Abstract

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)

where Avogadro constant is: NA= 6.02214076×10^23 mol−1

The stimulated absorption cross-section of the laser crystal is σa, the length of the crystal is L, and the transmittance of the crystal is T, then there is a relationship:

σ*σa=(-lnT)/(Ng*L)

where M is the molar mass (g/mol). N is the molar concentration of the active ions (mol/cm³).

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 Yb:YAG Crystal

For Yb:YAG crystal, the full name is: Ytterbium:Yttrium-Aluminium-Granat, and the chemical formula is: Y3:Al5O12. ρ=4.55g/cm^3, mY=88.9, mA=27.0, mO=16.0.

Then the Yb concentration is:

Ng=(3*4.55*6.02*1023*D)/(1*88.9+1*50.9+4*16.0)=1.38*1022*D/cm3

The stimulated absorption cross section of Yb:YAG is: σa=0.8×10-20cm2

Then the absorption coefficient of Yb:YAG crystal is:
αYb:YAG, 10%=σa*Ng=0.8×10-20 * 1.38 * 1022 * 0.1 = 11.04 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

Absorption coefficient of Pr:YLF Crystal

For Pr:YLF crystal, the full name is: Protactinium:Yttrium-Lithium-Fluoride, and the chemical formula is: Pr3+:LiYF4. ρ=3.95g/cm^3, mY=88.9, mLi=6.9, mF=19.0.

Then the Yb concentration is:

Ng=(1*3.95*6.02*1023*D)/(1*88.9+1*6.9+4*19.0)=1.384*1022*D/cm3

The stimulated absorption cross section of Pr:YLF is: σa=0.89×10-19cm2

Then the absorption coefficient of Pr:YLF crystal is:
αPr:YLF, 0.5%=σa*Ng=0.89×10-19 * 1.384 * 1022 * 0.005 = 6.159 cm-1