We report a stationary Fourier-transform spectrometer chip implemented in silicon microphotonic waveguides. The device comprises an array of 32 Mach-Zehnder interferometers (MZIs) with linearly increasing optical path delays between the MZI arms across the array. The optical delays are achieved by using Si-wire waveguides arranged in tightly coiled spirals with a compact device footprint of 12 mm 2 . Spectral retrieval is demonstrated in a single measurement of the stationary spatial interferogram formed at the output waveguides of the array, with a wavelength resolution of 40 pm within a free spectral range of 0.75 nm. The phase and amplitude errors arising from fabrication imperfections are compensated using a transformation matrix spectral retrieval algorithm. In a typical configuration, a waveguide array of MachZehnder interferometers (MZIs) with increasing path differences are used to implement the SHS concept [9,10]. For such a geometry, the source power spectrum and the output interferogram are related by the cosine FT. A similar MZI array geometry, including phase-correction circuits using independent heaters for each MZI, has also been demonstrated [13]. However, when long optical path delays are required for high spectral resolution, similar configurations yield prohibitively large devices.In this Letter, we present a compact FT spectrometer chip, in which a high spectral resolution of 40 pm with a compact device size is achieved by using tightly coiled spiral waveguide structures in an MZI array. Furthermore, a spectral retrieval algorithm with phase and amplitude error compensations is demonstrated for the first time to the best of our knowledge, obviating the need for dedicated phase correction circuits. The FT spectrometer is implemented as an array of N MZIs in silicon-on-insulator (SOI) waveguides (Fig. 1). Each MZI comprises a reference arm of constant length and a delay arm with a spiral waveguide. The length of the delay arm, i.e., spiral length, linearly increases by ΔL across the array. The high refractive index contrast of the SOI platform and the waveguide bend radius of ∼5 μm readily allows the making of spirals with geometrical lengths of over a centimeter within an area only a few hundred micrometers in diameter.For a given input spectral distribution, the dispersive property of the MZI array results in a wavelengthdependent spatial interferogram at the outputs of the array. The relation between the input spectral distribution and the interferogram Ix i is unambiguous within

Abstract:In this work we formulate the main properties of the gyrator operation which produces a rotation in the twisting (position -spatial frequency) phase planes. This transform can be easily performed in paraxial optics that underlines its possible application for image processing, holography, beam characterization, mode conversion and quantum information. As an example, it is demonstrated the application of gyrator transform for the generation of a variety of stable modes.

Permanent holographic storage has been demonstrated in a photopolymerizable organically modified silica glass. The glass was prepared by dispersing a titanocene photoinitiator and a high refractive index acrylic monomer in a porous silica matrix. This glass exhibits unprecedented sensitivity and refractive index change upon a moderate exposure to green light and can be fabricated in thickness up to several millimeters. A photopolymerizable storage medium of such a thickness with good holographic properties is needed for practical holographic storage devices. Lack of such medium has been considered the main obstacle in development of write-once holographic memories. In our glass, we have stored permanent volume holograms of diffraction efficiency approaching 100% and refractive index modulation up to 4.5×10−3, making this photopolymerizable material suitable for use in holographic data storage.

Improved performance of volume holographic sol‐gel materials—refractive index modulations in the 10–2 range, diffraction efficiencies near 100 %, and low levels of noise scattering—are reported that arise from the incorporation of Zr‐based high refractive index species capable of diffusing from dark to bright fringes of the interference pattern (see figure).

The gyrator transform (GT) promises to be a useful tool in image processing, holography, beam characterization, mode transformation, and quantum information. We introduce what we believe to be the first flexible optical experimental setup that performs the GT for a wide range of transformation parameters. The feasibility of the proposed scheme is demonstrated on the gyrator transformation of Hermite-Gaussian modes. For certain parameters the output mode corresponds to the Laguerre-Gaussian one. © 2007 Optical Society of America OCIS codes: 070.2590, 120.4820, 200.4740, 140.3300. where r i,o = ͑x i,o , y i,o ͒ are the input and output coordinates, respectively. This transform is additive and periodic with respect to ␣. For ␣ = 0 it corresponds to the identity transform, for ␣ = / 2 it reduces to the direct/inverse Fourier transform with rotation of the coordinates at / 2, and for ␣ = the reverse transform described by the kernel ␦͑r o + r i ͒ is obtained. The applications of the GT for spacevariant filtering, hyperbolic noise reduction, and encryption have been proposed in [5]. Moreover the GT corresponds to the movement on the main meridian of the orbital Poincaré spheres [6,7] introduced by the analogy to the polarization Poincaré sphere. The GT can be considered a universal mode converter, since it allows the generation of all essentially different structurally stable Gaussian modes, which can be obtained from the Hermite-Gaussian (HG) modes by the integral canonical transforms [7]. To use the GT for optical information processing we need an optical setup performing this operation for different parameters ␣. The design for such a system has been proposed in [9]. Based on the ABCD matrix formalism for the first-order lossless optical systems, it has been shown that the coherent optical system, which contains three generalized lenses with fixed distances between them [ Fig. 1(a)] is able to perform the GT for the large range of angles ␣. The transformation angle ␣ is changed by rotation of the cylindrical lenses, which forms the generalized lenses.In this paper the first experimental implementation of the flexible optical scheme for the GT is reported. The action of this system is demonstrated on the example of the transformation of the HG modes into the helicoidal Laguerre-Gaussian (LG) ones for ␣ = ͑2k +1͒ /4 (k is an integer) passing through intermediate modes [7,8] for other values ␣.We start from a detailed description of the symmetric optical setup constructed with three generalized lenses performing the GT [ Fig. 1(a)]. Every generalized lens is a combination of two convergent thin cylindrical lenses of the same power. The action of the generalized lens leads to the quadratic phase modulation written aswhere is the wavelength, f is the focal distance of a cylindrical lens, and angle indicates the position of the axis of symmetry of the cylindrical lenses. Thus the axis of the cylindrical lenses forms angle 1 =− and 2 = − / 2 with the vertical axis OY, respectively [10,11] [see Fig. 1(b)]. The first and t...