3D Finite-Difference Time-Domain Simulation
Interactive 3D FDTD simulation for accurate optical field analysis, mode analysis, and device optimization. Visualize electromagnetic field propagation, mode profiles, and device performance in real-time.
Adjust simulation parameters to analyze different device geometries and operating conditions.
Real-time 3D visualization of electromagnetic field propagation with interactive controls for different viewing angles and time steps.
Comprehensive mode analysis including effective index calculation, mode profiles, and dispersion characteristics.
Real-time calculation of key performance metrics including propagation loss, confinement factor, and bandwidth.
Automated optimization algorithms for device geometry and material parameters to achieve target performance specifications.
The Finite-Difference Time-Domain method solves Maxwell's equations in the time domain:
The FDTD method discretizes Maxwell's equations:
$$\nabla \times \vec{E} = -\mu \frac{\partial \vec{H}}{\partial t}$$
$$\nabla \times \vec{H} = \epsilon \frac{\partial \vec{E}}{\partial t} + \vec{J}$$
The Yee algorithm uses a staggered grid with electric and magnetic fields:
$$E_x^{n+1}(i,j,k) = E_x^n(i,j,k) + \frac{\Delta t}{\epsilon} \left[\frac{H_z^{n+1/2}(i,j+1,k) - H_z^{n+1/2}(i,j,k)}{\Delta y} - \frac{H_y^{n+1/2}(i,j,k+1) - H_y^{n+1/2}(i,j,k)}{\Delta z}\right]$$
The Courant-Friedrichs-Lewy (CFL) stability condition:
$$\Delta t \leq \frac{1}{c\sqrt{\frac{1}{(\Delta x)^2} + \frac{1}{(\Delta y)^2} + \frac{1}{(\Delta z)^2}}}$$