Liren Liu

Circular Dammann grating.

A circular Dammann grating that can produce circular equal intensities at various orders in the far field is described. A set of parameters such as order, circular number, uniformity, and diffraction efficiency has been defined to describe the novel diffractive phase elements. Numerical solutions of binary-phase (0, pi) circular Dammann gratings are given. The results of experiments with a four-order circular Dammann grating made by a lithographic technique are presented. This novel diffractive optical element should be highly interesting in a wide variety of practical applications.

Nonvolatile photorefractive holograms in LiNbO 3 :Cu:Ce crystals

We report experimental and theoretical studies of nonvolatile photorefractive holographic recording in LiNbO(3):Cu:Ce crystals with two illumination schemes: (1) UV light for sensitization and a red interfering pattern for recording and (2) blue light for sensitization and a red pattern for recording. The results show that the oxidized LiNbO(3):Cu:Ce crystals can provide high, persistent refractive-index modulation with weak light-induced scattering. The optimal working conditions and the prescription for doping and oxidation-reduction processing that yields the maximum refractive-index modulation are discussed.

Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous FRT’s and complex FRT’s are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy.

Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence

A theoretical study of the behaviour of partially coherent beams propagating through oceanic turbulence has been performed. Based on the previously developed knowledge of beam spreading of a partially coherent beam in the atmosphere and the spatial power spectrum of the refractive index of ocean water, we study the normalized root-mean-square width of a partially coherent beam on propagation through oceanic turbulence and its turbulence distance which may be a measure of turbulence resistance. Our analysis indicates that the behaviour of partially coherent beams on propagation may be described by the rate of dissipation of the mean-squared temperature chi(T) and that of salinity chi(S). In terms of a quantity w that defines the contributions of the temperature and salinity distributions to the distribution of the refractive index, chi(S) could be written as a function of chi(T) and w. Therefore, the behaviour of partially coherent beams on propagation can be characterized only by chi(T) for a given w. The results are shown for curved surfaces, from which one can see that partially coherent beams exhibit robust turbulence resistance when the water volume has a smaller chi(T).

Optoelectronic implementation of mathematical morphology.

An optoelectronic implementation based on optical neighborhood operations and electronic nonlinear feedback is proposed to perform morphological image processing such as erosion, dilation, opening, closing, and edge detection. Results of a numerical simulation are given and experimentally verified.

Talbot and Lau effects on incident beams of arbitrary wavefront, and their use.

Both the Talbot and the Lau effects of Ronchi and binary phase gratings on an incident wavefront of arbitrary wavefront are discussed. General and analytic solutions are obtained in terms of the Fresnel diffraction theory. Numerical simulations and supporting verification for Gaussian beams are demonstrated. It is found that the distortion of the self-image is closely linked to that of the far field distribution in a two-grating system, and both depend on the Talbot distance and the beam wavefront. Some interesting phenomena are explored such as light modulation and phase compensation. Possible applications are accordingly suggested.

Parallel optical negabinary arithmetic based on logic operations

On the basis of signed-digit negabinary representation, parallel two-step addition and one-step subtraction can be performed for arbitrary-length negabinary operands. The arithmetic is realized by signed logic operations and optically implemented by spatial encoding and decoding techniques. The proposed algorithm and optical system are simple, reliable, and practicable, and they have the property of parallel processing of two-dimensional data. This leads to an efficient design for the optical arithmetic and logic unit.

Prescription for optimizing holograms in LiNbO(3):Fe:Mn.

The photorefractive holographic dynamics of grating formation in photochromic doubly doped LiNbO(3):Fe:Mn crystal is studied numerically and analytically in terms of the two-center model of Kukhtarev et al. [Ferroelectrics 22, 949 (1979)]. The relations among the recorded and fixed space-charge fields and the doping densities, the oxidation-reduction states of the fields, and the intensities of UV-sensitizing and red recording beams are studied. Important conditions and effects are found, and an optimal prescription for material doping and oxidation-reduction processing is suggested in which the crystal can be strongly oxidized and the Mn-doping density is smaller than the Fe-doping density.

Lau cavity and phase locking of laser arrays

The Lau cavity is the self-imaging cavity with a phase corrector under the Lau reimaging condition. I propose the use of the Lau cavity to utilize both the Talbot and the Lau effects for phase locking one-dimensional and two-dimensional diode-laser arrays into a single-lobe coherent beam. Analyses on the self-reproducing of a coherent lasing field and the reimaging of initial incoherent radiation are given.

Optical implementation of parallel fuzzy logic

Abstract A multiple-imaging scheme with area-coding of input fuzzy variables and negations and thresholding of output intensity is proposed to perform basic fuzzy logic operations in parallel. Thus the pattern fuzzy logic described by a fuzzy logic function in disjunctive or conjunctive normal form can be easily realized in a two-stage optica system. The access of the required fuzzy logic function can be achieved by programming the lens-arrays and the thresholding devices. Simulations and experimental results are given, too.