Lijiang Zeng

Experimental verification of enhanced transmission through two-dimensionally corrugated metallic films without holes

We present experimental results to verify extraordinary optical transmission through two-dimensionally periodic, corrugated metallic films without holes as predicted by Bonod et al. [Opt. Express 11, 482 (2003)]. We also experimentally confirmed that using symmetric structures (metallic films sandwiched between two identical dielectric media) is advantageous for boosting the coupling of surface plasmons so as to create strong transmission peaks.

Fabrication of optical mosaic gratings with phase and attitude adjustments employing latent fringes and a red-wavelength dual-beam interferometer.

We present a method to make optical mosaic gratings that uses the exposure beams and the latent grating created by the previous exposure to adjust the lateral position and readjust the attitude of the substrate for the current exposure. As thus, it is a direct method without using any auxiliary reference grating(s) and it avoids the asynchronous drifts between otherwise independent exposure and alignment optical sub-systems. In addition, the method uses a red laser wavelength in the plane-mirror interferometers for the multi-dimensional attitude adjustment, so the adjustment can be done at leisure. The mosaic procedure is described step by step, and the principles to minimize substrate alignment errors are explained in detail. Experimentally we made several mosaics of (50 + 30) x 50 mm(2) final grating area. The typical peak-valley and root-mean-square values of the measured -1st-order diffraction wavefront errors are 0.036 lambda and 0.006 lambda, respectively.

Method of making mosaic gratings by using a two-color heterodyne interferometer containing a reference grating

We propose and demonstrate a two-color heterodyne interferometric method for making a perfect mosaic of two planar gratings that can substitute for a single and larger grating without introducing wavefront aberration at any wavelength. The lateral and longitudinal phase errors are separated and eliminated by use of two wavelengths in the interferometry. The accuracy of the phase difference measurement is improved by this heterodyne scheme. The method ensures that the lateral gap between the two subaperture gratings is an integer multiple of the grating period. For a pair of 0.72 microm period gratings we experimentally achieved a lateral alignment error of less than 1% of the grating period.

Fabrication of optical mosaic gratings: a self-referencing alignment method

We propose and demonstrate a self-referencing alignment technique to conveniently enlarge fabricated grating area. The latent image gratings are used as the reference objects to align (adjust and lock) the attitude and position of the substrate relative to the exposure beams between and during consecutive exposures. The adjustment system and the fringe-locking system are combined into the exposure system, eliminating the drift errors between them and making the whole system low-cost and compact. For the fabricated 1 × 4 mosaics of 50 × (30 + 30 + 30 + 30) mm(2) area and 1 × 2 mosaics of 90 × (80 + 80) mm(2) area, the typical peak-valley -1st-order wavefront errors measured by a 100-mm-diameter interferometer are not more than 0.06 λ and 0.09 λ, respectively.

Grating mosaic based on image processing of far-field diffraction intensity patterns in two wavelengths.

A practical grating mosaic method is proposed based on quantitative image processing of three far-field diffraction intensity patterns in two wavelengths. This method aims at making a perfect mosaic of two planar gratings that can substitute for a single and larger grating without introducing wavefront aberration at any wavelength. The zeroth-order and first-order far-field patterns of one wavelength are analyzed for separating and eliminating the angular mosaic errors. The first-order far-field patterns of two wavelengths are applied for separation of the lateral and longitudinal phase errors. Then the three patterns are considered together to enlarge the target range of coarse adjustment required for further fine adjustment in longitudinal position. Experimentally, angular and positional detection sensitivities of less than 6 microrad and 14 nm were achieved, respectively, and the periodicity in positional adjustment was checked, which departed less than 1.8% from the theoretical period. The performance of the perfect mosaic grating was diagnosed with the far-field diffraction intensity pattern in a third wavelength, and the necessity for a perfect mosaic was verified.

Accurate measurement of orthogonality of equal-period, two-dimensional gratings by an interferometric method

A two-dimensional grating can be used as a key component in planar encoders for measuring two-dimensional displacements or calibrating coordinate measuring machines. Ideally the two main periodic directions of the grating, the directions along which a translation by a grating period leaves the two-dimensional pattern indistinguishable from the untranslated one, should be perfectly orthogonal; any deviation from orthogonality causes cross-talk errors and necessitates system calibration. We present a method to measure the orthogonality, or the non-orthogonality angle of two-dimensional gratings precisely. This method uses interference fringes generated by diffracted beams of different orders to align the gratings periodic directions, and applies a new measurement strategy to directly measure the non-orthogonality angle by an autocollimator. Compared with traditional optical diffractometry, its angular position alignment is of higher sensitivity and its angle measurement is of lower uncertainty, and the measurement uncertainty is reduced. Orthogonalities of four gratings were measured and the standard uncertainty was 0.28u2009arcsec. The results agree well with the measurement results of optical diffractometry.

Optical mosaic gratings made by consecutive, phase-interlocked, holographic exposures using diffraction from latent fringes

We propose and demonstrate a method for fabricating large optical mosaic gratings, i.e., gratings made by consecutive, phase-interlocked, holographic exposures on single substrates. It takes advantage of the latent fringes generated by the preceding exposure to align the substrate for the following exposure. Good angular alignment accuracy and period consistency between the fringes recorded by consecutive exposures can be achieved by using the large-area moiré pattern produced by the latent fringes and the alignment beams. Phase-interlocking accuracy of less than 4 degrees between consecutive exposures was experimentally achieved by using the heterodyne detection technique.

Analysis and minimization of spacing error of holographic gratings recorded with spherical collimation lenses.

This research proposes a feedback method to adjust the dual-beam exposure system with spherical collimation lenses to achieve gratings with low spacing error. Through theoretical analysis and numerical calculation, it is proved that the interference aberration can be analyzed with the Zernike polynomials and the adjustment errors can be estimated according to the linear relationship between the errors and the polynomial coefficients. Moreover moving the substrate along its normal is proposed to decrease the spacing error but keep the gratings period unchanged. In the experiments, the wavefront measurement results of the ± 1st orders are used to deduce the spacing error. Based on the feedback adjustment method, the grating with a spacing error of 0.03 λ within 70 mm × 70 mm is fabricated with the collimation lenses of 0.6 λ spherical aberration.

Scatterometry specialized for a highly asymmetric triangular grating on a transparent substrate

We present a specialized scatterometry method to measure the groove profiles of highly asymmetric triangular gratings. Compared with the conventional scatterometry working in a specular way, this method utilizes diffraction spectra of the reflected ±1st orders and is good at measuring this kind of asymmetric grating with a higher sensitivity. In our work, diffraction efficiency angular spectra at a single wavelength are measured and passed on to a parameter optimization process to retrieve three profile defining parameters. Final results are compared with the ones from an atomic force microscope and discrepancies are discussed and explained.

A method to fabricate convex holographic gratings as master gratings for making flat-field concave gratings

Ion-beam etching blazed flat-field concave diffraction gratings (FFCG) to achieve high diffraction efficiency is a difficult task. This paper presents a new method to fabricate convex holographic gratings as master gratings for making FFCG. This method makes it convenient to fabricate blazed FFCG with corrected aberrations and uniform predetermined blaze angle over the grating surfaces. It can also be adapted to the commercial fabrication process. This method could be briefly described as follows: First, we make a convex grating using holographic recording method. The grooves are determined by the interference fringes of two spherical waves, one of which is divergent coming from the back side of the substrate, and the other is convergent coming from the front side. Leading-term aberrations can be corrected by optimizing the center positions of the two sphere waves. Second, the exposed convex grating is etched by ion beam to make a blazed convex grating. In this step, it is much easier to get a uniform blaze angle over the surface of a convex grating than over the surface of a concave grating. At last, the etched convex grating is used directly as a master grating to replicate blazed FFCG. An optimized example for a specific system structure is given in this paper. The advantages and difficulties of the method are discussed.