Incident light angle-Brewster's angle

I want to produce below figure:

I sweep it but never look like it!
simulation file:brewster.fsp (20.5 KB)
Can you help me?


Dear @m.dezyani

Please refer to Brewster’s angle example in KB page. After modifying the simulation file (setting the wavelength at 0.7 um, n2=1.5, and mesh accuracy of 2), here is the plot for P polarized light:

Please repeat the simulation for s-polarization and let me know if you have any further question.

brewster.fsp (24.7 KB)


Thank you, Mr @bkhanaliloo
Why did you use the gaussian source?

The Best

Hi @m.dezyani
Let’s talk about some basic features of laser beam. The laser differs from other incoherent light because it has some special features. One of those features is monochromaticity. Although it is never composed of only a single wavelength in laser cavity, laser
beam can be considered to be monochromatic because the oscillating laser consists
of very closely spaced, discrete, and narrow spectral lines (laser modes or cavity modes) compared with conventional light source whose emission covers frequency
bandwidth in the order of gigahertz.
For better monochromaticity, single mode can be achieved by forcing laser to
oscillate on a single transverse (usually, the fundamental TEM00 Gaussian mode ) and longitudinal mode. Other great feature is the manipulation of laser beam .
Focusing: Laser beam can be focused by curved mirrors or lenses to reduce its
spot size. The radius of focused Gaussian-mode laser beam (wf ) is the smallest
laser beam radius at the plane z = 0 as shown in the following figure

both the focused radius and depth of focus of a laser beam with Gaussian mode increase with the focal length of focusing optics. Another great feature is Shaping (spatial shaping): The commonly used laser beam for cutting purpose is the Gaussian beam (TEM00), but it can be shaped into other profiles such as tophat and rectangular beams, which have a complex power distributions rather than a Gaussian distribution .

Best regards

Hi @m.dezyani

We used Gaussian source in the KB example to demonstrate and compare the reflection profile for two polarizations, as it will not be very easy to visualize with plane waves.

However, you can use plane waves for your purpose. In your simulation file, when you use plane waves with PML boundaries, edge effects occur which might effect the accuracy of your simulations.Thus we recommend to use periodic BCs for injection angle of zero and Bloch boundaries for angled injections.

In your case please change the x and y BCs to Bloch and run the sweep. Please keep me updated with your results and simulation files for future references. I did a quick run and results seem to be reasonable to me.

@konslekk: Many thanks for providing information about the laser beam. That was very informative.



Hi @bkhanaliloo
I used plane wave with bloch BC.

There is big difference between (PML+Guassian) and (Bloch+plane wave).

Hi @m.dezyani

Here is my simulation result for plane wave with Bloch BCs:

These results seem to match better with theoretical expectations. Here is also my simulation file.

brewster_PlaneWaveBlochBC.fsp (23.9 KB)

The results between two simulations seem to match quite well. For these simulations I used a slightly longer pulse to make sure that injected light has a single frequency. This might increase simulation time but guarantees that light is emitted at expected angle.

Thanks you @bkhanaliloo

HI @bkhanaliloo

I have a follow up question

Do you think its still possible to get similar curve out from far field-ux-uy projections (or rather Back Focal plane) . So if incident light is X-polarized, i will see the brewster Null in the far field along respective axis (This i can already see in my simulation with High enough NA to cover the incident angle at which brewster effect happens ).

As far as i understand, the far field projections are arbitary magnitude which can only be normalized with injected power. which means I cannot get the same magnitude, TM Reflectance curve from Gaussian beam in far field. Is it right ?

Yes, power normalization would be difficult because you would not know the power of the incident light as a function of angle. For a farfield result, you can normalize with respect to the total power, or power inside a given range of angles, as shown on this page:

For this reason, while it should be possible to locate the Brewster angle by finding the angle where the reflection is zero(as you mentioned), I think it would be difficult to replicate the same curve that is obtained with the plane waves.

I hope this helps. Let me know if you have any questions.