A beam shaping method is presented where a diffractive optical element (DOE) is designed by optimizing the complex mode coefficient weights of a set of Gaussian beam modes. This method is compared with the more standard unidirectional approach. Differential evolution is used for the optimization in both the unidirectional and Gaussian beam mode optimization methods. For the particular transforms carried out, the Gaussian beam mode set optimization (GBMSO) approach achieved more optimal solutions. The GBMSO approach is extended to design DOEs that control the amplitude distribution of a beam at multiple planes, rather than at just a single plane (i.e., the far field).

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Beam shaping using Gaussian beam modes.

Special approaches unique to the waveband are required for the modelling of terahertz optical systems. Ray tracing is
inadequate because in typical instruments the propagating beams are not very many wavelengths in diameter and a
"quasi-optical" approach is required in which Fresnel diffraction effects can be efficiently and accurately simulated.
Typically, it is also necessary to be able to simulate the coupling of quasi-optical beams to feed antenna structures to
predict optical performance. In many systems the beams can be considered to be coherent and their propagation through
a beam guide consisting of re-focussing elements can be efficiently modelled using modal analysis, especially useful for
quick design purposes, beam control and optimisation. This modal approach has been extended to allow for aberrations
and truncation particularly relevant in compact mirror based systems. At the same time physical optics, although
computationally intensive, is also a useful tool when detailed analysis is required, particularly for providing crosspolarisation
information and high accuracy far-field beam patterns from large reflecting antennas, for example. However,
modal analysis in general is a very powerful tool, which enables one also to understand issues associated with throughput
when partially coherent systems are being considered. This is important for the efficient optical modelling of large arrays
systems now being developed for next generation astronomical instrumentation. In the presentation, we will discuss
these issues and present examples from real instrumentation. We also summarise our continuing work on the
development of computationally efficient modelling tools for fast quasi-optical design and analysis.

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Optical Modelling using Gaussian Beam Modes for the Terahertz Band

The nondiffracting Mathieu beams have highly localized distribution along the angular direction and sharply peak quasi-periodic structure along the radial direction. The beams can propagate a long distance without changing their transverse intensity distribution. The dielectric diffractive elements, which can convert plane wave and Gaussian beam to nondiffracting Mathieu beams at millimeter wavelength, are designed. The transverse intensity patterns of Mathieu beam generated by the proposed diffractive elements are in good agreements with the theoretical distributions, and the propagation distance of generated Mathieu beam is larger than the Gaussian beam.

Generation of Mathieu Beams in Millimeter Wave Band using Diffractive Elements

Bessel beams are diffraction-free beams and have many novel properties. In this paper, we designed the optical path to generate the Bessel beams in millimeter wave band using three elements. A dielectric hybrid-mode horn is designed to generate a Gaussian beam, a lens is used to transform the Gaussian beam, and an axicon is placed behind the transform lens to convert the Gaussian beam into a Bessel beam. The designed optical path is simulated by the finite-difference timedomain method. The transversal intensity distribution of the generated Bessel beam has good agreement with the ideal Bessel beam. It can propagate longer than 50mm and suffers little diffraction.

Optical path design of Bessel beams at W band by FDTD method

Bessel beams are a family of diffraction-free beams. They have many unique properties and prospective applications. Much attention has been focused to this subject in optics. Recently, the studies of such beams at mm- and submm- wavebands have been carried out in our group. The investigation results, including their theories, generation, propagation and potential applications, are presented in this paper.

Yanzhong Yu

Papers

Diffraction-Free Bessel Beams at mm- and Submm-Wavebands