Intensities from the Michelson Beamsplitter

[Identity]

(A laser monochromatic laser is shone in from the left, that's E_{in}.)

[PLAIN]http://img820.imageshack.us/img820/6184/beamsplitter.png

In the lecture notes, it says that:

E_{out1}=rE_2+tE_1, where E_1=-rE_{in}e^{i\phi} and E_2=tE_{in}e^{i\phi}

I don't really understand the signs (+/-) here.

According to the Fresnel equations, light reflecting off a material with a higher refractive index will experience a 180 degree phase shift, hence the minus sign in the E_1 equation. But then why isn't there also a minus sign here: E_{out1}=(-)rE_2+tE_1, is E_2 not also reflecting off a material with higher refractive index?

Thanks

 

[Charles Link]

This is an asymmetric beamsplitter as it necessarily is, with an AR (anti-reflection) coating on one of the faces. If $E_{out1}$ is down below, and $E_2$ coming from the right, with $E_1$ coming from above, they have the uncoated surface of the beamsplitter as being the upper surface, so that the reflection of $E_{inc}$ is off the higher index as it goes to the upper mirror and becomes $E_1$ and gets a $\pi$ phase change=-1 factor , and the $E_2$ coming from the right mirror reflects off the inside of the beam splitter, so there is no $\pi$ phase change. It should be noted their $t$ is actually a composite Fresnel coefficient that results from crossing both the surface with the AR coating and the surface that has no AR coating. See also: https://www.physicsforums.com/threads/if-maxwells-equations-are-linear.969743/#post-6159689