From the experiment, the ellipticity and intensity of circularly polarized 800 nm laser have changed after it is reflected by a R800/T400 dichromatic beamsplitter. Could someone tell me how to calculate or estimate the change of ellipticity?
It is usually done by using 'analyzers'. Probably the most easy-to-use system is a Babinet-Soleil compensator. There is an old -and nice- article, by Kent and Lawson, that explain how to measure the ellipticity (DOI:10.1364/JOSA.27.000117).
Obviously, you can also analyze the Stokes vector of the reflected beam by means of a 'Stokes vector bases' (Linear -45º, Linear 0º, elliptical 30º and elliptical 60º) or a circular analyzer (a quarter waveplate at 800nm and a polarizer).
Particularly, if you only need to measure the ellipticity, you can use a quarterwave plate (@800nm) placed between the source (laser, beamsplitter,...) and a polarizer, with its principal axes rotated 45º with respect to the polarizer. If you measure the intensity I1, and you rotate the polarizer 90º in order to measure the intensity I2, you obtain the beam ellipticity in a straight-forward way (sin(2e)=|I1-I2|/2).
I experienced the same problems ,when i guided my 800nm pulsed laser to the microscope for nonlinear emission. it was that the dichroic mirror induced a phase shift to the laser .That is ,when the input linearly polarized beam is not s- nor p-polarized,the output polarization state in the focus plane of the objective is changed into a elliptically polarized beam,not linearly polarized any more.
The similar problems had been addressed in this article : http://biomedicaloptics.spiedigitallibrary.org/article.aspx?articleid=1102565.
So i measured the phase shift and utilized a half-wave and quarter-wave plates combinations to control the polarization state output at the focus plane of objective in the microscope.it did work.and now with this combination, output light of any polarization state will be achieved.
As Guangcan stated the problem is that dichroic mirrors usually have different reflectivities for s and p polarizations. Because circularly polarized light can be thought as equal mixture of s and p polarizations which are 90 degrees out of phase any difference between s and p reflectivities will induce an elliptical polarization in the reflected beam. (you may also find that ultrafast dielectric mirrors cause similar problems.
An alternative to a Babinet-Soleil compensator is a Berek variable waveplate. We have had good results using this to pre-compensate the beam before it hits the dichroic. It should let you compensate for any amount of ellipticity. Even if you tune your laser to different wavelengths you can re-adjust the Berek waveplate to obtain the right polarization at the sample. .
>Could someone tell me how to calculate or estimate the change of ellipticity?
You may consider to directly MEASURE the state of polarization in your particular optical system, before and after the element of interest. You need a polarizer in a rotation mount and a power meter. Then, if necessary, playing with a half- and quater-wave plates, as suggested by Guangcan Li, will allow you to get the desired output polarization in almost any experimental situation.
Firstly, I would like thank you for your proposals about compensators, which is new for me! Usually, I just use a quarter waveplate combined with a polarizor to control the reflected polarization, as suggested Juan, Li and Sergei.
Following is my understanding about this issue. In general, the reflectivity of a dichroic mirror or BS depends on the polarization state of the beam. For example, if the input laser beam is s-polarized, it will be significantly attenuated after reflection but still s- polarized. As Michael mentioned, the circularly polarized light can be thought as equal mixture of s- and p- components. So the reflected beam should be elliptically polarized. If I know the reflectivity of s-polarized light by dichroic mirror/BS, I can calculate the polarization of reflected laser beam, which is originally circularly polarized.