COMSOL 6.4 - Single-Bit Hologram

A hologram is a holographically recorded object. When two coherent light beams intersect each other, an interference pattern is generated. If this occurs in a material that is sensitive to light intensities greater than a certain exposure threshold, the interference pattern is recorded in the material as a modulation of the refractive index. Such a material is called a holographic material and the process of recording is called holographic recording. When one of the two light beams is originally scattered by an object before entering the holographic material, the beam is called the object beam while the other beam is called the reference beam. In this case, the recorded hologram also contains the information about the scattering object. Now, if the hologram is illuminated by the reference beam alone in the same optical setup, the object beam will be regenerated from the holographic material. This process is called the holographic retrieval. This concept is depicted in Figure 1.

Figure 1: Holographic recording and retrieval.

Model Definition

In this model, the simplest example is chosen, in which the object beam has the same profile as the reference beam. The reference beam enters a holographic material from the left boundary while the object beam enters it from the top boundary. In the recording process, the two beams cross at 90 degree angle in the material and make interference fringes tilted at 45 degrees. For intensities above a certain exposure threshold, a refractive index modulation is induced in the holographic material on top of the constant background refractive index. In the retrieval, only the reference beam illuminates the hologram. Then this beam is partially transmitted and partially reflected off by the hologram, which regenerates the object beam. You can say that the hologram is working as a volume Bragg grating satisfying the Bragg condition for the reference beam.

Results and Discussion

Figure 2 shows the electric field distribution during the recording phase. Notice that the intensity pattern in the rightmost figure shows diagonal stripes that result in the striped refractive index modulation, shown in Figure 3.

Figure 2: Electric field distribution during recording. The left figure show the z-component of the electric field, whereas the right figure shows the squared norm of the electric field.

Figure 3: The refractive index distribution.

Figure 4 shows the intensity distribution across a cross section of the beam. The red line indicates the exposure threshold level for the holographic material. Notice that the refractive index modulation in Figure 5 starts at the location where the threshold level intersects the intensity distribution. In the wings of the beam, the intensity level is too low to induce any refractive index modulation.

Figure 4: The electric field distribution during recording. The blue curve shows the squared electric field norm, whereas the red line indicates the exposure threshold for the holographic material.

Figure 5: The induced refractive index modulation.

Finally, Figure 6 shows the electric field distribution during the retrieval phase. Here, only the reference beam is incident. However, as it is scattered by the induced refractive index grating, the object beam is regenerated and propagates toward the bottom of the figure.

Figure 6: The electric field distribution during the retrieval phase. The left figure shows the z-component of the electric field, whereas the right figure shows the norm of the electric field.

Wave_Optics_Module/Gratings_and_Metamaterials/single_bit_hologram

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

Start by loading the parameters that defines the model geometry and material properties.

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file single_bit_hologram_parameters.txt.

Geometry 1

The simulation domain consists of a rectangle with width L and height H.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type L.

In the text field, type H.

Locate the section. From the list, choose .

Click

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Refractive index, real part	n_iso ; nii = n_iso, nij = 0	n1	1	Refractive index
Refractive index, imaginary part	ki_iso ; kiii = ki_iso, kiij = 0	0	1	Refractive index

Definitions

A maximum operator will be used later when defining the refractive index variation of the hologram.

Maximum 1 (maxop1)

In the toolbar, click

and choose .

Select Domain 1 only.

Refractive Index During Recording

Now, define the refractive indices that will be used for the recording phase and the retrieval phase. This variable will later define the refractive index for the material. In the study steps, you later define which of the two refractive index variables that will be used for the different phases.

In the window, right-click and choose .

In the window for , type Refractive Index During Recording in the text field.

Locate the section. In the table, enter the following settings:


Name	Expression	Unit	Description
n	n1		Background refractive index

Modulated Refractive Index

Right-click and choose .

In the window for , type Modulated Refractive Index in the text field.

Locate the section. In the table, enter the following settings:


Name	Expression	Unit	Description
n_mod	n1+dn*(((ewfd.normE/maxop1(ewfd.normE))^2>threshold)-0.5)		Modulated refractive index

Refractive Index During Retrieval

In the window, right-click and choose .

In the window for , type Refractive Index During Retrieval in the text field.

Locate the section. In the table, enter the following settings:


Name	Expression	Unit	Description
n	withsol('sol2',n1+dn*(((ewfd.normE/maxop1(ewfd.normE))^2>threshold)-0.5))		Background refractive index

The withsol operator allows you to use expressions from a previous solution. In this case, it is the solution from the first study step, here denoted sol2, that will be used for defining the refractive index distribution during the second study step.

Materials

Material 1 (mat1)

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Refractive index, real part	n_iso ; nii = n_iso, nij = 0	n	1	Refractive index
Refractive index, imaginary part	ki_iso ; kiii = ki_iso, kiij = 0	0	1	Refractive index