A cyclically permutable code is a binary code whose codewords is cyclically distinct and has a full cyclic order. Important classes of these codes are the constant weight cyclically permutable codes. These codes have wide applications in optical code division multiple access communication systems. In this paper, we propose a tunable cyclic shifter based on the super-imposed holographic grating using photopolymer as the holographic medium, which can be used with a cyclically permutable code by applying appropriate strain to the photopolymer.
Proc. SPIE. 5636, Holography, Diffractive Optics, and Applications II
KEYWORDS: Mathematical modeling, Diffraction, Transformers, Gaussian beams, Diffractive optical elements, Coherence (optics), Detection and tracking algorithms, Deconvolution, Convolution, Global system for mobile communications
A novel design method of diffractive optical element for shaping Gaussian Schell model beams is investigated. In the design, it is important to solve a deconvolution problem for obtaining diffraction image with edge-sharpness degraded by the convolution effect of the partially coherent Gaussian Schell model beam. In this paper, a simple heuristic approach to the deconvolution problem is addressed. It is shown that an extra rim pattern around the target diffraction image can lighten the unwanted edge-blur of the diffraction image. The algorithm for generating the extra rim pattern is explained.
In this paper, we investigate photopolymer based holographic off-plane coupler experimentally. In our scheme, holograms are recorded inside the photopolymer slab waveguide by two-beam interference. The optical beams are vertically coupled into the waveguide through the recording position over the polymer substrate. The coupled optical beam propagates in the photopolymer slab waveguide. The beam profile radiated from the cut end of the waveguide and measured energy transfer efficiency are presented.
It is important to have a tunable encoder in optical channel coding for the purpose of coping with varying communication environment. In this paper, a tunable encoder based on the holographic grating (HG) using photopolymer as the holographic medium is described. The system is composed of photopolymer holographic grating as a demultiplexer, spatial light modulator (SLM), and other lens systems. The photopolymer grating acts as a demultiplexer to distribute optical wavelength channels on the SLM through its spatial dispersion property. Then, the SLM produces wavelength-endcoded data but its spatial amplitude/phase modulation. The merits of using the holographic grating are that it has relatively easy fabrication process, and that non-uniform grating structure and multiplexing can be exploited. In this setup, we can additionally change demultiplexing wavelengths by inducing strain gradient on the polymer grating, which is attached on the two XYZ linear stages. Hence a different set of wavelengths is incident to SLM and this enables another type of encoding pattern.
We examine and characterize a wavelength demultiplexer using a holographic grating for WDM multiple-channel applications. The holographic grating is a kind of volume grating recorded in a photopolymer, which is different from the general surface relief type diffraction gratings. The holographic grating disperses the wavelength components of incident wave into spatial domain so that through the coupling optics, different wavelength channels can be separated to the different output optical fibers. The characteristics of the polymeric holographic grating are compared to those of the relief type diffraction gratings. Overall demuliplexer characteristics is characterized by applying first order Born approximation with electro-magnetic vectorial analysis. It shows that the amplitude and group velocity (i.e., the chromatic dispersion) characteristics are determined by the holographic grating phase structure and out-coupling optics lens aberrations. The out-coupling lens aberration effect to the chromatic dispersion is examined and classified according to the lens aberration classification. The holographic grating phase perturbation (i.e., chirping) can be used to minimize the lens aberration caused chromatic dispersion to improve the demultiplexer performance. The demultiplexer polarization dependent loss is also examined in relation to the spatial dispersion and diffraction efficiency characteristics.
We propose and characterize nanowire-embedding in photonic crystal. This embedding method becomes a novel fabrication process for photonic crystal line defect, which enhances freedom in waveguide manufacturing. The characteristics of the nanowire defect waveguide are investigated by using a cascaded low pass filter model in circuit theory. We can find that the wave propagation characteristics correspond to the specific case of optical branch phonon vibration in solid crystals, where diatomic vibration occurs with multiple particle interaction. Actually, the dispersion characteristics of the proposed system are similar to the optical branch phonon vibration of the transition metal compounds. There are multiple modes (i.e., different Bloch wave numbers) for an optical frequency with local minimum of frequency at the lower wave number. Waveguide bending ability was confirmed by using FDTD (finite difference time domain) simulations. Nanowire-embedding in photonic crystal is expected to open a new territory to the field of photonic integrated circuit from fabrication process to waveguide and various photonic devices.
We propose a model of a holographic grating (HG) filter for WDM applications and provide a method to control the chromatic dispersion of WDM demultiplexer as one of its specific applications. The general filter characteristics can be described as a correlation between the scattered mode from the HG and the out-coupling optic mode. We note that the HG phase distribution and lens aberration of out-coupling optics provide effective phase modulation for the chromatic dispersion of the filtered output. Also the amplitude distributions of the two modes perform a kind of weighting function (i.e., apodization), which controls the overall filter spectrum. This filter scheme can exploit wavelength dependent diffraction angle transition (i.e., spatial dispersion) and can be used for multi-channel demultiplexer in WDM system. In this case, lens aberrations of the out-coupling optics cause chromatic dispersion problems in each separated channel and among the channels. The problems can be managed by controlling the HG phase distribution so that the overall chromatic dispersion of the demultiplexer can be reduced and managed over the demultiplexed channels. We characterize the chromatic dispersion properties according to the third order lens aberrations and propose methods to control them by using HG phase distribution.
A tunable demultiplexer based on the holographic grating (HG) using photopolymer is described. The system is based on the 1st order Born approximation of volume diffraction, optical aberration of the lens system, and mode correlation of fiber coupling. The merits of the holographic grating are that it has relatively easy fabrication process, non-uniform grating period and multiplexing are possible, and anisotropic diffraction can be exploited. And also the strain tuning method on the polymer grating for wavelength tuning is proposed. In the setup, the polymer grating is attached on the two XYZ linear stages. If one stage is fixed and the other stage moves away, the polymer grating is extended. Hence all the transmission wavelengths move to longer wavelength with grating period variation caused by the strain induced on the polymer. The objective of this method is to change the transmission wavelengths of the demultiplexer linearly or arbitrarily.
In this paper, the applications of holographic devices for optical communications are reviewed and discussed. In dense wavelength division multiplexing (DWDM) optical communication systems, holographic devices have some potential applications to satisfy the complex requirements of the systems. We explain recent accomplishment in this field using holographic gratings (HGs) recorded in a photorefractive crystal or a photopolymer. General properties of the HG as a filter are reviewed. We note that the photopolymer HG can be used as a wavelength demultiplexer in DWDM system. It uses spatial dispersion properties of diffraction grating, which provides wavelength-dependent diffraction angle change to separate the multiplexed wavelength channels. The HG device has inherent advantages compared to the other device technologies. As specific applications of the device, we propose chromatic dispersion management of the multiple channel wavelength demultiplexer, channel wavelength tuning of the device output, and double band demultiplexer using superposed HGs. Also, we discuss optical signal routing using computer-generated holograms (CGHs) on a phase spatial light modulator. We expect that these HG devices and CGH system can exploit phase control, tunability, multiplexing and dynamic imaging control of holograms to cope with various DWDM system requirements.
We propose and characterize the remote multiplexing of holograms with random pattern references from a multimode fiber bundle. The random pattern reference is modeled by using the superposition and concatenation of propagation modes of multimode fibers and free space. We compare two laser-coupling methods to the fiber bundle, i.e., direct coupling and lens coupling, for angle, shift, and wavelength remote multiplexings. The optimum laser-coupling method for each multiplexing is analyzed based on the theoretical model and experimental results. Retrieved hologram images show that 1-D intensity variation of the image might occur for the 90-deg geometry holograms in relation to the random pattern properties. Environmental variation effects such as vibration and temperature variation are also discussed and examined. These remote multiplexing methods can be applied to general multimode waveguide arrays to construct compact and integrated optical systems, where multiplexing can be performed at remote places.