Juhani Huttunen

FRESNEL DIFFRACTION IN FRACTIONAL TALBOT PLANES : A NEW FORMULATION

We consider field distributions in fractional Talbot planes behind a periodic two-dimensional complex-amplitude transparency that is illuminated by a unit-amplitude plane wave. In the paraxial approximation the field in various fractional Talbot planes is expressed as a sum of contributions from a finite number of points in the plane of the transparency, yielding compact algebraic formulas for the diffracted field. Given the desired intensity distribution in the fractional Talbot plane, we synthesize the transmission function from nonlinear equations. An experimental illustration that uses a binary phase grating is given.

Double-ion-exchange process in glass for the fabrication of computer-generated waveguide holograms.

We experimentally optimize double-ion-exchange process parameters to achieve a designed phase modulation for a wave front passing through a computer-generated waveguide hologram and numerically analyze the effects of fabrication errors. We also demonstrate a gradient-thickness waveguide hologram for ? beam splitting.

Computer-generated guided-wave holography: application to beam splitting

The use of guided-wave synthetic holograms in integrated optics is extended beyond the conventional Fresnel lens and Bragg grating technology. As an example, beam splitters based on Fourier-domain holograms are proposed as an alternative to the usual channel waveguide devices. We demonstrate fanout to six with +/-5% (+/-0.2-dB) uniformity error using a binary phase grating and fanout to eight with +/-20% (+/-0.8-dB) uniformity error using a multilevel grating.

Volume diffraction effects in computer-generated guided-wave holography

An integrated-optics equivalent of any one-dimensional computer-generated hologram can, in principle, be formed by a patterning a (scaled) cross-sectional slice of the surface relief profile on the waveguide. Because of the small effective-index modulation, the thickness of such a computer-generated waveguide hologram must be far greater than that of its free-space counterpart. Considerable volume diffraction effects are thus introduced. An analysis of such effects is carried out with the thin-grating-decomposition method, using Fourier-plane-grating multiple beam splitters as an example. It is shown that the index-modulation profile must be reoptimized to obtain a good reconstruction fidelity in the presence of volume effects, and methods of achieving this are introduced.

Phase images of grooves in a perfectly conducting surface

Scattering of an arbitrary two-dimensional electromagnetic field by an isolated rectangular groove in a perfectly conducting substrate is modeled using a rigorous electromagnetic diffraction formalism. By calculating the phase of that part of the scattered field, which propagates in directions that fall within the numerical aperture of a microscope objective, we examine the resolution limits of a Linnik-type interference microscope with focused coherent illumination. It is shown that accurate groove width and depth determination by phase measurement should be possible, even when the groove width is somewhat smaller than the optical wavelength, if use is made of reference data obtained by rigorous computations. However, our results do not support some recent experimental results that suggest the possibility of achieving superresolution by interference microscopy.

Synthesis of wide-field diffractive waveguide lenses

Abstract A synthesis algorithm is presented for wide-field diffractive focusing lenses in waveguides. Analytic optimization of the phase transformation is used to widen the angular field, and the efficiency is improved by parametric optimization of the local grating profile. If the effective-index modulation is Δ n eff ≈ 0.1, a curved F:5 singlet in contact with the pupil can achieve a diffraction-limited angular field of approximately ±3°, whereas a planar lens in a telecentric configuration can achieve ∼ ±8°.

High-efficiency diffractive waveguide lenses by parametric optimization.

The first-order diffraction efficiency of a waveguide diffraction grating is maximized, for a wide range of grating periods, by optimization of the effective-index modulation profile. Three different values of effective-index modulation in the range of 0.02-0.11 are considered. The analysis is performed with the thin-grating-decomposition method. The results are verified by electromagnetic grating theory and applied to the construction of diffractive waveguide lenses with an improved overall efficiency. In the neighborhood of the optical axis, the optimized lens structure is a close approximation of a gradient-thickness Fresnel lens. Significant deviations from this shape appear when the local grating period reduces below ~ 15-25λ, where ~ is the wavelength of the guided mode. Near the edges of a high-numerical-aperture lens, where the local period is ~ 3-6λ, an approximate Bragg grating structure is obtained.

Planar Fresnel lens photoimprinted in a germanium-doped silica optical waveguide

A gradient-thickness Fresnel lens was photoimprinted in the germanium-doped core layer of a single-mode planar waveguide on silica by exposure to ultraviolet light through a mask, which increases the refractive index in the lens region by approximately 5 x 10(-3). The lens is used to collimate the output of a standard single-mode optical fiber butt coupled to the waveguide at a wavelength of 1.3 microm. The method is applicable to the mass production of complex diffractive elements in a planar waveguide geometry.

Experimental optimization of double-ion exchange in glass for computer-generated waveguide holograms

We optimize experimentally the double ion-exchange process parameters to achieve a designed phase modulation for a wavefront passing through a computer-generated waveguide hologram. We also demonstrate a gradient-thickness waveguide hologram (kinoform) for 1/8 beam splitting.

Synthetic holographic beamsplitters for integrated optics

We propose the application of computer-generated Fourier domain holograms to wavefront synthesis and manipulation in integrated optics. In particular, we describe the use of such diffractive optical elements to split a guided plane wave into several equal-intensity output waves. Gratings with fan-out to 6, 7, and 8 are demonstrated with about +/- 25% (approximately +/- 1 dB) array uniformities.