The threshold logic filter is an important nonlinear filter class, which is defined by a threshold logic function of binary input values. It is proved in this paper that not all positive self-dual logical functions are threshold functions if the number of input variables is 5 or more. The positive self-dual logical filter is a limited class but includes almost all filters for noise removal. Our result means that not all positive self-dual filters can be expressed by one operation of the threshold logic filters. In the sense of the filter expression by neural networks, the two-layer network cannot always optimize even this limited class.

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We show analytically that application of an identity in conformal invariant field theories to multidimensional guided-wave optics predicts a generic family of modes with algebraic (power-law) tails in the evanescent field.

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In systematic research on a series of new nonlinear organic materials, we found that Bis (4-nitrophenoxy) methane (BNPM) showed a large intensity of second harmonic light, which was 4.4 times as large as that of urea crystal by powder technique and easily crystallized from a solution. The crystal structure of BNPM, obtained by the X-ray diffraction method, was orthorhombic, space group P2₁2₁2 (point group 222), with unit-sell dimension a=10.205 b=12.854 c=4.8822 In addition, we found that the absorption edge of BNPM was 430 nm with a 0.9-mm-thick crystal, and we observed the second harmonic light with BNPM single crystal at the wavelength of 1064 nm and in the range from 906 nm to 990 nm.

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A binary phase grating capable of shaping an incident Gaussian beam to a flattop beam in a Fourier domain is designed iteratively. It is essential in grating design to consider the phases of diffracted waves by the grating, in addition to their amplitude uniformity and diffraction efficiency. The optimized grating phase produces the in-phase diffracted waves that interfere constructively to form a uniform amplitude and phase profile. The dependence of the shaped profile on the illuminating amplitude distribution, the grating misalignment, and the lens focusing error is investigated by computer simulation and optical experiment.

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This paper describes invariance of the normalized optical spectrum for a particular class of optical fields propagated in the far zone from a secondary, spatially, partially coherent source. The optical field across the secondary planar source is inhomogeneous to give the complex degree of spectral coherence such that h{αω(ρ₁-ρ₂)}exp{iεω(ρ₁²-ρ₂²)}, where α, ε are constants, ω is optical frequency, and ρ₁, ρ₂ denote two points in the secondary source. This expression for is the same as obtained in the Fresnel zone from a primary, spatially incoherent source. The invariance law does not hold for the spectrum of the light propagated from the primary source.

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Morphological techniques are applied to binary image processors in a multiple-imaging optical system and the following algorithms are proposed: performing morphological basic operations, extraction of boundary lines, detection of characteristic points in small-scale patterns, elimination of salt noises with few pixels, and smoothing of boundaries. Techniques for processing a complicated binary image are demonstrated using the algorithms and a hybrid parallel computing system with a simple optical multiple-imaging system and a personal computer.

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In this paper a new type element that can implement perfect shuffle (PS) network of free spatial optical interconnection is presented. It is a microoptics array element consisting of a series of sub-blazed gratings with different spatial frequency. The array has highly efficient light energy and a very simple setup. It can realize 1-D, 2-D PS networks and their inverse transforms. Also, the array can conveniently realize microminiaturization and multilevel interconnection and other forms of interconnections.

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In lightwave community antena television (CATV) systems as well as other optical fiber communication networks, a transmitted optical signal is known to be degraded by an intensity noise produced within the fiber due to the interference between the signal and doubly reflected light. We report on the improvements to the signal degradation due to the double Rayleigh backscattering by inserting optical isolators in the trunk lines of the systems. A carrier-to-noise ratio (CNR) has been calculated as a function of the number and the insertion loss of the isolators. The calculated results indicate that there is an optimum number of isolators, and if the insertion loss is less than 0.3 dB, the CNR degradation can be restored by more than 60%. To test the calculated results, we conducted experiments for the specific case of employing one isolator, and obtained good agreements between the two.

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The characteristics of intra-cavity distributed Bragg reflector (DBR) quasi-phase-matched (IDQPM) second-harmonic-generation (SHG) lasers are theoretically studied. In the IDQPM-SHG laser, a QPM device and a DBR for feedback are separately fabricated on the same substrate with the QPM device placed between the DBR and a semiconductor laser. The threshold current of the IDQPM-SHG laser depends on the coupling efficiency between the laser diode and the QPM waveguide and the reflectivity of the DBR. The SH output of the IDQPM-SHG laser is strongly dependent on the generalized SHG conversion efficiency, κ. This laser has the potential to attain an SH output over a 30-mW using a currently available 50-mW semiconductor laser for the fundamental light source, when highly efficient QPM device (κ=2.2 W^-1) is used. Its tolerance for various deviations from the initial design and the problems to develop a commercially available IDQPM-SHG laser are also discussed.

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Optical multistability of a Fabry-Perot semiconductor laser is analyzed when multi-optical inputs detuned from the cavity-resonant wavelength of a semiconductor laser are injected. Many split branches are shown to be produced in the optical output versus optical input characteristics for different detuned optical inputs. It is also shown that optical outputs can be switched in any one of the optical input wavelengths by optical input pulses, based on the optical output versus input characteristics with multi-split branches.

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Self-pumped four wave mixing (SPFWM) in a single BaTiO₃ crystal is experimentally studied because of its fast response and rather simple optical system. The origins of unstable operations are shown and classified: unstable operation of self-pumped phase conjugate mirror (SPPCM), floating dust in the laser beam path, competition between beam path loops, and competition between groups of index gratings. The reflectivities and the buildup times are measured as they relate to incident conditions, i.e. the geometry of beam paths and interaction regions, and four cases are given. Large reflectivity was obtained when buildup time was short, probably because of large coupling strength. The measured buildup times lie between 0.5 s and 0.6 s at the total incident beam power of about 5.5 mW, so that fast response of SPFWM was confirmed.

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In topography measurements of a local ocular fundus of the human eye using a grating-pattern projection technique, a pre-processing method to detect fringes accurately and a generalized Fourier transform method to analyze the fringe deformations are proposed. The method of analysis compensates for fringe deformations caused by instrumental characteristics. By combining the two methods, depth information can be determined with high accuracy. It is shown that the topographic parameters of the optic disc and the fundus slopes in the rim area are obtained with good reproducibility.

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Although it has long been recognized that the effects of photon multiple scattering generally need to be accounted for in the analysis of lidar cloud returns, this is a difficult problem and current approaches are still rudimentary. The multiple scattering process is controlled by the size of the lidar beamwidth and the distance to the cloud, which jointly determine the lidar footprint, but cloud microphysical content (i.e., particle size, concentration, and shape) exerts a strong influence on the range distribution and depolarization of the returned energy. Since clouds are inherently inhomogeneous with height, it is our premise that vertically homogeneous cloud simulations based on idealized particle size distributions lead to misleading results. We offer a more realistic approach based on the contents of growing water droplet clouds predicted by a sophisticated adiabatic cloud model, which are offered for use as new standard vertically-inhomogeneous cloud models. Lidar returned signal and depolarization profiles derived from our analytical double-scattering method are given for intercomparison purposes.

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