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This paper introduces a new way of two-dimensional wavefront reconstruction based on the Fourier modal method. Expending the target wavefront by using Fourier series, calculating the expansion coefficient based on the differential phase measured from the experiment, and fitting the coefficients at the missing points by averaging adjacent values, the target wavefront could be reconstructed eventually by using inverse Fourier transform on the expansion coefficients. The paper also introduces our numerical simulation study on the precisions of both the wavefront reconstruction under ideal situation and under the situation with simulated noise respectively. Corresponding verification experiment for the two-dimensional wavefront reconstruction based on the Fourier modal method is also done by using a two-grating lateral shearing interferometry system, with the 3D profile of the sample obtained.

We investigate the development of the mode occupations in tapered structures using the Fourier modal method. In order to use the Fourier modal method, tapered structures are divided into layers of uniform refractive index in the propagation direction and the optical modes are found within each layer. This is not very efficient and in this proceeding we take the first steps towards a more efficient formalism for treating tapered structures using the Fourier modal method. We show that the coupling coefficients through the structure are slowly varying and that only the first few modes are occupied. We exploit both of these properties in the developing of a more efficient formalism.

Focusing the light onto nanostructures thanks to spherical lenses is a first step to enhance the field, and is widely used in applications, in particular for enhancing non-linear effects like the second harmonic generation. Nonetheless, the electromagnetic response of such nanostructures, which have subwavelength patterns, to a focused beam can not be described by the simple ray tracing formalism. Here, we present a method to compute the response to a focused beam, based on the B-spline modal method. The simulation of a gaussian focused beam is obtained thanks to a truncated decomposition on plane waves computed on a single period, which limits the computation burden.

The continuously increasing complexity of opto-electronic devices and the rising demands of simulation accuracy lead to the need of solving very large systems of linear equations making iterative methods promising and attractive from the computational point of view with respect to direct methods. In particular, iterative approach potentially enables the reduction of required computational time to solve Maxwell’ s equations by Eigenmode Expansion algorithms. Regardless of the particular eigenmodes finding method used, the expansion coefficients are computed as a rule by scattering matrix (S-matrix) approach or similar techniques requiring order of M 3 operations. In this work we consider alternatives to the S-matrix technique which are based on pure iterative or mixed direct–iterative approaches. The possibility to diminish the impact of M 3 -order calculations to overall time and in some cases even to reduce the number of arithmetic operations to M 2 by applying iterative techniques are discussed. Numerical results are illustrated to discuss validity and potentiality of the proposed approaches. Keywords: iterative approach, scattering matrix, modal method, opto-electronic simulations, Maxwell’s equations solver

Hartmann and Shack-Hartmann, instead of measuring the wavefront deformations directly they measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods had been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., model and zonal. In this work we briefly describe a modal method to integrate Hartmann, and Shack-Hartmann patterns. Using orthogonal wavefront slope aberration polynomials, instead of the commonly used Zernike polynomials for the wavefront deformations.

Rapid progress of exposure systems for IC manufacturing is pushing their performance from sub-micrometer to nanometer and catadioptric projection optics have been developed to fulfill this trend. The catadioptric projection optics will produce an annular wavefront. In our system with catadioptric projection optics, the Hartmann wavefront sensor is employed for the test. The wavefront reconstruction method is essential to the accuracy of inspection. For typical annular wavefronts with smaller and larger obscuration ratios, the wavefront reconstructed via modal method with Zernike annular polynomials, modal method with Zernike circular polynomials and zonal method are compared. Simulation results show that both the modal method with Zernike annular polynomials and zonal method are qualified to guarantee the accuracy of reconstruction in both cases. While the modal method with Zernike circular polynomials fail in the case of larger obscuration ratios. The wavefront reconstruction with different terms of Zernike annular polynomials, Zernike circular polynomials and the wavefront fit following the zonal method with a different number of Zernike polynomials are conducted as well.

We describe a FMM (Fourier Modal Method) based rigorous vector diffraction method that can be applied to trapezoidal groove structures. Applying this method to the calculation of the electric field on the surface of the recording layer for DVR groove-only recording media, we found a significant difference of the electric field distributions between two recording schemes, one when the light spot is focused on-groove, the other when it is focused in-groove. These calculation results clearly explained the measured differences of the recording power sensitivities and the cross-writing characteristics between the two schemes.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.