# Oh, so that what it is called “optical isolator”

One of the reason why I do like study engineering course especially photonics is the application of the mathematical modelling in making/proofing/calculating or even inventing something that has not even invented before, and now it has become a reality, being used widely in the world.

Recently, I get an interesting problem from one of my course,

An optical isolator transmits light travelling in one direction and blocks it in the opposite direction. Show that isolation of the light reflected by a planar mirror may be achieved by using a combination of a linear polarizer and a quarter-wave retarder with axes 45° with respect to the transmission axis of the polarizer.

The first step I do when I get the problem is, asking to myself: Umm.. What is it? How does it work? How does the scheme look like? How does the device physically representated?

So, I found out like this,

Physically, it similar with the fiber optic. But in reality, it does not and works totally different. So, this device is used in combination with laser in order to prevent back reflection to the source (laser). Obviously, the source will get damaged when they received any signal back to the local system. So, that is why this device exists.

The scheme for this system, mostly based on Faraday rotator. But in this problem, I put them in with the description explained. What is Faraday rotator? Hmm.. I will explain it when I get them.

So, I designed something like this,

Ahh.. Those are transfer blocks. LP, QWR and M are standing for linear polarizer, quantum wave retarder and mirror, respectively. So, each optical component is described by matrix called “Jones matrix”. This matrix has several definition for different optical component. The ones we used in here are:

In short, we will have a complete mathematical equation as follows,

In this problem, we do not care with the input wave. We will only deal with the LP, QWR and M, and it is denoted in Tt.

After a long matrix multiplication, we will arrive in this result:

Whoa! It is really zero!