Dielectric Surface-relief Gratings Research Articles

Features of the Resonance in a Rectangular Dielectric Surace-Relief Gratings Illuminated with a Limited Cross Section Gaussian Beam.

In this work the features of the resonance in a rectangular dielectric surface-relief gratings, illuminated with a limited cross-section Gaussian beam, have been studied. The rigorous coupled wave method and beam decomposition into the plane waves by the Fourier transform have been used. It is shown that there is a resonant wavelength for each thickness of the dielectric grating. The value of resonant wavelength depends on the beam angle of incidence on the gratings. Moreover, the two types of resonances can occur in the grating at certain grating parameters. The power reflection coefficient is practically equal to unity for the first type of resonance and is much smaller than unity, for the second one. The obtained results extend the knowledge regarding the nature of the waveguide resonance in the dielectric grating, considering the limited cross section beam, and they can increase its use in many applications.

Tunable directional beaming assisted by asymmetrical SPP excitation in a subwavelength metallic double slit

We present a design for tunable directional beaming through a subwavelength metallic double slit surrounded by dielectric surface-relief gratings. On-axis and off-axis beaming can be switched by controlling the incident angle to asymmetrically excite surface plasmon polaritons (SPPs) that are subsequently coupled out to propagating beams by the two gratings on the left and the right sides of the double slit. Furthermore, the division of optical power into two off-axis beaming directions can be tuned smoothly by varying the incident angle while keeping the total power almost unchanged. The mechanism of this effect is analyzed theoretically and verified using rigorous numerical simulations.

Coated phase masks for proximity printing of Bragg gratings

Binary dielectric surface-relief gratings can be used as phase masks in exposure of high-spatial-frequency gratings in fibers and waveguides. Ideally, the phase mask should generate only diffraction orders ±1, but also the zero order appears if the period is small. We show that the zero order can always be easily suppressed below 1% by coating the grating with a thin high-refractive-index dielectric film. A demonstration is provided.

Infrared quarter-wave reflection retarders designed with high-spatial-frequency dielectric surface-relief gratings on a gold substrate at oblique incidence

One- and two-dimensional high-spatial-frequency dielectric surface-relief gratings on a Au substrate are used to design a high-reflectance quarter-wave retarder at 70° angle of incidence and 10.6-μm light wavelength. The equivalent homogeneous anisotropic layer model is used. It is shown that equal and high reflectances (>98.5%) for the p and the spolarizations and quarter-wave retardation can be achieved with two-dimensional ZnS surface-relief gratings. Sensitivities to changes of incidence angle, light wavelength, grating filling factor, and grating layer thickness are considered.

Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs

The validity of various homogeneous layer models for high-spatial-frequency rectangular-groove (binary) dielectric surface-relief gratings is examined for both nonconical and conical diffraction. In each model the grating is described by a slab of uniaxial material with its optic axis parallel to the grating vector. The ordinary and principal extraordinary indices of the slab depend on the grating filling factor, the substrate and cover refractive indices, and the ratio of the wavelength to the grating period. These indices can be determined by solving two transcendental equations. Higher-order indices are defined as the exact solution to these equations. Second-order indices (second-order dependence on the wavelengthto- period ratio) and first-order indices (no dependence on the wavelength-to-period ratio) are defined by approximate solutions to these equations. Layer models using higher-order and second-order indices are shown to be accurate for high-spatial-frequency gratings, even at wavelength-to-period ratios near the onset of higher-order propagating diffracted waves. These models are used to design example antireflecting gratings on silicon substrates, including designs for conical incidence. All designs are evaluated and optimized by exact rigorous coupled-wave analysis.

Three-dimensional diffraction analysis of dielectric surface-relief gratings

Diffraction of the general angle of incidence by dielectric surface-relief gratings is analyzed by use of a differential method. The method is applied to sinusoidal, rectangular, and triangular gratings. In all our results, error in energy conservation is of the order of 10−4 to groove depths as deep as 2.5 grating periods. It is also shown that, in conical diffraction mountings, when conditions of incidence upon these gratings are controlled, the gratings function as if a polarizing beam splitter had been cascaded with a rotatable half-wave retardation plate.

Electromagnetic theory of Talbot imaging

Electromagnetic diffraction theory is applied to investigate self-imaging of optical fields transmitted by lamellar diffraction gratings. We consider both conventional and fractional Talbot imaging of metallic Ronchi rulings and dielectric surface-relief gratings. Our rigorous approach takes fully into account diffraction inside the modulated grating structure as well as non-paraxial propagation of the electromagnetic field into the observation plane, and it is valid for any grating period. We also show that, for certain grating periods, the transmitted electromagnetic field self-images exactly, regardless of the grating profile.

Diffraction by surface-relief gratings with conic cross-sectional grating shapes

Diffraction of plane waves by dielectric surface-relief gratings with conic (elliptic, hyperbolic, parabolic) cross-sectional grating shapes is analyzed, using a simple transmittance theory. Integral expressions for the complex amplitudes of the diffracted waves are given for these structures. The calculated results indicate new types of diffraction behavior compared with corresponding results for the commonly studied grating shapes (sinusoidal, rectangular, triangular). In particular, these structures are shown to exhibit a large number of diffracted waves with similar intensities. It is also shown that a bandpasslike behavior (a variable number of fairly even-intensity orders with reasonably sharp cutoff) is obtainable.

Zero-reflectivity homogeneous layers and high spatial-frequency surface-relief gratings on lossy materials

The required thickness and complex refractive index of single homogeneous layers on lossy substrates to produce zero reflectivity are calculated by a rigorous impedance matching approach. The analysis is applicable to both TE and TM polarization and to any angle of incidence. The filling factor and groove depth of a rectangular-groove grating, equivalent to a single homogeneous lossy layer in the long-wavelength limit, are calculated. The method reduces to that previously found for dielectric surface-relief gratings in the limit of no losses. The antireflection behavior of the gratings is verified using the rigorous (without approximations) coupled-wave analysis of metallic surface-relief grating diffraction. It is shown that multiple zeroreflectivity solutions exist for both TE and TM polarizations and for any angle of incidence for an arbitrary complex-refractive-index substrate. Example zero-reflectivity gold gratings for incident free space wavelengths from 0.44 to 12.0 microm are presented.

Dielectric surface-relief gratings with high diffraction efficiency

Diffraction properties of dielectric surface-relief gratings were investigated by solving Maxwell’s equations numerically using the differential method. The diffraction efficiency of a grating with a groove depth about twice as deep as the grating period is comparable with the efficiency of a volume phase grating. Dielectric surface-relief gratings interferometrically recorded in photoresist can possess a high diffraction efficiency of up to 94% (throughput efficiency 85%). Calculated results were also found in good agreement with the experimental data.

Diffraction analysis of dielectric surface-relief gratings: erratum

Diffraction analysis of dielectric surface-relief gratings: erratum

Diffraction analysis of dielectric surface-relief gratings

Diffraction by a dielectric surface-relief grating is analyzed using rigorous coupled-wave theory. The analysis applies to arbitrary grating profiles, groove depths, angles of incidence, and wavelengths. Example results for a wide range of groove depths are presented for sinusoidal, square-wave, triangular, and sawtooth gratings. Diffraction efficiencies obtained from the present method of analysis are compared with previously published numerical results. To obtain large diffraction efficiencies (greater than 85%) for gratings with typical substrate permittivities, it is shown that the grating profile should possess even symmetry.