01/31/2017 17:52:37

Scientists have simplified the simulation of high-precision optical instruments

Physicists from MIPT and University Jean Monnet (France) have developed a new simulation method for optical elements that form the basis of numerous modern instruments and devices. The researchers’ paper, presenting a description of the method which enables complex optical devices to be designed on gaming graphics cards, has been published in one of the leading optical journals – the Journal of Quantitative Spectroscopy and Radiative Transfer.

Alexey Shcherbakov, an employee of the Laboratory of Nanooptics and Plasmonics at MIPT’s Center of Nanoscale Optoelectronics, and his colleague from University Jean Monnet Alexandre Tishchenko (1958–2016) proposed a new approach to calculating the optical parameters of complex diffraction gratings and diffractive elements. The possibilities of the newly developed method are significantly greater than those offered by other widely used methods for a variety of optical structures. The results of the study therefore open new perspectives for the highly efficient optimization of modern optical and optoelectronic devices.

Alexey Shcherbakov demonstrates the diffraction pattern from a two-dimensional grating, credit: MIPT’s Press Office  

Diffraction gratings are optical elements which form the basis of many modern devices in spectroscopy, telecommunications, and laser technologies. They are one- or two-dimensional periodic structures containing hundreds and thousands of regular elements: e.g. a series of parallel strips of microscopic width. Diffraction gratings are capable of splitting white light into a spectrum, reflecting rays of different wavelengths in different directions – this is why they are used in virtually all spectrometers.

A good and very simple example of a diffraction grating is an ordinary compact disc. If it is illuminated with light of a fixed frequency, using a red laser pointer for example, one can see that instead of a single reflected beam there appears a set of beams. They are referred to as diffraction orders. The directions in which these beams propagate are fixed and depend on the grating period (the distance between adjacent elements), the angle of incidence and the radiation frequency. This relationship is very simple and is even studied in some advanced physics courses in schools. Calculating the intensity of each diffraction order, i.e., what amount of the incident light power is reflected in each direction, is far more difficult. Performing these types of calculations with high precision is extremely important from a practical viewpoint, since they are vital for the optimization of a wide variety of instruments and devices.

The capability of diffraction gratings to split light into a spectrum is used in spectrometers: devices that use the spectrum analysis to determine the composition of various substances, ranging from chemical solutions to interstellar gases. Diffraction simulation is essential for manufacturing lithography masks used in modern microelectronic fabrication, and for designing special polarizers in laser metal processing technology. In addition, periodic structures are used to increase the efficiency of solar concentrators and photovoltaic cells (by increasing light absorption) and make it more difficult to forge documents and money: a pattern of fine metallic strips on paper that reflect light in a certain way can act as a protective element.

Coordinate planes of a curvilinear coordinate system introduced in a region near a two-dimensional sinusoidal diffraction grating so that one of the planes coincides with the grating surface (an opaque surface).

A rigorous calculation of the diffraction order efficiency is only possible by solving Maxwell’s equations – fundamental equations that describe the electromagnetic field and, in particular, the electromagnetic wave propagation. They were formulated more than a hundred years ago, but a wide variety of solutions that these equations admit in different cases still motivates many scientists all over the world to continue to study methods of their solution. And describing complex optical diffraction gratings using Maxwell’s equations is only possible with the aid of numerical methods.

This means that instead of a ready-to-use formula, a finite precision algorithm has to be implemented. To analyze and optimize complex diffraction gratings, researchers use modern computers and computer clusters. A whole field of science, combining mathematical physics, numerical analysis, programming, and other areas, is devoted to exploring how to write computer programs and perform these computations in the most efficient way. The development of this field is being spurred on by advances in technologies of diffraction structures fabrication: more and more precise devices pose increasingly high requirements to simulation methods at the design level.

In their publication, the researchers developed the Generalized Source Method (GSM), which helped to significantly reduce the consumption of computing resources compared to other methods. The idea of the method is based on the utilization of hypothetical sources of the electromagnetic radiation which substitute structural inhomogeneity. According to Alexey Shcherbakov, a senior researcher of the Laboratory of Nanooptics and Plasmonics, and a graduate of the Department of General and Applied Physics, this idea can, with certain limitations, be illustrated as follows: “Let’s suppose we throw stones into the center of a circular pond. The waves generated by the stones will be circular and will spread out from the center of the pond to the water’s edge. Now let us ask ourselves, what shape will the waves have if a boat is floating somewhere in the pond. It turns out that if we remove the boat and throw lots of small stones in the place where it was floating, these small stones can be chosen so that the total number of waves generated by them and the stone that we throw into the center will be the same as if the boat were still floating in the pond. This hypothetical substitution may seem to be complicating the task, but, in practice, this principle allows scientists to efficiently solve very complex problems of wave propagation.”

The key idea of the new method based on the GSM was to use curvilinear coordinate transformations in the grating region. Within the method rationale, a rough grating surface is stretched to a plane which makes it very simple to calculate the reflection and refraction of waves. In order to preserve the physical effects caused by the roughness, one should simultaneously change the properties of the environment near the surface in a certain way upon such stretching. Thus, instead of being reflected at the corrugated grating surface, waves appear to pass through an inhomogeneous space, which slows down their propagation differently in different locations. This technique significantly improves calculations, and allows one to obtain far more accurate results in the same calculation time.

In addition to the analytical development of the new approach with metric sources, the researchers also demonstrated the possibility of efficient parallelization of the method and performing simulations on graphic cards. This means that it is possible to use commercially produced components, which all gamers are familiar with, to simulate very complex diffraction gratings. The computing power of graphics chips is already greater than the power of processors, which is why graphics cards have found a place in many laboratories all over the world. In the published research, comparing simulations on graphics cards and ordinary processors showed that a graphics chip is able to do the task dozens of times faster.

The research was supported by Grant 16-29-11747-ofi_m of the Russian Foundation for Basic Research and MIPT’s Project 5-100 program.

Link to the original article: A.A. Shcherbakov, A.V. Tishchenko, Generalized source method in curvilinear coordinates for 2D grating diffraction simulation // Journal of Quantitative Spectroscopy and Radiative Transfer 187, 76-96 (2017).

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