Difference in polarizability of active ions in the excited and ground states 
$\Delta p$

$2\cdot {10}^{26}\text{\hspace{0.17em}}{\mathrm{cm}}^{3}$
[11] 
$4\cdot {10}^{26}\text{\hspace{0.17em}}{\mathrm{cm}}^{3}$
[14] 
Refractive index 
${n}_{0}$
 1.82 [1] 
Frequency of transition
$1\to 0$

${\nu}_{10}$

$1.84\times {10}^{13}\text{\hspace{0.17em}}{\mathrm{s}}^{1}$
[1] 
$6.00\times {10}^{13}\text{\hspace{0.17em}}{\mathrm{s}}^{1}$
[1] 
Frequency of transition
$2\to 1$

${\nu}_{21}$

$2.91\times {10}^{14}\text{\hspace{0.17em}}{\mathrm{s}}^{1}$
[1] 
$2.82\times {10}^{14}\text{\hspace{0.17em}}{\mathrm{s}}^{1}$
[1] 
Frequency of transition
$3\to 2$

${\nu}_{32}$

$8.91\times {10}^{12}\text{\hspace{0.17em}}{\mathrm{s}}^{1}$
[1] 
$3.02\times {10}^{13}\text{\hspace{0.17em}}{\mathrm{s}}^{1}$
[1] 
Frequency of transition
$4\to 2$

${\nu}_{42}$
 
$2.82\times {10}^{14}\text{\hspace{0.17em}}{\mathrm{s}}^{1}$
[10] 
Absorption cross section 
${\sigma}_{03}$

$7.7\times {10}^{21}\text{\hspace{0.17em}}{\mathrm{cm}}^{2}$
[1] 
$7.7\times {10}^{20}\text{\hspace{0.17em}}{\mathrm{cm}}^{2}$
[1] 
Emission cross section 
${\sigma}_{21}$

$2.1\times {10}^{20}{\mathrm{cm}}^{2}$
[1] 
$2.8\times {10}^{19}\text{\hspace{0.17em}}{\mathrm{cm}}^{2}$
[1] 
Lifetime of the upper laser level 
${\tau}_{21}$

$0.951\text{\hspace{0.17em}}\mathrm{ms}$
[1] 
$0.23\text{\hspace{0.17em}}\mathrm{ms}$
[1] 
Upconversion coefficient 
${\alpha}_{\mathit{\text{up}}\mathit{conv}}$
 
$5\times {10}^{17}\text{\hspace{0.17em}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{1}$
[10] 
Thermal expansion coefficient 
${\alpha}_{T}$

$7.5\times {10}^{6}\text{\hspace{0.17em}}{\mathrm{K}}^{1}$
[1] 
Thermooptic coefficient 
$\partial n\u2215\partial T$

$7.3\times {10}^{6}\text{\hspace{0.17em}}{\mathrm{K}}^{1}$
[1],
$9\times {10}^{6}\text{\hspace{0.17em}}{\mathrm{K}}^{1}$
[10] 
Effective thermooptic coefficient (for rods) 
${(dn\u2215dT)}_{\mathit{eff}}$

${10}^{5}\text{\hspace{0.17em}}{\mathrm{K}}^{1}$
[2] 
Density 
ρ

$4.56\text{\hspace{0.17em}}\mathrm{g}\cdot {\mathrm{cm}}^{3}$
[1] 
Specific heat 
${C}_{p}$

$0.59\text{\hspace{0.17em}}\mathrm{J}\cdot {\mathrm{g}}^{1}\cdot {\mathrm{K}}^{1}$
[1] 
Thermal conductivity 
K

$0.065\text{\hspace{0.17em}}\mathrm{W}\cdot {\mathrm{cm}}^{1}\cdot {\mathrm{K}}^{1}$
[19] (for 9 at.%) 
$0.1\text{\hspace{0.17em}}\mathrm{W}\cdot {\mathrm{cm}}^{1}\cdot {\mathrm{K}}^{1}$
[5] (for 1 at.%) 
 
$0.09\text{\hspace{0.17em}}\mathrm{W}\cdot {\mathrm{cm}}^{1}\cdot {\mathrm{K}}^{1}$
[19] (for 2 at.%)  
Heat transfer coefficient 
H

$2\text{\hspace{0.17em}}\mathrm{W}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{2}\phantom{\rule{0.2em}{0ex}}{\mathrm{K}}^{1}$
[1] 
Young modulus 
E

$3.1\times {10}^{7}\text{\hspace{0.17em}}\mathrm{kg}\cdot {\mathrm{cm}}^{2}$
[1] 
Tensile strength  
$2\times {10}^{4}\text{\hspace{0.17em}}\mathrm{kg}\cdot {\mathrm{cm}}^{2}$
[1] 
Poisson ratio 
ν
 0.3 [1] 
Active ion concentration at 1% doping  
$1.38\times {10}^{20}\text{\hspace{0.17em}}{\mathrm{cm}}^{3}$
[1] 
Simulated parameters of laser elements 
Doping concentration for rods   2 at.%  1 at.% 
Doping concentration for disks   9 at.%  1 at.% 
Length of the rods 
L

$15\text{\hspace{0.17em}}\mathrm{mm}$

Thickness of CWpumped disks 
L

$0.1\u20130.8\text{\hspace{0.17em}}\mathrm{mm}$

Thickness of pulsepumped disks 
L

$0.3\text{\hspace{0.17em}}\mathrm{mm}$

Pump power for rods in CW mode 
P

$20\text{\hspace{0.17em}}\mathrm{W}$

Pump power for rods in pulse mode 
P

$40\text{\hspace{0.17em}}\mathrm{W}$

Pump power for disks 
P

$1\text{\hspace{0.17em}}\mathrm{kW}$

Pump radius for disks 
${w}_{p}$

$4\text{\hspace{0.17em}}\mathrm{mm}$

Pump radius for rods in CW mode 
${w}_{p}$

$0.1\u20130.9\text{\hspace{0.17em}}\mathrm{mm}$

Pump radius for rods in pulse mode 
${w}_{p}$

$0.5\text{\hspace{0.17em}}\mathrm{mm}$

Constant characterizing ASE in rods 
${\gamma}_{\mathit{ASE}}$

$(2.2\xf7178.0)\times {10}^{24}\text{\hspace{0.17em}}{\mathrm{cm}}^{3}$

Constant characterizing ASE in disks 
${\gamma}_{\mathit{ASE}}$

$(3.3\xf726.4)\times {10}^{22}\text{\hspace{0.17em}}{\mathrm{cm}}^{3}$
