Beam Splitter

A beam splitter is used for splitting a beam of light in two. One way of making a splitter is to deposit a thin layer of metal between two glass prisms. The beam is slightly attenuated within the layer and then split into two paths. This example models the thin metal layer using a transition boundary condition, which reduces the memory requirements. Losses in the metal layer are also computed.

Figure 1: A beam splitter composed of two prisms with a thin layer of metal between them.

Model Definition

Model the beam splitter in the 2D plane, as shown in Figure 1, under the assumption that the electric field is polarized perpendicular to the plane. A Gaussian beam of wavelength 700 nm propagates in the x direction through the glass prism of refractive index n = 1.5. A 13 nm thin layer of silver sandwiched between the two prisms splits the beams.

The model geometry is a square region around the region where the Gaussian beam crosses the silver layer. The focus of the beam is at the left boundary, so the expression for the beam intensity at the focal plane can be used as the excitation. The expression for the relative electric field intensity at the focal plane of a Gaussian is

where w = 3500 nm is the beam waist, and the y = 0 line is the centerline of the beam. Use this expression in a Scattering Boundary Condition on the left side to model the incident beam. Model all the other domain boundaries using Scattering Boundary Conditions. These conditions are appropriate when they are placed several wavelengths away from any scattering objects and the wave is known to be traveling at normal or almost normal incidence.

The thin silver layer is modeled using a Transition Boundary Condition. At a free-space wavelength of 700 nm, the dielectric of silver is about εr = −16.5 −1.06i, where the imaginary part accounts for the losses. Thus, you can set the conductivity of the metal to zero. This boundary condition allows for a discontinuity in the fields across the interface by splitting the mesh at the boundary. It can introduce both losses and a phase shift across the interface. It does not require a mesh of the thickness of the domain, and thus saves significant memory. Mesh the two domains with triangular elements, with the maximum size set such that there are six elements per wavelength in the glass.

The second part of this tutorial uses the Electromagnetic Waves, Beam Envelopes interface to model the beam splitter. In this case a coarser mesh is used, making the simulation time much shorter.

Results and Discussion

Figure 2 shows the electric field intensity in the modeling domain. The beam is split into two beams, one propagating in the x direction and the other one in the y direction. The splitting can be evaluated by computing the flux crossing the incoming boundary and the two outgoing boundaries. Figure 3 plots the power crossing these boundaries as well as the losses at the mirror.

Figure 4 also shows the electric field norm, as inFigure 2, but is the result of using the Electromagnetic Waves, Beam Envelopes interface.

Figure 2: The electric field intensity shows that the incoming beam is split into two beams of approximately equal intensity.

Figure 3: The power flux crossing the input boundary and the two output boundaries as well as the losses at the silver surface.

Figure 4: The electric field intensity when simulated with the Electromagnetic Waves, Beam Envelopes interface (compare with Figure 2).

Wave_Optics_Module/Optical_Scattering/beam_splitter

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
lda0	700[nm]	7E-7 m	Vacuum wavelength
lda	lda0/1.5	4.6667E-7 m	Material wavelength
f0	c_const/lda0	4.2827E14 1/s	Frequency
eps_Ag	-16.5-1.06*i	-16.5-1.06i	Relative dielectric constant, Silver
w0	5*lda0	3.5E-6 m	Spot radius

Here, c_const is a predefined COMSOL constant for the speed of light in vacuum and lda is the material wavelength, defined as the vacuum wavelength divided by the refractive index. In this case, 1.5 is the refractive index of the glass material that will be used in the model.

Geometry 1