Waveguide Diffraction Research Articles

Simulation of gradient period polarization volume gratings for augmented reality displays

Augmented reality (AR) displays are gaining attention as next-generation intelligent display technologies. Diffractive waveguide technologies are progressively becoming the AR display industry's preferred option. Gradient period polarization volume holographic gratings (PVGs), which are considered to have the potential to expand the field of view (FOV) of waveguide display systems due to their wide bandwidth diffraction characteristics, have been proposed as coupling elements for diffraction waveguide systems in recent years. Here, what we believe to be a novel modeling method for gradient period PVGs is proposed by incorporating grating stacking and scattering analysis utilizing rigorous coupled-wave analysis (RCWA) theory. The diffraction efficiency and polarization response were extensively explored using this simulation model. In addition, a dual-layer full-color diffractive waveguide imaging simulation using proposed gradient period PVGs is accomplished in Zemax software using a self-compiled dynamic link library (DLL), achieving a 53° diagonal FOV at a 16:9 aspect ratio. This work furthers the development of PVGs by providing unique ideas for the field of view design of AR display.

Radiation of a TM mode from an open end of a three-layer dielectric capillary

Abstract Modern trends in beam-driven radiation sources include the interaction of Cherenkov wakefields in open-ended circular waveguides with complicated dielectric linings, with a three-layer dielectric capillary recently proposed to reduce radiation divergence being a representative example [Opt. Lett. 45 5416 (2020)]. We present a rigorous approach that allows for an analytical description of the electromagnetic processes that occur when the structure is excited by a single waveguide TM mode. In other words, the corresponding canonical waveguide diffraction problem is solved in a rigorous formulation. This is a continuation of our previous papers which considered simpler cases with a homogeneous or two-layer dielectric filling. Here we use the same analytical approach based on the Wiener–Hopf–Fock technique and deal with the more complicated case of a three-layer dielectric lining. Using the obtained rigorous solution, we discuss the possibility of manipulating the far-field radiation pattern using a third layer made of a low permittivity material.

Study on Two-Dimensional Exit Pupil Expansion for Diffractive Waveguide Based on Holographic Volume Grating

Diffraction gratings are becoming a preferred option for waveguide head-mounted in–out coupling devices due to their flexible optical properties and small size and light weight. At present, diffraction waveguide coupling devices for AR head-mounted displays (HMD) have difficulties such as a long development cycle and complicated processing. In this paper, we first establish a set of two-dimensional (2D) grating ray tracing models, based on which we determine the initial architecture of the dual-region two-dimensional exit pupil expansion (2D-EPE) AR-HMD holographic waveguide diffraction system. Second, we propose a honeycomb coupled grating array and optimize the optical energy utilization and brightness uniformity of the holographic waveguide and use a custom dynamic linked library (DLL) function to implement the ray tracing of the 2D grating and add a probabilistic splitting function to the DLL, which reduces the single simulation time from 11.853 min to 1.77 min. We also propose a holographic lithography device composed of holographic optical elements (HOEs) and a method for preparing HOEs. Finally, in order to obtain the diffraction efficiency preoptimized by the above DLL for the uniformity of the exit pupil brightness and light energy utilization, we inverse design with the preparation process parameters as the optimization variables and develop the adaptable electromagnetic calculation program Holo-RCWA. Using Holo-RCWA with nondominated sorting genetic algorithm II (NSGA-II), we inverse design to obtain the process parameters satisfying the diffraction efficiency distribution, and the optimization time of the whole system is reduced from 2–3 days to 10 h. This work is of great significance for AR/VR applications.

SYMBOLIC-NUMERICAL IMPLEMENTATION OF THE GALERKIN METHOD FOR APPROXIMATE SOLUTION OF THE WAVEGUIDE DIFFRACTION PROBLEM

In this paper, we construct a symbolic-numerical implementation of the Galerkin method for approximate solution of the waveguide diffraction problem at the junction of two open planar three-layer waveguides. The Gelerkin method is implemented in the Maple computer algebra system by symbolic manipulations; its software implementation is based on the scprod symbolic-numerical procedure, which enables the numerical calculation of scalar products for the Galerkin method based on symbolic expressions. The use of symbolic manipulations makes it possible to speed up the calculation of integrals in the Galerkin method owing to single-run symbolic calculation of integrals typical for the problem, rather than multiple numerical integration.

Space-time duality in magnonics: Temporal diffraction in magnonic waveguides

In the present paper, we address the issue of the magnonic features due to the quadratic character of the dispersion of purely exchange SWs becoming more and more important due to a rapid progress in the technology of excitation of ultra-short SWs. Our interpretation in terms of time diffraction of the theoretical results and numerical simulations relies on the space/time duality principle that has already been successfully applied in ultrafast optics in the description of temporal evolution of short optical pulses. It was shown that time diffraction related effects lead to a considerable transformation of the signals transmitted through a magnonic channel in spintronic logic and computing devices that can be either detrimental or beneficial for the procedure of information processing. Specifically, time diffraction results in pulse expansion severely limiting the rate of information transfer. On the positive side, this feature can be effectively used to realize such important functionalities as pulse focusing/ compression and Fourier analysis which opens up novel promising opportunities in information processing.

Diffraction at the Open End of Dielectric-Lined Circular Waveguide

A rigorous approach for solving canonical circular open-ended dielectric-lined waveguide diffraction problems is presented. This is continuation of our recent paper [1] where a simpler case of uniform dielectric filling has been considered. Here we deal with the case of an open-ended circular waveguide with layered dielectric filling which is closer to potential applications. The presented method uses the solution of corresponding Wiener-Hopf-Fock equation and leads to an infinite linear system for reflection coefficients (S-parameters) of the waveguide, the latter can be efficiently solved numerically using the reducing technique. As a specific example directly applicable to beam-driven radiation sources based on dielectric-lined capillaries, diffraction of a slow TM symmetrical mode at the open end of the described waveguide is considered. A series of such modes forms the wakefield (Cherenkov radiation field) generated by a charged particle bunch during its passage along the vacuum channel axis. Calculated S-parameters were compared with those obtained from COMSOL simulation and an excellent agreement was shown. This method is expected to be very convenient for analytical investigation of various electromagnetic interactions of Terahertz (THz) waves (both free and guided) and charged particle bunches with slow-wave structures prospective in context of modern beam-driven THz emitters, THz accererators and THz-based bunch manipulation and bunch diagnostic systems.

Selective Couplers Based on Multiplexed Volume Holographic Gratings for Waveguide Displays

Diffraction waveguides are widely used in augmented reality devices as information display systems for the introduction of data into the human visual field in order to supplement information about the world around us. This paper formulates the principles of radiation conversion in diffraction waveguides made of photo-thermo-refractive glass on the basis of multiplexed volume holographic gratings, and the advantages and disadvantages of high spectral-angular selectivity are analyzed. In the optical scheme, each of the superimposed volume holographic gratings in the diffraction waveguide forms a corresponding part of the composite angular field of view of the augmented reality device. A proposed mathematical model based on angular multiplexing made it possible to synthesize the diffraction optical element for a new type of diffraction waveguide made from photo-thermo-refractive glass and to create a prototype with an angular resolution of at least 3.0 ± 0.5′, with a brightness change in the image of less than 20% and with a composite angular field of view of 32°.

Directional color routing assisted by switchable Fano resonance in bimetallic metagrating

AbstractGreat progress in nanophotonics has been demonstrated in tailoring the impinging beams. The physics behind those intriguing effects is to a large extent governed by the parameter of the optical phase. While, simple nanostructures usually suffer from fundamental limitations on their efficiency in wave transformation, especially in the transmission system, associated with their inadequate phase accumulation, challenge their implementation in practical application. Here, we describe a transparent nanostructure built from a pair of partially overlapped gold and aluminum semi-nanoshells that show almostπphase accumulation through material-dependent plasmon resonances. Combined with an optical slab waveguide, the bimetallic metagratings exhibit prominent directional color routing properties in transmission light, which result from switchable Fano resonances between plasmon resonances of bimetallic nanostructures and ±1 order waveguide diffraction modes at two opposite oblique incidences due to sufficient phase shift provided by the asymmetric and bimetallic plasmon resonators. Both theoretical and experimental results show that the Fano-resonance-assisted color routing exhibits a relatively broadband tuning range (∼150 nm with an efficiency of up to 50%) and a color routing efficiency of up to 70% at the central wavelength ofλ = 600 nm.

Diffraction at the Open-Ended Dielectric-Loaded Circular Waveguide: Rigorous Approach

An elegant and convenient rigorous approach for solving circular open-ended dielectric-loaded waveguide diffraction problems is presented. It uses the solution of corresponding Wiener-Hopf-Fock equation and leads to an infinite linear system for reflection coefficients (S-parameters) of the waveguide, the latter can be efficiently solved numerically using the reducing technique. As a specific example directly applicable to beam-driven radiation sources based on dielectric-lined capillaries, diffraction of a slow TM symmetrical mode at the open end of a circular waveguide with uniform dielectric filling is considered. A series of such modes forms the wakefield (Cherenkov radiation field) generated by a charged particle bunch during its passage along the waveguide axis. Calculated S-parameters were compared with those obtained from COMSOL simulation and an excellent agreement is shown. This method is expected to be very convenient for analytical investigation of various electromagnetic interactions of Terahertz (THz) waves (both free and guided) and charged particle bunches with slow-wave structures prospective in context of modern beam-driven THz emitters, THz accererators and THz-based bunch manipulation and bunch diagnostic systems.

Physical problems of diffraction waveguide used in large field of view

Diffraction gratings have been widely used in waveguides. They can transmit light beams or images from the in-coupling end to the out-coupling end at predetermined positions. However, when they are applied to augmented reality and virtual reality with large field of view and color light sources, there will arise some problems such as mismatch and missing field of view, non-uniform emission, and others. Therefore, starting from these physical problems, the upper limit of the field of view for diffractive waveguide and the complete theoretical boundary formula of the field of view are derived, and on this basis, in-depth research is conducted on monochromatic waves and multicolor waves, respectively. It is concluded that the single-layer diffractive waveguide supports the theoretical upper limit of the monochromatic wave field angle of about 48° under normal high refractive index of <i>n</i> = 1.75, and supports the theoretical upper limit of the multicolor wave field angle of 26.4° for coefficient <i>q</i> = 1.3. Clearly, a larger field of view requires a higher refractive index <i>n</i> and a smaller <i>q</i> value. The boundary conditions of field integrity indicate that reducing the maximum diffraction angle of the long wave and thinning the thickness of the waveguide layer can solve the problem of missing field of view. The practical maximum diffraction angle generally does not exceed 75°, and the thickness of the waveguide layer is about 0.5 to 1.0 mm generally based on the incident field of view. Finally, a method of expanding each total internal reflection field of view into a ray tracing diagram and a distribution function of pupils to receive light energy at various angles are obtained. In this way, the optimal position of the out-coupling grating region can be achieved, and the inverse of the distribution function is used to constrain the angular distribution of the projected light or the grating efficiency, and then receiving uniform exit image at any position becomes possible. The uniformity of the monochromatic waveguide increases from 0.27 to 0.15, and the uniformity of the long wave in the single grating multicolor waveguide rises from 0.4 to 0.28. The results of these studies will undoubtedly help to solve the problem in the diffractive waveguides used in large field of view and multicolor light.

The Method of Integral Equations in Problems of Wave Diffraction in Waveguides

This paper studies the propagation of steady-state oscillations in an irregular rectangular waveguide. The irregularity of the waveguide is caused by the presence inside it of a metallic inclusion in the form of a cylindrical inductive cylinder. To solve the problem in a complete electrodynamic formulation, it is necessary to investigate the boundary problem for the system of Maxwell equations. To study the waveguide system consisting of a waveguide with a well-conducting inclusion, the method of integral equations was applied. The cores of the integral equations are defined through the Green functions of the unfilled waveguide, written in terms of the waveguide modes. Algorithms for their calculation are developed on the basis of the selection of a logarithmic singularity, and algorithms for summing up the series belonging to them are created. The possibilities of the method of integral equations are illustrated with examples of calculating the reflection and transmission coefficients from inductive pins.

Design of achromatic surface microstructure for near-eye display with diffractive waveguide

Dispersion problem has always constrained the development of see-through near-eye displays with diffractive waveguide. Here, we propose a design method and optical systems for one-layer achromatic surface microstructure composed with a triple-carved-sub-grating. The triple-carved-sub-grating with specified period is designed based on rigorous coupled wave theory, corresponding to Red (R), Green (G) and Blue (B) wavelengths, respectively. The surface microstructure with period of 18.9um is realized by synthesizing the three sub-gratings together, and it is verified numerically that the diffractive angle of R, G, and B wavelengths is 35°under the normal incidence of TE polarization, which imply that the surface microstructure diffracts the certain RGB wavelengths achromatically. A diffraction waveguide with achromatic surface microstructure is also modeled to analysis the stray light and color correction, and the results indicate that the diffraction waveguide transmits image with little stray light. Via proper duplication it could be utilized as the combining optics of diffractive-waveguide near-eye display and head-up display because of its light and compact features.

Diffraction-less propagation beyond the sub-wavelength regime: a new type of nanophotonic waveguide

Sub-wavelength grating (SWG) metamaterials have garnered a great interest for their singular capability to shape the propagation of light. However, practical SWG implementations are limited by fabrication constraints, such as minimum feature size. Here, we present a new nanophotonic waveguide grating concept that exploits phase-matching engineering to suppress diffraction effects for a period three times larger than those with SWG approaches. This long-period grating not only facilitates fabrication, but also enables a new diffraction-less regime with additional degrees of freedom to control light propagation. More specifically, the proposed phase-matching engineering enables selective diffraction suppression, providing new tools to shape propagation in the grating. We harness this flexible diffraction control to yield single-mode propagation in, otherwise, highly multimode waveguides, and to implement Bragg filters that combine highly-diffractive and diffraction-less regions to dramatically increase light rejection. Capitalizing on this new concept, we experimentally demonstrate a Si membrane Bragg filter with record rejection value exceeding 60 dB. These results demonstrate the potential of the proposed long-period grating for the engineering of diffraction in nanophotonic waveguides and pave the way for the development of a new generation of high-performance Si photonics devices.

Ring-Gaussian laser pulse filamentation in a self-induced diffraction waveguide

Self-action in air of a high-power femtosecond laser pulse with the spatial form of a ring-Gaussian beam (‘dressed’ beam) is studied theoretically. Pulse self-focusing and filamentation is analyzed in detail through the numerical solution of the spectral propagation equation, taking into account medium optical nonlinearity and plasma generation. Pulse propagation dynamics and energy fluxes inside the beam are visualized by means of averaged diffraction ray tracing. We clearly show that, in terms of diffraction optics, the outer ring forms a specific nonmaterial diffractive waveguide, favoring long-range self-channeling of the central part of a beam by delivering optical energy to a filament. The spatial robustness and stability of such diffractive waveguides strongly depends on the energy stored in the ring, as well as on its position relative to the beam axis. The striking advantage of such ‘dressed’ beams is their reduced angular divergence during plasma-free (post-filamentation) evolution.

A numerical solution of the layer-to-layer transition problem as a waveguide diffraction problem

Application of net-point methods to the solution of the layer-to-layer transition problem leads to the necessity to restrict the domain and formulate artificial boundary conditions. In the present work the introduction of an artificial coaxial for reducing the original problem to a waveguide diffraction problem is applied. The test results of the finite-element program that we developed, which demonstrate the high accuracy of the method, are considered. The investigated dependence of the solution on the artificial boundary location shows the rapid convergence of the method.

Photorefractive direct laser writing

We demonstrate a simple technique to create a large number of arbitrary optical structures in photorefractive Fe-doped lithium niobate (Fe:LN). The technique consists in directly writing with a focused laser beam at visible wavelength the desired optical structures on a sample, taking advantage of the photorefractive effect. Using a computer-controlled translation stage, arbitrary 1D patterns can be recorded allowing diffraction gratings or waveguide arrays to be realized. In contrast to other laser-writing approaches, our method exploits solely the large photorefractive sensitivity of Fe:LN as the mechanism to induce the refractive index change. Thanks to this, commonly available, low power cw lasers are sufficient to obtain the desired structures.The resulting refractive index modulations are characterized by an interferometric technique and positively compared with the one-center photorefractive model.The proposed method offers interesting advantages in terms of simplicity, flexibility and cost effectiveness, making it very interesting for rapid prototyping of complicated diffractive optical elements.

Analytical study of dispersion relations for shear horizontal wave propagation in plates with periodic stubs

The coupled mode theory with coupling of diffraction modes and waveguide modes is usually used on the calculations of transmission and reflection coefficients for electromagnetic waves traveling through periodic sub-wavelength structures. In this paper, I extend this method to derive analytical solutions of high-order dispersion relations for shear horizontal (SH) wave propagation in elastic plates with periodic stubs. In the long wavelength regime, the explicit expression is obtained by this theory and derived specially by employing an effective medium. This indicates that the periodical stubs are equivalent to an effective homogenous layer in the long wavelength. Notably, in the short wavelength regime, high-order diffraction modes in the plate and high-order waveguide modes in the stubs are considered with modes coupling to compute the band structures. Numerical results of the coupled mode theory fit pretty well with the results of the finite element method (FEM). In addition, the band structures’ evolution with the height of the stubs and the thickness of the plate shows clearly that the method can predict well the Bragg band gaps, locally resonant band gaps and high-order symmetric and anti-symmetric thickness-twist modes for the periodically structured plates.

Control of dissipative solitons in a waveguide trap

A planar package of waveguides with heterogeneously implanted impurity resonance atoms is considered. The conditions of formation of dissipative solitons due to a competition of Kerr saturating nonlinearity and diffraction in the waveguide traps formed by impurity media are determined. It is shown that applying a constant electric field to an impurity resonance medium with a constant dipole moment makes it possible to control the propagation of solitons in Y-shaped waveguide traps.

Guided-wave acoustooptic Bragg diffraction in silica waveguides

A rigorous theoretical analysis of the optical guided-wave, surface acoustic wave and AO Bragg interaction between the optical guided-wave and surface acoustic wave in Si-based silica waveguide is presented. The mechanical displacement, strains and acoustic power of the SAW are studied for various SAW frequencies and ZnO layer thickness. The effects of SAW frequency, ZnO layer thickness, waveguide thickness, acoustic power and acoustic apertures on the AO Bragg interaction are provided as well.

Interference pattern generation in evanescent electromagnetic waves for nanoscale lithography using waveguide diffraction gratings

The generation of interference patterns of evanescent electromagnetic waves with an essentially subwavelength period using dielectric waveguide diffraction gratings is considered. Using simulations within the framework of the electromagnetic theory, the possibility of obtaining high-quality interference patterns due to enhancement of evanescent diffraction orders under resonance conditions is demonstrated. The contrast of the interference patterns in the case of TE polarisation of the incident wave is close to unity. The field intensity in the near-field interference maxima exceeds the intensity of the incident wave by 25–100 times. The possibility of generation of the interference patterns of evanescent waves corresponding to higher diffraction orders is shown. The use of higher orders reduces the requirements to the fabrication technology and allows generation of interference patterns with a high spatial frequency, using diffraction gratings with a low spatial frequency. Examples of generating interference patters with periods six times smaller than those of the used diffraction gratings are presented.