# Wave Optics Module

# Wave Optics Module

### Analyze Micro- and Nano-Optical Devices with the Wave Optics Module

#### Software for Simulating Optical Design Components

The Wave Optics Module provides dedicated tools for electromagnetic wave propagation in linear and nonlinear optical media for accurate component simulation and optical design optimization. With this module you can model high-frequency electromagnetic wave simulations in either frequency- or time-domain in optical structures. It also adds to your modeling of optical media by supporting inhomogeneous and fully anisotropic materials, and optical media with gains or losses. Several 2D and 3D formulations are available in the Wave Optics Module for eigenfrequency mode analysis, frequency-domain, and time-domain electromagnetic simulation. You can calculate, visualize, and analyze your phenomena using postprocessing tools, such as computation of transmission and reflection coefficients.

#### Analysis for All Types of Optical Media

It is straightforward to simulate optical sensors, metamaterials, optical fibers, bidirectional couplers, plasmonic devices, nonlinear optical processes in photonics, and laser beam propagation. This can be done in 2D, 2D axisymmetric, and 3D spatial domains. Ports can be defined for inputs and outputs, as well as for automatic extraction of S-parameters matrices that contain the full transmission and reflection properties of an optical structure with, potentially, multiple ports. A variety of different boundary conditions can be applied to simulate scattering, periodic, and discontinuity boundary conditions. Perfectly-matched layers (PMLs) are ideal for simulating electromagnetic wave propagation into unbounded, free space while keeping computational costs down. The postprocessing capabilities allow for visualization, evaluation, and integration of just about any conceivable quantity, since you can freely compose mathematical expressions of fields and derived quantities.

#### Additional Images:

*DRUDE-LORENTZ SLIT: An incoming plane wave pulse with a flat front and a Gaussian temporal shape is illuminated over a geometry consisting of a single dispersive slab with a subwavelength slit. Periodic boundary conditions are applied to create an array of slits.*

#### A Variety of Tools for Simplifying Optics Simulation

The Wave Optics Module allows for simulation of optical media with inhomogeneous, anisotropic, nonlinear, and dispersive material properties, such as conductivity, refractive index, permittivity, or permeability. To do this, COMSOL Multiphysics gives you access to the relevant 3-by-3 tensor, if your property is anisotropic, or allows you to enter any arbitrary algebraic equations for these material properties for nonlinear, inhomogenous, and dispersive materials. For sweeps over wavelength or frequency, you can define material properties that include expressions in the frequency or wavelength variable. This flexibility in accessing the underlying equations and mathematics that describe the material properties makes the Wave Optics Module perfect for modeling hard-to-describe materials, such as gyromagnetic and metamaterials with engineered properties. It also includes valuable features for simulating Floquet-periodic structures with higher-order diffraction modes, and graded index materials.

#### Consider the Effects of Other Phenomena on Wave Optics

As with all COMSOL products, the Wave Optics Module seamlessly integrates with COMSOL Multiphysics and the other add-on modules. That integration enables you to couple other physics with the propagation of electromagnetic waves. For instance, you can monitor laser heating, or the effect of structural stresses and deformations on the propagation of light through your optical devices and components.

#### Accurate Optical Modeling with the Innovative Beam Envelope Method

In time-dependent studies of electromagnetic wave propagation you often assume that all variations in time occur as sinusoidal signals, making the problem time-harmonic in the frequency domain. The Wave Optics Module has a number of interfaces for simulating such phenomena. You can also simulate nonlinear problems where the distortion of the signal is small, thanks to certain features included in the module. If the nonlinear influence is strong, a full time-dependent study of your device is required.

When solving optics propagation problems using traditional methods, a significant number of elements is required to resolve each propagating wave. Small wavelengths are invariably involved when simulating light propagation. Typically, large amounts of computational resources are required when you are modeling components and devices that are large as compared with the wavelength. Instead, the Wave Optics Module approaches these types of simulations using the innovative beam envelope method.

This novel method for electromagnetic full-wave propagation overcomes the need for traditional approximations, by direct discretization of Maxwell’s equations. Here, the electric field is expressed as the product of a slowly varying envelope function and a rapidly varying exponential phase function. This allows for accurate simulations of optically large systems where the geometric dimensions can be much larger than the wavelength, and where light waves cannot be approximated with rays. The conventional electromagnetic full-wave propagation method is also available in the Wave Optics Module, and can be appropriately used in smaller geometries.

# Wave Optics Module

### Product Features

- In-plane, axisymmetric, and full-wave 3D electromagnetic wave propagation
- Specialized beam envelope method for efficient simulation of large structures
- User-defined materials that can be graded index, frequency-dependent, anisotropic, and lossy
- Negative-index and metamaterials
- Optical materials library with over 1400 materials including a large number of glasses used for lenses, semiconductor materials, and other areas

- Multiphysics enabled optics analysis coupled to heat transfer, structural analysis, and fluid flow
- Frequency-domain, time-domain, and eigenmode analyses
- Periodic structures with higher-order Floquet modes
- Perfectly matched layers (PMLs) for optimal representation of infinite domains

- Scattered field formulation for planar, cylindrical, spherical, Gaussian, or user-defined incident fields
- Transmission and reflection through scattering parameters (S-parameters)
- Advanced visualization capabilities for arbitrary field quantities
- Drude-Lorentz, Debye, and Selmeier dispersion models

### Application Areas

- Photonic devices
- Integrated optics
- Waveguides
- Couplers
- Fiber optics
- Photonic crystals
- Fiber Bragg gratings

- Nonlinear optics
- Harmonic generation with frequency mixing
- Optical scattering
- Surface scattering
- Scattering from nanoparticles
- Lasers and amplifiers

- Semiconductor lasers
- Rod, slab, and disk laser design
- Laser heating
- Optoelectronics
- Optical lithography
- Optical sensors

### Supported File Types

File Format | Extension | Import | Export |
---|---|---|---|

Touchstone | .s2p, .s3p, .s4p, ... | No | Yes |

Nanorods

*A Gaussian electromagnetic wave is incident on a dense array of very thin wires (or rods). The distance between the rods and, thus, the rod diameter is much smaller than the wavelength. Under these circumstances, the rod array does not function as a diffraction grating (see the Plasmonic Wire Grating model). Instead, the rod array behaves as if ...*

Optical Scattering Off of a Gold Nanosphere

*This model demonstrates the simulation of the scattering of a plane wave of light by a gold nanosphere. The scattering is computed for the optical frequency range over which gold can be modeled as a material with negative complex-valued permittivity. The far-field pattern and losses are computed.*

Time-Domain Modeling of Dispersive Drude-Lorentz Media (Wave Optics)

*This tutorial shows how to solve the full time-dependent wave equation in dispersive media such as plasmas and semiconductors. The 2D TM in-plane wave model solves for the vector potential from the wave equation and for an auxiliary electric polarization density from an ordinary differential equation.
The geometry consists of a single dispersive ...*

Hexagonal Grating (Wave Optics)

*A plane wave is incident on a reflecting hexagonal grating. The grating cell consists of a protruding semisphere. The scattering coefficients for the different diffraction orders are calculated for a few different wavelengths.*

Defining a Mapped Dielectric Distribution of a Material (Wave Optics)

*In this example, the properties of an engineeredmaterial are modeled by a spatially varying dielectric distribution. Specifically, a convex lens shape is defined via a known deformation of a rectangular domain. The dielectric distribution is defined on the undeformed, original rectangular domain and is mapped onto the deformed shape of the lens. ...*

Modeling a Negative Refractive Index (Wave Optics)

*It is possible to engineer the structure of materials such that both the permittivity and permeability are negative. Such materials are realized by engineering a periodic structure with features comparable in scale to the wavelength. It is possible to model both the individual unit cells of such a material, as well as, to model to properties of a ...*

Single-Bit Hologram

*When two coherent light beams intersect, an interference pattern appears. If this occurs in a material that is sensitive to light, with intensities greater than a certain exposure threshold, the interference pattern is recorded in the material as a modulation of the refractive index and a hologram is produced.
In this tutorial model, a beam ...*

Gaussian Beam Incident at the Brewster Angle

*This model demonstrates the polarization properties for a Gaussian beam incident at an interface between two media at the Brewster angle.
The model shows how to use the Electromagnetic Waves, Beam Envelopes physics interface with a User defined phase specification. Matched Boundary Condition features are used for absorbing waves incident to ...*

Fresnel Equations (Wave Optics)

*A plane electromagnetic wave propagating through free space is incident at an angle upon an infinite dielectric medium. This model computes the reflection and transmission coefficients and compares the results to the Fresnel equations.*

Second Harmonic Generation

*It is more difficult to generate laser emissions in the short-wavelength part of the visible and near visible part of the electromagnetic spectrum than in the long-wavelength part. Nonlinear frequency mixing makes it easier to generate new short wavelengths from existing laser wavelengths.
This tutorial model describes the second harmonic ...*

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