OPTOS formalism

Last updated

OPTOS (optical properties of textured optical sheets) is a simulation formalism for determining optical properties of sheets with plane-parallel structured interfaces. The method is versatile as interface structures of different optical regimes, e.g. geometrical and wave optics, can be included. It is very efficient due to the re-usability of the calculated light redistribution properties of the individual interfaces. [1] It has so far been mainly used to model optical properties of solar cells and solar modules but it is also applicable for example to LEDs or OLEDs with light extraction structures.

Contents

History

The development of the OPTOS formalism started in 2015 at the Fraunhofer Institute for Solar Energy Systems ISE in Freiburg, Germany. The mathematical formulation has been described in detail in several open access publications. [2] [3] [4] A basic version of the code including documentation with function references has been available since the end of 2015 at the homepage of Fraunhofer ISE. [5] Continuous updates and a list of OPTOS related publications can be found on ResearchGate. [6]

OPTOS simulation procedure

One key aspect of OPTOS simulations is the division of the modeled system into interface and propagation regions. The light redistribution properties are calculated with the most appropriate method for each interface individually and depending on the relevant structure dimension. Large scale structures can for example be modeled via ray tracing while for interfaces with structure dimensions in the range of the wavelength wave optical approaches like RCWA, FDTD or FEM can be used.

Simulation procecure of the OPTOS formalism Simulation procecure of the OPTOS formalism.png
Simulation procecure of the OPTOS formalism

System description

The discretization of the complete angular space into a fixed number of angle channels, as second key aspect of the OPTOS formalism, allows representing the angular power distribution within the system by a vector v which consists of one entry for each angle channel. The value of the entry is the power fraction of the corresponding angle channel with respect to the total incident power.

Interface interaction

The light redistribution properties of an interface are represented by the so-called reflection and transmission matrices, R and T. They store for each of the angle channels the redistribution information into other angle channels for light incident onto a certain interface with a certain wavelength. There are in total four different redistribution matrices for each interface, characterized by the incidence direction as well as reflection or transmission redistribution.

Propagation through the sheet

The incoherent propagation of light through the sheet can also be represented by a matrix. If no light redistribution takes occurs on the path, the propagation matrix D is a diagonal matrix. The single entries consist of the Lambert-Beer absorption factor, including cosine of the polar angle and the absorption coefficient of the respective material.

Calculation of optical properties

Using the pre-calculated matrices described above, optical properties like reflectance, transmittance or absorptance within the sheet can be calculated via matrix multiplications [2–4] and can be performed within seconds or minutes using a standard personal computer. Also a depth-dependent absorption profile can be calculated. This is of special importance for the subsequent electrical simulation of structured silicon solar cells.

OPTOS simulation characteristics

Strengths

Limitations

OPTOS couples redistribution properties of different interfaces. If there is no accurate modeling technique to calculate redistribution matrices, such interfaces cannot be included in OPTOS. OPTOS models the propagation through the sheet incoherently. If the sheet thickness becomes very low and interference effects play a significant role, this needs to be handled coherently and not as “thick” sheet. However, as coherently modeled sub-system, it can be included in OPTOS as effective interface. Circular or elliptical polarization effects are not taken into account as all phase information is neglected during the propagation.

Application Examples

The main application of OPTOS has so far been the simulation of:

Alternative fields of application could be:

Related Research Articles

<span class="mw-page-title-main">Optics</span> Branch of physics that studies light

Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Light is a type of electromagnetic radiation, and other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

<span class="mw-page-title-main">Polarization (waves)</span> Property of waves that can oscillate with more than one orientation

Polarization is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves in solids.

Ray transfer matrix analysis is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element is described by a 2×2 ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system. The same mathematics is also used in accelerator physics to track particles through the magnet installations of a particle accelerator, see electron optics.

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

<span class="mw-page-title-main">Reflection (physics)</span> "Bouncing back" of waves at an interface

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected.

<span class="mw-page-title-main">Ellipsometry</span> Optical technique for characterizing thin films

Ellipsometry is an optical technique for investigating the dielectric properties of thin films. Ellipsometry measures the change of polarization upon reflection or transmission and compares it to a model.

<span class="mw-page-title-main">Anti-reflective coating</span> Optical coating that reduces reflection

An antireflective, antiglare or anti-reflection (AR) coating is a type of optical coating applied to the surface of lenses, other optical elements, and photovoltaic cells to reduce reflection. In typical imaging systems, this improves the efficiency since less light is lost due to reflection. In complex systems such as cameras, binoculars, telescopes, and microscopes the reduction in reflections also improves the contrast of the image by elimination of stray light. This is especially important in planetary astronomy. In other applications, the primary benefit is the elimination of the reflection itself, such as a coating on eyeglass lenses that makes the eyes of the wearer more visible to others, or a coating to reduce the glint from a covert viewer's binoculars or telescopic sight.

An epitaxial wafer is a wafer of semiconducting material made by epitaxial growth (epitaxy) for use in photonics, microelectronics, spintronics, or photovoltaics. The epi layer may be the same material as the substrate, typically monocrystaline silicon, or it may be a silicon dioxide (SoI) or a more exotic material with specific desirable qualities. The purpose of epitaxy is to perfect the crystal structure over the bare substrate below and improve the wafer surface's electrical characteristics, making it suitable for highly complex microprocessors and memory devices.

<span class="mw-page-title-main">Solar cell</span> Photodiode used to produce power from light on a large scale

A solar cell or photovoltaic cell is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect. It is a form of photoelectric cell, a device whose electrical characteristics vary when it is exposed to light. Individual solar cell devices are often the electrical building blocks of photovoltaic modules, known colloquially as "solar panels". The common single-junction silicon solar cell can produce a maximum open-circuit voltage of approximately 0.5 to 0.6 volts.

In optics, a ray is an idealized geometrical model of light or other electromagnetic radiation, obtained by choosing a curve that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray optics or geometrical optics does not describe phenomena such as diffraction, which require wave optics theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model.

<span class="mw-page-title-main">Computational electromagnetics</span> Branch of physics

Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment using computers.

Interference lithography is a technique for patterning regular arrays of fine features, without the use of complex optical systems or photomasks.

In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces, complicating analysis. Ray tracing solves the problem by repeatedly advancing idealized narrow beams called rays through the medium by discrete amounts. Simple problems can be analyzed by propagating a few rays using simple mathematics. More detailed analysis can be performed by using a computer to propagate many rays.

<span class="mw-page-title-main">Transfer-matrix method (optics)</span>

The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium; a stack of thin films. This is, for example, relevant for the design of anti-reflective coatings and dielectric mirrors.

TracePro is a commercial optical engineering software program for designing and analyzing optical and illumination systems. The program's graphical user interface (GUI) is 3D CAD-based creating a virtual prototyping environment to perform software simulation before manufacture.

Eigenmode expansion (EME) is a computational electrodynamics modelling technique. It is also referred to as the mode matching technique or the bidirectional eigenmode propagation method. Eigenmode expansion is a linear frequency-domain method.

<span class="mw-page-title-main">Luminescent solar concentrator</span>

A luminescent solar concentrator (LSC) is a device for concentrating radiation, solar radiation in particular, to produce electricity. Luminescent solar concentrators operate on the principle of collecting radiation over a large area, converting it by luminescence and directing the generated radiation into a relatively small output target.

<span class="mw-page-title-main">Rigorous coupled-wave analysis</span> Semi-analytic method of computational electromagnetism

Rigorous coupled-wave analysis (RCWA), also known as Fourier modal method (FMM), is a semi-analytical method in computational electromagnetics that is most typically applied to solve scattering from periodic dielectric structures. It is a Fourier-space method so devices and fields are represented as a sum of spatial harmonics.

<span class="mw-page-title-main">Diffractive beam splitter</span>

The diffractive beam splitter is a single optical element that divides an input beam into multiple output beams. Each output beam retains the same optical characteristics as the input beam, such as size, polarization and phase. A diffractive beam splitter can generate either a 1-dimensional beam array (1xN) or a 2-dimensional beam matrix (MxN), depending on the diffractive pattern on the element. The diffractive beam splitter is used with monochromatic light such as a laser beam, and is designed for a specific wavelength and angle of separation between output beams.

The Fraunhofer Institute for Solar Energy Systems ISE is an institute of the Fraunhofer-Gesellschaft. Located in Freiburg, Germany, The Institute performs applied scientific and engineering research and development for all areas of solar energy. Fraunhofer ISE has three external branches in Germany which carry out work on solar cell and semiconductor material development: the Laboratory and Service Center (LSC) in Gelsenkirchen, the Technology Center of Semiconductor Materials (THM) in Freiberg, and the Fraunhofer Center for Silicon Photovoltaics (CSP) in Halle. From 2006 to 2016 Eicke Weber was the director of Fraunhofer ISE. With over 1,100 employees, Fraunhofer ISE is the largest institute for applied solar energy research in Europe. The 2012 Operational Budget including investments was 74.3 million euro.

References

  1. Tucher, N.; Eisenlohr, J.; Goldschmidt, J. C.; Bläsi, B. "A versatile formalism for optical simulation of textured sheets", SPIE Newsroom, doi : 10.1117/2.1201509.006104
  2. Eisenlohr, J.; Tucher, N.; Höhn, O.; Hauser, H.; Peters, M.; Kiefel, P.; Goldschmidt, J. C.; Bläsi, B. "Matrix formalism for light propagation and absorption in thick textured optical sheets" Optics Express doi : 10.1364/oe.23.00a502
  3. 1 2 Tucher, N.; Eisenlohr, J.; Kiefel, P.; Höhn, O.; Hauser, H.; Peters, M.; Müller, C.; Goldschmidt, J. C.; Bläsi, B. "3D optical simulation formalism OPTOS for textured silicon solar cells" Optics Express, doi : 10.1364/oe.23.0a1720
  4. 1 2 Tucher, N.; Eisenlohr, J.; Gebrewold, H.; Kiefel, P.; Höhn, O.; Hauser, H.; Goldschmidt, J. C.; Bläsi, B. "Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS" Optics Express, doi : 10.1364/oe.24.0a1083
  5. "Simulation of optical properties of textures: The "OPTOS" Formalism - Fraunhofer ISE". Fraunhofer Institute for Solar Energy Systems ISE. Retrieved 2017-06-01.
  6. "OPTOS - optical properties of textured optical sheets". ResearchGate. Retrieved 2017-06-01.
  7. 1 2 Tucher, Nico; Müller, Björn; Jakob, Peter; Eisenlohr, Johannes; Höhn, Oliver; Hauser, Hubert; Goldschmidt, Jan Christoph; Hermle, Martin; Bläsi, Benedikt (2017-07-04). "Optical performance of the honeycomb texture – a cell and module level analysis using the OPTOS formalism". Solar Energy Materials and Solar Cells. 173: 66–71. doi:10.1016/j.solmat.2017.06.004.
  8. Chen, Yang; Höhn, Oliver; Tucher, Nico; Pistol, Mats-Erik; Anttu, Nicklas (2017-08-07). "Optical analysis of a III-V-nanowire-array-on-Si dual junction solar cell". Optics Express. 25 (16): A665–A679. doi: 10.1364/oe.25.00a665 . ISSN   1094-4087. PMID   29041038.
  9. Pearce, Phoebe (2021-09-27). "RayFlare: flexible optical modelling of solar cells". Journal of Open Source Software. 6 (65): 3460. doi: 10.21105/joss.03460 . ISSN   2475-9066.

OPTOS page at Fraunhoer ISE website (includes documentation and download of basic version)

OPTOS project on ResearchGate (with continuous updates and a list of OPTOS related publications)