How to calculate absorption coefficient of laser crystal?

Question

In the laser system design, we need to know the absorption coefficient of the pump light by the crystal to determine the required length of the laser crystal. Usually, the crystal manufactures often provide the doping amount of the crystal, which is generally expressed in at.%. The following describes how to calculate the absorption coefficient of the laser crystal from the doping amount expressed as at.%.

It is known that a:AxByCz. a, A, B and C are the names of elements. x, y and z are the composition coefficients of the chemical formula. ‘a’ is the active medium, replace ‘A’. The density of AxByCz is ρ (g/cm^3). mA, mB, and mC are the atomic weights of A, B, and C respectively, and the doping amount D expressed in atomic ratio at.%.

Then the calculation formula of the doping concentration of ‘a’ is:

Ng=(x*ρ*D*NA)/(x*mA+y*mB+ z*mC)

Absorption coefficient of Nd:YAG Crystal

For Nd:YAG crystal, the full name is: Neodymium:Yttrium-Aluminium-Granat, and the chemical formula is: Nd:Al5O12. ρ=4.55g/cm^3, mY=88.9, mA=27.0, mO=16.0.

Then the Nd concentration is:

Ng=(3*4.55*6.02*1023*D)/(3*88.9+5*27.0+12*16.0)=1.38*1022*D/cm3

The stimulated absorption cross section of Nd:YAG is 

σa=6.7×10-20cm2

Then the absorption coefficient of Nd:YAG rod is:

αNd:YAG, 1%=σa*Ng=6.7×10-20 * 1.38 * 1022 * 0.01 = 9.246 cm-1

Absorption coefficient of Nd:YVO4 crystal

For Nd:YVO4 crystal, the calculation is slightly different because only a single neodymium ion can occupy a YVO4 unit:

Ng=(1*4.55*6.02*1023*D)/(1*88.9+1*50.9+4*16.0)=1.25*1022*D/cm3

Answer 1

A good way to calculate the absorption coefficient of laser crystal is to use the formula: α = (1/d) * ln(I0/It), where α is the absorption coefficient, d is the thickness of the crystal, I0 is the intensity of the incident light, and It is the intensity of the transmitted light through the crystal; essentially, you measure the intensity of light before and after passing through the crystal at a specific wavelength, then use the thickness to calculate the absorption coefficient.

You can calculate the absorption coefficient using this formula: α=2.303*A/d, where d is thickness, A is absorption and α is the absorption coefficient, respectively.