By restriction to a dielectric we avoid absorption eå ects and emphasize the transmission mode of operation. The re¯ection mode of operation may be considered analogously. The xy planes through z in and z out indicate the input and output planes of the system.According to the spectrum of plane waves representation (e.g. see [1] section 3.2) the input wave U in …x ; y ; z µ z in † and the output wave U out …x ; y ; z ¶ z out † are completely speci® ed by the ® elds U inˆUin …x ; y ; z in † and U outˆUout …x ; y ; z out † respectively. Thus, in what follows we consider the input and output ® elds U in and U out .

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Section: Customary Beam Shaping Approachmentioning

confidence: 99%