Nonlinear multiwavelength conversion based on an aperiodic optical superlattice in lithium niobate.

We have demonstrated what is to our knowledge the first successful achievement of multiwavelength conversion in an aperiodic optical superlattice (AOS) lithium niobate crystal with equalized gain. The two AOS devices in our experiment, numerically synthesized from 2857 crystal blocks with a unit block thickness of 3.5 microm, have fundamental wavelengths of 1540 and 1545 nm for double-wavelength second-harmonic generation (SHG) and of 1540, 1545, and 1553 nm for triple-wavelength SHG at 50 degrees C. Our experiment and simulation show that the output spectrum of an AOS wavelength converter is fairly insensitive to typical fabrication errors.

Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution.

We first present nonparaxial designs for a microcylindrical axilens with different long focal depths and rigorously analyze electromagnetic field distributions of the axilens using integral equations and the boundary-element method. Numerical results show that the designed axilenses indeed have the special feature of attaining a long focal depth while keeping high transverse resolution for numerical apertures of 2.4, 2.0, and 1.0. The ratio between the extended focal depth of the designed axilens and the focal depth of the conventional focal lens is 1.41, the corresponding maximal extended focal depth of the axilens can reach 28 microm, and the spot size of the focal beam is approximately 10 microm over the focal range.

Entirely electromagnetic analysis of microlenses without a beam-shaping aperture.

We suggest an approach for numerically studying the performance of cylindrical microlenses without a beam-shaping aperture based on the boundary-element method (BEM). We divide the infinite microlens boundary into two components: The first part is an infinite expanded flat interface excluding the curved interface, and the second part is only the originally curved microlens interface. The resulting transmitted field can be regarded as the composition of two fields: One is generated by the first boundary, and the other is contributed from the second boundary. We carry out numerical simulations for two microlens systems, with or without aperture. We find that, for the nonapertured system, an ideal focusing feature is still observed; however, the axial distribution of the transmitted field exhibits an oscillation, different from the apertured system. It is expected that the current approach may provide a useful technique for the analysis of micro-optical elements.

Design of polarization-selective diffractive phase elements in a laser cavity.

We report a new design for a polarization-selective laser cavity with birefringent diffractive phase elements. This laser cavity can create two modes with different polarizations and profiles launched separately from two end mirrors. The numerical simulation results show that the constructed laser cavity can successfully generate two orthogonal polarization modes with a uniform circular shaped pattern output from one end mirror and a uniform square-shaped pattern output from another end mirror.

Diffractive phase elements that synthesize color pseudo-nondiffracting beams.

The design of diffractive phase elements (DPE's) for generating color pseudo-nondiffracting beams (PNDB's) in a multiple-wave illuminating system by the conjugate-gradient method is described. The axial-intensity distributions for dual-color PNDB's generated by the DPE's are shown. The color PNDB's behave as segmented axial-intensity distributions; in each of segments only one color persists. The sequence of wavelength components in the color PNDB's can be arbitrarily preset. Three-dimensional plots of a dual-color PNDB indicate the characteristics of a beam with high transverse resolution.

Optical implementations of the Radon-Wigner display for one-dimensional signals.

New optical implementations of the Radon-Wigner display for a one-dimensional signal are proposed based on the fractional Fourier transform. The setups involve only one varifocal lens. Furthermore, the same magnification can be realized simultaneously for all the fractional transform orders, which is quite convenient for practical applications.

Beam shaping and its solution with the use of an optimization method.

We present an exact mathematical description of beam shaping and indicate that a rigorous solution does not exist: only an optimal solution can be found. An optimization method is proposed to search for the solution. The simulation results for an example are given in detail.

Rotation-invariant and controllable space-variant optical correlation.

We propose a method for designing a correlator for achieving rotation-invariant and controllable space-variant optical correlation. The design concept is based on a combination of fractional correlation and circular-harmonic decomposition of the reference object. The suggested method is described and analyzed in detail. Numerical simulations show that this new correlator might provide potential applications in practice.

Recursive algorithm for phase retrieval in the fractional fourier transform domain.

We first discuss the discrete fractional Fourier transform and present some essential properties. We then propose a recursive algorithm to implement phase retrieval from two intensities in the fractional Fourier transform domain. This approach can significantly simplify computational manipulations and does not need an initial phase estimate compared with conventional iterative algorithms. Simulation results show that this approach can successfully recover the phase from two intensities.

Implementation of pseudo-nondiffracting beams by use of diffractive phase elements.

We report the experimental implementation of pseudo-nondiffracting beams by use of diffractive phase elements (DPE's). Based on the conjugate-gradient method presented in J. Opt. Soc. Am. A 15, 144-151 (1998), these DPE's are designed and fabricated on a flat quartz substrate. The experimental results show that the performance of the fabricated DPE's is in good agreement with the theoretical prediction.

Fractional Gabor transform.

A fractional Gabor transform (FRGT) is proposed. This new transform is a generalization of the conventional Gabor transform (GT) based on the Fourier transform to the windowed fractional Fourier transform (FRFT). The FRGT provides analyses of signals in both the real space and the FRFT frequency domain simultaneously. The space-FRFT frequency pattern can be rotated as the fractional order changes. The FRGT has an additional freedom, compared with the conventional GT, i.e., the transform order. The FRGT may offer a useful tool for guiding optimal filter design in the FRFT domain in signal processing.

Design and fabrication of a diffractive phase element for wavelength demultiplexing and spatial focusing simultaneously.

The design of a diffractive phase element (DPE) that simultaneously implements wavelength demultiplexing and focusing is carried out on the basis of the general theory of amplitude-phase retrieval. The designed DPE is fabricated with optical contact lithography. Three masks are needed to produce the surface-relief structure of the DPE with eight quantized levels in depths. Experiments demonstrate that the designed DPE can successfully implement both the functions of demultiplexing three different-wavelength beams and focusing each component at a predesignated position simultaneously. Experimental measurements are in good agreement with the results of numerical simulations.

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.

Diffractive-phase-element design that implements several optical functions.

A scheme for the design of diffractive phase elements (DPE's) that integrates several optical functions is presented in a consistent sense based on the general theory of amplitude-phase retrieval and the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)]. We extend the original Yang-Gu algorithm to treat a system illuminated by a beam of incident light whose components are at different wavelengths, and a set of equations for determining the phase distribution of the DPE is derived. The profile of a surface-relief DPE can be designed with an iterative algorithm. Numerical simulations are carried out for the design of one-dimensional DPE's capable of both demultiplexing different wavelength components and focusing each partial wave at predetermined positions. The influence of the extension of sampling points in the DPE's from ideal geometric points to physical spots on design results is also investigated. The numerical simulation results show that the new algorithm can be used successfully to design the desired DPE's. It is therefore expected to be useful in the design of DPE's for micro-optical systems.

Design of diffractive phase elements that produce focal annuli: a new method.

A new optimization method based on the general theory of amplitude-phase retrieval is proposed for designing the diffractive phase elements (DPE's) that produce focal annular patterns. A set of equations for determining the phase distribution of the DPE is given. The profile of a surface-relief DPE can be designed with an iterative algorithm. Numerical calculations are carried out for several examples. A comparison of the performance of the DPE's designed with the Gerchberg-Saxton algorithm and the new algorithm is presented. The effect of quantization of the phase distribution of the DPE's on the results is also investigated. The results show that the new algorithm can successfully achieve the design of the DPE's that convert the uniform incident beam into the focal annular patterns.

Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison.

A detailed comparison of the original Gerchberg-Saxton and the Yang-Gu algorithms for the reconstruction of model images from two intensity measurements in a nonunitary transform system is presented. The Yang-Gu algorithm is a generalization of the Gerchberg-Saxton algorithm and is effective in solving the general amplitude-phase-retrieval problem in any linear unitary or nonunitary transform system. For a unitary transform system the Yang-Gu algorithm is identical to the Gerchberg-Saxton algorithm. The reconstruction of images from data corrupted with random noise is also investigated. The simulation results show that the Yang-Gu algorithm is relatively insensitive to the presence of noise in data. In all cases studied the Yang-Gu algorithm always resulted in a highly accurate recovered phase.