Harmonic diffractive lenses

The harmonic diffractive lens is a diffractive imaging lens for which the optical path-length transition between adjacent facets is an integer multiple m of the design wavelength λ(o). The total lens thickness in air is mλ(o)/(n - 1), which is m times thicker than the so-called modulo 2π diffractive lens. Lenses constructed in this way have hybrid properties of both refractive and diffractive lenses. Such a lens will have a diffraction-limited, common focus for a number of discrete wavelengths across the visible spectrum. A 34.75-diopter, 6-mm-diameter lens is diamond turned in aluminum and replicated in optical materials. The sag of the lens is 23 μm. Modulation transfer function measurements in both monochromatic and white light verify the performance of the lens. The lens approaches the diffraction limit for 10 discrete wavelengths across the visible spectrum.     

Efficiency analysis of diffractive lenses

Multilevel diffractive optical elements are necessary for achieving high-efficiency performance. Here the diffraction efficiency of a multilevel phase-only diffractive lens is analyzed. Approximate, as well as more accurate, approaches are presented. Both plane-wave and Gaussian illumination are discussed. It is shown that for many practical cases the diffraction efficiency can be determined by only a single parameter that takes into account the spatial bandwidth product as well as the focal length of the lens and the illumination wavelength. The analysis is based on the scalar theory and the thin-element approximation. Justification for doing this is presented. The results are valid for lenses with at least F/5.     

Spectral properties of multiorder diffractive lenses

Diffractive lenses have been traditionally designed with the first diffracted order. The spectral characteristics of diffractive lenses operating in higher diffracted orders differ significantly from the first-order case. Multiorder diffractive lenses offer a new degree of freedom in the design of broadband and multispectral optical systems that include diffractive optical elements. It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets. The wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses. Experiments that illustrate lens performance in two spectral bands are described, and the results show excellent agreement with the theoretical predictions.     

Preoptimization improvements to subwavelength diffractive lenses

We present preoptimization strategies for improving the design of diffractive lenses in the electromagnetic domain, with few or no electromagnetic analyses. We find that improvements can be substantial, in some cases even to the point that extensive electromagnetic optimization gives only marginal additional improvement.     

Radiation characteristics of waveguide diffractive doublets

The radiation characteristics of waveguide diffractive doublets consisting of double gratings located on two surfaces of waveguide cladding film are modeled based on a singular perturbation method. We determine the conditions under which the presence of the upper grating does not affect the radiation characteristics of the waveguide diffractive doublet as a whole. This allows independent performance of the upper grating, which may be replaced by a general diffractive optical element, and of the lower grating as a waveguide grating coupler. The results obtained provide an alternative method for determining the thickness of cladding film in the waveguide diffractive doublets for guided-wave manipulation.     

Integrated waveguide diffractive doublet for guided-wave manipulation

An integrated waveguide diffractive doublet consisting of a uniform grating coupler and a diffractive optical element is proposed. Design of this waveguide diffractive doublet for guided-wave manipulation is described in detail. Experimental results for a fabricated waveguide diffractive doublet are also presented to demonstrate the device principles. It was found that this waveguide diffractive doublet can enhance device functionality while remaining simple and compact and having a planar structure. Furthermore, this device can be fabricated by use of all-optical lithography.     

Aberration measurement of photolithographic lenses by use of hybrid diffractive photomasks

In optical lithography the degradation of image quality due to aberrations present in the exposure tool is a serious problem. Therefore it is desirable to establish a reliable aberration measurement procedure based on the analysis of printed images in the photoresist. We present what is to our knowledge a new method for characterizing the aberrations of an exposure tool using a hybrid diffractive photomask. By utilizing each different impact on the aberrated image from each diffracted illumination, we were able to extract the aberration present in the stepper system. We experimentally verified this method with a G-line stepper and verified its spherical aberration astigmatism.     

High-efficiency blazed diffractive optical elements for the violet wavelength fabricated by electron-beam lithography

Blazed diffractive optical elements (DOEs) were studied for the violet wavelength by electron-beam lithography. By optimizing electron-beam writing parameters and electron-dose distributions, we fabricated eight kinds of grating (period A = 10-0.54 microgm) with excellent blazed structure. It has been demonstrated that the measured diffraction efficiency values agreed well with the rigorous theoretical ones. For the fine period of 0.54 microm, we confirmed a peak appearance of 75.6% (TE) experimentally. A wave aberration as small as approximately 0.01 lambda (rms) was obtained for the first-order diffracted wave from the fabricated DOEs. Blazed DOEs for the violet wavelength could be used as key devices in a high-density optical disk pickup of the next generation.     

Focusing waveguide grating coupler using a diffractive doublet

A novel focusing waveguide grating coupler comprising an integrated uniform grating coupler and binary-phase-only diffractive lens is proposed, designed, and fabricated. Experimental results are also presented to demonstrate the device performance. This device is in direct competition with single-element focusing grating couplers defined by direct-write electron-beam lithography and its structure is attractive because the fabrication procedure is better suited for mass production.     

Diffracted-ray approach to the fast evaluation of diffractive lenses

We employ a combination of asymptotic methods to speed up the computation of fields in the focal region of a diffractive lens (DL). The DL is treated locally as a linear grating with a slowly varying period and groove orientation. We employ rigorous electromagnetic diffraction theory locally to obtain the field just behind the DL. A simple diffracted-ray formula is derived for the field in the focal region of the DL at observation points that are not in the immediate vicinity of the optical axis. A careful study of the range of validity of this formula is made. For observation points that are not in the immediate vicinity of the optical axis the new algorithm is 3 x 10(5) times faster than the application of numerical integration to the double integrals involved and approximately 1000-1200 times faster than a recently published algorithm based on using asymptotic theory to replace the double integral with a single integral.     

Fractional Fourier transform optical system with programmable diffractive lenses

We present experimental results for a fractional Fourier transform (FRFT) system implemented with programmable lenses written onto a liquid-crystal spatial light modulator (LCSLM). Because the focal length can be changed, different orders of the FRFT can be obtained without changing the optical setup. The LCSLM can very easily implement more complicated operations, including the realization of simultaneous orders of the FRFT and anamorphic transforms.     

Fabrication of large-aperture lightweight diffractive lenses for use in space

We describe the advantages of using diffractive (Fresnel) lenses on thin membranes over conventional optics for, among others, future space telescope projects. Fabrication methods are presented for lenses on two types of freestanding membrane up to 50 cm in size. The first is a Fresnel lens etched into a thin (380-mum) glass sheet, and the second is an ~50-mum-thick polymer membrane containing a Fresnel lens made by replication process from a specially made fused-silica master. We show optical performance analysis of all the lenses that are fabricated, including a diffraction-limited Airy spot from a 20-m- focal-length membrane lens in a diffractive telescope system.     

Apodized multilevel diffractive lenses that produce desired diffraction-limited focal spots

An apodized, multilevel diffractive lens that can produce a desired diffraction-limited focal spot is proposed for many applications, such as focusing, imaging, optical storage, and optical trapping. The three key points for the design are the innovative idea of complex conjugate subzones, the use of Babinet's principle, and the equivalent-pupil (or aperture) function theory of diffractive focusing elements composed of concentric transparent rings. As a concrete example, we numerically design a mixed multilevel diffractive lens (the highest phase level is 8) to produce a diffraction-limited Gaussian focal spot. Some related problems, such as the validity range and the combination with high-numerical-aperture refractive lenses, are also discussed.     

Point-spread function for binary diffractive lenses fabricated with misaligned masks

The influence of mask-alignment errors on the fabrication of four-level binary lenses has been investigated. The pupil function was derived as a function of the amount of misalignment between the two mask patterns based on scalar diffraction theory. It was found that the phase term in the pupil function affects only the location of the point-spread function, whereas the uneven light transmittance degrades the image quality in the direction of the misalignment. The Strehl intensity was found to decrease almost linearly with respect to the amount of error.     

High-efficiency continuously tunable single-frequency doubly resonant optical parametric oscillator

We report a high-efficiency continuously tunable single-frequency doubly resonant optical parametric oscillator (OPO) based on periodically poled KTiOPO4. Pumped by a frequency-doubled Nd:YLF laser at 526.5 nm, the OPO has a low threshold of 30 mW and can deliver up to 156 mW single-frequency output at 0.8 μm and 89 mW single-frequency output at 1.5 μm with 390 mW of pump power. Coarse and continuous frequency tuning are also demonstrated experimentally.     

Broadband parametric amplification in Bragg reflection waveguide

A novel scheme for enhancing the bandwidth of optical parametric amplification using asymmetric Bragg reflection waveguides is presented. The unique dispersion characteristics exhibited by the Bragg reflection waveguides are exploited for countering the rapidly falling signal gain as one moves away from the phase-matching wavelength. The role of the periodic cladding on the gain and bandwidth of optical parametric amplification in a lithium niobate based Bragg reflection waveguide is analysed. Such an idea could be used in any nonlinear up conversion or down conversion process for enhancing the bandwidth significantly and for easing fabrication tolerances.     

High-efficiency mid-infrared ZnGeP2 optical parametric oscillator in a multimode-pumped tandem optical parametric oscillator

We demonstrate a high-efficiency ZnGeP(2) optical parametric oscillator (OPO) pumped by another KTP OPO in a multimode-pumped tandem OPO configuration. The maximum optical-to-optical and slope efficiencies were 32% and 42.5%, respectively. Our setup also provides tunable multiband radiation in the 2.03-2.32-mum range and the 2.9-6.2-mum range simultaneously.     

Collimating cylindrical diffractive lenses: rigorous electromagnetic analysis and scalar approximation

Practical collimating diffractive cylindrical lenses of 2, 4, 8, and 16 discrete levels are analyzed with a sequential application of the two-region formulation of the rigorous electromagnetic boundary-element method (BEM). A Gaussian beam of TE or TM polarization is incident upon the finite-thickness lens. F/4, F/2, and F/1.4 lenses are analyzed and near-field electric-field patterns are presented. The near-field wave-front quality is quantified by its mean-square deviation from a planar wave front. This deviation is found to be less than 0.05 free-space wavelengths. The far-field intensity patterns are determined and compared with the ones predicted by the approximate Fraunhofer scalar diffraction analysis. The diffraction efficiencies determined with the rigorous BEM are found to be generally lower than those obtained with the scalar approximation. For comparison, the performance characteristics of the corresponding continuous Fresnel (continuous profile within a zone but discontinuous at zone boundaries) and continuous refractive lenses are determined by the use of both the BEM and the scalar approximation. The diffraction efficiency of the continuous Fresnel lens is found to be similar to that of the 16-level diffractive lens but less than that of the continuous refractive lens. It is shown that the validity of the scalar approximation deteriorates as the lens f-number decreases.     

Scaling of diffractive and refractive lenses for optical computing and interconnections

We discuss both numerically and analytically how the space-bandwidth product and the information density of lenses scale as functions of their diameter and f-number over many orders of magnitude. This information may be useful for the design of optical computing and interconnection systems. For diffractive lenses, cost is defined as the number of resolution elements the lithographic production system must have; the relationship of this quantity to the space-bandwidth product and information density is also given.     

Analytic description of wave fields in focal regions of diffractive lenses

Abstract

On the assumption that the transmission function of a diffractive lens is periodical, the Kirchhoff diffraction integral is evaluated analytically in the paraxial region. The amplitude of the wave is expressed in terms of the infinite series which rapidly converges in the vicinity of the focal point. Hence, only a small number of terms provides an acceptable approximation of the amplitude in this region. The new formalism also includes axial locations outside the focal planes. By means of the derived analytical expressions, the image parameters (resolution, depth of field) may be related to the parameters of the diffractive lens.