Wave Optics Module Updates

For users of the Wave Optics Module, COMSOL Multiphysics® version 5.2a brings a new Polarization domain feature for easier simulation of nonlinear frequency mixing and nonlinear parametric processes, increased flexibility in the Electromagnetic Waves, Beam Envelopes interface, and more. Review all of the Wave Optics Module updates in further detail below.

Polarization Domain Feature

Different frequency-domain interfaces can be coupled with the new Polarization domain feature. This simplifies simulations of nonlinear frequency mixing, like sum- and difference-frequency generation; and nonlinear parametric processes. The Polarization feature is available as a subnode for the Electromagnetic Waves, Frequency Domain and the Electromagnetic Waves, Beam Envelopes interfaces.

Application Library path for an example utilizing the Polarization Domain feature:

Wave_Optics_Module/Verification_Examples/second_harmonic_generation_frequency_domain

New App: Polarizing Beam Splitter

Polarizing beam splitter cubes consist of two right-angled prisms where a dielectric coating is applied to the intermediate surface. The cube transmits part of the incident wave while reflecting the other part. An advantage of using this cube design, instead of a plate design, for beam splitters is that ghost images are avoided.

This new app demonstrates the basic MacNeille design, which consists of pairs of layers with alternating high and low refractive indices, and where you can select how many layers will make up your splitter. You can enter refractive indices for the prisms and the layers in the dielectric stack, either directly or through a predefined material list.

Sweeps can be performed over a range of wavelengths or spot radii. The app displays the norm of the total electric field and the electric field for the first and second wave for a given wavelength or spot radius and polarization. Also presented is the reflectance and transmittance.

Application Library path:

Wave_Optics_Module/Applications/polarizing_beam_splitter

Screenshot of the Polarizing Beam Splitter app. The graphics window to the right displays the beam, incident from the left, that is reflected upwards by the thin-film stack applied to the boundaries between two prisms. Parameter sweeps over the wavelength or the spot radius can be performed. The electric field, the reflectance and transmittance, and the refractive index profiles can be displayed in the graphics window, in addition to the geometry and the mesh. Screenshot of the Polarizing Beam Splitter app. The graphics window to the right displays the beam, incident from the left, that is reflected upwards by the thin-film stack applied to the boundaries between two prisms. Parameter sweeps over the wavelength or the spot radius can be performed. The electric field, the reflectance and transmittance, and the refractive index profiles can be displayed in the graphics window, in addition to the geometry and the mesh.

Screenshot of the Polarizing Beam Splitter app. The graphics window to the right displays the beam, incident from the left, that is reflected upwards by the thin-film stack applied to the boundaries between two prisms. Parameter sweeps over the wavelength or the spot radius can be performed. The electric field, the reflectance and transmittance, and the refractive index profiles can be displayed in the graphics window, in addition to the geometry and the mesh.

User-Defined Wave Vector Specification

More flexibility has been added to the Electromagnetic Waves, Beam Envelopes physics interface by way of a new section in the Settings window called User Defined Wave Vector Specification. This was added so that you are able to set the wave vector correctly for perfectly matched layer (PML) domains when you want to specify a User defined phase. The default settings can be erroneous in that situation. By selecting User defined in the Type of phase specification list, you will see the new User Defined Wave Vector Specification section, which allows you to specify special settings in, for example, the Perfectly Matched Layer domains.

Updated App: Plasmonic Wire Grating Analyzer

Surface plasmon-based circuits are being used in applications such as plasmonic chips, light generation, and nanolithography. The Plasmonic Wire Grating Analyzer application computes the coefficients of refraction, specular reflection, and first-order diffraction as functions of the angle of incidence for a plasmonic wire grating on a dielectric substrate.

The model describes a unit cell of the grating, where Floquet boundary conditions define the periodicity. Postprocessing functionality allows you to expand the number of unit cells and extract the visualization into the third dimension.

Built into the app is the ability to sweep the incident angle of a plane wave from the normal angle to the grazing angle on the grating structure. The app also allows you to vary the radius of a wire as well as the periodicity or size of the unit cell. Further parameters that can be varied are the wavelength and orientation of the polarization.

The application presents results for the electric field norm for multiple grating periodicity for selected angles of incidence, the incident wave vector and wave vectors for all reflected and transmitted modes, and the reflectance and transmittance.

Application Library path:

Wave_Optics_Module/Applications/plasmonic_wire_grating

The Plasmonic Wire Grating Analyzer app computes diffraction efficiencies for the transmitted and reflected waves and the first and second diffraction orders for a wire grating on a dielectric substrate. The wavelength, polarization, material properties, wave periodicity, and radius can be changed. The Plasmonic Wire Grating Analyzer app computes diffraction efficiencies for the transmitted and reflected waves and the first and second diffraction orders for a wire grating on a dielectric substrate. The wavelength, polarization, material properties, wave periodicity, and radius can be changed.

The Plasmonic Wire Grating Analyzer app computes diffraction efficiencies for the transmitted and reflected waves and the first and second diffraction orders for a wire grating on a dielectric substrate. The wavelength, polarization, material properties, wave periodicity, and radius can be changed.

New Tutorial Model: Second Harmonic Generation in the Frequency Domain

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 generation (SHG) process, where light at the fundamental frequency is passed through a crystal with nonlinear optical properties that generates light at the second harmonic frequency.

The tutorial model couples the physics from two Electromagnetic Waves, Frequency Domain interfaces — one for the fundamental wave and one for the second harmonic — by using the Domain Polarization feature for each interface.

Results show that energy is transferred from the fundamental to the second harmonic wave, causing the amplitude for the fundamental wave to decrease, whereas the amplitude for the second harmonic wave starts at zero and increases during the propagation through the crystal. These results are compared against the analytical solution from the slowly varying envelope approximation (SVEA).

Application Library path:

Wave_Optics_Module/Verification_Examples/second_harmonic_generation_frequency_domain

Plot of the y-polarization of the electric field for the fundamental wave (top) and the second harmonic wave (bottom). Notice that the amplitude for the second harmonic wave increases with propagation, as energy is transferred to it from the fundamental wave. It is also evident from the plot that the wavelength of the second harmonic wave is half that of the fundamental wave. Plot of the y-polarization of the electric field for the fundamental wave (top) and the second harmonic wave (bottom). Notice that the amplitude for the second harmonic wave increases with propagation, as energy is transferred to it from the fundamental wave. It is also evident from the plot that the wavelength of the second harmonic wave is half that of the fundamental wave.

Plot of the y-polarization of the electric field for the fundamental wave (top) and the second harmonic wave (bottom). Notice that the amplitude for the second harmonic wave increases with propagation, as energy is transferred to it from the fundamental wave. It is also evident from the plot that the wavelength of the second harmonic wave is half that of the fundamental wave.

New Tutorial Model: 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 enters a holographic material from the left boundary while another enters it from the top boundary. This simulates a bit-by-bit holographic data storage, including data recording and retrieval. In the recording process, the two beams intersect and create an interference fringe pattern, which is recorded in the hologram carrying the single-bit data.

Application Library path:

Wave_Optics_Module/Gratings_and_Metamaterials/single_bit_hologram

Plot of the interference pattern during the recording process. The reference beam is incident from the left and the object beam is incident from the top. The left plot represents the summed electric field from the two beams, whereas the right plot represents the intensity pattern from the two interfering beams. Plot of the interference pattern during the recording process. The reference beam is incident from the left and the object beam is incident from the top. The left plot represents the summed electric field from the two beams, whereas the right plot represents the intensity pattern from the two interfering beams.

Plot of the interference pattern during the recording process. The reference beam is incident from the left and the object beam is incident from the top. The left plot represents the summed electric field from the two beams, whereas the right plot represents the intensity pattern from the two interfering beams.