Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation

A compensation technique for reducing the effect of nonlinear optical frequency swept in an optical frequency-domain reflectometer (OFDR) is proposed. The instantaneous sweep optical frequency of an OFDR laser source is directly obtained by analysis of the interference signal from an auxiliary interferometer with a Hilbert transformation. Beating OFDR data from a main interferometer are regenerated with respect to the measured instantaneous optical frequency. We show that this technique dramatically improves the spatial resolution of a conventional OFDR and can be applied to an optical frequency-domain medical imaging system to eliminate the problem of a nonlinear frequency sweep effect.     

Synthesis of fiber Bragg grating parameters from experimental reflectivity: a simplex approach and its application to the determination of temperature-dependent properties

A simple, accurate, and fast method to synthesize the physical parameters of a fiber Bragg grating numerically from its reflectivity is proposed and demonstrated. Our program uses the transfer matrix method and is based on a Nelder-Mead simplex optimization algorithm. It can be applied to both uniform and nonuniform (apodized and chirped) fiber Bragg gratings. The method is then used to synthesize a uniform Bragg grating from its reflectivity taken at different temperatures. It gives a good estimate of the thermal expansion coefficient and the thermo-optic coefficient of the fiber.     

Rapid characterization of the ultraviolet induced fiber Bragg grating complex coupling coefficient as a function of irradiance and exposure time

We report the application of optical frequency domain reflectometry and a discrete-layer-peeling inverse scattering algorithm to the spatial characterization of the UV induced complex coupling coefficient during fiber Bragg grating growth. The fiber grating is rapidly characterized using this technique to give irradiance dependent growth as a function of exposure time, thereby providing the complete characterization of the coupling coefficient in the form of a "growth surface," which is related to the fiber's photosensitivity. We compare measurements of fiber Bragg grating growth in SMF-28 when exposed to continuous wave 244 nm irradiation from 0 to 90 W cm(-2) for exposure times up to 3230 s with a selection of other fibers including high germanium concentration fiber and erbium doped fiber.     

Influence of grating parameters on the linewidths of external-cavity diode lasers

We investigate experimentally the influence of the grating reflectivity, grating resolution, and diode facet antireflection (AR) coating on the intrinsic linewidth of an external-cavity diode laser built with a diffraction grating in a Littrow configuration. Grating lasers at 399, 780, and 852 nm are determined to have typical linewidths between 250 and 600 kHz from measurements of their frequency noise power spectral densities. The linewidths are little affected by the presence of an AR coating on the diode facet but narrow as the grating reflectivity and grating resolution are increased, with the resolution exerting a greater effect. We also use frequency noise measurements to characterize a laser mount with improved mechanical stability.     

Experimental reconstruction of a highly reflecting fiber Bragg grating by using spectral regularization and inverse scattering

We demonstrate experimentally, for the first time to our knowledge, a reconstruction of a highly reflecting fiber Bragg grating from its complex reflection spectrum by using a regularization algorithm. The regularization method is based on correcting the measured reflection spectrum at the Bragg zone frequencies and enables the reconstruction of the grating profile using the integral-layer-peeling algorithm. A grating with an approximately uniform profile and with a maximum reflectivity of 99.98% was accurately reconstructed by measuring only its complex reflection spectrum.     

Analysis of a dephased complex-coupled distributed-feedback laser by the power-series method

A novel power-series method to solve the coupled-wave equations is introduced. The method is used to calculate the threshold gain margins of a complex-coupled distributed-feedback laser as functions of the ratio of gain coupling to index coupling (|kappa(g)|/|kappa(n)|) and of the phase difference between the index and the gain gratings. For coupling coefficient |kappa|l < ., the laser shows a mode degeneracy at specific values of the ratio |kappa(g)|/|kappa(n)| for cleaved facets. At phase differences pi/2 and 3pi/2 between the gain and the index gratings, an antireflection-coated complex-coupled laser becomes multimode, and a different mode starts to lase. The effect of facet reflectivity (both magnitude and phase) on the gain margin of a complex-coupled DFB laser is also investigated. Although the gain margin varies slowly with the magnitude of the facet's reflectivity, it shows large variations as a function of the phase. Spatial hole burning was found to be minimum at phase difference npi, n =, ..., and maximum at phase differences pi/2 and 3pi/2.     

Reconstruction of fiber grating refractive-index profiles from complex bragg reflection spectra

Reconstruction of the refractive-index profiles of fiber gratings from their complex Bragg reflection spectra is experimentally demonstrated. The amplitude and phase of the complex reflection spectrum were measured with a balanced Michelson interferometer. By integrating the coupled-mode equations, we built the relationship between the complex coupling coefficient and the complex reflection spectrum as an iterative algorithm for reconstructing the index profile. This method is expected to be useful for reconstructing the index profiles of fiber gratings with any apodization, chirp, or dc structures. An apodized chirped grating and a uniform grating with a depression of index modulation were used to demonstrate the technique.     

Single-element imaging spectrograph

A spectrograph concept designed for both high wavelength and high spatial resolution (in one dimension) is briefly described. This design is referred to as a single-element imaging spectrograph (SEIS). It is a one-bounce diffractive system that combines the spectral properties of a Rowland mount spectrograph with the imaging (spatial resolution) properties of a Wadsworth mount spectrograph through the use of a toroidal diffraction grating. No primary optics are necessary, making the system especially attractive for use in the extreme and far ultraviolet, where low reflectivity of common optical coatings can severely limit instrument sensitivity.     

Improved reflectivity and velocity model for aluminum gratings on YZ LiNbO3

Lithium niobate has recently been used for SAW tags and temperature sensors because of its high coupling coefficient and high reflectivity. To increase the device operating frequency for a given electrode line resolution, harmonic operation of the reflector is a very attractive option. When used in conjunction with harmonically operated transducers, the device operating frequency can be increased for a given photolithographic line width resolution. To design and accurately predict the behavior of these devices, it is necessary to model the electrode reflectivity and velocity for both fundamental and second-harmonic operation. The coupling of modes (COM) model has been used to model these devices, however the COM model uses empirically determined coefficients to model reflectivity. In this paper, the reflectivity and velocity of aluminum electrodes is extracted experimentally for fundamental and second-harmonic operation versus metalization ratios ranging from 0.2 to 0.9 and versus normalized metal thickness ranging from 0.4% to 4%. A least-squares fit is then performed on the data using physical terms in the transmission line model to yield equations that can be used in the COM model to predict device behavior over varying metallization ratios and normalized metal thicknesses. Orthogonal frequency-coded (OFC) SAW tags were designed and fabricated and experimentally obtained data are compared with the COM modeled responses for the tags at fundamental and second-harmonic operation to verify the predictions.     

Solid-immersion imaging interferometric nanoscopy to the limits of available frequency space

Imaging interferometric nanoscopy (IIN) is a synthetic aperture approach offering the potential of optical resolution to the linear-system limit of optics (~λ/4n). The immersion advantages of IIN can be realized if the object is in close proximity to a solid-immersion medium with illumination and collection through the substrate and coupling this radiation to air by a grating on the medium surface opposite the object. The spatial resolution as a function of the medium thickness and refractive index as well as the field-of-view of the objective optical system is derived and applied to simulations.     

Examination of the +1, −1 Surface Plasmon Mini-gap on a Gold Grating

Abstract

An energy gap in the excitation of surface plasmons is found for light at normal incidence to a gold grating. This gap occurs at the crossing of the plus and minus first order surface plasmons. It arises directly as a consequence of distortion of the grating from sinusoidality, the first harmonic of the grating providing coupling between the plus and minus one orders. Experiments have been performed using both wavelength scans, where at a fixed angle of incidence the wavelength of excitation is varied, and angle of incidence scans, where for a fixed wavelength the angle of incidence is varied a few degrees either side of normal to the grating. By fitting the angular dependent reflectivity scans using grating modelling theory the gold grating is characterized at all wavelengths. This then allows a detailed comparison of the theoretical dispersion curve with that obtained experimentally. The agreement for both p-polarized light (for angle dependence with the plane of incidence normal to the grating grooves) and for s-polarized light (angle dependence with the plane of incidence perpendicular to the grating grooves) is excellent. An apparent momentum gap in the lower energy branch of the dispersion curve, attributed to the loss of coupling strength, is found to move to the upper branch if the grating profile is inverted.     

Interdigitated electrode-induced phase grating with an electrically switchable and tunable period

A new design for an adjustable electro-optic phase grating inside a waveguide is proposed. The electric field and the refractive-index distribution induced inside a waveguide by voltage applied to double-sided periodic interdigitated electrode arrays are calculated rigorously on the basis of an original analytical technique. The modeling was carried out with the Mathcad software. It is shown that the fundamental periodicity of the induced grating inside the waveguide can be switched between l and 2l by application of the appropriate voltage, where l is the spatial periodicity of the interdigitated electrodes. One can also fine tune the peak grating reflectivity by changing the constant component of the induced refractive index with the help of the constant component of the electric field inside the waveguide. The suggested design can be used as a basic idea for a variety of optical communication networking applications, including switching, modulation, deflection, and data processing.     

High-resolution frequency-domain reflectometry by estimation ofmodulated superimposed complex sinusoids

By assuming a parametric model for a linear one-port or two-port, the time-domain resolution of a vector network analyzer can be significantly improved with respect to the Rayleigh limit. The measurement problem is formulated as a nonlinear least squares parameter estimation problem involving the extremization of a cost function. An extremization algorithm with good global convergence properties is presented for the case of discontinuities of small reflectivity modeled as simple lumped frequency-dependent elements. The reflection coefficient at either port of the device under test is modeled as a superposition of modulated complex sinusoids. Through optimization of a sequence of cost functions, the algorithm produces a sequence of fits for models that incorporate an increasing number of discontinuities     

Cost-effective and high-resolution wavelength interrogation unit using an incomplete asymmetric arrayed waveguide grating

This paper presents a wavelength interrogation unit using an incomplete asymmetric arrayed waveguide grating (AWG) without output waveguides. The incomplete asymmetric AWG converts the wavelengths of the incident light into a spatial intensity distribution. The center of the spatial distribution is determined by a one-dimensional position sensitive detector (PSD). The simulation results show that wavelength shifts can be precisely interrogated by the device with a wavelength resolution of 3.5 pm. The device can be applied to the interrogation of fiber Bragg grating (FBG) temperature sensors with the temperature resolution of 0.3°C.     

Inverse scattering algorithm for reconstructing lossy fiber Bragg gratings

We demonstrate an inverse scattering algorithm for reconstructing the structure of lossy fiber Bragg gratings. The algorithm enables us to extract the profiles of the refractive index and the loss coefficient along the grating from the grating transmission spectrum and from the reflection spectra, measured from both sides of the grating. Such an algorithm can be used to develop novel distributed evanescent-wave fiber Bragg sensors that measure the change in both the refractive index and the attenuation coefficient of the medium surrounding the grating. The algorithm can also be used to analyze and to design fiber Bragg gratings written in fiber amplifiers. A novel method to overcome instability problems in extracting the parameters of the lossy grating is introduced. The new method also makes it possible to reduce the spectral resolution needed to accurately extract the grating parameters.     

Characteristics of grating-assisted couplers.

Characteristics of grating-assisted coupling between two parallel waveguides are analyzed. The influence of the grating parameters, such as groove depth, duty cycle, and refractive indices is considered. Chirped and parallel gratings as well as gratings with sinusoidal envelope periodicity are also addressed. The analysis is based on a unified coupled-mode formalism, with the transfer-matrix method as a general solution technique. It is shown how to modify the grating parameters to provide a specific spectral response (reflectivity and transmission coefficients). As an example, two parallel gratings are used to obtain a similar response to a single grating of double length. The location of the grating between the two waveguides as well as the light-wave injection direction are very important. The presented methods and effects may be useful for design and analysis in the fields of optical communications, sensing, and processing.     

Quantitative determination of higher harmonic content in the soft x-ray spectra of toroidal grating monochromator using a reflection multilayer

Use of a grating monochromator causes a problem of higher harmonic contaminations in a synchrotron beamline operating in the soft x ray/vacuum ultraviolet region. Generally gratings are used to experimentally determine the higher harmonic contaminations. In this method, the relative contribution of contaminant wavelengths is measured with respect to the first harmonic wavelength (desired wavelength). The quantitative fit of grating spectra is rather complex, and therefore qualitative analysis is carried out. Analysis of multilayer reflectivity data has become rather simple with recent advances in the theoretical modeling. Therefore we propose to use a multilayer mirror and analyze its reflectivity data for quantitative determination of harmonic contamination in a soft x ray beamline. In the present study we used a Mo/Si multilayer of d=97 ? to quantify the spectral purity of 600 lines/mm toroidal grating at the reflectivity beamline of Indus-1 450 MeV synchrotron source. The measured reflectivity spectra at each wavelength is analyzed and the actual contribution of higher harmonics in the incident beam is obtained. Details of methodology and results are discussed.     

Design of a high-efficiency volume grating coupler for line focusing

A volume grating for outcoupling and line focusing of waveguided infrared light is designed and optimized. A local grating vector approach is used in combination with the rigorous coupled-wave analysis. By design, this volume grating coupler is holographically constructed on top of a waveguide by the interference of two coherent 364-nm ultraviolet waves formed with two aberration-optimized cylindrical lenses. This focusing coupler exhibits preferential-order coupling (92.9%) into the cover as well as very low focal intensity side lobes. This is accomplished through a chirped, slanted-fringe volume grating with a designed spatial variation in the attenuation coefficient (describing the outcoupling of the guided mode) along the length of the grating. This is achieved by a specific variation in the grating slant angle along the grating length. By design, the 1000-mum-length coupler focuses an 850-nm infrared guided wave to a line with an intensity FWHM of 3.32 mum and a 90% power width of 5.53 mum at a focal distance of 4 mm directly above the grating. Its performance is compared with that of a corresponding electron-beam-written surface-relief coupler design.     

Reconstruction of gratings from noisy reflection data

The worst-case error amplification factor in reconstructing a grating from its complex reflection spectrum is shown to be of the order 1/T(min), where T(min) is the minimum transmissivity through the grating. For a uniform grating with coupling coefficient-length product kappaL, the error amplification is exp(2kappaL). The exponential dependence on the grating strength shows that spatial characterization of gratings from a measured reflection spectrum is impossible if the grating is sufficiently strong. For moderately strong gratings, a simple regularization technique is proposed to stabilize the solution of the inverse-scattering problem of computing the grating structure from the reflection spectrum.