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