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 :\nabla \times \mu^{-1} \nabla \times \mathbf{E} - \omega^2\epsilon\mathbf{E} = - i \omega \mathbf{J} :\nabla\cdot \epsilon\mathbf{E} = 0. for given sources \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 :\nabla \times \mu^{-1} \nabla \times \mathbf{E} = \epsilon\omega^2\mathbf{E} :\mathbf{E} = \mathbf{E}(x,y) e^{i k_z z}. Due to the symmetry of the problem, the electrical field \mathbf{E} can be expressed as product of a field \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 \mathbf{E}(x,y) and the corresponding propagation constant (wavenumber) k_z. JCMsuite also solves the corresponding formulation for the magnetic field \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 \omega and corresponding resonating fields have to be computed. No incident waves or interior sources are present. JCMsuite determines pairs of \mathbf{E} and \omega or \mathbf{H} and \omega fulfilling the time-harmonic Maxwell's curl-curl equation, e.g., :\nabla \times \mu^{-1} \nabla \times \mathbf{E} = \epsilon\omega^2\mathbf{E} :\nabla\cdot \epsilon\mathbf{E} = 0. for a pair of \mathbf{E} and \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 T within a body is governed by the
heat equation :\partial_t\left(c\rho T\right) = \nabla\cdot k\nabla T + q where c is the specific heat capacity, \rho is the mass density, k is the heat conductivity, and q is a thermal source density. Given a thermal source density q JCMsuite computes the temperature distribution 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 :\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 C_{ijkl}, the linear strain \epsilon_{ij}, the prescribed initial strain \epsilon_{ij}^\text{init}, the displacement u_i (due to thermal expansion), and the prescribed force F_i. The linear strain \epsilon_{ij} relates to the displacement u_i by \epsilon_{i j} = \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 ==