Diffractive optical elements with modulated zone sizes

Abstract

The standard design for phase-only diffractive optical elements comprises a transformation of the continuous phase function into a surface relief by means of wrapping the phase into regular intervals of M2π. This results in a structure with diffractive zones aligned in a horizontal plane. We present an alternative design concept with modulated zone sizes leading to non-periodic boundary positions and non-aligned surface structures. The diffractive properties are compared to those of conventional diffractive optical elements. It can be shown that they are fully equivalent for the design wavelength, but exhibit a different spectral behaviour for deviating wavelengths. These properties are exploited for the improvement of the optical performance of blazed gratings and diffractive lenses under conditions of deviating wavelengths. Special emphasis is put on the optimization of the ratio between diffractive efficiencies of the design order and other orders for blazed gratings and focusing diffractive lenses, as well as the suppression of interference effects within Gaussian beams collimated with diffractive lenses.     

Diffractive optical elements for intra-cavity beam-shaping of laser modes

Abstract

Diffractive optical elements (DOE) are applied as intra-cavity mode selection devices for customizing the fundamental mode of laser resonators for high power laser systems. Using a phase-conjugating mode selecting element (MSE) in a laser oscillator, we are able to produce a good approximation to a super-Gaussian mode with a near flat intensity profile. This offers higher energy extraction from any following laser amplifiers compared to an unmodified Gaussian TEM₀₀ mode. Two different designs for operation in a 1 m cavity length Nd:YAG master oscillator are presented. Both designs are surface relief phase elements fabricated in fused silica using photolithography with reactive-ion etching to produce 16 level elements for use in transmission. One element is designed to replace the cavity end mirror, while the other stands off an arbitrary distance from the end mirror. A novel iterated design for these transmissive elements is introduced. Numerical results and experimental measurements are presented and discussed.     

Diffractive optical elements for simultaneous operation in reflection and transmission

It is advantageous for some diffractive optical element (DOE) applications to produce different output patterns in different circumstances. There has been considerable work on the design of wavelength multiplexing DOEs and in devices where the polarization of the incident light determines the output. One parameter that has not, to our knowledge, been exploited for pattern formation DOEs is the mode of operation, i.e., whether the element works in reflection or transmission. We present an approach for designing such devices and design an element with modeled efficiency, mean square error (MSE), and cross-talk of 65.9, 2.52, and 4.2% in transmission and 66.6, 2.50, and 3.5% in reflection. The element has been successfully fabricated and has measured efficiencies of 58.3% +/- 2 in reflection and 68.8% +/- 5 in transmission are reported.     

Diffractive optical elements for beam shaping of monochromatic spatially incoherent light

Fresnel-type diffractive optical elements (DOEs) for general beam shaping of monochromatic, spatially incoherent light are demonstrated. Direct and indirect methods, i.e., adding a lens' phase to the designed Fraunhofer-type DOEs, are used for the design. The indirect method can reduce the calculation time by approximately half without loss of design accuracy. Two different design examples are shown. For one design the direct method gives a maximum sidelobe intensity of 5.0% of the maximum intensity in the signal window. For the second design the indirect method gives 23.0% of this value. The generated patterns can maintain their basic shapes over a long distance. The elements have been fabricated by directly using gray-scale commercial slides as masks. Experimental results are in close agreement with numerical predictions.     

Diffractive optical elements in hybrid lenses: modeling and design by zone decomposition

We propose to model hybrid optical systems (i.e., lenses with conventional and diffractive optical elements) as multiaperture systems in which the images formed by each zone of the diffractive optical element should be summed up coherently. This new zone decomposition concept is explained and compared with the standard diffraction-order expansion with the help of a hybrid triplet example.     

Diffractive optical elements for the formation of "light bottle" intensity distributions

Application of the two-photon polymerization (2PP) technique for the fabrication of binary radial diffractive optical elements (DOEs) to form a bottle-like intensity distribution, or "light bottle," is studied. Computer modeling and fabrication of a binary DOE for the formation of the desired light distributions are realized. The results of scanning electron microscopy analysis of the diffractive relief produced by the 2PP technique and an investigation of the optical properties of the fabricated elements are presented.     

Diffractive optical elements based on Fourier optical techniques: a new class of optics for extreme ultraviolet and soft x-ray wavelengths

A diffractive optical element, based on Fourier optics techniques, for use in extreme ultraviolet/soft x-ray experiments has been fabricated and demonstrated. This diffractive optical element, when illuminated by a uniform plane wave, will produce two symmetric off-axis first-order foci suitable for interferometric experiments. The efficiency of this optical element and its use in direct interferometric determination of optical constants are also discussed. Its use in direct interferometric determination of optical constants is also referenced. Its use opens a new era in the use of sophisticated optical techniques at short wavelengths.     

Diffractive optics applied to free-space optical interconnects

The optimum design of free-space optical interconnection systems utilizing diffractive optics is determined from a practical engineering standpoint for systems ranging from space invariant to fully space variant. System volume is calculated in terms of parameters such as the f-number of the diffractive lens, the wavelength of light, and also the total number, size, and separation of the optical sources and detectors. Performance issues such as interconnection complexity, diffraction efficiency, and signal-tonoise ratio are discussed. Diffractive optics fabricated by electron-beam direct-write techniques are used to provide experimental results for both shuffle-exchange and twin-butterfly free-space optical interconnects.     

Diffractive optical chemical sensor based on light absorption

A new type of chemical sensor based on light absorption is proposed. An array of zones alternatively containing the pH indicator thymolphthalein is formed in a gelatin film. By changing the sample solution from acidic to alkaline, a blue stripe appears in the gelatin film. This acts as a transmission grating and diffracts the introduced laser beam. Theory predicts that this method, which is based on light absorption/beam diffraction, is as sensitive as or more sensitive than fluorometry.     

Diffractive optical Hough transform implemented with phase singularities

The conventional Hough transform is implemented with a computer-generated hologram. The transmission function of the computer-generated hologram is computed with an extension of Bryngdahl's technique, which incorporates branch-point phase singularities. With this implementation it is shown that the branch-point technique can be used to implement point transforms successfully with an implicit transformation equation such as the Hough transform. This is done first by expression of the implicit transform in terms of several explicit transforms. After computation of the complex-valued transmission functions of the explicit transform, the functions are added together to form the transmission function for the implicit transform. Results are obtained by computation of Fresnel diffraction patterns of the Hough-transform computer-generated hologram, illuminated by different input images.     

Diffractive optical element design with memory-matrix-based identification methodology

We present a new technique for the design of diffractive optical elements (DOE's) that is based on previous nonlinear least squares (NLS) and phase-shifting quantization methods [Appl. Opt. 36, 7297-7306 (1997)]. The technique uses a memory-matrix-based identification (MMBI) optimization procedure. We compare results from the MMBI method with those from iterative Fourier transform and NLS methods. In comparison, the MMBI DOE designs produce better-quality reconstructions for DOE's with eight or more fabrication phase levels and generally have a higher signal-to-noise ratio and better uniformity.     

Uniform and graded multilayers as x-ray optical elements

A detailed comparison of the performance of uniform and graded multilayers as soft x-ray monochromators and normal incidence collectors has been made. In particular, the responses of flat depth-, and laterally graded multilayers to Al K(alpha) radiation, lambda = 8.34 A, have been computed and compared with the corresponding uniform multilayer. Furthermore, the efficiency of graded and uniform multilayers as normal incidence x-ray collectors has been calculated in terms of effective areas for parabolic reflectors tuned to the O K(alpha) line, lambda = 23.7 A. Finally, the effective areas of four strong solar emission lines in the 30-60 A region have been computed for uniform multilayers. Normal incidence multilayer mirrors are well suited for spectroheliograph type of applications.     

Diffractive phase elements for pattern formation: phase-encoding geometry considerations

Space-invariant, multilevel, diffractive phase elements are designed for large-scale pattern-formation tasks. The importance of the design algorithm and the phase-encoding geometry of the diffractive element is discussed with regard to the performance of both on- and off-axis reconstruction, notably for pixelated gratings. A new phase-encoding scheme is presented that results in an increase of the diffraction efficiency for the off-axis case.     

Diffractive optical isolator made of high-efficiency dielectric gratings only

The working principle of an optical isolator made of two corrugated dielectric gratings is introduced. One grating acts as a polarizer, and the other acts as a quarter-wave plate used in conical incidence converting linearly polarized light into circularly polarized light. Global maxima of diffraction efficiency for surface-corrugated gratings with binary, sinusoidal, and pyramidal ridge shapes with dependence on the material index are identified. Regarding technological feasibility for use in the visible wavelength range, high-frequency gratings with a binary shape were realized. With these gratings, an extinction ratio of more than 40 dB for the polarizer is theoretically possible, and more than 20 dB was experimentally achieved. A good correlation between theoretically calculated efficiencies and birefringences based on rigorous methods and the experimental results is demonstrated.     

Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators

Diffractive optical elements (DOEs) realized by spatial light modulators (SLMs) often have features that distinguish them from most conventional, static DOEs: strong coupling between phase and amplitude modulation, a modulation versus steering parameter characteristic that may not be precisely known (and may vary with, e.g., temperature), and deadspace effects and interpixel cross talk. For an optimal function of the DOE, e.g. as a multiple-beam splitter, the DOE design must account for these artifacts. We present an iterative design method in which the optimal setting of each SLM pixel is carefully chosen by considering the SLM artifacts and the design targets. For instance, the deadspace-interpixel effects are modeled by dividing the pixel to be optimized, and its nearest neighbors, into a number of subareas, each with its unique response and far-field contribution. Besides the customary intensity control, the design targets can also include phase control of the optical field in one or more of the beams in the beam splitter. We show how this can be used to cancel a strong unwanted zeroth-order beam, which results from using a slightly incorrect modulation characteristic for the SLM, by purposely sending a beam in the same direction but with the opposite phase. All the designs have been implemented on the 256 x 256 central pixels of a reflective liquid crystal on silicon SLM with a selected input polarization state and a direction of transmission axis of the output polarizer such that for the available different pixel settings a phase modulation of ~2pi rad could be obtained, accompanied by an intensity modulation depth as high as >95%.     

Short-pulse properties of optical frequency comb generators

An optical frequency comb generator, based on a simple electro-optic modulator in an optical resonator, can produce high-repetition-rate picosecond pulses. Unlike conventional picosecond lasers, the properties of these pulses are greatly affected by detuning the optical cavity and by dispersion caused by the electro-optic crystal. Picosecond pulses were studied in a physical device by numerical simulation and intensity autocorrelation measurements. The pulse width and pulse-to-pulse spacing were greatly affected by detuning the input laser frequency and the resonance of the optical resonator, and the numerical simulations showed that dispersion causes temporal ripples that are antisymmetric between pulse pairs.     

Achromatic optical elements

The principles of wavefront reconstruction by means of a geometric-optical reflection of radiation from surfaces of interference fringe maxima are discussed. The optical elements based on these principles should be achromatic. Two methods of the optical elements design are proposed. The first method is a direct holographic recording of the interference fringe structure containing only a few periods, and the second method is a combination of the measurement of the object wavefront shape with digital holography methods.     

Diffractive incremental and absolute coding principle for optical rotary sensors

Rotary sensors are an essential component in numerous applications where a rotation movement has to be detected. With optical encoders, a high angular resolution can be achieved. As a disadvantage, the resolution enhancement is associated with increasing cost. To overcome this issue, a coding principle is presented that uses a diffractive solid measure on a microstructured plastic disc. Like a DVD, this encoder disc can be manufactured in a cost effective injection molding process. For this approach, a differential incremental code, as well as an absolute code, has been developed.     

Diffractive phase elements for beam shaping: a new design method

A design method based on the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)] is proposed for computing the phase distributions of an optical system composed of diffractive phase elements that achieve beam shaping with a high transfer efficiency in energy. Simulation computations are detailed for rotationally symmetric beam shaping in which a laser beam with a radially symmetric Gaussian intensity distribution is converted into a uniform beam with a circular region of support. To present a comparison of the efficiency and the performance of the designed diffractive phase elements by use of the geometrical transformation technique, the Gerchberg-Saxton algorithm and the Yang-Gu algorithm for beam shaping, we carry out in detail simulation calculations for a specific one-dimensional beam-shaping example.