2004/12/05 | 光束分离器[Beamsplitter]
类别(Ω〖物理〗) | 评论(0) | 阅读(61) | 发表于 11:55

A beamsplitter is an optical element that allows part of an electromagnetic wave to pass through while reflecting the other part. A simple dielectric can therefore serve as a beamsplitter. Consider the dielectric illustrated above with index of refraction n,thickness d,and Fresnel reflection and transmission coefficients r and t , and let and , and incident electric field intensity . Let be the phase of the single-reflected beam, the phase of the doubly-reflected beam, and so on. Then the zeroth-order term is






(1)

where is the phase difference upon passing through the dielectric. Similarly, the first-order term is


(2)



(3)









(4)

and the second-order term is


(5)



(6)






(7)

Therefore, by induction,

(8)

Now define
(9)

If all rays are collected,







(10)

so the power transmission is
(11)

But
(12)

where k is the wavenumber and l is the distance difference, and
(13)

(14)


Writing
(15)

then gives
(16)

The plots above show T as a function of frequency for various beamsplitter thicknesses.

Note that only the rays up to n = k are included, then






(17)
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