JCMsuite

JCMsuite
Basic data
developer	JCMwave GmbH
Publishing year	2001
Current  version	3.6.1 (01/27/2017)
operating system	Microsoft Windows , Linux
category	CAE program , finite element method
License	Proprietary EULA
jcmwave.com

JCMsuite is software for the simulation and analysis of physical processes of electromagnetism, elasticity and heat conduction, which can also be coupled with one another. The solution of the underlying partial differential equations is based on the finite element method . The main areas of application of the software are the analysis and optimization of nano-optical and micro-optical systems. The software was used in research and development projects in the areas of scatterometry , photolithography , photonic crystal fibers , VCSELs , quantum dot emitters , absorption amplification in solar cells and surface plasmons .

Numerical method

JCMsuite uses the finite element method to solve the partial differential equations. The software functions can be controlled by the script languages MATLAB and Python so that parameter-dependent geometries can be defined and parameter scans can be carried out. Details of the numerical implementation have been published in several scientific papers, e.g. B. in. The performance of the numerical method was compared with alternative numerical methods. Due to the high achievable accuracy, the JCMsuite was used as a reference for evaluating analytical (approximate) methods.

Problem classes

JCMsuite enables different physical problem classes to be dealt with.

Light scattering

In the case of electromagnetic scattering problems, the geometry of the scattering objects (ie the spatial distribution of permeability and permittivity ), the incident waves and, if necessary, internal sources are specified. We are looking for the system response in the form of the reflected, refracted and scattered electromagnetic waves . The time harmonic problem with a frequency is solved in the frequency space . The time dependence of the electromagnetic fields can then be split off as a time-dependent phase factor, ie and . Based on the Maxwell equations this leads z. B. for the electric field on the time harmonic differential equations ${\displaystyle \mu }$ ${\displaystyle \epsilon }$ ${\displaystyle \omega }$ ${\displaystyle \mathbf {E} (\mathbf {r} ,t)=\Re (\mathbf {E} (\mathbf {r} )e^{-i\omega t})}$ ${\displaystyle \mathbf {H} ({\vec {r}},t)=\Re (\mathbf {H} ({\vec {r}})e^{-i\omega t})}$ ${\displaystyle \mathbf {E} (\mathbf {r} )}$

${\displaystyle \nabla \times \epsilon ^{-1}\nabla \times \mathbf {E} -\mu \epsilon ^{2}\mathbf {E} =-i\omega \mathbf {J} }$,

${\displaystyle \nabla \cdot \epsilon \mathbf {E} =0}$.

It is the source current density z. B. generated by electric dipoles . In the case of scattering problems, the electromagnetic fields outside the scattering objects are viewed as a superposition of the incident and scattered fields. The scattered fields meet an emission condition at the edge of the computation area because they move away from the scattered objects. In order to avoid non-physical reflections at the edge of the calculation area, a perfectly matched layer boundary condition is used. ${\displaystyle \mathbf {J} }$

Fiber optic design

Optical waveguides are structures which are invariant in one spatial direction (e.g. in the direction) and have any structure in the other two transverse spatial directions. Analogous to the case of light scattering, a time-harmonic problem is solved in that the time-dependent phase factor is split off from the electromagnetic fields. Due to the symmetry of the problem, the fields and can furthermore be represented as the product of a phase factor and a field that only depends on the transverse coordinates and . Based on the Maxwell equations this leads z. B. for the electric field on the time harmonic differential equation ${\displaystyle z}$ ${\displaystyle e^{-i\omega t}}$ ${\displaystyle \mathbf {E} (\mathbf {r} )}$ ${\displaystyle \mathbf {H} (\mathbf {r} )}$ ${\displaystyle e^{ikz}}$ ${\displaystyle x}$ ${\displaystyle y}$ ${\displaystyle \mathbf {E} (\mathbf {r} )}$

${\displaystyle \nabla \times \epsilon ^{-1}\nabla \times \mathbf {E} =\mu \omega ^{2}\mathbf {E} }$,

with . ${\displaystyle \mathbf {E} =\mathbf {E} (x,y)e^{ikz}}$

For a given frequency and waveguide geometry, JCMsuite determines pairs of propagation constants (wave numbers) and associated fields . JCMsuite also calculates the corresponding differential equations for the magnetic field . Effects of bending the waveguide can be determined by using curvilinear coordinate systems. ${\displaystyle \omega }$ ${\displaystyle k}$ ${\displaystyle \mathbf {E} _{k}(x,y)}$ ${\displaystyle \mathbf {H} (x,y)}$

Optical resonances

In the case of resonance problems, the one, two or three-dimensional geometry of the resonance body is specified. In contrast to the case of light scattering, there are no incident fields or source current densities. This leads e.g. B. for the electric field on the time harmonic differential equations ${\displaystyle \mathbf {E} (\mathbf {r} )}$

${\displaystyle \nabla \times \epsilon ^{-1}\nabla \times \mathbf {E} =\mu \omega ^{2}\mathbf {E} }$,

${\displaystyle \nabla \cdot \epsilon \mathbf {E} =0}$.

JCMsuite determines pairs of resonance frequencies and associated resonance fields (resp. ) That satisfy the time-harmonic differential equations. Typical applications are the calculation of eigenmodes of optical resonators (e.g. of semiconductor lasers ), of plasmonic modes or of band structures of photonic crystals . ${\displaystyle \omega }$ ${\displaystyle \mathbf {E} (\mathbf {r} )}$ ${\displaystyle \mathbf {H} (\mathbf {r} )}$

Conduction

The ohmic losses of the electromagnetic fields generate heat that spreads over the objects and can change their refractive index . The temperature distribution of a body is given by the heat conduction equation ${\displaystyle T}$

${\displaystyle \partial _{t}\left(c\rho T\right)=\nabla \cdot k\nabla T+q}$

certainly. Here are the heat capacity , the mass density, the thermal conductivity and is the volumetric heat flow density . For a given heat flow density , the JCMsuite determines the temperature distribution. Heat convection or heat radiation within the body are not supported. The temperature profile can be used as input for optical calculations in order to take into account the temperature dependence of the refractive index up to the linear order. ${\displaystyle c}$ ${\displaystyle \rho }$ ${\displaystyle k}$ ${\displaystyle q}$ ${\displaystyle q}$ ${\displaystyle T.}$

Linear elasticity

Heating due to ohmic losses can lead to thermal expansion and thus to tension within an object. Due to the photoelastic effect , this can change the birefringent behavior of an object. In order to determine the stresses occurring within a geometry, the JCMsuite solves equations for the linear elasticity of a body, which follow the minimum principle for elastic energy

${\displaystyle \int _{\Omega }\epsilon _{ij}C_{ijkl}\left(\epsilon _{kl}-\epsilon _{kl}^{\text{init}}\right)-u_{i}F_{i}\rightarrow \min .}$

Free or fixed boundary conditions also apply. Thereby are the elasticity tensor , the linear stress tensor , the tensor of the given initial stress, the linear displacement (through thermal expansion) and a given force field. The linear stress tensor is related to shift over . The stress calculated by the JCMsuite can be used as input for optical calculations in order to take into account the dependence of the refractive index on material stresses. ${\displaystyle C_{ijkl}}$ ${\displaystyle \epsilon _{ij}}$ ${\displaystyle \epsilon _{ij}^{\text{init}}}$ ${\displaystyle u_{i}}$ ${\displaystyle F_{i}}$ ${\displaystyle \epsilon _{ij}}$ ${\displaystyle u_{i}}$ ${\displaystyle \epsilon _{ij}={\frac {1}{2}}\left(\partial _{i}u_{j}+\partial _{j}u_{i}\right)}$

Web links

• Manufacturer's website (in English)
• Documentation of the software (in English)

Individual evidence

1. ↑ J. Potzick, R. Dixson, R. Quintanilha, M. Stocker, A. Vladar: International photomask linewidth comparison by NIST and PTB . tape 7122 , January 1, 2008, p. 71222P-71222P-14 , doi : 10.1117 / 12.801435 .
2. ↑ Hannah Marlowe, Randall L. McEntaffer, James H. Tutt, Casey T. DeRoo, Drew M. Miles: Modeling and empirical characterization of the polarization response of off-plane reflection gratings . In: Applied Optics . tape 55 , no. 21 , July 20, 2016, ISSN  1539-4522 , doi : 10.1364 / ao.55.005548 ( osapublishing.org [accessed February 4, 2017]).
3. Jump up ↑ Mark-Alexander Henn, Bryan M. Barnes, Hui Zhou, Martin Sohn, Richard M. Silver: Optimizing the nanoscale quantitative optical imaging of subfield scattering targets . In: Optics Letters . tape 41 , no. 21 , November 1, 2016, ISSN  1539-4794 , doi : 10.1364 / ol.41.004959 ( osapublishing.org [accessed February 4, 2017]).
4. ↑ Yoshihiro Tezuka, Jerry Cullins, Yuusuke Tanaka, Takeo Hashimoto, Iwao Nishiyama: EUV exposure experiment using programmed multilayer defects for refining printability simulation . tape 6517 , January 1, 2007, p. 65172M-65172M-12 , doi : 10.1117 / 12.711967 .
5. ↑ Ramin Beravat, Gordon KL Wong, Michael H. Frosz, Xiao Ming Xi, Philip St J. Russell: Twist-induced guidance in coreless photonic crystal fiber: A helical channel for light . In: Science Advances . tape 2 , no. 11 , November 1, 2016, ISSN  2375-2548 , p. e1601421 , doi : 10.1126 / sciadv.1601421 , PMID 28138531 ( sciencemag.org [accessed February 4, 2017]).
6. ↑ GKL Wong, MS Kang, HW Lee, F. Biancalana, C. Conti: Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber . In: Science . tape 337 , no. 6093 , July 27, 2012, ISSN  0036-8075 , p. 446-449 , doi : 10.1126 / science.1223824 , PMID 22837523 ( sciencemag.org [accessed February 4, 2017]).
7. ↑ F. Couny, F. Benabid, PJ Roberts, PS Light, MG Raymer: Generation and Photonic Guidance of Multi-Octave Optical Frequency Combs . In: Science . tape 318 , no. 5853 , November 16, 2007, ISSN  0036-8075 , p. 1118–1121 , doi : 10.1126 / science.1149091 , PMID 18006741 ( sciencemag.org [accessed February 4, 2017]).
8. ↑ V. Shchukin, NN Ledentsov, J. Kropp, G. Steinle, N. Ledentsov: Single-Mode Vertical Cavity Surface Emitting Laser via Oxide-Aperture-Engineering of Leakage of High-Order Transverse Modes . In: IEEE Journal of Quantum Electronics . tape 50 , no. 12 , December 1, 2014, ISSN  0018-9197 , p. 990-995 , doi : 10.1109 / JQE.2014.2364544 ( ieee.org [accessed February 4, 2017]).
9. ↑ M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt: Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography . In: Nature Communications . tape 6 , July 16, 2015, ISSN  2041-1723 , doi : 10.1038 / ncomms8662 , PMID 26179766 ( nature.com [accessed February 4, 2017]).
10. ↑ G. Yin, P. Manley, M. Schmid: Light absorption enhancement for ultra-thin Cu (In1 - xGax) Se2 solar cells using closely packed 2-D SiO2 nanosphere arrays . In: Solar Energy Materials and Solar Cells . tape 153 , August 1, 2016, p. 124–130 , doi : 10.1016 / j.solmat.2016.04.012 ( sciencedirect.com [accessed February 4, 2017]).
11. ↑ ^{a b} David Shapiro, Daniel Nies, Oleg Belai, Matthias Wurm, Vladimir Nesterov: Optical field and attractive force at the subwavelength slit . In: Optics Express . tape 24 , no. 14 , July 11, 2016, ISSN  1094-4087 , doi : 10.1364 / oe.24.015972 ( osapublishing.org [accessed February 4, 2017]).
12. ↑ Jan Pomplun, Sven Burger, Lin Zschiedrich, Frank Schmidt: Adaptive finite element method for simulation of optical nano structures . In: physica status solidi (b) . tape 244 , no. 10 , October 1, 2007, ISSN  1521-3951 , p. 3419–3434 , doi : 10.1002 / pssb.200743192 ( wiley.com [accessed February 5, 2017]).
13. Jump up ↑ Johannes Hoffmann, Christian Hafner, Patrick Leidenberger, Jan Hesselbarth, Sven Burger: Comparison of electromagnetic field solvers for the 3D analysis of plasmonic nanoantennas . tape 7390 , January 1, 2009, p. 73900J-73900J-11 , doi : 10.1117 / 12.828036 .
14. ↑ Bjorn Maes, Jiří Petráček, Sven Burger, Pavel Kwiecien, Jaroslav Luksch: Simulations of high-Q optical nanocavities with a gradual 1D bandgap . In: Optics Express . tape 21 , no. 6 , March 25, 2013, ISSN  1094-4087 , doi : 10.1364 / oe.21.006794 ( osapublishing.org [accessed February 5, 2017]).
15. ↑ Viktoriia E. Babicheva, Sergey S. Vergeles, Petr E. Vorobev, Sven Burger: Localized surface plasmon modes in a system of two interacting metallic cylinders . In: Journal of the Optical Society of America B . tape 29 , no. 6 , June 1, 2012, ISSN  1520-8540 , doi : 10.1364 / josab.29.001263 ( osapublishing.org [accessed February 5, 2017]).