Symmetric Gratings Research Articles

Plasmon-polariton band structures of asymmetric T-shaped plasmonic gratings

It is shown that asymmetric T-shaped plasmonic gratings can display plasmon-polariton band structures with wide range of band gaps and tunable group velocities. A structure gap is introduced in the post of Tshaped plasmonic gratings and it is found that the size of this gap plays an important role in controlling the plasmon-polariton band gap and group velocities. We obtained variation of energy band gap ranging from 0.4 eV to 0.0323 eV by changing the size of the structure gap from 0 to 250 nm. The plasmon-polariton band structures were obtained by using Rigorous Coupled Wave Analysis. We studied the difference between symmetric and asymmetric T-shaped gratings and found that the symmetric structure has a momentum gap in the photonic band structure, which can be avoided in the asymmetric structure. Furthermore, by varying the post and spacer (made of SiO2) thicknesses we can tune the energy band gap from 0.1 eV to 0.148 eV and from 0.183 eV to 0.19 eV, respectively. In this device, we obtain tunable group velocities ranging from one to several orders of magnitude smaller than the speed of light in the vacuum. This asymmetric T-shaped plasmonic grating is expected to have applications in surface plasmon polariton (SPP) based optical devices, such as filters, waveguides, splitters and lasers, especially for applications requiring large photonic band gap.

High-Q terahertz Bragg resonances within a metal parallel plate waveguide

One-dimensional (1D) Bragg waveguides are demonstrated at terahertz (THz) frequencies. Lithographically made 1D symmetric and asymmetric dielectric gratings on metallized high conductivity Si chips are incorporated within metal parallel plate waveguides to form Bragg waveguides. These waveguides have high throughput and have Bragg resonances with linewidths approaching 6 GHz and Q as high as 430. These high-Q resonant Bragg waveguides are excellent structures for applications in THz sensing.

Surface plasmon resonance transmission filters at 1053 nm based on metallic grating with narrow slit

Metallic gratings with narrow slits can lead to special optical properties such as strongly enhancing the transmission and considerably strengthening the polarized effect. A narrow-band filter suitable for application in optical communication is designed by sandwiching a metallic grating between two identical dielectric films. The maximum transmission can reach 96% after optimizing the parameters of films and grating at a central wavelength of 1053 nm. It is the first time, to our knowledge, that such high transmission has been reported since the discovery of the extraordinarily high transmission through periodic holes or slits; moreover, the extremely polarized effect is also found in P mode of this symmetric grating.

Azimuthally symmetric long-period fibre grating fabrication with a TEM01∗-mode CO2 laser

We present a fabrication method that produces azimuthally symmetric long-period fibre gratings using a carbon dioxide laser operating in the TEM01∗-mode. The outlay and optimization of the optical system are introduced, and the long-period fibre grating fabrication method is outlined. A uniform long-period grating written in a boron-doped fibre exhibited a maximum transmission loss of 10.83 dB at 1538.5 nm. The peak transmission loss of a non-uniform long-period grating also written in the boron-doped fibre yielded a value of 10.25 dB at 1552.6 nm. The polarization properties of the fabricated long-period fibre gratings were investigated to determine the quality of the grating structures. The uniform long-period grating structure exhibited a maximum polarization-dependent loss of 0.97 dB at 1542.1 nm, and the non-uniform long-period grating yielded a maximum polarization-dependent loss of 2.48 dB at 1551.4 nm.

Inverse symmetric Dammann gratings

Inverse symmetric Dammann grating is a special grating, whose transition points are reflection symmetric about the midpoint with inverse phase offset in one period. It can produce even-numbered or odd-numbered array illumination when the phase modulations are π or a specific value. Numerical solutions optimized by the steepest-descent algorithm for binary phase and multilevel phases with splitting ratio from 1×4 to 1×14 are given. Fabrication of 1×6 array without the zero-order intensity and 1×7 array with the zero-order intensity are made from the same amplitude mask. A 6×6 output without the crossed zero-orders was achieved by crossing two one-dimensional 1×6 inverse symmetric Dammann gratings. This grating may have potential value for practical applications.

Efficient design of spatially symmetric Bragg gratings for add/drop multiplexers

A simple and fast numerical procedure is presented for designing spatially symmetric Bragg gratings with no need for iteratively solving the coupled mode equations. Using a unique relation between the phase and the amplitude of the reflection spectra valid for spatially symmetric gratings, the grating spectra are suitably optimized to fit given specifications. At the end of the design process an inverse-scattering algorithm determines the spatial structure of the corresponding Bragg grating. This method is particularly useful for the design of add/drop multiplexers, where symmetry can be a crucial prerequisite.

Energy redistribution and polarization transformation in conical mount diffraction under resonance excitation of surface waves

This paper presents an analytical theory of resonance diffraction in the conical mount. The resonance is caused by plasmon polariton excitation via diffraction from a highly reflecting shallow grating of arbitrary profile. Single and double resonance configurations are considered in detail. The dependence of polarization, intensity, and phase of specular and resonance waves on the parameters of the problem is presented in explicit form and examined for arbitrary polarization of the incident wave as a function of the angle of incidence and the grating period, orientation, form, and height. The results obtained enable us to indicate gratings with specific properties, for instance, gratings, ensuring transformation of arbitrarily polarized incident wave into the linearly polarized specular wave. Properties of two-dimensional transformation matrix relating polarization amplitudes of incident and specular reflected waves are analyzed. It is shown that the transformation matrix is antisymmetric even for asymmetric gratings (for symmetric gratings, this property is exact one, and it follows from the reciprocity theorem) for an arbitrary grating profile. The comparison of the results obtained shows the remarkable agreement with the data of the polarization conversion experiments. Both concrete results and the approach presented may be of use in constructing gratings with unique parameters and, therefore, in solving problems of designing optical devices, which are selective with respect to the polarization, wavelength, and orientation.

Fabrication of Axially Symmetric Long-Period Gratings With a Carbon Dioxide Laser

We demonstrate a simple but effective method of creating an axially symmetric refractive index change in an optical fiber using the infrared beam from a carbon dioxide laser. Symmetric exposure of the fiber is achieved by using a single incident laser beam and placing a special reflector behind the fiber. Long-period gratings produced with this method exhibit clean spectra and very low insertion loss (<0.1 dB), similar to those induced by ultraviolet light

Phase constraint for the waves diffracted by lossless symmetrical gratings at Littrow mount

The energy conservation of grating diffraction is analyzed in a particular condition of incidence in which two incident waves reach a symmetrical grating from the two sides of the grating normal at the first-order Littrow mounting. In such a situation the incident waves generate an interference pattern with the same period as the grating. Thus in each direction of diffraction, interference occurs between two consecutive diffractive orders of the symmetrical incident waves. By applying only energy conservation and the geometrical symmetry of the grating profile to this problem it is possible to establish a general constraint for the phases and amplitudes of the diffracted orders of the same incident wave. Experimental and theoretical results are presented confirming the obtained relations.

Optimization technique for simple reconstruction of the index modulation profile of symmetric fiber Bragg gratings from their reflective spectrum

We propose a new and simple method to reconstruct the refractive-index modulation of a symmetric fiber Bragg grating (FBG) from its magnitude reflection spectrum (i.e., phase information is not required). The reconstruction method uses an FBG model based on some known parameters of the fabricated FBG (grating length, number of subgratings, and grating period) and an optimization technique, namely, the Quasi-Newton method, to find the local parameter values of the FBG. To our knowledge, this is the first time that the reconstruction of FBG is experimentally realized by an optimization technique. Compared with other reconstruction methods, the proposed method is so simple that it requires only the reflection spectrum of the fabricated FBG.

Propagation properties of planar Bragg waveguides studied by an analytical Bloch-mode method

We use an analytic Bloch-mode approach to investigate one-dimensional planar Bragg waveguides (PBWGs) with an air- or a glass-core layer sandwiched within two symmetric Bragg gratings formed by alternate arrays of air and glass layers. The calculation results show that there exist simultaneously two kinds of guided modes as the gap-guided modes resulting from the photonic band-gap effect and the index-guided modes formed by the total internal reflection effect. We calculate the electromagnetic (EM)-field distributions of these guided modes with different parallel wave vectors and find remarkably different EM-field profiles between the index-guided modes and the gap-guided modes. In order to explore the propagation properties of the PBWGs, we analyze the group velocity and the group-velocity dispersion of different types of guided modes. The results show that the guided mode properties are significantly influenced by the core material as well as the cladding structure. The analytic Bloch-mode approach can help to investigate and design the PBWGs in a simple, efficient, and accurate manner.

Reflective Display Configurations Based on Total Internal Reflection and Grating-Grating Coupling of Holographic Polymer Dispersed Liquid Crystals (H-PDLC)

ABSTRACT We report on a novel electro-optical reflective configuration based on total internal reflection and grating-grating coupling fabricated in Holographic Polymer Dispersed Liquid Crystals (H-PDLC) materials. In this device, two symmetric slanted gratings are temporally multiplexed into a single film. A narrowband light is selected and diffracted from two coupled Bragg gratings creating a reflected image. These reflective configurations have switching voltages that are at least one-half that of H-PDLC reflective displays reported in the literature, and therefore have potential as low power, reflective display devices.

N-fold symmetric gratings as gain-flattening filters

We present N-fold symmetric gratings as gain-flattening filters, since they are polarization insensitive and capable of exhibiting low back reflection. These gratings consist of N superimposed identical tilted gratings which are evenly distributed azimuthally. The coupling interactions between the forward propagating core mode and the backward propagating cladding modes are analyzed, including the limit when N/spl rarr//spl infin/ which is a rotationally symmetric grating. The fiber grating parameters are optimized to equalize the gain profile of a typical erbium doped fiber amplifier to within 0.07 dB. Finally, we examine how the performance of the gain-flattening filter depends on the blaze angle and the effect of an uneven azimuthal distribution of the grating.

Control of spontaneous emission by complex nanostructures.

Spontaneous emission in the presence of complex nanostructures is discussed by use of a calculational scheme that permits us to deal with interfaces of arbitrary shape. Control over the field associated with the emission is shown to be attainable. In particular, decay rates are offered for geometries that lead to focusing and collimation of near- and far-field distributions. Emission from axially symmetric gratings is shown to lead to narrow angular distributions of emission, and focusing at the foci of dielectric ellipsoids is achieved for dimensions comparable with the wavelength. In the latter case the total emission rate for two atoms in an ellipsoidal cavity is shown to be enhanced in a way that deviates from the predictions of the Dicke effect by means of intermediate- and far-field contributions.

Hankel transform-domain analysis of scattered fields in multilayer planar waveguides and lasers with circular gratings

Radiation patterns of scattered fields with arbitrary azimuthal orders in multilayer planar waveguides and laser cavities with circularly symmetric gratings are formulated based on the volume current method. Full-wave Green's function analysis based on the integral transform method lies at the heart of this approach. Unlike the conventional approach, the dyadic Green's function relates some auxiliary fields to some auxiliary sources in the spectral domain. These auxiliary functions are defined to facilitate the spectral domain formulation in the cylindrical coordinate system and the use of transfer matrix method for obtaining a closed-form solution of the spectral Green's function in multilayer planar structures. More importantly, it is shown that the far-field pattern of the scattered field can be expressed directly in terms of the auxiliary fields in the Hankel transform domain.

Ultralow threshold and single-mode lasing in microgear lasers and its fusion with quasi-periodic photonic crystals

The GaInAsP microgear laser is a kind of microdisk laser but has a rotationally symmetric grating, which matches with the profile of the whispering gallery mode. In this study, we achieved the room temperature continuous-wave lasing with a threshold photopump power of 14 /spl mu/W for the smallest gear diameter of 2.02 /spl mu/m. We also observed the single-mode lasing in a deep grating device, where the /spl pi/-phase-shifted nonlasing mode completely disappeared. The experimental results were well explained by a three-dimensional finite-difference time-domain calculation and a consideration on the surface recombination. In addition, to increase the variety of the microgear, we proposed its fusion with a quasi-periodic photonic crystal (QPC), which also has a rotational symmetry. We theoretically estimated a sufficiently high Q of 21 600 for a QPC gear with a point defect of 1.6-/spl mu/m diameter, which is the smallest limit for a normal microdisk at a wavelength of 1.5-1.6 /spl mu/m.

P‐111: Reflective Display Based on Total Internal Reflection and Grating‐Grating Coupling

AbstractWe report on a novel reflection‐type display based on total internal reflection and grating‐grating coupling fabricated in H‐PDLC materials. In this display, two symmetric slanted gratings are temporally multiplexed into a single film. A narrowband light is selected and diffracted from two coupled Bragg gratings creating a reflected image. These holographic pixels have switching voltages that are at least one‐half that of H‐PDLC reflective displays reported in the literature.

Equivalent circuit of Bragg gratings and its application to Fabry-Pérot cavities.

An equivalent circuit of both uniform and apodized symmetrical Bragg gratings is proposed, consisting of an ideal partially reflecting mirror placed between two wavelength-dependent uniform propagating sections. The model is simple, exact, and valid for every wavelength; it can be combined with other port-based models and is of great aid in the analysis and design of devices containing two or more Bragg gratings. As an application, the synthesis of dispersive Bragg gratings based Fabry-Pérot cavities is demonstrated. The conditions under which a Bragg-grating-based Fabry-Pérot cavity behaves exactly as an ideal dispersive Fabry-Pérot cavity are discussed. Experimental results that confirm the theoretical spectral response calculated by using the equivalent circuit are reported.

Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework

In this work, a computationally fast, numerically stable, and memory-efficient cascading and doubling algorithm is proposed within the method of lines framework to model long planar waveguide gratings having thousands of periods in the propagation direction. This algorithm can model 2/sup n/ grating periods in n calculational steps and needs N/sup 2/ matrices for N sample points in the problem space. It can model periodic, quasi-periodic, symmetric, and asymmetric gratings efficiently. Different deep waveguide gratings are modeled using this scheme and results for the fundamental TE mode spectral reflectivity are compared with published results showing excellent agreement.

Design of flat-top bandpass filters based on symmetric multiple phase-shifted long-period fiber gratings

We analyze the transmission response of symmetric multiple phase-shifted long-period fiber gratings (LPGs). In particular, we present the optimal design parameters for two and three phase-shifted LPGs having a flat-top passband response. Similarities and differences between symmetric multiple phase-shifted LPGs and fiber Bragg gratings (FBGs) are highlighted.