Have a question about Gaussian beam.

gudong

An ideal paraxial lens is used to focus a Gaussian beam of free-space wavelength l0 to a spot of diameter d at the waist. The same (identical, the lens and illumination are the same) optical setup is then used to focus a spot inside a block of glass of index n.
a)What is the diameter of the beam at the waist inside the glass?
b)How has the Rayleigh range of the beam changed?
c)What is the ABCD matrix that you would use to model the glass interface?

after

我认为：
a）在玻璃中光束大小要看追迹结果；
b）瑞利范围要看传输后束腰大小；
c）传输矩阵将不同面的焦距代入即可得出；

zemax

如果简单估算的话，焦斑大小为焦距和入射光的发散角的乘积
在玻璃中，由于玻璃会使焦距变长，焦点会变大，位置会变远，具体的修正量与焦点离玻璃表面的距离和玻璃折射率决定。
有了光腰的大小，利用高斯光束的那套公式，你就可以得到其他得参数。
只要用玻璃中得波长就可以。

gudong

Thank you very much for the answer. Let me make sure I understand correctly:
first about the focus length: assume input z0 is  focal length f of the length ( which is the assumption of 焦斑大小为焦距和入射光的发散角的乘积), then index/z’’=1/f, so because of glass, new focal length is n*f away.
the divergeence angle is (2 * wavelength)/(pi*2*W0) if we use wavelength in glass, then index of glass is canceled, which means the diameter of beam is the same, but Rayleigh range is n times. (z0=pi*w0^2/wavelength in glass)

Am I right? Thanks