Optical microscopy of quasi-periodic structures induced upon excitation of waveguide TE and TM modes under irradiation of AgCl-Ag films by a laser beam

This paper reports on the results of analyzing the conditions under which quasi-periodic structures induced in AgCl-Ag photosensitive films by a linearly polarized Gaussian laser beam (λ=633 nm) can be clearly observed with the use of an optical microscope. It is shown that quasi-periodic structures with vectors K ∥ E (where E is the vector of polarization of the inducing beam) and periods d > λ are effectively formed upon excitation of waveguide TM₀ modes at a large angle of incidence (φ=70°) and the p polarization of the inducing beam. Exposure of the film on a 60° glass prism to a p-polarized beam incident on the sample at an angle φ=60° from the side of the glass leads to the effective formation of primary gratings with vectors K⊥E (due to the excitation of waveguide TM₀ modes) and secondary oblique gratings. The specific features of the quasi-periodic structures and the correlation between the primary and secondary gratings are revealed and analyzed.     

Influence of two-dimensional bragg diffraction on the competition of the waveguide TE<Subscript>0</Subscript> and TM<Subscript>0</Subscript> modes during formation of spontaneous gratings in AgCl-Ag thin films

An intricate space-time instability of patterns of small-angle scattering and diffraction of a laser beam on the structures appearing in AgCl-Ag films under exposure to the same beam is investigated. The instability is related to the formation of spontaneous gratings in the film resulting from the interference of the incident beam with the waveguide modes scattered in the film. The existence of a two-dimensional Bragg diffraction on the TE₀ and TM₀ modes with subsequent formation of secondary spontaneous gratings is revealed and is theoretically substantiated. It is established that the difference in the indicatrices of the radiation scattered into the TE₀ and TM₀ modes for the s-and p-polarizations manifests itself in different kinds of diffraction and small-angle scattering patterns at the output of illuminated samples.     

Spatial-temporal instability and optical turbulence upon the formation of spontaneous gratings by S-polarized light in waveguide AgCl-Ag films

The spatial-temporal instability of the spontaneous gratings formed in waveguide AgCl-Ag films under irradiation with an S-polarized laser beam is investigated. The studies are based on the simultaneous observation of diffraction (D) patterns formed by the S _? gratings and small-angle scattering (SAS). The transverse instability of D and SAS patterns was found to be associated with excitation of TE₀ modes at different angles with respect to the plane of incidence by scattering centers of Rayleigh type with the following formation of microgratings by the scattered modes and with their competition. It is shown that the time evolution of the form and the dynamic shift of the D patterns is also connected with the time dependence of the effective refractive index for TE₀ modes. In the case when a focused laser beam was used, the optical turbulence was found in the SAS and D patterns, caused, mainly, by the competition of S _?-and S ₊-microgratings, which eventually leads to the destruction of the latter.     

Small-angle scattering during formation of periodic structures in light-sensitive films subjected to laser radiation

Patterns of small-angle scattering that appear in thin AgCl films containing granular silver upon the formation of spontaneous periodic structures by p-polarized and circularly polarized laser beams (He-Ne laser, P=8 mW, λ = 632.8 nm) are studied. It is found that, at angles of incidence exceeding 4° regardless of the type of polarization, the diffraction of the waveguide modes excited by the dominant C gratings from neighboring microgratings with the vectors K ≠ K c dominantly contributes to the small-angle scattering. In the case of circularly polarized light, the pattern of small-angle scattering becomes more complicated as a result of the formation of S _? gratings and related secondary regular gratings.     

Nonpolarizing and tunable perpendicular dual-grating guided-mode resonance filter

A perpendicular dual-grating (PDG) guided-mode resonance filter was constructed by placing two identical waveguide gratings close to and their grooves perpendicular to each other. Multilayer waveguide theory was used to estimate the resonant wavelength for the TE and TM polarization incidences, and the rigorous coupled wave analysis (RCWA) was used to investigate the resonant wavelength, the lineshape and linewidth of the resonant peaks for arbitrary polarization incidences. The filter presents identical spectral characteristics for normally incident wave with arbitrary polarization. The separation of the resonant reflection peaks corresponding to the TE₀ and TM₀ split modes were realized by properly selecting the geometrical and material parameters of the grating layers and the waveguide layers. Measurement of the nano air gap between 0 and 0.4 p by determining one of the two resonant reflection peaks of the TE₀/TM₀ split modes was achieved without being interfered by the TM₀/TE₀ split modes.     

A nonlinear dynamic effect of formation of photo-induced periodic structures in waveguiding As<Subscript>2</Subscript>S<Subscript>3</Subscript>-Ag thin films

A nonlinear effect of spatiotemporal transformations of a focused linearly polarized Gaussian beam of a He-Ne laser obliquely incident (S and P polarizations) upon an As₂S₃-Ag film containing a small amount of chlorine and deposited onto a glass substrate is found and interpreted. The effect consists in the appearance, in the process of exposure, of beams diffracted and anisotropically scattered by periodic structures arising due to excitation of the waveguide TE₀ and TM₀ modes in the film. The diffraction measurements of the effective refractive indices for the TE₀ and TM₀ modes make it possible to calculate the refractive index and the thickness of the film from dispersion equations. Along with slow evolution of the diffraction and scattering patterns, we have found a persistent optical turbulence in the fringes of scattering from the structures related to excitation of the TE₀ modes. It is suggested that the turbulence is an indication of existence of reversible processes in the mechanism of photosensitivity.     

Peculiarities of spontaneous grating generation in light-sensitive waveguide layers during holographic grating formation

The generation of spontaneous (noise) gratings during the simultaneous formation of a holographic grating in thin (on the order of the cutoff thickness of the TE₀ waveguide mode) AgCl-Ag films by two laser beams with λ = 532 nm and polarization vectors that make an angle of 45° with the plane of incidence have been studied. The electron microscopy images and diffraction patterns have revealed a significant difference of the spontaneous-grating structure from the structure obtained under irradiation by one laser beam. The spontaneous gratings have a significant spread in the directions of their wave vector, and the diffraction pattern (recorded using a probe beam with λ = 337 nm) has the form of a bundle of diverging arcs that intersect at one point. This difference is caused by self-diffraction from the holographic grating, which is responsible for the main diffraction peaks with odd orders, the growth of spontaneous gratings because of the interference of the beams diffracted by the holographic grating with the waveguide TE₀ modes scattered in the film, and silver transport to the interference minima. The diffraction patterns are quantitatively analyzed and the period of the new (formed under two-beam irradiation) spontaneous gratings is calculated. The calculation results are in good agreement with the experimental data.     

On‐chip silicon 8‐channel hybrid (de)multiplexer enabling simultaneous mode‐ and polarization‐division‐multiplexing

An 8‐channel hybrid (de)multiplexer to simultaneously achieve mode‐ and polarization‐division‐(de)multiplexing is proposed and demonstrated experimentally on a silicon‐on‐insulator platform to improve the link capacity of an on‐chip optical interconnect. The present hybrid (de)multiplexer has four channels for each polarization. A polarization beam splitter based on a three‐waveguide coupler is used to combine/separate the fundamental modes of TE‐ and TM‐polarizations (TE₀ and TM₀). Six asymmetric directional couplers are cascaded for (de)multiplexing the high‐order modes (TE₁, TE₂, TE₃, TM₁, TM₂, and TM₃). The experimental results show all eight channels have low loss and low crosstalk (<−10 dB) over a ∼ 30 nm wavelength range.     

A partially reflecting metal cladding: its effect on the modes of dielectric optical waveguides

If the metal cladding of a dielectric optical waveguide is sufficiently thin to be only partially reflecting, then the waveguide modes differ from those of the conventional metal-clad waveguide. The TE modes are little affected by a variation in the metal thickness but the TM modes change considerably due to a coupling between the waveguide modes and the surface plasma waves supported by both the metal: dielectric interfaces and the metal film. It is the refractive index of the dielectric cladding which is remote from the guiding core that determines whether the lowest order TM mode is the TM₀ or TM₁ mode. This dielectric cladding also strongly influences the attenuation of the TM modes and, if the guide supports a TM₀ mode, then the attenuation of the TM modes far from cut-off are an order of magnitude higher than that of the corresponding modes when the guide cannot support a TM₀ mode. If the guide can support a TM₀ mode then its dimensions can be chosen such that it will support the TE_N and TM_N modes with equal phase velocities. A lossless approximation is used to develop an expression which will specify the required guide dimensions directly and parametric plots of these dimensions are discussed.     

Minimization of losses and calculation of the optical properties of Bragg fiber waveguides with a hollow core

A numerical method for solving the inverse problem of determining the geometry of the multilayer shell of a Bragg waveguide that has the lowest waveguide losses for a given mode has been developed with the use of the genetic algorithm. For the calculated designs of waveguides, the distribution of the coordinates of the boundaries of shell layers has been found to be aperiodic under the condition r ₁ ≤ λ due to the axial symmetry of the problem. Waveguide losses for the TE ₀₁, TM ₀₁, and HE ₁₁ modes satisfy the conditions \(\alpha _{TM_{01} } > \alpha _{HE_{11} } > \alpha _{TE_{01} } \). It follows from the dependence of n _eff obtained for these modes on the core radius and number of shell layers that any change in the structure of the waveguide leads to the violation of the optimal propagation regime for these modes. A Bragg fiber waveguide with a hollow core that is designed for the TE ₀₁ mode and directs light in the single-mode regime is presented. The main fraction of losses in this waveguide is attributed to material absorption.     

Dual-core leaky optical waveguide as an integrated-optic polarizer

We present a design of a dual-core leaky waveguide that can be used as an integrated-optic polarizer. The proposed polarizer works on the principle of mode filtering. The structure is characterized by two cores, namely core-1 and core-2 and a high index layer in the upper-most region, such a structure supports leaky modes. The leakage losses of the modes have been calculated by using the transfer matrix method (TMM). Single polarization operation is ensured by high differential leakage loss between fundamental TE and TM modes. We show TE-pass operation with 0.5 dB/mm loss in TE₀ mode and 13 dB/mm loss in TM₀ mode, and TM-pass operation with 0.36 dB/mm loss in TM₀ mode and 7.45 dB/mm loss in TE₀ mode. Besides single-polarization operation, single-mode operation of the structure is ensured by high leakage loss of all the other higher-order modes.     

Optical interconnection between different spatial modes using double phase conjugate mirror with polarization alignment system

We propose a fundamental interconnection method using a polarization alignment system for waveguides having different spatial modes. In addition, as an example for the verification of the fundamental operation, we demonstrate an interconnection between a photonic crystal fiber and a laser that have obviously different spatial modes. The polarization alignment system operates synergistically with a self-written waveguide formed with a double phaseconjugate mirror. This technique enables us to interconnect a photonic crystal fiber with a laser source without complicated and time-consuming optical alignment. In this method, although it is not necessary to perform an external control for interconnection, the waveguide most suitable for connection is formed autonomously in a Sn₂P₂S₆:Sb crystal developed for this purpose. There was a marked reduction in the polarization dependence of coupling efficiency, compared with that observed using a stand-alone double phase-conjugate mirror.     

TE and TM interactive waves in successive nonKerr nonlinear dielectric planar layer structures

The interactive TE and TM modes in the most general case of a multilayer nonlinear optical waveguide consisting of successive nonKerr nonlinear media are herewith presented. The structure we consider here consists of three successive nonlinear films in a linear environment. A discussion of the numerical results indicates that the existence of the inner nonlinear layer may cause significant perturbation in the interactive areas of the _TE – _TM plane as computed with simpler models.     

Analysis and design of grating couplers

Based on an accurate perturbation analysis of the guiding properties of dielectric gratings, simple design criteria are developed for grating couplers which transfer the energy of a beam into or out of an optical waveguide. Gratings having arbitrary groove shapes are considered and explicit formulae are given for the leakage parameters of gratings with symmetric profiles. The results cover TE_v and TM_v modes and they apply to both shallow and deep grating grooves. The variation of the leakage parameter α in rectangular gratings is examined in detail; these rectangular gratings are then used as basic configurations for predicting the characteristics of other grating profiles. Particular attention is given to trapezoidal and triangular profiles and gratings with asymmetric profiles are also discussed.     

Effect of light polarization on holographic recording in glassy azocompounds and chalcogenides

Light polarization effects on a holographic grating recording in a glassy chalcogenide a-As₄₀S₁₅Se₄₅ film has been experimentally studied and compared with previously studied glassy molecular azobenzene film 8a at 633, using s − s,p − p, CE-1 and CE-2 circular-elliptic recording-beam polarizations (differing by light electric field rotation directions). The azocompound exhibited much higher self-diffraction efficiency (SDE) and diffraction efficiency whereas chalcogenide was more sensitive. Their recording efficiency polarization dependences also were different. SDE up to 45% was achieved in 8a with p − p and up to 2.6% in a-As₄₀S₁₅Se₄₅ with CE-2 polarized recording beams. The polarization changes in the diffraction process were studied as well in these and other materials (11, 16, 19 and a-As₂S₃ film, LiTaO₃:Fe crystal). It was found that light polarization changes in the process of diffraction from gratings recorded vectorially by s−p polarizations depended on chemical composition, wavelength, and exposure time. Vector gratings with SDE up to 25% were recorded in 8a, rotating a linear polarization by 90°. No light polarization changes were found in azobenzene 19 and chalcogenide films and in LiTaO₃:Fe crystal, thus showing a vector recording of scalar holograms. The recording mechanisms in azocompounds and chalcogenides are discussed and compared.     

Sub-wavelength imaging of photo-induced refractive index pattern in chalcogenide glass films

Mapping of refractive index patterns with sub-wavelength resolution is achieved using Near-field Scanning Optical Microscopy (NSOM) in reflection mode. Imaging of index pattern is performed on surface gratings photo-imprinted in As₂S₃ films. The NSOM is adapted with a near infrared laser which wavelength (785 nm) is chosen to be within the transparency window of the glass film therefore allowing consistent measure of reflected light. Quantitative measurements of photo-induced index changes can then be obtained from knowledge of the initial film index. Images of gratings with a period of 0.5 micron are easily collected therefore demonstrating sub-wavelength spatial resolution. The technique permits to concurrently obtain a topographic image and index image of the gratings thereby permitting to quantify the extent of photodarkening and photoexpansion simultaneously. It is shown that relief gratings tend to vanish in films aged in air for several months however the index gratings remain.     

Field structure in a photorefractive holographic grating in a planar waveguide

A theoretical investigation is made of the field structure in a holographic grating formed by TE₀ modes in a planar photorefractive waveguide by the photogalvanic recording mechanism. Waveguides with three characteristic refractive index profiles are considered, namely, a step function, a parabola, and a hyperbolic secant squared. A comparison is made between the light field distributions of TE₀ modes in waveguides having the different profiles. The field structure of the space charge in planar holographic gratings is analyzed for their initial formation phase. It is shown that the space charge field has a similar structure for all three waveguide types considered when planar photorefractive gratings are recorded by TE₀ modes.Institute of Automated Control Systems and Radio Electronics, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 85–92, November, 1993.     

Spatial evolutions of inversionless gain and lasing field intensity in an open V-type system with SGC

This paper studies manly spatial evolution of gain without inversion (GWI) and the Rabi frequency E (intensity ?_p) of the probe field in an open V-type three-level inversionless lasing system with spontaneously generated coherence (SGC) for both cases with and without Doppler broadening. We found that: (1) Varying sizes of SGC strength (measured by angle θ), atomic exit rate (r₀) and ratio (S) of the atomic injection rates has remarkable effect on spatial evolutions of GWI and E (?_p). This effect in the case with Doppler broadening is similar to but weaker than that in the case without Doppler broadening. (2) Regardless of that Doppler broadening is present or not, GWI and E (?_p) increase with increase of θ, r₀ and S in certain value ranges of θ, r₀ and S; in the case with SGC we can obtain GWI and E (?_p) much larger than those in the case without SGC, while by choosing values of γ₀ and S, in the open system we can obtain LWI gain and E (?_p) much larger than those in the corresponding closed system. (3) The propagation distance in which GWI exists in the case with Doppler broadening is longer than that in the case without Doppler broadening; in the case without Doppler broadening, we can obtain larger GWI than that in the case with Doppler broadening; but in the case with Doppler broadening, we can obtain larger E (?_p) than that in the case without Doppler broadening.     

基于二维结构薄膜的偏振选择相位光栅的研究

利用二维结构薄膜构建了具有偏振选择特性的新型相位光栅,借助严格耦合波分析(RCWA)方法计算了光栅各级衍射强度随入射光波长及入射角的变化,发现在垂直入射情况下,波长600—640 nm范围内,相位光栅对横向电学(TE)模主要产生0级衍射,而对横向磁学(TM)模产生±1级衍射,在波长633nm处,0级衍射光的偏振消光比为109.8,±1级衍射光的偏振消光比为334.6.利用时域有限差分方法对这种相位光栅的偏振分束现象进行了模拟,偏振分离角在玻璃基板内可以达到10°左右,最后模拟了入射角为23°时光栅对不同偏     

Radiative plasmon polaritons in multilayer structures with a two-dimensional electron gas

Two-dimensional plasmon polaritons are analyzed for a typical experimental configuration in which a layer of two-dimensional electrons with a finite mobility lies on the top of a dielectric waveguide formed by the substrate (a wafer of finite thickness). Two-dimensional plasmons couple strongly to the radiative modes of this dielectric waveguide. It is shown that, as a result of the competition between collisional and radiative processes, a family of eight quasi-stationary normal modes arises. Six of them decay carrying energy to infinity. The two remaining plasmon-polariton modes are nonradiative. One of these modes, the TM-type plasmon polariton, in the limiting case where retardation is disregarded corresponds to the conventional longitudinal two-dimensional plasmon. The other mode, the TE-type plasmon polariton, exists only for a finite thickness of the substrate. All of them are characterized by different dispersion relations of the complex frequency ω(q) = Reω + iImω and differ in both polarization (longitudinal and transverse) and symmetry with respect to the direction of decay (symmetric and asymmetric). The latter modes decay slowly, propagating into free space to plus or minus infinity. The conditions under which the Q factors of certain modes are arbitrarily high are found. In this case, Imω(q ₀) = 0, and dissipative losses in the two-dimensional electron gas are compensated by external sources. As a result, the reflection coefficient for a plane wave whose angle of incidence is determined by the vector q ₀ vanishes.