- #1

zeronem

- 117

- 1

- TL;DR Summary
- Question on deriving the operator for a beam splitter of a specific ratio of split

Hello. I have a question. In the book I am reading, They derive the U

I'm having a hard time deciphering whether the formula for beam splitter operator is for a beam splitter at 50/50 ratio only, or for any ratio of a photon state with amplitudes "a" and "b" of the photon going in from the left.

I feel this derivation was based off the a beam splitter at a ratio of 50/50 which means a and b would have to be 1/2.

If a and b of the photon state were not based on a 50/50 split, but rather a 70/30 split would that change the U

_{bs}operator applied on a photon state with the beam splitter at a ratio of 50/50. A beam splitter that is used in the Mach-Zehnder interferometer.I'm having a hard time deciphering whether the formula for beam splitter operator is for a beam splitter at 50/50 ratio only, or for any ratio of a photon state with amplitudes "a" and "b" of the photon going in from the left.

I feel this derivation was based off the a beam splitter at a ratio of 50/50 which means a and b would have to be 1/2.

If a and b of the photon state were not based on a 50/50 split, but rather a 70/30 split would that change the U

_{bs}operator? Or would I go about an a = sqrt(7/10) and b = sqrt(3/10)? In the formula in the picture above?