Slanted Gratings Research Articles

Transparent Slanted Phase Gratings in Emissive Waveguides

A new front-illumination principle is demonstrated for use in energy efficient and bright reflective liquid crystal displays (LCDs). The new emissive waveguide principle presented is based on Bragg diffraction of waveguided light at a tuned holographic grating. The frontlight exhibits negligible image deterioration due to an excellent transparency and a high preference for (linearly polarized) light emission towards the display.

Characteristics of DuPont photopolymers for slanted holographic grating formations

The characteristic parameters of DuPont OmniDex613 photopolymers including the shrinkage factor, diffusion coefficient, and nonlocal response length are studied for slanted holographic gratings recorded at the UV wavelength of 363.8 nm by application of the rigorous coupled-wave analysis in conjunction with an angular-selectivity measurement, a real-time diffraction-monitoring technique, and a nonlocal diffusion model. Both small (<20 deg) and large (>40 deg) slant-angle gratings are presented. Depending on the exposure intensity, the recording shrinkage factor of the photopolymer varies from ~2.75% to ~4.20%. Furthermore, the effects of postbaking conditions on the refractive-index modulations and the shifts of Bragg angles for slanted holographic gratings are also investigated systematically. It is found that the postbaking processing can not only increase the refractive-index modulations from Δn1~0.013 to ~0.028 for a small slant-angle grating and from Δn1~0.011 to ~0.022 for a large slant-angle grating, but can also compensate the recording shrinkage.

Design of an integrated optical add-drop multiplexer with low cross-talk and low back-reflection

The design of an integrated optical add-drop multiplexer (OADM), using an adiabatic transition and a symmetric coupler with a superimposed slanted grating, is presented. Through optimization of the shape function of the adiabatic transition, extinction ratio is kept high at both the symmetric coupler and the end of the adiabatic transition. By increasing the separation between the two waveguides of the symmetric coupler, the resultant similarity of the square distributions of the two eigenmodes ensures that the two self-coupling coefficients can reach zero simultaneously with the cross-coupling coefficient being near maximum. Therefore, the design has low cross-talk and low back-reflection at the input and add ports. The simulations show that the back-reflection at both ports can be kept below −43 dB and the cross-talk below −33 dB, and the process tolerances are acceptable, which are critical to mass production.

Optical Add/Drop Multiplexers Using Slanted Fiber Bragg Gratings

Novel optical add/drop multiplexers (OADMs) using slanted fiber Bragg gratings (S-FBGs) are proposed. The S-FBGs couple the guided mode to radiation modes, and they also couple specific radiation modes to the guided mode. A set of S-FBGs located near each other function as OADMs. Output light beams from an optical fiber couple to the other fiber by the slanted gratings. The proposed OADM does not require optical circulators that are components of conventional multiplexers using FBGs. Low-cost and small-size optical filters may be constructed. Calculation results successfully show the possibilities of OADMs.

Compact slanted grating couplers

We present a compact and efficient design for slanted grating couplers (SLGC's) to vertically connect fibers and planar waveguides without intermediate optics. The proposed SLGC employs a strong index modulated slanted grating. With the help of a genetic algorithm-based rigorous design tool, a 20microm-long SLGC with 80.1% input coupling efficiency has been optimized. A rigorous mode analysis reveals that the phase-matching condition and Bragg condition are satisfied simultaneously with respect to the fundamental leaky mode supported by the optimized SLGC.

Frequency response of second-order extremely asymmetrical scattering in wide uniform holographic gratings

Second-order extremely asymmetrical scattering (EAS) and grazing-angle scattering (GAS) are types of Bragg scattering in slanted wide periodic gratings. They occur when the second diffracted order satisfies the Bragg condition and has a wavevector parallel (for EAS) and almost parallel (for GAS) to the grating boundaries. In this paper, for the first time, a rigorous numerical study of the frequency responses of second-order EAS and GAS is presented for bulk TE electromagnetic waves in planar holographic gratings. A highly unusual pattern of strong optical resonances in the side-lobe structure of these frequency responses is predicted. A relationship between these resonances and the previously predicted GAS resonances (at zero detunings of the Bragg condition) is established and analysed. A special new type of eigenmodes in slanted wide periodic gratings with strong frequency detunings are predicted in the case of second-order EAS and GAS. The eigenmodes are shown to be guided by the grating alone without any conventional guiding effect in the structure. The typical field structure in such eigenmodes is investigated and discussed.

The characteristics of fiber slanted gratings in multimode fiber

We report what is believed to the first example of graded index multimode fiber slanted grating. The gratings are realized by the same technique as the single mode fiber gratings. The periodic perturbation causes fundamental core mode to higher order core modes, cladding modes and radiation modes coupling. There is a unique feature in the spectra of certain angle-slanted gratings (2.5°–4°). Hope this phenomenon can cause a new type of fiber components that can be widely used in the LAN and sensing systems.

3D near‐field model for uniform slanted fiber gratings

AbstractA 3D near‐field model for a uniform slanted fiber Bragg grating (FBG) is presented. This model, based on antenna theory, allows for the calculation of the radiated near field in the space surrounding a fiber that contains a tilted uniform fiber Bragg grating. Radiation patterns can also be obtained. The model has been successfully checked via experiments. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 428–432, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11081

Active U-turn electrooptic switch formed in patterned holographic polymer-dispersed liquid crystals

We have developed an active U-turn device by spatially patterning two identical holographic polymer dispersed liquid-crystal gratings. In the field-OFF state, the holographic planes of both gratings are slanted such that the angle of the diffraction beam is beyond the total internal reflection angle of the air-glass interface. The diffraction beam is trapped in the device until diffracted by the second slanted grating. In the field-ON state, the holographic grating is erased and the incident beam propagates directly through the sample. The index modulation is determined to be 0.059 /spl plusmn/ 0.006 at 1.55 /spl mu/m. Low switching voltage and sub-millisecond response times are reported.

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.

Rigorous analysis of grazing-angle scattering of electromagnetic waves in periodic gratings

Grazing-angle scattering (GAS) is a type of Bragg scattering of waves in slanted non-uniform periodic gratings, when the diffracted order satisfying the Bragg condition propagates at a grazing angle with respect to the boundaries of a slab-like grating. Rigorous analysis of GAS of bulk TE electromagnetic waves is undertaken in holographic gratings by means of the enhanced T-matrix algorithm. A comparison of the rigorous and the previously developed approximate theories of GAS is carried out. A complex pattern of numerous previously unknown resonances is discovered and analysed in detail for gratings with large amplitude, for which the approximate theory fails. These resonances are associated not only with the geometry of GAS, but are also typical for wide transmitting gratings. Their dependence on grating amplitude, angles of incidence and scattering, and grating width is investigated numerically. Physical interpretation of the predicted resonances is linked to the existence and the resonant generation of special new eigenmodes of slanted gratings. Main properties of these modes and their field structure are discussed.

Second-order grazing-angle scattering in uniform wide holographic gratings

Grazing-angle scattering (GAS) is a type of Bragg scattering in slanted wide periodic gratings. It occurs when the diffracted order satisfying the Bragg condition (scattered wave) propagates at a grazing angle to the grating boundaries. Previous research has been concerned only with first-order GAS, which has been shown to be a highly unusual type of scattering characterised by a strong resonant increase of amplitudes of the scattered and incident waves in the grating. In this paper, a rigorous numerical study of second-order GAS is presented for the case of bulk TE electromagnetic waves in planar holographic gratings. A highly unusual pattern of strong resonances in the grating, which is strongly different from that for first-order GAS, is predicted, described, and discussed. Physical interpretations of the predicted results are presented. In particular, a special new type of eigenmodes in a slanted wide periodic grating with large amplitude is predicted. These eigenmodes are shown to be guided by the grating alone without any conventional guiding effect in the structure. The typical field structure in such eigenmodes is investigated and discussed.

Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method.

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings.

Extremely asymmetrical scattering in gratings with varying mean structural parameters

Extremely asymmetrical scattering (EAS) is an unusual type of Bragg scattering in slanted periodic gratings with the scattered wave (the +1 diffracted order) propagating parallel to the grating boundaries. Here, a unique and strong sensitivity of EAS to small stepwise variations of mean structural parameters at the grating boundaries is predicted theoretically (by means of approximate and rigorous analyses) for bulk TE electromagnetic waves and slab optical modes of arbitrary polarization in holographic (for bulk waves) and corrugation (for slab modes) gratings. The predicted effects are explained using one of the main physical reasons for EAS—the diffractional divergence of the scattered wave (similar to divergence of a laser beam). The approximate method of analysis is based on this understanding of the role of the divergence of the scattered wave, while the rigorous analysis uses the enhanced T-matrix algorithm. The effect of small and large stepwise variations of the mean permittivity at the grating boundaries is analysed. Two distinctly different and unusual patterns of EAS are predicted in the cases of wide and narrow (compared to a critical width) gratings. Comparison between the approximate and rigorous theories is carried out.

Fast Fourier factorization method applied to modal analysis of slanted lamellar diffraction gratings in conical mountings

A new formulation of the Fourier modal method that applies fast Fourier factorization [J. Opt. Soc. Am. A 17 (2000) 1773] is presented for slanted lamellar gratings in conical mountings. A new eigenvalue problem in the grating region is derived, and used to study metallic gratings. Comparison of the convergence speed of the numerical results given by the conventional methods and the new one shows a spectacular improvement. The fast Fourier factorization method can be also applied to various volume slanted-fringe gratings with discontinuous permittivity variations.

Sensitivity of slanted fibre Bragg gratings toexternalrefractive index higher than that of silica

The influence of external refractive index higher than that of silica on the transmission spectra properties of slanted fibre Bragg gratings is investigated. An analytical method is presented for their potential use as refractometers for refractive index ranges beyond 1.45.

Rigorous analysis of extremely asymmetrical scattering of electromagnetic waves in slanted periodic gratings

Extremely asymmetrical scattering (EAS) is a new type of Bragg scattering in thick, slanted, periodic gratings. It is realised when the scattered wave propagates parallel to the front boundary of the grating. Its most important feature is the strong resonant increase in the scattered wave amplitude compared to the amplitude of the incident wave: the smaller the grating amplitude, the larger the amplitude of the scattered wave. In this paper, rigorous numerical analysis of EAS is carried out by means of the enhanced T-matrix algorithm. This includes investigation of harmonic generation inside and outside the grating, unusually strong edge effects, fast oscillations of the incident wave amplitude in the grating, etc. Comparison with the previously developed approximate theory is carried out. In particular, it is demonstrated that the applicability conditions for the two-wave approximation in the case of EAS are noticeably more restrictive than those for the conventional Bragg scattering. At the same time, it is shown that the approximate theory is usually highly accurate in terms of description of EAS in the most interesting cases of scattering with strong resonant increase of the scattered wave amplitude. Physical explanation of the predicted effects is presented.

Modeling and design of planar slanted volume holographic gratings for wavelength-division-multiplexing applications

Holographic gratings are modeled and designed for path-reversed substrate-guided-wave wavelength-division demultiplexing (WDDM) as a continuation of earlier research [Appl. Opt. 38, 3046 (1999)]. An efficient and practical method is developed to simulate the slanted volume holographic gratings. The trade-off between dispersion and the bandwidth of the holograms is analyzed. A 60 degrees (incident angle of the grating)/60 degrees (diffraction angle of the grating in air) grating structure is selected to demultiplex optical signals in the 1555-nm spectral region, and a 45 degrees /45 degrees grating structure is chosen for the spectral region near 800 nm. Experimental results are consistent with the simulation results for these two WDDM devices. A four-channel WDDM is also demonstrated at a center wavelength of 1555 nm and with a channel spacing of 2 nm.

Slanted gratings UV-written in photosensitive claddingfibre

Experimental results concerning slanted gratings photo-written in a photosensitive cladding fibre and in a standard step index fibre are presented. The improvements concerning back reflection for an FWHM bandwidth suitable for erbium-doped fibre amplifier gain equalisation are demonstrated in the case of slanted gratings realised within photosensitive cladding fibre.

Reflection Holograms Formed Using Polymer-Dispersed Liquid Crystals

The electrical switching characteristics of reflection gratings formed using polymer-dispersed liquid crystals are explored. First, an explanation for the lack of switching in previously formed gratings formed using E7 as the liquid crystal is proposed based on experiments on slightly slanted gratings. These confirm that the LC director orientation within the anisotropically-shaped LC domains is parallel to the grating vector(and applied electric field direction). Slight modification of the syrup leads to transmission gratings with different polarization dependencies and reflection gratings (non-slanted) that switch completely with a modest electric field. These differences are attributed to a 90° rotation in the preferred LC director orientation within the LC domains. This change in orientation results in strong coupling of the electric field with the LC dipoles in a reflection geometry thereby leading to easier switching. The microstructure of these grating structures are explored using low-voltage scanning electron microscopy and bright-field transmission electron microscopy.