For illumination of green light on the sample through 1 layer of approximate 1cm thick quartz surafce, what should be the power of laser source?
You need to calculate the transmittance T of your sample, for which you require calculation of its attenuation coefficient μ, assumed to be constant throughout the optical path, at the relevant frequency (i.e. photon energy).*) For this, consult the following references:
https://www.nist.gov/pml/x-ray-mass-attenuation-coefficients
https://doi.org/10.1016/j.radphyschem.2009.03.077
*) http://bit.ly/2rLJEly
https://en.wikipedia.org/wiki/Attenuation_coefficient#Napierian_and_decadic_attenuation_coefficients
The first question to ask is what green power needs to reach the sample from your laser?
While Benham Farid's references appear sound, the mass attenuation coefficients in the NIST paper are for ionising radiation with photon energies greater than 1 keV. For green light at 555 nm (540 THz), photon energy is only 2.23 eV.
The term "quartz" is often used rather loosely. Quartz is a crystalline form of silica. Fused quartz is manufactured by melting crystalline quartz to form a glassy material. Optical grades are transparent, but translucent forms are available which scatter light due to the presence of small bubbles.
High purity silica glass, particularly synthetic silica, is available with very low absorption of visible light. Transmission through a 10 mm thick window is typically around 93%. https://www.thorlabs.com/NewGroupPage9.cfm?ObjectGroup_ID=3983
At normal incidence almost all of the light lost is by reflection rather than absorption. Fresnel reflection accounts for approximately 3.5% loss at each surface, although transmission is improved with appropriate anti-reflection coatings.
If your laser has a stable output polarisation, a beam launched with the correct p-polarisation at the Brewster angle will have close to 100% transmission. https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=919
If your window is made of crystalline quartz, the absorption coefficient will depend on the purity and presence of any intended or unintended dopants. Crystalline quartz is birefringent, so the refractive index and Fresnel reflection coefficient depends on the polarisation state of the incident beam, its angle of incidence, and the orientation of the crystal lattice.
https://refractiveindex.info/?shelf=main&book=SiO2&page=Ghosh-o shows a graph of the reflection coefficient as a function of angle of incident angle for the ordinary ray of crystalline quartz. Use the 'page' menu to select the ordinary ray or results for fused silica.
https://en.wikipedia.org/wiki/Quartz
https://en.wikipedia.org/wiki/Fused_quartz
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