# Quadrature Separation in Homodyne Detector

I am wondering in Homodyne detector structure with a beamsplitter, why phase of input beam to beamsplitter can be conjugated? I mean for example for an input beam operator b onto the beamsplitter at homodyne detector output we will have

$$y=j \left[ b \exp(i \phi) - b \exp(-i \phi) \right]$$

I am concerned to know why either incident beam phase or phi can be conjugated?

Any comment regarding this concept would be greatly appreciated.

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I put your equation into LaTeX. I hope you don't mind. –  Colin K Jul 16 '11 at 3:55
""why phase of input beam to beamsplitter can be conjugated?"" What do You mean with "conjugated", and to what is this conjugation? ""why either incident beam phase or phi can be conjugated?"" Same question. –  Georg Jul 16 '11 at 20:51
I find the question as asked very hard to understand. Perhaps this is because it concerns a specialized subfield, but perhaps you could write a few more words explaining what you are asking about to give the non-specialist a hint. –  dmckee Jul 21 '11 at 16:19
This could be a good question if some clarifying context were added. Perhaps a diagram? –  nibot Aug 27 '11 at 21:24