Hi.  Please no not merge to a similar thread.

A laser beam travels trough air, enters glass, then a rhodamine+ dye, changing its green wavelength to yellow :

 

If the dye is a thin layer, should the green beam pass trough it as yellow ?   Or, if the dye is 'sandwiched' between glass 'slides' , would it exit the second glass as yellow ?  Will it be coherent and monochromatic ?

3 hours ago, Externet said:

Hi.  Please no not merge to a similar thread.

A laser beam travels trough air, enters glass, then a rhodamine+ dye, changing its green wavelength to yellow :

 

If the dye is a thin layer, should the green beam pass trough it as yellow ?   Or, if the dye is 'sandwiched' between glass 'slides' , would it exit the second glass as yellow ?  Will it be coherent and monochromatic ?

The yellow is fluorescence. The emitted light will be scattered from the beam and will not be coherent. It will be near monochromatic if only one transition is excited in the fluorescence process but will have the line shape of that emission line. In a thin film some of the beam may emerge on the far side but if it does it will be what remains of the original beam, i.e. green.

There's an interesting phenomenon that you may have observed.
If you have a sheet of fluorescent plastic, the edges seem to glow brighter than the faces.

It's due to internal reflection. The amount of light emitted is the same from all teh faces, but the smaller faces are brighter.

It could be coherent if a resonant cavity were used. It’s how dye lasers work.