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This work presents recent results derived from the rigorous modelling of holographic polymer-dispersed liquid crystal (H-PDLC) gratings. More precisely, the diffractive properties of transmission gratings are the focus of this research. This work extends previous analysis performed by the authors but includes new features and approaches. More precisely, full 3D numerical modelling was carried out in all analyses. Each H-PDLC sample was generated randomly by a set of ellipsoid geometry-based LC droplets. The liquid crystal (LC) director inside each droplet was computed by the minimisation of the Frank elastic free energy as a function of the applied electric field. The analysis carried out considered the effects of Frank elastic constants K11, K22 and K33, the anchoring strength W0, and even the saddle-splay constant K24. The external electric field induced an orientation of the LC director, modifying the optical anisotropy of the optical media. This effect was analysed using the 3D split-field finite-difference time-domain (SF-FDTD) method. In order to reduce the computational costs due to a full 3D tensorial analysis, a highly optimised method for high-performance computing solutions (HPC) was developed. The influences of the anchoring and voltage on the diffraction efficiencies were investigated, showing the potential of this approach.

This work shows the redesign of an elemental experience based on the Helmholtz resonator using 3D printing. A Helmholtz resonator is based on a volume and at least one opening that can include a tube or not. The air column inside the tube can be considered the mass of the system, whereas the volume represents the system's stiffness. Due to these analogies between acoustics and mechanics, the Helmholtz resonator is an interesting example of a harmonic oscillator. The relevance of harmonic motions is well known, and this topic is present in the syllabus of many technical and scientific education degrees. In this work, a bottle has been designed and fabricated using 3D printer technology. The design aimed to create a Helmholtz resonator with a variable frequency of resonance. Different mouthpieces have also been designed. The bottle is composed of a set of cylindrical sections that can be attached, enlarging the length of the container. For ensuring that the different parts set a tight enclosure, an O-ring seal has also been designed and fabricated. As more rings and O-seal junctions are attached, the volume of the resonator grows. By blowing the mouth of the Helmholtz resonator with different sections, different resonance frequencies can be measured. From these measurements, several parameters can be estimated indirectly, such as the speed of sound waves, the room temperature, and air density. 3D printing permits to analyse several scenarios without using uncomfortablestrategies to vary the bottle's volume, such as water, reducing the hazard in a laboratory with electronic instrumentation. This research was funded by the Ministerio de Ciencia e Innovación (Spain) under Projects FIS2017-82919-R (MINECO/AEI/FEDER, UE) and PID2019-106601RB-I00, by the ‘Redes-I3CE Research Program in university education of the Institute of Education Sciences of the University of Alicante (2020–21 call)’. Reference: 5310.

In this work we study and characterize and holographic waveguide system composed of two volume diffraction gratings, which act as optical couplers and a glass substrate that acts as a waveguide. The features such us high diffraction efficiencies and Bragg angle selectivity exhibited by volume diffraction gratings allow the appropriated adjustment of the incident light to be diffracted in the direction of total reflection condition inside the glass substrate with high efficiency. In this work the holographic waveguide is recorded on different photopolymer materials, which optimization is controlled to obtain high spatial frequencies and stable fringes. The effect of the shrinkage of the holograms after recording in the quality of the image obtained from the optical waveguide is also studied. To perform the experiments two kind of photopolymers were studied: a nanoparticle-(thiol-ene) polymer composite, NPC, and a penta/hexa-acrylate based polymer with dispersed nematic liquid crystal molecules, PDLC. The holographic characteristics such as diffraction efficiency or wavelength selectivity obtained with the waveguides recorded on the different photopolymers were also studied and compared. This work was supported by the “Ministerio de Economía Industria y Competitividad” (Spain) under projects FIS2017- 82919-R (MINECO/AEI/FEDER, UE) and FIS2015-66570-P (MINECO/FEDER). and by “Generalitat Valenciana” (Spain) (PROMETEOII/2015/015).

In this paper, we present a method to characterize a complete optical Holographic Data Storage System (HDSS), where we identify the elements that limit the capacity to register and restore the information introduced by means of a Liquid Cristal on Silicon (LCoS) microdisplay as the data pager. In the literature, it has been shown that LCoS exhibits an anamorphic and frequency dependent effect when periodic optical elements are addressed to LCoS microdisplays in diffractive optics applications. We tested whether this effect is still relevant in the application to HDSS, where non-periodic binary elements are applied, as it is the case in binary data pages codified by Binary Intensity Modulation (BIM). To test the limits in storage data density and in spatial bandwidth of the HDSS, we used anamorphic patterns with different resolutions. We analyzed the performance of the microdisplay in situ using figures of merit adapted to HDSS. A local characterization across the aperture of the system was also demonstrated with our proposed methodology, which results in an estimation of the illumination uniformity and the contrast generated by the LCoS. We show the extent of the increase in the Bit Error Rate (BER) when introducing a photopolymer as the recording material, thus all the important elements in a HDSS are considered in the characterization methodology demonstrated in this paper. This was supported by Ministerio de Economía, Industria y Competitividad (Spain) under projects FIS2017-82919-R (MINECO/AEI/FEDER, UE) and FIS2015-66570-P (MINECO/FEDER), Generalitat Valenciana (Spain) under project PROMETEO II/2015/015 and Universidad de Alicante (Spain) under project GRE17-06.

In this work, an accurate numerical modeling of the diffraction properties of transmission holographic polymer dispersed liquid crystal (H-PDLC) gratings is presented. The method considers ellipsoid geometry-based liquid crystal (LC) droplets with random properties regarding size and location across the H-PLDC layer and also the non-homogeneous orientation of the LC director within the droplet. The direction of the LC director inside the droplets can be varied to reproduce the effects of the external voltage applied in H-PDLC-based gratings. From the LC director distribution in the droplet, the permittivity tensor is defined, which establishes the optical anisotropy of the media, and it is used for numerically solving the light propagation through the system. In this work, the split-field finite-difference time-domain method (SF-FDTD) is applied. This method is suited for accurately analyzing periodic media, and it considers spatial and time discretisation of Maxwell’s equations. The scheme proposed here is used to investigate the influence on the diffraction properties of H-PDLC as a function of the droplets size and the bulk fraction of LC dispersed material. Work supported by Ministerio de Economía, Industria y Competitividad of Spain under projects FIS2017-82919-R (MINECO/AEI/FEDER) and FIS2015-66570-P (Mineco/FEDER) and by Generalitat Valenciana of Spain under project PROMETEO II/2015/015.

In recent works, we demonstrated the accuracy and physical relevance of a highly simplified reverse-engineering analytical model for a parallel-aligned liquid crystal on silicon devices (PA-LCoS). Both experimental measurements and computational simulations applying the rigorous split-field finite difference time domain (SF-FDTD) technique led to this conclusion in the low applied voltages range. In this paper, we develop a complete rigorous validation covering the full range of possible applied voltages, including highly non-linear liquid crystal (LC) tilt angle profiles. We demonstrate the applicability of the model for spectral and angular retardation calculations, of interest in spatial light modulation applications. We also show that our analytical model enables the calculation of the retardance for novel PA-LC devices as a function of the LC compound and cell gap, becoming an appealing alternative to the usual numerical approaches for PA-LC devices design. Ministerio de Economía, Industria y Competitividad (Spain) under projects FIS2017-82919-R (MINECO/AEI/FEDER, UE) and FIS2015-66570-P (MINECO/FEDER), and by Generalitat Valenciana (Spain) under project PROMETEO II/2015/015.

Liquid crystal on silicon (LCoS) displays have become the most attractive microdisplays for all sort of spatial light modulation applications. Among the different LCoS technologies, parallel aligned LCoS (PA-LCoS) are especially interesting. They offer unique capabilities as spatial light modulators (SLM), since they enable phase-only modulation without coupled amplitude modulation, and with millions of addressable pixels. In this work we evaluate and demonstrate the various capabilities offered by a novel and simplified physical model for parallel aligned liquid crystal devices (PA-LC), thus also applicable to PA-LCoS microdisplays. The model provides the voltage dependent retardance values, necessary for spatial light modulation applications, for a very wide range of incidence angles and any wavelength in the visible. First, it needs to be calibrated through a reverse-engineering approach. In this calibration, the values obtained for two of the three parameters provide the correct values for important internal properties of these devices related with the birefringence, cell gap and director profile. Therefore, the proposed model can be used as a means to inspect internal physical properties of the cell. Last but not least the model is useful to simulate the retardance for novel PA-LC devices as a function of the LC compound and cell gap. Therefore, it is not only a reverse-engineering model but it also constitutes an analytical alternative to the usual numerical approaches for PA-LC devices design and construction. This work was supported by Ministerio de Economía, Industria y Competitividad (Spain) under projects FIS2017-82919-R (MINECO/AEI/FEDER, UE) and FIS2015-66570-P (MINECO/FEDER), by Generalitat Valenciana (Spain) under project PROMETEO II/2015/015 and by Universidad de Alicante under project GRE17-06.

Holographic data storage systems (HDSS) have been a promising and very appealing technology since the first laser developments in the sixties. Impact of ongoing advances in the various components needs to be explored in its specific application to HDSS. In this sense, continuous progress is being produced in spatial light modulator (SLM) technology where parallel-addressed liquid crystal on silicon (PA-LCoS) microdisplays have replaced previous liquid-crystal displays (LCD) in most of optics and photonics applications. PA-LCoS microdisplays are well adapted to display phaseonly elements without coupled amplitude. In this paper, we analyse how PA-LCoS devices can also be used to display the widely applied binary intensity modulated (BIM) data pages. We also investigate hybrid-ternary modulated (HTM) data pages, which are very much demanding on the phase and amplitude modulation properties of an SLM. HTM data pages combine the ease of detection of BIM data pages, together with a large reduction of the DC term of the Fourier Transform of the data page. This reduction is necessary to avoid saturation of the recording material dynamic range. Simulated results show the magnitude of the expected DC term in the Fourier plane. We have verified the good performance of PA-LCoS to display BIM data pages. We have also obtained that pure HTM data pages cannot be produced with PA-LCoS devices, however, a rather close performance is obtained when implementing the pseudo-HTM data pages. In this work a more complete study of pseudo-HTM modulation is offered. This work was supported by the “Ministerio de Economía y Competitividad” (projects FIS2014-56100-C2-1-P and FIS2015-66570-P) and by the “Generalitat Valenciana” of Spain (projects PROMETEOII/2015/015 and ISIC/2012/013).

The holographic storage of information is based on the interference of two waves: the reference wave and the object wave, the latter is generated by using a spatial light modulator, and in the case of applications of data storage this corresponds to a binary pattern of one and zeros. The interference pattern is recorded in a photosensitive medium (photopolymers, photographic emulsions, photorefractive, etc.), so that when illuminated by the reference wave the object wave is reproduced. In order to properly investigate the characteristics of the generated hologram it is necessary to adequately study the interaction of electromagnetic radiation with the recording medium. In this work we develop a completely vectorial formalism for solving the Helmholtz equation that allows investigation of electromagnetic dispersion in dielectric media in which the refractive index varies spatially. The method is based on the technique of Green's tensor and allows to correctly simulate the behavior of a volume hologram. This method is compared with the method of discrete dipoles and a formalism based on the first Born approximation to determine the intensity of light scattered by a volume hologram. This work was supported by the Ministerio de Trabajo y Competitividad of Spain under projects FIS2014-56100-C2-1- P and FIS2015-66570-P and by the Generalitat Valenciana of Spain (under projects PROMETEOII/2015/015 and ISIC/2012/013) and by the University of Alicante (GRE12- 14).

De entre los sistemas de reproducción de sonido 3D, Wavefield Synthesis (WFS) presenta una serie de ventajas sobre el resto, principalmente en lo que respecta al gran realismo y sensación de inmersión acústica que proporciona. Otra gran ventaja adicional, es que la zona útil de escucha es muy amplia, superando al resto de sistemas disponibles en la actualidad. La teoría de WFS fue propuesta a finales de los 80 y principios de los 90, no siendo hasta el siglo XXI cuando se han puesto en marcha los primeros prototipos de estos sistemas, aunque muchos aspectos no contemplados en la teoría inicial siguen siendo en la actualidad retos importantes. La presente tesis aborda el estudio de la implementación de los sistemas de WFS aportando soluciones prácticas a las limitaciones tecnológicas que presentan estos sistemas, así como otra serie de problemas de implementación y funcionamiento en tiempo real que, aunque en una primera instancia no se describen como limitaciones físicas, suponen un problema a superar cuando se busca un sistema que funcione eficientemente. El objetivo final de esta tesis es aportar soluciones que contribuyan al desarrollo de un sistema de WFS totalmente funcional, por lo que durante su desarrollo ha sido necesario encontrar soluciones particulares y originales a multitud de problemas de diferente índole. Esta serie de problemas proviene por un lado de las limitaciones físicas de WFS y por otro de la implementación práctica del sistema. Por otro lado también se ha trabajo en los aspectos computacionales relacionados con la implementación en tiempo real de sistemas de WFS, los cuales necesitan una gran potencia de cálculo para dicho funcionamiento en tiempo real sin cortes ni grandes latencias. Este último se ha tratado de forma rigurosa dedicando un capítulo completo para su análisis y propuesta de soluciones eficientes y efectivas en coste., Bleda Pérez, S. (2009). Contribuciones a la implementación de sistemas Wave Field Synthesis [Tesis doctoral no publicada]. Universitat Politècnica de València. doi:10.4995/Thesis/10251/6685.

The split-field finite-difference time-domain method is extended to second-harmonic generation in two-dimensionally periodic structures. Making use of the full coefficient-tensor formalism, a coupled nonlinear system of equations, which must be solved at each update of the electromagnetic field, is developed. The accuracy of the method is verified by comparing the results to well-known one-dimensional problems. The results for L-shaped arrays are compared with results obtained with the Fourier modal method. This work is partially supported by the “Ministerio de Economía y Competitividad” of Spain under project FIS2011-29803-C02-01; by the “Generalitat Valenciana” of Spain under projects PROMETEO/2011/021, ISIC/2012/013, and GV/2014/076; and by the “Universidad de Alicante” of Spain under project GRE12-14.

In this work, we present a method of manufacturing an optical see-through display based on a holographic waveguide with transmission holograms that couple the incident light between air and the glass substrate, accomplishing total internal reflection. The holograms (slanted transmission gratings with a spatial frequency of 1700 lines/mm) were recorded on a polyvinyl alcohol acrylamide (PVA/AA) photopolymer. We will also show that the addition of N,N′-methylene-bis-acrylamide (BMA) to the composition of the photopolymer allows the achievement of the index modulations necessary to obtain high diffraction efficiencies in non-slanted diffraction gratings of 1000 and 2200 lines/mm, and also in slanted gratings of 1700 lines/mm (which are the base of the optical system proposed). Work supported by the “Ministerio de Economía, Industria y Competitividad” of Spain (projects FIS2014-56100-C2-1-P and FIS2015-66570-P) and by the “Generalitat Valenciana” of Spain (projects PROMETEO II/2015/015).

We present a modified coupled wave theory to describe the properties of nonslanted reflection volume diffraction gratings. The method is based on the beta value coupled wave theory, which will be corrected by using appropriate boundary conditions. The use of this correction allows predicting the efficiency of the reflected order for nonslanted reflection gratings embedded in two media with different refractive indices. The results obtained by using this method will be compared to those obtained using a matrix method, which gives exact solutions in terms of Mathieu functions, and also to Kogelnik’s coupled wave theory. As will be demonstrated, the technique presented in this paper means a significant improvement over Kogelnik’s coupled wave theory. This work was supported by “Ministerio de Economía y Competitividad” of Spain (Grants FIS2011-29803-C02-01 and FIS2011-29803-C02-02), “Generalitat Valenciana” of Spain (Grants PROMETEO/2011/021 and ISIC/2012/013), and the University of Alicante (Grant GRE12-14).

The accurate consideration of propagation losses in arbitrarily shaped waveguide-based structures is studied in this paper. For such a purpose, a software tool based on the perturbation of the boundary conditions on the waveguide metallic walls and on the boundary integral resonant mode expansion method has been developed. To show the advantages of the proposed technique with respect to the classic power-loss method, the complex propagation wavenumbers of a double ridge and an elliptical waveguide have been first computed and compared with results of a commercial software based on the finite element technique. Next a circular, a sectorial shaped and a triangular shaped waveguide have been considered. Then, a computer-aided design software package based on this modal analysis tool has been applied to predict the propagation loss effects in complex waveguide structures, such as an evanescent mode ridge waveguide filter, a traditional dual mode filter with circular cavities and a twist component for K-band applications., This work has been supported by the Ministerio de Economia y Competitividad (MINECO), Spanish Government, by the coordinated R&D project TEC 2010-21520-C04 and the Grant JC 2009-0221, and by University of Alicante under the project GRE 10-22.

A set of simplified and rigorous electromagnetic vector theories is used for analyzing the transmittance characteristics of diffraction phase gratings. The scalar diffraction theory and the effective medium theory are validated with the exact results obtained via the rigorous coupled-wave theory and the finite-difference time-domain method. The effects of surface profile parameters and also the angle of incidence is demonstrated to be a limiting factor in the accuracy of these theories. Therefore, the error of both simplified theories is also analyzed in non-paraxial domain with the intention of establishing a specific range of validity for both simplified theories. This work was supported by the Ministerio de Economía y Competitividad of Spain under projects FIS2011-29803-C02-01, FIS2011-29803-C02-02 and by the Generalitat Valenciana of Spain under projects PROMETEO/2011/021, ISIC/2012/013, ACOMP/2013/075 and GV/2012/099.

The implementation of split-field finite difference time domain (SF-FDTD) applied to light-wave propagation through periodic media with arbitrary anisotropy method in graphics processing units (GPUs) is described. The SF-FDTD technique and the periodic boundary condition allow the consideration of a single period of the structure reducing the simulation grid. Nevertheless, the analysis of the anisotropic media implies considering all the electromagnetic field components and the use of complex notation. These aspects reduce the computational efficiency of the numerical method compared with the isotropic and nonperiodic implementation. Specifically, the implementation of the SF-FDTD in the Kepler family of GPUs of NVIDIA is presented. An analysis of the performance of this implementation is done, and several applications have been considered in order to estimate the possibilities provided by both the formalism and the implementation into GPU: binary phase gratings and twisted-nematic liquid crystal cells. Regarding the analysis of binary phase gratings, the validity of the scalar diffraction theory is evaluated by the comparison of the diffraction efficiencies predicted by SF-FDTD. The analysis for the second order of diffraction is extended, which is considered as a reference for the transmittance obtained by the SF-FDTD scheme for periodic media. This work was supported by the Ministerio de Economía y Competitividad of Spain under projects FIS2011-29803-C02-01 and FIS2011-29803-C02-02 and by the Generalitat Valenciana of Spain under projects PROMETEO/2011/021, ISIC/2012/013, and GV/2012/099.

Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. Explicit approximate solutions are then expressed as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function cn. Then we obtain other approximate expressions for these solutions, which are expressed in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean is used and the rational harmonic balance method is applied to obtain the periodic solution of the original nonlinear oscillator. This work was supported by the “Generalitat Valenciana” of Spain, under Project PROMETEO/2011/021, and by the “Vicerrectorado de Tecnología e Innovación Educativa” of the University of Alicante, Spain, under Project GITE-09006-UA.

The implementation of the Split-Field Finite Difference Time-Domain (SP-FDTD) method in Graphics Processing Units is described in this work. This formalism is applied to light wave propagation through periodic media with arbitrary anisotropy. The anisotropic media is modeled by means of a permittivity tensor with non-diagonal elements and absorbing boundary conditions are also considered. The split-field technique and the periodic boundary condition allow to consider a single period of the structure reducing the simulation grid. Nevertheless, the analysis of anisotropic media implies considering all the electromagnetic field components and the use of complex notation. These aspects reduce the computational efficiency of the numerical method compared to the isotropic and non-periodic implementation. With the upcoming of the new generation of General-Purpose Computing on Graphics Units many scientific applications have been accelerated and others are being developed into this new parallel digital computing architecture. Specifically, the implementation of the SP-FDTD in the Fermi family of GPUs of NVIDIA is presented. An analysis of the performance of this implementation is done and several applications have been considered in order to estimate the possibilities provided by both the formalism and the implementation into GPU. The formalism has been used for analyzing different structures and phenomena: binary phase gratings and twisted-nematic liquid crystal cells. The numerical predictions obtained by means of the FDTD method here implemented are compared with theoretical curves achieving good results, thus validating the accuracy and the potential of the implementation. This work was supported by the "Ministerio de Economía y Competitividad" of Spain under projects FIS2011-29803-C02-01, FIS2011-29803-C02-02 and by the "Generalitat Valenciana" of Spain under projects PROMETEO/2011/021, ISIC/2012/013 and GV/2012/099.

In this work a set of simplified theories for predicting diffraction efficiencies of diffraction phase and triangular gratings are considered. The simplified theories applied are the scalar diffraction and the effective medium theories. These theories are used in a wide range of the value Λ/λ and for different angles of incidence. However, when 1 ≤ Λ/λ ≤ 10, the behaviour of the diffraction light is difficult to understand intuitively and the simplified theories are not accurate. The accuracy of these formalisms is compared with both rigorous coupled wave theory and the finite-difference time domain method. Regarding the RCWT, the influence of the number of harmonics considered in the Fourier basis in the accuracy of the model is analyzed for different surface-relief gratings. In all cases the FDTD method is used for validating the results of the rest of theories. The FDTD method permits to visualize the interaction between the electromagnetic fields within the whole structure providing reliable information in real time. The drawbacks related with the spatial and time resolution of the finite-difference methods has been avoided by means of massive parallel implementation based on graphics processing units. Furthermore, analysis of the performance of the parallel method is shown obtaining a severe improvement respect to the classical version of the FDTD method. This work was supported by the “Ministerio de Economía y Competitividad” of Spain under projects FIS2011-29803-C02-01 and FIS2011-29803-C02-02 and by the “Generalitat Valenciana” of Spain under project PROMETEO/2011/021.

In this work a vectorized and parallel version of the Finite-Difference Time-Domain method (FDTD) is applied to Volume Holographic Gratings (VHG) and Thin-Film Filters (TFF). In particular, in this work gratings with a grating period vector forming an arbitrary angle with the perpendicular to the plane of incidence are analyzed. Angular and wavelength selectivity are obtained by means of the normalized diffraction efficiency. These parameters are positively compared with experimental values and also with analytical closed expressions, thus validating our method. Furthermore, analysis of the performance of the parallel method is shown obtaining a severe improvement with respect to the classical version of the FDTD method. This improvement of the algorithm provides a feasible and accurate scheme for simulating a wide range of optical devices. This work was supported by the ”Ministerio de Ciencia e Innovación” of Spain under projects FIS2008-05856-C02-01 and FIS2008-05856-C02-02.

The present paper describes an optimized C++ library for the study of electromagnetics. The implementation is based on the Finite-Difference Time-Domain method for transient analysis, and the Finite Element Method for electrostatics. Both methods share the same core and are optimized for CPU and GPU computing. To illustrate its running, FEM method is applied for solving Laplace’s equation analyzing the relation between surface curvature and electrostatic potential of a long cylindrical conductor, whereas FDTD is applied for analyzing Thin Film Filters at optical wavelengths. Furthermore, a comparison of the performance of both CPU and GPU versions is analyzed as a function of the grid size simulation. This approach allows the study of a wide range of electromagnetic problems taking advantage of the benefits of each numerical method and the computing power of the modern CPUs and GPUs. This work was supported by the “Ministerio de Economía y Competitividad” of Spain under projects FIS2011-29803-C02-01, FIS2011-29803-C02-02 and by the “Generalitat Valenciana” of Spain under projects PROMETEO/2011/021 and ISIC/2012/013.

In this work we present an analysis of non-slanted reflection gratings by using a corrected Coupled Wave Theory which takes into account boundary conditions. It is well known that Kogelnik's Coupled Wave Theory predicts with great accuracy the response of the efficiency of the zero and first order for volume phase gratings, for both reflection and transmission gratings. Nonetheless, since this theory disregard the second derivatives in the coupled wave equations derived from Maxwell equations, it doesn't account for boundary conditions. Moreover only two orders are supposed, so when either the thickness is low or when high refractive index high are recorded in the element Kogelnik's Theory deviates from the expected results. In Addition, for non-slanted reflection gratings, the natural reflected wave superimpose the reflection order predicted by Coupled Wave theories, so the reflectance cannot be obtained by the classical expression of Kogelnik's Theory for reflection gratings. In this work we correct Kogelnik's Coupled Wave Theory to take into account these issues, the results are compared to those obtained by a Matrix Method, showing good agreement between both theories. This work was supported by the “Ministerio de Ciencia e Innovación" of Spain under projects FIS2008-05856-C02-01 and FIS2008-05856-C02-02, and by the “Generalitat Valenciana" of Spain under project PROMETEO/2011/021.

In this work we present an analysis of non-slanted holographic reflection gratings by using a matrix method. A transfer matrix which relates the values of the electric field and its derivatives is obtained for a permittivity which varies cosenoidally for one period. The coefficients of this matrix can be calculated in terms of Mathieu's functions and their derivatives. Then the matrix of the entire medium is obtained as the Nth power of the matrix for one period. Since the reflectance and transmittance coefficients are related to the coefficients of the medium matrix, it is possible to calculate the efficiencies of orders -1 (reflected) and 0 (transmitted) by using this method. The results obtained by using the Transference Matrix Method are compared to those obtained using Kogelnik's expressions for the transmission and diffraction efficiency. As will be seen there is good agreement between the results obtained by the Transference Matrix Method and those of the Coupled Wave Theory. This work was supported by the "Ministerio de Ciencia e Innovación", Spain (project FIS2008-05856-C02-02).