# JCMsuite

Type Private company Computer software Berlin, Germany (2001) Berlin, Germany JCMsuite www.jcmwave.com
Developer(s) JCMwave GmbH 3.6.1 / January 27, 2017; 18 months ago Windows, Linux Finite element analysis Proprietary EULA www.jcmwave.com/JCMsuite/doc/html/

JCMsuite is a finite element analysis software package for the simulation and analysis of electromagnetic waves, elasticity and heat conduction. It also allows a mutual coupling between its optical, heat conduction and continuum mechanics solvers. The software is mainly applied for the analysis and optimization of nanooptical and microoptical systems. Its applications in research and development projects include dimensional metrology systems,[1][2][3] photolithographic systems,[4] photonic crystal fibers,[5][6][7] VCSELs,[8] Quantum-Dot emitters,[9] light trapping in solar cells,[10] and plasmonic systems.[11] The design tasks can be embedded into the high-level scripting languages MATLAB and Python, enabling a scripting of design setups in order to define parameter dependent problems or to run parameter scans.

## Problem Classes

JCMsuite allows to treat various physical models (problem classes).

### Optical Scattering

Scattering problems are problems, where the refractive index geometry of the objects is given, incident waves as well as (possibly) interior sources are known and the response of the structure in terms of reflected, refracted and diffracted waves has to be computed. The system is described by time-harmonic Maxwell's Equation

${\displaystyle \mu ^{-1}\nabla \times \epsilon ^{-1}\nabla \times \mathbf {E} -\omega ^{2}\mathbf {E} =-i\omega \epsilon ^{-1}\mathbf {J} }$
${\displaystyle \nabla \cdot \epsilon \mathbf {E} =0}$.

for given sources ${\displaystyle \mathbf {J} }$ (current densities, e.g. electric dipoles) and incident fields. In scattering problems one considers the field exterior to the scattering object as superposition of source and scattered fields. Since the scattered fields move away from the object they have to satisfy a radiation condition at the boundary of the computational domain. In order to avoid reflections at the boundaries, they are modelled by the mathematical rigorous method of a perfectly matched layer (PML).

### Optical Waveguide Design

Waveguides are structures which are invariant in one spatial dimension (e. g. in z-direction) and arbitrarily structured in the other two dimensions. To compute waveguide modes, the Maxwell's curl-curl Equation is solved in the following form

${\displaystyle \nabla \times \epsilon ^{-1}\nabla \times \mathbf {E} =\mu \omega ^{2}\mathbf {E} }$
${\displaystyle \mathbf {E} =\mathbf {E} (x,y)e^{ik_{z}z}.}$

Due to the symmetry of the problem, the electrical field ${\displaystyle \mathbf {E} }$ can be expressed as product of a field ${\displaystyle \mathbf {E} (x,y)}$ depending just on the position in the transverse plane and a phase factor. Given the permeability, permittivity and frequency, JCMsuite finds pairs of the electric field ${\displaystyle \mathbf {E} (x,y)}$ and the corresponding propagation constant (wavenumber) ${\displaystyle k_{z}}$. JCMsuite also solves the corresponding formulation for the magnetic field ${\displaystyle \mathbf {H} (x,y)}$. A mode computation in cylindrical and twisted coordinate systems allows to compute the effect of fiber bending.

### Optical Resonances

Resonance problems are problems in 1D, 2D, or 3D where the refractive index geometry of resonating objects is given, and the angular frequencies ${\displaystyle \omega }$ and corresponding resonating fields have to be computed. No incident waves or interior sources are present. JCMsuite determines pairs of ${\displaystyle \mathbf {E} }$ and ${\displaystyle \omega }$ or ${\displaystyle \mathbf {H} }$ and ${\displaystyle \omega }$ fulfilling the time-harmonic Maxwell's curl-curl equation, e.g.,

${\displaystyle \nabla \times \epsilon ^{-1}\nabla \times \mathbf {E} =\mu \omega ^{2}\mathbf {E} }$
${\displaystyle \nabla \cdot \epsilon \mathbf {E} =0}$.

for a pair of ${\displaystyle \mathbf {E} }$ and ${\displaystyle \omega }$.

Typical applications are the computation of cavity modes (e.g., for semiconductor lasers), plasmonic modes and photonic crystal band-structures.

### Heat Conduction

Ohmic losses of the electromagnetic field can cause a heating, which distributes over the object and changes the refractive index of the structure. The temperature distribution ${\displaystyle T}$ within a body is governed by the heat equation

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

where ${\displaystyle c}$ is the specific heat capacity, ${\displaystyle \rho }$ is the mass density, ${\displaystyle k}$ is the heat conductivity, and ${\displaystyle q}$ is a thermal source density. Given a thermal source density ${\displaystyle q}$ JCMsuite computes the temperature distribution ${\displaystyle T.}$ Heat convection or heat radiation within the body are not supported. The temperature profile can be used as an input to optical computations to account for the temperature dependence of the refractive index up to linear order.

### Linear Elasticity

A heating due to Ohmic losses may also induce mechanical stress via thermal expansion. This changes the birefringence of the optical element according to the photoelastic effect and hence may influence the optical behavior. JCMsuite can solve linear problems of continuum mechanics. The equations governing linear elasticity follow from the minimum principle for the elastic energy

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

subject to fixed or free displacement boundary conditions. The quantities are the stiffness tensor ${\displaystyle C_{ijkl}}$, the linear strain ${\displaystyle \epsilon _{ij}}$, the prescribed initial strain ${\displaystyle \epsilon _{ij}^{\text{init}}}$, the displacement ${\displaystyle u_{i}}$ (due to thermal expansion), and the prescribed force ${\displaystyle F_{i}}$. The linear strain ${\displaystyle \epsilon _{ij}}$ relates to the displacement ${\displaystyle u_{i}}$ by ${\displaystyle \epsilon _{ij}={\frac {1}{2}}\left(\partial _{i}u_{j}+\partial _{j}u_{i}\right)}$. The computed strain can be used as an input to optical computations to account for the stress dependence of the refractive index. Stress and strain are related by Young's modulus.

## Numerical Method

JCMsuite relies on the finite element method. Details of the numerical implementation have been published in various contributions, e.g.[12] The performance of the methods has been compared to alternative methods in various benchmarks, e.g.[13][14] Due to the attainable high numerical accuracy JCMsuite has been used as reference for results obtained with analytical (approximative) methods, e.g.[15][11]

## References

1. ^ Potzick, J.; et al. (2008). "International photomask linewidth comparison by NIST and PTB". Proc. SPIE. Photomask Technology 2008. 7122: 71222P. Bibcode:2008SPIE.7122E..2PP. doi:10.1117/12.801435.
2. ^ Marlowe, H.; et al. (2016). "Modeling and empirical characterization of the polarization response of off-plane reflection gratings". Appl. Opt. 21 (21): 5548. Bibcode:2016ApOpt..55.5548M. doi:10.1364/AO.55.005548.
3. ^ Henn, M.-A.; et al. (2016). "Optimizing the nanoscale quantitative optical imaging of subfield scattering targets". Opt. Lett. 41 (21): 4959. Bibcode:2016OptL...41.4959H. doi:10.1364/OL.41.004959.
4. ^ Tezuka, Y.; et al. (2007). "EUV exposure experiment using programmed multilayer defects for refining printability simulation". Proc. SPIE. Emerging Lithographic Technologies XI. 6517: 65172M. Bibcode:2007SPIE.6517E..2MT. doi:10.1117/12.711967.
5. ^ Beravat, R.; et al. (2016). "Twist-induced guidance in coreless photonic crystal fiber: A helical channel for light". Sci. Adv. 2 (11): e1601421. Bibcode:2016SciA....2E1421B. doi:10.1126/sciadv.1601421.
6. ^ Wong, G. K. L.; et al. (2012). "Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber". Science. 337 (6093): 446–9. Bibcode:2012Sci...337..446W. doi:10.1126/science.1223824. PMID 22837523.
7. ^ Couny, F.; et al. (2007). "Generation and Photonic Guidance of Multi-Octave Optical-Frequency Combs". Science. 318 (5853): 1118–21. Bibcode:2007Sci...318.1118C. doi:10.1126/science.1149091. PMID 18006741.
8. ^ Shchukin, V.; et al. (2014). "Single-Mode Vertical Cavity Surface Emitting Laser via Oxide-Aperture-Engineering of Leakage of High-Order Transverse Modes". IEEE J. Quant. Electron. 50 (12): 990. Bibcode:2014IJQE...50..990S. doi:10.1109/JQE.2014.2364544.
9. ^ Gschrey, M.; et al. (2015). "Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography". Nat. Commun. 6: 7662. Bibcode:2015NatCo...6E7662G. doi:10.1038/ncomms8662. PMC . PMID 26179766.
10. ^ Yin, G.; et al. (2016). "Light absorption enhancement for ultra-thin Cu(In1−xGax)Se2 solar cells using closely packed 2-D SiO2 nanosphere arrays". Solar Energy Materials and Solar Cells. 153: 124. doi:10.1016/j.solmat.2016.04.012.
11. ^ a b Shapiro, D.; et al. (2016). "Optical field and attractive force at the subwavelength slit". Opt. Express. 24 (14): 15972–7. Bibcode:2016OExpr..2415972S. doi:10.1364/OE.24.015972. PMID 27410865.
12. ^ Pomplun, J.; et al. (2007). "Adaptive finite element method for simulation of optical nano structures". Physica Status Solidi B. 244 (10): 3419. arXiv:. Bibcode:2007PSSBR.244.3419P. doi:10.1002/pssb.200743192.
13. ^ Hoffmann, J.; et al. (2009). "Comparison of electromagnetic field solvers for the 3D analysis of plasmonic nano antennas". Proc. SPIE. Modeling Aspects in Optical Metrology II. 7390: 73900J. arXiv:. Bibcode:2009SPIE.7390E..0JH. doi:10.1117/12.828036.
14. ^ Maes, B.; et al. (2013). "Simulations of high-Q optical nanocavities with a gradual 1D bandgap". Opt. Express. 21 (6): 6794–806. Bibcode:2013OExpr..21.6794M. doi:10.1364/OE.21.006794. PMID 23546062.
15. ^ Babicheva, V.; et al. (2012). "Localized surface plasmon modes in a system of two interacting metallic cylinders". J. Opt. Soc. Am. B. 29 (6): 1263. arXiv:. Bibcode:2012JOSAB..29.1263B. doi:10.1364/JOSAB.29.001263.