U(2). The set of all 2 × 2 unitary matrices is called U(2).
We have shown that linear optical...

Question

U(2). The set of all 2 × 2 unitary matrices is called U(2).
We have shown that linear optical elements are always represented by members of
U(2). But do all of the members of U(2) represent physically possible linear
optical elements? Show that this is so by proving that any matrix in U(2) can
be written as a product of the matrices for phase shifters and balanced beam
splitters. We can therefore use these basic devices as component parts to
construct any imaginable linear optical element. Hint: Tackle a simpler problem
first. Figure out how to construct any unitary matrix with only real entries of
the form

Banasree · Accepted Answer

Ans. 
A phase shifter device is used to provide a phase shift of RF value. This RF value is normally for a phase change of 180˚ or 360 ˚. 
Therefore,

U(2). The set of all 2 × 2 unitary matrices is called U(2). We have shown that linear optical elements are always represented by members of U(2). But do all of the members of U(2) represent physically...

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