Harald Aagedal

Theory of speckles in diffractive optics and its application to beam shaping

Abstract The design of diffractive phase elements (DPEs) for solving the general beam shaping problem where the signal wave is specified by an intensity distribution on a continuous support in a finite signal window is considered. In this case serious design problems due to speckles may arise. After introducing a mathematical definition and description of speckles, the influence of the phase of the signal wave on the design process is examined. It turns out that depending on the application a pseudo-random or a spherical phase should be used as an initial phase of the signal wave for an iterative design procedure. Due to its smoothness the spherical phase prevents the occurrence of speckles during the iteration process whereas the pseudo-random phase is accompanied by speckle effects. For applications where the imaging properties of the spherical phase are undesirable, a soft coding method is presented which significantly reduces the number of speckles of the pseudo-random phase. For cases where speckles ...

ANALYTICAL BEAM SHAPING WITH APPLICATION TO LASER-DIODE ARRAYS

In contrast to numerical methods for beam shaping, analytical beam shaping consists of two steps: first, finding a purely geometrical distortion between the input plane and the output plane redistributing the intensity of the incoming wave front; and, second, computing a phase-only element realizing this coordinate transform. For the latter the method of stationary phase may be applied. The known classes of possible analytical wave transformation are extended to comprise separable and isotropic super-Gaussian-to-super-Gaussian conversion as well as transformation of Gaussian arrays to super-Gaussian distributions, and vice versa. The resulting optical phase elements contain no spiral phase dislocation and may thus be realized as refractive or diffractive elements. In addition, the outgoing wave front does not contain spiral phase dislocations.

Analysis of optical elements with the local plane-interface approximation.

The local plane-interface approximation (LPIA) is a method for propagating electromagnetic fields through the inhomogeneous regions (e.g., elements) of an optical system. The LPIA is the superclass of all approximations that replace the usually curved optical interfaces with local tangential planes. Therefore the LPIA is restricted to smooth optical surfaces. A maximum radius of curvature of the optical interface of the order of a few wavelengths is a rough estimate for the validity of the LPIA. Two important approximation levels of the LPIA are the thin-element approximation (TEA) and a geometric-optical version of the LPIA (LPIA(ray)). The latter combines the wave-optical propagation of an electromagnetic field in the homogeneous region of an optical system with a ray-tracing step in the inhomogeneous region. We discuss the regions of validity of the LPIA in general and the approximation levels LPIA(ray) and TEA in detail.

Fabrication of micro-optical surface profiles by using grayscale masks

The fabrication of surface profile may become an interesting technology in the field of micro optics and micromachining. Recently, surface profiles are known and widely used in optics, especially in diffractive optics. In the last few years the demand on deep and arbitrarily shape profiles increased drastically. Laser beam writing and e-beam writing are technologies suitable for the fabrication of such profiles, but only for a limited range of profile depth. Photolithography is also able to realize surface profiles, much deeper profiles can be realized by combining of different technologies. In this paper we report about a strategy for arbitrary deep profile generation as well as results we achieved by using single and combined technologies of special gray scale masks (based on HEBS glass), e-beam lithography and photolithography.

Comparison of resonator-originated and external beam shaping.

The spatial shaping of laser beams is a subject of research in modern optics. Recently the introduction of diffractive elements in laser resonators has offered an alternative to external beam-shaping optics by mode shaping within the resonator. We describe the specification of the laser resonator mirrors to obtain by means of internal mode shaping a desired beam outside the resonator. Modal discrimination of the modified resonator and the mirror alignment sensitivity is discussed. Basic features of resonator-originated and external beam shaping are compared.

Consequence of illumination wave on optical function of non-periodic diffractive elements

Abstract Non-periodic diffractive elements may be used to generate a specified light distribution as the diffraction pattern. The illumination wave has a severe influence on the optical function of the DE. First steps on the analysis of this situation are performed for coherent and incoherent illumination. In the coherent case, an iterative algorithm is introduced.

On pixel-oriented structure parametrization for design of diffractive elements

Abstract In two dimensions the design of paraxially operating diffractive elements is typically based on a pixel-oriented parametrization of the structure of the element. Various algorithms have been suggested to optimize such a set of parameters in order to obtain a diffractive element with satisfying optical properties. In particular projection-type algorithms such as the iterative Fourier transform algorithm have been proven to be well adapted to this kind of parametrization. Because of the significant progress which has been made in the availability of computer memory the number of pixels is no longer a serious bottleneck of a pixel-oriented parametrization and therefore the benefit of projection-type algorithms has been increased in recent years. This is demonstrated by comparing designs of diffractive elements as they can be obtained by different methods. Moreover, an additional constraint for projection-type algorithms is described and implemented which allows the control of the minimum feature siz...

Design of paraxial diffractive elements with the computer-aided design (CAD) system DigiOpt

User-friendly computer-aided design tools for the implementation of diffractive optical elements may on the one hand influence the acceptance of diffractive optics in industry and on the other help to simplify research work in this area. In the present paper we describe the software system DIGIOPT which was designed to fulfill our demands on the design of paraxial diffractive elements for optical information processing applications.

Upper bound of signal-relevant efficiency of constrained diffractive elements.

We define the signal-relevant efficiency (SRE) of a diffractive optical element as a measure of the proportion of the incident field power that ends up in the desired output signal. An upper bound for SRE is determined in the presence of arbitrary constraints imposed on the element, such as phase-dependent loss due to absorption within the microstructure and quantization of the surface profile. We apply the theory to the important class of diffractive elements that contain only one desired diffraction order (such as diffractive lenses) and derive the surface profile that provides the highest efficiency allowed by the constraints.

Algorithms and software for diffractive optics

The present paper describes the requirements for software for diffractive optics and briefly explains some basic facts and algorithms. Examples from an academically developed software package are given.