Optics - Re-aligning P Polarization with Brewster Windows

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SteveeGeorge
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Hi all,

I have a problem, and in need of some help.

I am an optical engineer, currently designing an attentuator for near infrared lasers (10.6μm). The attenuator consists of two enhanced ZnSe Brewster windows that rotate in opposite directions and different angles to exactly re-align polarization.

I have attached my calculations as images, so to display each step of my workings. I have accounted for the refractive indexes and transmission coefficients of both brewster windows. My objective is to formulate an expression for the 2nd brewster window angle in respects to the 1st brewster window angle to perfectly realign the P polarization, which I have taken to be in the X direction:

Handwritten derivation of coordinate rotation matrices for two Brewster windows at angles theta 1 and theta 2, with transmission expressions for the first window.

Here is the coordinate transforms and the transmission of the first Brewster windows (internal and external surfaces).

Handwritten derivation of transmitted electric field components through two Brewster windows, using rotation terms with angles theta1 and theta2 and transmission coefficients 0.99499 and 0.14142.

After calculating the final transmission of both windows, I assumed that since the angle of polarization is respective to x direction, the J component equates to zero (Re-alignment).

How do I formulate an expression for theta2, respective to theta1?

If anyone could shine some light on my problem, it would be greatly appreciated!

Thanks

-Steve
 
Attachments
  • Handwritten derivation setting an expression to zero, with terms in cos and sin of theta1 and theta2, divided by cos theta2 and rewritten using trig identities, leading to an expanded expression with tan theta2.
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  • Handwritten algebra on lined paper: an equation dividing by cos^2 theta1, expanded in tan theta2 and sin/cos terms, then rearranged into a quadratic in x = tan theta2 with the quadratic formula applied, giving x = tan theta2 as a ratio with 1.69859 sin theta1 cos theta1 in the denominator.
    Scan0020.jpg
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