Cryogenic nanosecond and picosecond high average and peak power (HAPP) pump lasers for ultrafast applications

David C. Brown; Sten Torneg?rd; Joseph Kolis

doi:10.1017/hpl.2016.12

Journals >High Power Laser Science and Engineering >Volume 4 >Issue 2 >Page 02000e15 > Article

High Power Laser Science and Engineering
Vol. 4, Issue 2, 02000e15 (2016)

Cryogenic nanosecond and picosecond high average and peak power (HAPP) pump lasers for ultrafast applications

David C. Brown¹, Sten Torneg?rd¹, and Joseph Kolis²

Author Affiliations

¹Snake Creek Lasers, LLC, 26741 State Route 267, Friendsville, PA 18818, USA

²Clemson University, Department of Chemistry, Clemson, SC, USA

show less

DOI: 10.1017/hpl.2016.12 Cite this Article Set citation alerts

David C. Brown, Sten Torneg?rd, Joseph Kolis. Cryogenic nanosecond and picosecond high average and peak power (HAPP) pump lasers for ultrafast applications[J]. High Power Laser Science and Engineering, 2016, 4(2): 02000e15 Copy Citation Text

EndNote(RIS)

BibTex

Plain Text

show less

$Thermal conductivity for $\text{Al}_{2}\text{O}_{3}$ as a function of temperature for the $c$-axis (green circles) and the $a$-axis (blue squares); also shown are the thermal expansion coefficient values for the $c$-axis (pink triangles) and the $a$-axis (red squares).$

Fig. 1. Thermal conductivity for $\text{Al}_{2}\text{O}_{3}$ as a function of temperature for the $c$-axis (green circles) and the $a$-axis (blue squares); also shown are the thermal expansion coefficient values for the $c$-axis (pink triangles) and the $a$-axis (red squares).

Download full size | View in the Article

YAG thermal conductivity (blue diamonds), thermal expansion coefficient (red squares) and $(dn/dT)$ (green triangles) as a function of absolute temperature.

Fig. 2. YAG thermal conductivity (blue diamonds), thermal expansion coefficient (red squares) and $(dn/dT)$ (green triangles) as a function of absolute temperature.

Download full size | View in the Article

Fig. 3. LuAG thermal conductivity (red squares), thermal expansion coefficient (blue diamonds) and $(dn/dT)$ (green triangles) as a function of absolute temperature.

Download full size | View in the Article

Fig. 4. YLF thermal conductivity along $a$-axis (blue diamonds) and $c$-axis (green triangles), thermal expansion coefficient along $a$-axis (red squares) and $c$-axis (black diamonds), and $(dn/dT)$ along the $a$-axis (pink circles) and the $c$-axis (orange circles), all as a function of absolute temperature.

Download full size | View in the Article

Fig. 5. LuLF thermal conductivity along $a$-axis (blue diamonds) and $c$-axis (green triangles), thermal expansion coefficient along $a$-axis (red squares) and $c$-axis (black triangles), and $(dn/dT)$ along the $a$-axis (pink circles) and the $c$-axis (orange circles), all as a function of absolute temperature.

Download full size | View in the Article

$YALO thermal conductivity along $a$-axis (blue diamonds), $b$-axis (red squares) and $c$-axis (green triangles), thermal expansion coefficient along the $a$-axis (black crosses), $b$-axis (blue squares) and $c$-axis (long dashes), and $(dn/dT)$ along the $a$-axis (light blue diamonds), $b$-axis (short dashes) and $c\text{-}\text{axis}(\text{pink}~\text{triangles})$, all as a function of absolute temperature.$

Fig. 6. YALO thermal conductivity along $a$-axis (blue diamonds), $b$-axis (red squares) and $c$-axis (green triangles), thermal expansion coefficient along the $a$-axis (black crosses), $b$-axis (blue squares) and $c$-axis (long dashes), and $(dn/dT)$ along the $a$-axis (light blue diamonds), $b$-axis (short dashes) and $c\text{-}\text{axis}(\text{pink}~\text{triangles})$, all as a function of absolute temperature.

Download full size | View in the Article

$$\text{Y}_{2}\text{O}_{3}$ thermal conductivity (red circles), thermal expansion coefficient (blue diamonds) and $(dn/dT)$ (green triangles) as a function of absolute temperature.$

Fig. 7. $\text{Y}_{2}\text{O}_{3}$ thermal conductivity (red circles), thermal expansion coefficient (blue diamonds) and $(dn/dT)$ (green triangles) as a function of absolute temperature.

Download full size | View in the Article

$$\text{Sc}_{2}\text{O}_{3}$ thermal conductivity (blue circles), thermal expansion coefficient (green diamonds) and $(dn/dT)$ (red squares) as a function of absolute temperature.$

Fig. 8. $\text{Sc}_{2}\text{O}_{3}$ thermal conductivity (blue circles), thermal expansion coefficient (green diamonds) and $(dn/dT)$ (red squares) as a function of absolute temperature.

Download full size | View in the Article

$$\text{GdVO}_{4}$ thermal conductivity along $a$-axis (blue diamonds) and $c$-axis (green triangles), thermal expansion coefficient along $a$-axis (black triangles) and $c$-axis (red triangles), and $(dn/dT)$ along the $a$-axis (orange circles) and the $c$-axis (pink squares), all as a function of absolute temperature.$

Fig. 9. $\text{GdVO}_{4}$ thermal conductivity along $a$-axis (blue diamonds) and $c$-axis (green triangles), thermal expansion coefficient along $a$-axis (black triangles) and $c$-axis (red triangles), and $(dn/dT)$ along the $a$-axis (orange circles) and the $c$-axis (pink squares), all as a function of absolute temperature.

Download full size | View in the Article

$$\text{CaF}_{2}$ thermal conductivity (red squares, blue diamonds and pink circles), thermal expansion coefficient green triangles) and $(dn/dT)$ (black circles) as a function of absolute temperature.$

Fig. 10. $\text{CaF}_{2}$ thermal conductivity (red squares, blue diamonds and pink circles), thermal expansion coefficient green triangles) and $(dn/dT)$ (black circles) as a function of absolute temperature.

Download full size | View in the Article

Fig. 11. Number of waves distortion per unit output power for Yb:YAG at 300 (blue line) and 77 K (red line), and the ratio of the number of waves at 300 to 77 K pink), all as a function of laser extraction efficiency.

Download full size | View in the Article

$Temporal repetitively diode-pumped sequence showing pump pulses of duration $T$, repetition rate ${\it\nu}_{R}$, the temporal variation of the initial inversion density $n_{i}$ and the inversion from a previous pulse $n_{\text{fp}}$, and the difference inversion density ${\rm\Delta}n$ due to extraction.$

Fig. 12. Temporal repetitively diode-pumped sequence showing pump pulses of duration $T$, repetition rate ${\it\nu}_{R}$, the temporal variation of the initial inversion density $n_{i}$ and the inversion from a previous pulse $n_{\text{fp}}$, and the difference inversion density ${\rm\Delta}n$ due to extraction.

Download full size | View in the Article

Fig. 13. Schematic diagram of the Thor-300 Cryo Amplifier system; the gray boxes represent copper heat sinks that are coupled to closed-cycle cryogenic coolers, the disks are shown on opposite faces of the heat sinks. Green arrows represent 940 nm pump beams used to optically pump the disks, A more detailed description may be found in the text.

Download full size | View in the Article

Fig. 14. Thor-300 Yb:YAG pump chamber showing entrance window, vacuum, window, and mounting flanges, and a pulse-tube He closed-cycle cryocooler mounted on top.

Download full size | View in the Article

$Evolution of the energy/pulse in Thor-300 cryogenic laser system as a function of the optical element number and at a 1 kHz repetition rate. The pump pulse duration is $500~{\rm\mu}\text{s}$. The Gaussian beam radius in elements 1-82 is 2 mm; after beam expansion at element 82, the beam radius is 3.5 mm.$

Fig. 15. Evolution of the energy/pulse in Thor-300 cryogenic laser system as a function of the optical element number and at a 1 kHz repetition rate. The pump pulse duration is $500~{\rm\mu}\text{s}$. The Gaussian beam radius in elements 1-82 is 2 mm; after beam expansion at element 82, the beam radius is 3.5 mm.

Download full size | View in the Article

$Evolution of the intensity in Thor-300 cryogenic laser system as a function of the optical element number and at a 1 kHz repetition rate. The pump pulse duration is $500~{\rm\mu}\text{s}$. The Gaussian beam radius in elements 1-82 is 2 mm; after beam expansion at element 82, the beam radius is 3.5 mm.$

Fig. 16. Evolution of the intensity in Thor-300 cryogenic laser system as a function of the optical element number and at a 1 kHz repetition rate. The pump pulse duration is $500~{\rm\mu}\text{s}$. The Gaussian beam radius in elements 1-82 is 2 mm; after beam expansion at element 82, the beam radius is 3.5 mm.

Download full size | View in the Article

$Evolution of the intensity (blue line) in Thor-300 cryogenic laser system as a function of the optical element number and at a 1 kHz repetition rate. Also shown is the laser damage threshold for each optical element (red line). The pump pulse duration is $500~{\rm\mu}\text{s}$. The Gaussian beam radius in elements 1-82 is 2 mm; after beam expansion at element 82, the beam radius is 3.5 mm.$

Fig. 17. Evolution of the intensity (blue line) in Thor-300 cryogenic laser system as a function of the optical element number and at a 1 kHz repetition rate. Also shown is the laser damage threshold for each optical element (red line). The pump pulse duration is $500~{\rm\mu}\text{s}$. The Gaussian beam radius in elements 1-82 is 2 mm; after beam expansion at element 82, the beam radius is 3.5 mm.

Download full size | View in the Article

Fig. 18. Evolution of the energy/pulse in Thor-300 cryogenic laser system as a function of the optical element number and at a 1 kHz repetition rate. The pump pulse duration is $500~{\rm\mu}\text{s}$. The Gaussian beam radius in elements 1-82 is 2 mm; after beam expansion at element 82, the beam radius is 3.5 mm.

Download full size | View in the Article

Fig. 19. Evolution of the intensity in Thor-300 cryogenic laser system as a function of the optical element number and at a 1 kHz repetition rate. The pump pulse duration is $500~{\rm\mu}\text{s}$. The Gaussian beam radius in elements 1-82 is 2 mm; after beam expansion at element 82, the beam radius is 3.5 mm.

Download full size | View in the Article

Fig. 20. Evolution of the intensity (blue line) in Thor-300 cryogenic laser system as a function of the optical element number and at a 1 kHz repetition rate. Also shown is the laser damage threshold for each optical element (red line). The pump pulse duration is $500~{\rm\mu}\text{s}$. The Gaussian beam radius in elements 1-82 is 2 mm; after beam expansion at element 82, the beam radius is 3.5 mm.

Download full size | View in the Article

Elastic parameters	$E_{0}$ (0 K)	$a$ ($10^{-4}/\text{K}$)	$E$ (300 K)	$B_{0}$ (0 K)	$b$ ($10^{-4}/\text{K}$)	$B$ (300 K)	${\it\nu}$
	(GPa)		(GPa)	(GPa)		(GPa)
$\text{Al}_{2}\text{O}_{3}$	393	1.33	377	241	0.84	235	0.23
CaF	—	—	110	—	—	—	0.30
$\text{Lu}_{2}\text{O}_{3}$	204	1.03	198	161	0.24	160	0.29
$\text{MgAl}_{2}\text{O}_{4}$	278	1.98	262	187	1.97	176	0.25
MgO	310	1.63	295	164	1.23	158	0.19
$\text{Sc}_{2}\text{O}_{3}$	229	1.22	221	148	0.98	144	0.24
$\text{Y}_{2}\text{O}_{3}$	176	1.37	169	147	1.93	139	0.30
YAG	—	—	302	—	—	—	0.24
YbAG	—	—	257	—	—	—	0.25
$\text{LiYF}_{4}$	—	—	77	—	—	—	0.33

Table 1. Young’s modulus, bulk modulus and Poisson’s ratio for selected laser materials (from Ref. [3]).

View in the Article

Crystal	$k$	${\it\alpha}$ ($10^{-6}$)	${\it\beta}$ ($10^{-6}$)	${\it\eta}_{h}^{\text{QD}}$	${\it\nu}$	$E$ ($10^{9}$)	${\rm\Gamma}_{T}$ ($10^{10}$)	${\rm\Gamma}_{S}$ ($10^{-5}$)	${\rm\Gamma}$	$T$
	($\text{W}/(\text{cm}\text{-}\text{K})$)	($1/\text{K}$)	($1/\text{K}$)			($\text{g}/\text{cm}^{2}$)	$(\text{W}\text{-}\text{K})/\text{cm}$	$(\text{W}\text{-}\text{cm})/\text{g}$	$(\text{W}\text{-}\text{cm})/\text{g}$	(K)
YAG	0.112	6.14	7.80	0.086	0.24	3.080	2.72	5.23	6.71	300
	0.461	1.95	0.90	0.086	0.24	3.080	305.44	67.83	753.7	100
LuAG	0.083	6.13	8.30	0.086	0.25	2.872	1.90	4.11	4.95	300
	0.254	2.46	0.70	0.086	0.25	2.872	171.5	31.35	447.86	100
YLF-$a$	0.053	10.05	$-4.60$	0.045	0.33	0.785	2.55	10.00	21.74	300
	0.242	3.18	$-0.50$	0.045	0.33	0.785	338.23	144.34	453.93	100
YLF-$c$	0.072	14.31	$-6.60$	0.045	0.33	0.785	1.69	9.54	14.45	300
	0.337	2.36	$-1.80$	0.045	0.33	0.785	176.29	270.81	1504.50	100
YALO-$a$	0.117	2.32	7.70	0.096	0.23	3.220	6.82	12.56	16.31	300
	0.649	$-1.16$	1.00	0.096	0.23	3.220	582.79	139.36	1393.60	100
YALO-$b$	0.100	8.08	11.70	0.096	0.23	3.220	1.10	3.08	2.63	300
	0.544	3.24	4.50	0.096	0.23	3.220	388.66	41.82	92.93	100
YALO-$c$	0.133	8.70	8.30	0.096	0.23	3.220	1.92	3.81	4.59	300
	0.776	3.00	1.20	0.096	0.23	3.220	224.54	64.43	536.92	100
$\text{Lu}_{2}\text{O}_{3}$	0.114	6.10	7.1^*	0.080	0.29	2.019	3.29	8.22	11.58	300
	0.340	2.90	2.3^*	0.080	0.29	2.019	63.72	51.54	224.09	100
$\text{Sc}_{2}\text{O}_{3}$	0.147	6.40	8.12	0.088	0.24	2.254	3.21	8.80	10.84	300
	0.455	0.75	2.20	0.088	0.24	2.254	313.36	265.66	1207.55	100
$\text{Y}_{2}\text{O}_{3}$	0.130	6.30	6.08	0.074	0.30	1.723	4.59	11.33	18.64	300
	0.520	0.90	2.40	0.074	0.30	1.723	325.33	156.86	653.58	100
$\text{CaF}_{2}$	0.080	19.20	$-12.70$	0.091	0.30	1.122	0.36	2.86	2.25	300
	0.390	10.60	$-7.5$^*	0.091	0.30	1.122	5.32	25.22	23.79	100
$\text{Al}_{2}\text{O}_{3}$-$c$	0.330	5.15	9.80	0.335	0.23	3.844	1.95	3.83	3.91	300
	5.150	0.71	4.05	0.335	0.23	3.844	534.62	433.72	1070.91	100
$\text{Al}_{2}\text{O}_{3}$-$a$	0.360	5.93	12.80	0.335	0.23	3.844	1.42	3.63	2.84	300
	3.440	0.90	1.90	0.335	0.23	3.844	600.51	228.55	1202.89	100

Table 2. Thermal conductivity

$k$

, thermal expansion coefficient

${\it\alpha}$

, thermo-optic coefficient

${\it\beta}$

, quantum-defect heat fraction

${\it\eta}_{h}^{\text{QD}}$

, Poisson’s ratio

${\it\nu}$

, Young’s modulus

$E$

, and calculated figures of merit

${\rm\Gamma}_{T}$

${\rm\Gamma}_{S}$

and

${\rm\Gamma}$

for selected laser crystals at 100 and 300 K. Absolute values of negative parameter values were used to calculate figures of merit. Table is reproduced from Ref. [3].

View in the Article

Crystal	Crystal	${\it\delta}{\it\lambda}_{\text{abs}}$ (FWHM)	${\rm\Delta}{\it\lambda}_{\text{abs}}$	${\it\sigma}_{\text{abs}}^{P}$	${\it\lambda}_{\text{em}}^{P}$	${\rm\Delta}{\it\lambda}_{\text{em}}$	${\it\sigma}_{\text{em}}^{P}$	${\it\tau}_{F}$	Temp.	References
	type	${\it\lambda}_{\text{abs}}^{P}$ (nm)	(FWHM)	($\text{cm}^{2}$)	(nm)	(FWHM)	($\text{cm}^{2}$)	(${\rm\mu}\text{s}$)	(K)
			(nm)	($10^{-20}$)		(nm)	($10^{-20}$)
$\begin{array}{@{}l@{}}\text{Ti}^{3+}\text{:}\text{Al}_{2}\text{O}_{3}\\ E\Vert c~({\rm\pi})\end{array}$	U	$\begin{array}{@{}c@{}}455{-}580\\ 493\end{array}$	120.0	6.45	790	225.0	3.0	3.2	300	[37, 38]
$\begin{array}{@{}l@{}}\text{Ti}^{3+}\text{:}\text{Al}_{2}\text{O}_{3}\\ E\Vert a~({\it\sigma})\end{array}$	U	$\begin{array}{@{}c@{}}455{-}575\\ 493\end{array}$	122.0	2.79	800	236.0	1.5	3.2	300	[37, 38]
$\begin{array}{@{}l@{}}\text{Cr}^{3+}\text{:LiSAF}\\ E\Vert c\end{array}$	U	$\begin{array}{@{}c@{}}600{-}703\\ 637\end{array}$	97.7	5.4	850	192.0	4.8	67	300	[39]
$\begin{array}{@{}l@{}}\text{Cr}^{3+}\text{:LiSAF}\\ E\Vert a\end{array}$	U	$\begin{array}{@{}c@{}}593{-}693\\ 637\end{array}$	102.3	2.6	850	171.4	1.6	67	300	[39]
$\begin{array}{@{}l@{}}\text{Cr}^{3+}\text{:LiCAF}\\ E\Vert c\end{array}$	U	$\begin{array}{@{}c@{}}585{-}680\\ 647\end{array}$	85.8	2.95	763	127.0	1.3	175	300	[39]
$\begin{array}{@{}l@{}}\text{Cr}^{3+}\text{:LiCAF}\\ E\Vert a\end{array}$	U	$\begin{array}{@{}c@{}}580{-}680\\ 647\end{array}$	92.7	2.00	763	127.0	0.9	175	300	[39]
$\text{Yb}^{3+}\text{:BOYS}$	A	$\begin{array}{@{}c@{}}972{-}978\\ 975\end{array}$	6.0	0.90	1062	60.0	0.43	1100	300	[40, 41]
$\text{Yb}^{3+}\text{:CaF}_{2}$	A	$\begin{array}{@{}c@{}}915{-}970\\ 979\end{array}$	$\begin{array}{@{}c@{}}53.3\\ 21.8\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.83\\ \phantom{0}0.57\end{array}$	1030	26.7	0.25	1900	300	[42]
$\text{Yb}^{3+}\text{:CaF}_{2}$	A	$\begin{array}{@{}c@{}}915{-}970\\ 980\end{array}$	$\begin{array}{@{}c@{}}53.3\\ \phantom{00}2.93\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.88\\ \phantom{0}1.57\end{array}$	$\begin{array}{@{}c@{}}1033\\ 990\end{array}$	$\begin{array}{@{}c@{}}43.3\\ 10.7\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.50\\ \phantom{0}0.83\end{array}$	1900	77	[42]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:CALGO}\\ E\Vert c~({\rm\pi})\end{array}$	U	$\begin{array}{@{}c@{}}974{-}984\\ 979\end{array}$	6.60	2.7	1040	80	0.25	420	300	[43, 44]^*
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:CALGO}\\ E\Vert a~({\it\sigma})\end{array}$	U	$\begin{array}{@{}c@{}}974{-}984\\ 979\end{array}$	7.90	1.0	1040	80	0.75	420	300	[43, 44]^*
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:GdCOB}\\ E\Vert Z\end{array}$	B	$\begin{array}{@{}c@{}}902\\ 949\\ 976\end{array}$	$\begin{array}{@{}c@{}}13.5\\ 10.8\\ \phantom{0}2.4\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.48\\ \phantom{0}0.13\\ \phantom{0}1.10\end{array}$	$\begin{array}{@{}c@{}}976\\ 1003\\ 1032\\ 1070\end{array}$	$\begin{array}{@{}c@{}}4.1\\ 18.9\\ 27.0\\ 32.4\end{array}$	$\begin{array}{@{}c@{}}0.5\\ 0.3\\ 0.6\\ 0.2\end{array}$	2440	300	[45]^*
$\text{Yb}^{3+}$:GSO	B	$\begin{array}{@{}c@{}}889{-}981\\ 897\\ 922\\ 940\\ 976\end{array}$	$\begin{array}{@{}c@{}}17.0\\ 26.0\\ 24.0\\ 10.0\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.33\\ \phantom{0}0.60\\ \phantom{0}0.39\\ \phantom{0}0.51\end{array}$	$\begin{array}{@{}c@{}}1011\\ 1030\\ 1047\\ 1080\end{array}$	72	$\begin{array}{@{}c@{}}\phantom{0}0.27\\ \phantom{0}0.18\\ \phantom{0}0.34\\ \phantom{0}0.27\\ \phantom{0}0.46\end{array}$	1560	300	[46]^*
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:KGW}\\ E\Vert a\end{array}$	B	$\begin{array}{@{}c@{}}927{-}983\\ 934\\ 981\end{array}$	$\begin{array}{@{}c@{}}14.0\\ \phantom{0}3.2\end{array}$	$\begin{array}{@{}c@{}}3.0\\ 12.0\phantom{0}\end{array}$	$\begin{array}{@{}c@{}}988\\ 1000\\ 1025\end{array}$	$\begin{array}{@{}c@{}}6.6\\ 12.0\\ 13.8\end{array}$	$\begin{array}{@{}c@{}}15.1\phantom{0}\\ 8.1\\ 2.8\end{array}$	243	300	[47]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:KGW}\\ E\Vert b\end{array}$	B	$\begin{array}{@{}c@{}}939{-}982\\ 952\\ 979\end{array}$	$\begin{array}{@{}c@{}}25.5\\ \phantom{0}5.1\end{array}$	$\begin{array}{@{}c@{}}2.0\\ 2.0\end{array}$	$\begin{array}{@{}c@{}}981\\ 1001\\ 1031\end{array}$	$\begin{array}{@{}c@{}}9.0\\ 15.1\\ 18.0\end{array}$	$\begin{array}{@{}c@{}}3.3\\ 2.6\\ 2.1\end{array}$	243	300	[47]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:KGW}\\ E\Vert c\end{array}$	B	$\begin{array}{@{}c@{}}946{-}982\\ 953\\ 979\end{array}$	$\begin{array}{@{}c@{}}14.0\\ \phantom{0}5.1\end{array}$	$\begin{array}{@{}c@{}}0.8\\ 2.0\end{array}$	$\begin{array}{@{}c@{}}981\\ 1001\\ 1024\end{array}$	$\begin{array}{@{}c@{}}7.8\\ 12.0\\ 21.1\end{array}$	$\begin{array}{@{}c@{}}2.5\\ 1.2\\ 0.8\end{array}$	243	300	[47]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:KYW}\\ E\Vert a\end{array}$	B	$\begin{array}{@{}c@{}}928{-}983\\ 934\\ 954\\ 981\end{array}$	$\begin{array}{@{}c@{}}12.1\\ 20.2\\ \phantom{0}3.4\end{array}$	$\begin{array}{@{}c@{}}2.9\\ 1.3\\ 13.1\phantom{0}\end{array}$	$\begin{array}{@{}c@{}}937\\ 1006\\ 1032\end{array}$	$\begin{array}{@{}c@{}}7.8\\ 8.6\\ 8.6\end{array}$	$\begin{array}{@{}c@{}}15.6\phantom{0}\\ 3.4\\ 2.2\end{array}$	233	300	[47]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:KYW}\\ E\Vert b\end{array}$	B	$\begin{array}{@{}c@{}}928{-}984\\ 933\\ 952\\ 980\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}9.4\\ 19.5\\ \phantom{0}7.4\end{array}$	$\begin{array}{@{}c@{}}1.9\\ 3.5\\ 2.8\end{array}$	$\begin{array}{@{}c@{}}982\\ 1002\\ 1032\end{array}$	$\begin{array}{@{}c@{}}8.6\\ 17.2\\ 22.4\end{array}$	$\begin{array}{@{}c@{}}8.5\\ 2.9\\ 1.4\end{array}$	233	300	[47]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:KYW}\\ E\Vert c\end{array}$	B	$\begin{array}{@{}c@{}}925{-}984\\ 932\\ 952\\ 979\end{array}$	$\begin{array}{@{}c@{}}13.5\\ 13.5\\ 10.1\end{array}$	$\begin{array}{@{}c@{}}1.0\\ 0.8\\ 2.0\end{array}$	$\begin{array}{@{}c@{}}982\\ 1000\\ 1024\end{array}$	$\begin{array}{@{}c@{}}15.5\\ 31.0\\ 25.9\end{array}$	$\begin{array}{@{}c@{}}28.0\phantom{0}\\ 2.2\\ 0.7\end{array}$	233	300	[47]
$\text{Yb}^{3+}\text{:LSO}$	B	$\begin{array}{@{}c@{}}894{-}985\\ 900\\ 924\\ 977\end{array}$	$\begin{array}{@{}c@{}}13.0\\ 25.0\\ 15.0\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}0.21\\ \phantom{00}0.36\\ \phantom{00}1.30\end{array}$	$\begin{array}{@{}c@{}}1004\\ 1012\\ 1032\\ 1055\\ 1083\end{array}$	73	$\begin{array}{@{}c@{}}\phantom{0}0.34\\ \phantom{0}0.32\\ \phantom{0}0.33\\ \phantom{0}0.21\\ \phantom{0}0.14\end{array}$	1680	300	[46]^*
$\text{Yb}^{3+}\text{:}\text{Lu}_{2}\text{O}_{3}$	A	$\begin{array}{@{}c@{}}899{-}977\\ 903\\ 950\\ 976\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}8.1\\ 12.1\\ \phantom{0}4.0\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}1.1\\ \phantom{0}1.4\\ \phantom{0}3.1\end{array}$	$\begin{array}{@{}c@{}}976\\ 1033\\ 1078\end{array}$	$\begin{array}{@{}c@{}}4.1\\ 14.2\\ 12.1\end{array}$	$\begin{array}{@{}c@{}}3.3\\ 1.9\\ 0.9\end{array}$	820	300	[48, 49]
$\text{Yb}^{3+}\text{:LuAG}$	A	$\begin{array}{@{}c@{}}913{-}972\\ 917\\ 941\\ 970\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}8.5\\ 21.3\\ \phantom{0}3.2\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}0.61\\ \phantom{00}0.95\\ \phantom{00}1.02\end{array}$	1030	3.4	2.50	950	295	[48, 50]
$\text{Yb}^{3+}\text{:LuAG}$	A	$\begin{array}{@{}c@{}}916{-}970\\ 917\\ 941\\ 969\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}2.8\\ \phantom{00}4.8\\ \phantom{00}1.2\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}1.35\\ \phantom{00}1.80\\ \phantom{00}2.50\end{array}$	1030	1.1	13.90	950	100	[48, 51]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:LSB}\\ E\Vert c~({\rm\pi})\end{array}$	U	$\begin{array}{@{}c@{}}894{-}975\\ 899\\ 938\\ 971\end{array}$	$\begin{array}{@{}c@{}}11.0\\ 40.4\\ \phantom{0}7.4\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}0.30\\ \phantom{00}0.14\\ \phantom{00}0.37\end{array}$	$\begin{array}{@{}c@{}}938\\ 988\\ 1042\end{array}$	36	$\begin{array}{@{}c@{}}\phantom{0}0.33\\ \phantom{0}0.29\\ \phantom{0}0.28\end{array}$	1150	300	[52]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:LSB}\\ E\Vert a~({\it\sigma})\end{array}$	U	$\begin{array}{@{}c@{}}894{-}992\\ 899\\ 939\\ 980\end{array}$	$\begin{array}{@{}c@{}}11.0\\ \text{—}\\ 23.3\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}0.20\\ \text{—}\\ \phantom{00}0.96\end{array}$	$\begin{array}{@{}c@{}}1080\\ 988\\ 980\end{array}$	55	$\begin{array}{@{}c@{}}\phantom{0}0.16\\ \text{—}\\ \phantom{0}0.12\end{array}$	1150	300	[52]
$\text{Yb}^{3+}\text{:Sc}_{2}\text{O}_{3}$	A	$\begin{array}{@{}c@{}}890{-}977\\ 893\\ 942\\ 976\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}6.9\\ 23.8\\ \phantom{0}2.3\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.6\\ \phantom{0}1.0\\ \phantom{0}4.4\end{array}$	$\begin{array}{@{}c@{}}1041\\ 1095\end{array}$	$\begin{array}{@{}c@{}}13.4\\ 10.7\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}1.44\\ \phantom{0}0.33\end{array}$	800	300	[51]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:S-FAP}\\ E\Vert c~({\rm\pi})\end{array}$	U	$\begin{array}{@{}c@{}}898{-}937\\ 900\\ 936\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}3.5\\ {<}1\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}9.5\\ \phantom{0}6.6\end{array}$	$\begin{array}{@{}c@{}}986\\ 1048\\ 1119\end{array}$	$\begin{array}{@{}c@{}}{<}1\\ 3.5\\ 9.5\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}6.6\\ \phantom{0}7.3\\ \phantom{0}0.1\end{array}$	1140	300	[53]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:S-FAP}\\ E\Vert a~({\it\sigma})\end{array}$	U	$\begin{array}{@{}c@{}}898{-}987\\ 900\\ 952\\ 986\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}4.0\\ \phantom{0}3.0\\ {<}1\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}3.9\\ \phantom{0}1.1\\ 10.8\end{array}$	$\begin{array}{@{}c@{}}986\\ 1048\\ 1119\end{array}$	$\begin{array}{@{}c@{}}{<}1\\ 4.0\\ \text{—}\end{array}$	$\begin{array}{@{}c@{}}10.8\\ \phantom{0}1.4\\ \text{—}\end{array}$	1140	300	[53]
$\text{Yb}^{3+}\text{:SSO}$	B	$\begin{array}{@{}c@{}}905{-}988\\ 914\\ 956\\ 976\end{array}$	$\begin{array}{@{}c@{}}18.0\\ 19.0\\ 24.0\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}0.68\\ \phantom{00}0.50\\ \phantom{00}0.90\end{array}$	$\begin{array}{@{}c@{}}1006\\ 1036\\ 1062\\ 1087\end{array}$	57	$\begin{array}{@{}c@{}}\phantom{00}0.26\\ \phantom{00}0.44\\ \phantom{00}0.38\\ \phantom{00}0.10\end{array}$	1640	300	[46]^*
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:SYS}\\ E\Vert c~({\rm\pi})\end{array}$	U	$\begin{array}{@{}c@{}}896{-}982\\ 918\\ 979\end{array}$	$\begin{array}{@{}c@{}}43.0\\ \phantom{0}5.4\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}0.87\\ \phantom{00}0.40\end{array}$	1040	73	0.44	800	300	[41, 54]^*
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:SYS}\\ E\Vert a~({\it\sigma})\end{array}$	U	$\begin{array}{@{}c@{}}897{-}981\\ 918\\ 979\end{array}$	$\begin{array}{@{}c@{}}43.0\\ \phantom{0}4.3\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}1.22\\ \phantom{00}0.34\end{array}$	1040	—	—	800	300	[41, 54]^*
$\text{Yb}^{3+}\text{:Y}_{2}\text{O}_{3}$	A	$\begin{array}{@{}c@{}}901{-}978\\ 904\\ 950\\ 976\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}6.1\\ 10.7\\ \phantom{0}3.8\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.7\\ \phantom{0}0.9\\ \phantom{0}2.4\end{array}$	$\begin{array}{@{}c@{}}1031\\ 1076\end{array}$	$\begin{array}{@{}c@{}}14.3\\ 15.6\end{array}$	$\begin{array}{@{}c@{}}\phantom{00}1.06\\ \phantom{00}0.42\end{array}$	850	300	[51]
$\text{Yb}^{3+}$:YAG	A	$\begin{array}{@{}c@{}}911{-}970\\ 915\\ 941\\ 969\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}8.1\\ 18.9\\ \phantom{0}2.5\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.5\\ \phantom{0}0.9\\ \phantom{0}0.9\end{array}$	1029	8.5	2.3	951	300	[2, 17]
$\text{Yb}^{3+}$:YAG	A	$\begin{array}{@{}c@{}}914{-}968\\ 916\\ 941\\ 968\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}3.9\\ \phantom{0}6.9\\ \phantom{0}0.1\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.8\\ \phantom{0}1.8\\ 37.0\end{array}$	1029	1.5	11.0	951	75–80	[2, 17]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:YCOB}\\ E\Vert X\end{array}$	B	$\begin{array}{@{}c@{}}893{-}978\\ 900\\ 950\\ 977\end{array}$	$\begin{array}{@{}c@{}}14.7\\ 14.7\\ \phantom{0}2.3\end{array}$	$\begin{array}{@{}c@{}}0.3\\ 0.2\\ 0.9\end{array}$	$\begin{array}{@{}c@{}}977\\ 1033\\ 1084\end{array}$	$\begin{array}{@{}c@{}}2.2\\ 48.2\\ 16.5\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}1.1\\ \phantom{0}0.3\\ \phantom{0}0.1\end{array}$	2200	300	[52]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:YCOB}\\ E\Vert Y\end{array}$	B	$\begin{array}{@{}c@{}}894{-}978\\ 900\\ 950\\ 977\end{array}$	$\begin{array}{@{}c@{}}12.0\\ 20.0\\ \phantom{0}2.0\end{array}$	$\begin{array}{@{}c@{}}0.2\\ 0.1\\ 1.5\end{array}$	$\begin{array}{@{}c@{}}977\\ 1033\\ 1084\end{array}$	$\begin{array}{@{}c@{}}1.3\\ 20.0\\ \text{—}\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}1.7\\ \phantom{0}0.3\\ \text{—}\end{array}$	2200	300	[52]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:YCOB}\\ E\Vert Z\end{array}$	B	$\begin{array}{@{}c@{}}894{-}978\\ 900\\ 950\\ 977\end{array}$	$\begin{array}{@{}c@{}}12.7\\ 14.7\\ \phantom{0}2.2\end{array}$	$\begin{array}{@{}c@{}}0.5\\ 0.1\\ 0.8\end{array}$	$\begin{array}{@{}c@{}}977\\ 1033\\ 1084\end{array}$	$\begin{array}{@{}c@{}}2.6\\ 28.9\\ \text{—}\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.9\\ \phantom{0}0.5\\ \text{—}\end{array}$	2200	300	[52]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:YLF}\\ E\Vert c~({\it\pi})\end{array}$	U	$\begin{array}{@{}c@{}}954{-}974\\ 959\\ 971\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}9.5\\ {\approx}5.1\phantom{0}\end{array}$	$\begin{array}{@{}c@{}}1.0\\ 0.4\end{array}$	1020	36.0	0.8	2080	300	[2, 55, 56]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:YLF}\\ E\Vert a~({\it\sigma})\end{array}$	U	$\begin{array}{@{}c@{}}927{-}981\\ 931\\ 946\\ 959\\ 972\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}8.3\\ \phantom{0}5.2\\ 15.5\\ 16.5\end{array}$	$\begin{array}{@{}c@{}}0.6\\ 0.6\\ 0.4\\ 0.3\end{array}$	1020	27.0	0.7	2080	300	[2, 55, 56]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:YLF}\\ E\Vert c~({\it\pi})\end{array}$	U	$\begin{array}{@{}c@{}}958{-}971\\ 959\\ 971\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}2.1\\ \text{—}\end{array}$	$\begin{array}{@{}c@{}}6.8\\ 1.3\end{array}$	1020	8.0	1.8	1990	79	[2, 55, 56]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:YLF}\\ E\Vert a~({\it\sigma})\end{array}$	U	$\begin{array}{@{}c@{}}930{-}971\\ 934\\ 946\\ 960\\ 971\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}8.2\\ \phantom{0}3.1\\ \phantom{0}1.5\\ \text{—}\end{array}$	$\begin{array}{@{}c@{}}0.8\\ 1.0\\ 2.4\\ 2.8\end{array}$	1020	28.0	1.0	1990	79	[2, 55, 56]
$\text{Yb}^{3+}\text{:YSO}$	B	$\begin{array}{@{}c@{}}892{-}984\\ 899\\ 917\\ 950\\ 977\end{array}$	$\begin{array}{@{}c@{}}15.0\\ 24.0\\ 31.0\\ 13.0\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}0.31\\ \phantom{0}0.32\\ \phantom{0}0.28\\ \phantom{0}0.64\end{array}$	$\begin{array}{@{}c@{}}980\\ 1003\\ 1040\\ 1056\\ 1081\end{array}$	48	$\begin{array}{@{}c@{}}\phantom{00}0.24\\ \phantom{00}0.39\\ \phantom{00}0.23\\ \phantom{00}0.17\\ \phantom{00}0.12\end{array}$	1740	300	[46]^*
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:YVO}_{4}\\ E\Vert c~({\it\pi})\end{array}$	U	$\begin{array}{@{}c@{}}383{-}991\\ 987\end{array}$	7.6	7.2	987	7.6	9.6	310	300	[57]
$\begin{array}{@{}l@{}}\text{Yb}^{3+}\text{:YVO}_{4}\\ E\Vert a({\it\sigma})\end{array}$	U	$\begin{array}{@{}c@{}}952{-}992\\ 970\\ 987\end{array}$	$\begin{array}{@{}c@{}}35.6\\ \phantom{0}9.9\end{array}$	$\begin{array}{@{}c@{}}1.9\\ 1.7\end{array}$	$\begin{array}{@{}c@{}}975\\ 987\\ 1009\end{array}$	$\begin{array}{@{}c@{}}26.5\\ 13.6\\ 17.4\end{array}$	$\begin{array}{@{}c@{}}\phantom{0}1.4\\ \phantom{0}2.3\\ \phantom{0}1.1\end{array}$	310	300	[57]

Table 3. Spectral properties of legacy and Yb-based ultrafast laser materials at room and cryogenic temperatures. Part of Table 3 is reproduced from Ref. [3].

View in the Article

Crystal type	Crystal	$E$ field orientation	Wavelength (nm)	$n_{0}$	$n_{2}$ (esu) $10^{-13}$	${\it\gamma}_{N}$ ($\text{cm}^{2}/\text{W}$) $10^{-16}$	Reference
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	1064	1.76	1.30	3.09	[61]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	532	1.78	1.40	3.30	[61]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	355	1.80	1.60	3.72	[61]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	266	1.82	2.60	5.98	[61]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	650	1.77	1.36	3.21	[62]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	700	1.77	1.33	3.17	[62]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	750	1.76	1.32	3.14	[62]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	800	1.76	1.31	3.11	[62]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	850	1.76	1.30	3.09	[62]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	900	1.76	1.29	3.06	[62]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	950	1.76	1.28	3.04	[62]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	1000	1.76	1.26	3.01	[62]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	1050	1.76	1.26	2.99	[62]
SC	$\text{Al}_{2}\text{O}_{3}$	$E\Vert C$	1100	1.75	1.24	2.97	[62]
SC	LiSAF	Unspecified	850	1.39	1.10	3.30	[63]
SC	LiCAF	Unspecified	850	1.38	1.22	3.70	[63]
SC	LiSGAF	Unspecified	850	1.39	1.10	3.30	[63]
SC	$\text{Mg}_{2}\text{SiO}_{4}$	Unspecified	1240	1.64	0.78	2.00	[63]
GM	$\text{SiO}_{2}$	I	1064	1.45	0.95	2.74	[64]
GM	$\text{SiO}_{2}$	I	527	1.46	1.05	3.00	[64]
GM	$\text{SiO}_{2}$	I	351	1.48	1.27	3.60	[64]
GM	BK-7	I	1064	1.52	1.46	4.00	[61]
SC	YAG	I	1064	1.82	2.51	5.78	[65]
SC	YAG	I	1064	1.82	2.70	6.21	[66]
CER	YAG	I	1064	1.82	2.49	5.73	[65]
SC	YALO	$E\Vert C$	1064	1.91	3.33	7.30	[26]
SC	YLF	Unoriented measurement	1064	1.46 (o) 1.48 (e)	0.60	1.72	[67]
SC	LuAG	I	1064	2.14	5.50	10.77	[66]
SC	$\text{Y}_{2}\text{O}_{3}$	I	1064	1.78	5.33	12.54	[66]
CER	$\text{Y}_{2}\text{O}_{3}$	I	1064	1.78	5.79	13.63	[65]
CER	$\text{Sc}_{2}\text{O}_{3}$	I	1064	1.85	5.32	12.05	[65]
CER	$\text{Lu}_{2}\text{O}_{3}$	I	1064	1.83	3.96	9.06	[65]
SC	MgO	I	1064	1.74	1.61	3.88	[66]
SC	$\text{MgAl}_{2}\text{O}_{4}$	I	1064	1.72	1.50	3.65	[66]
SC	$\text{CaF}_{2}$	I	1064	1.43	0.43	1.26	[66]
SC	$\text{YVO}_{4}$	$E\Vert C$	1080	2.25	8.06	15.00	[68]
SC	$\text{YVO}_{4}$	$E\Vert A$	1080	1.96	8.89	19.00	[68]
SC	$\text{YVO}_{4}$	Unoriented measurement	1064	2.06^*	10.62	21.60	[69]
SC	$\text{GdVO}_{4}$	Unoriented measurement	1064	2.08^*	8.34	16.80	[69]
SC	KGW	$E\Vert \text{Nm}$	800–1600	1.99	9.50	20.00	[70]
SC	KGW	$E\Vert \text{Np}$	800–1600	2.03	7.27	15.00	[70]
SC	KYW	$E\Vert \text{Nm}$	1080	2.01	4.80	10.00	[68]
Gas	Air	I	400	1	0.00128	0.00536	[71]
Gas	Air	I	800	1	0.00072	0.00301	[71]

Table 4. Reported room-temperature values of the linear index, nonlinear index and nonlinear coefficient for a number of important laser crystals and optical materials. Also shown are the crystal type (SC – single crystal, GM – glassy material, or CER – ceramic), the

$E$

-field orientation (parallel to specified crystal axis, unspecified, and I – isotropic), and the measurement wavelength. Table reproduced from Ref. [3].

View in the Article

Crystal	Wavelength (nm)	$n_{0}$	${\it\beta}_{1}$ ($\text{fs}/\text{mm}$)	${\it\beta}_{2}$ ($\text{fs}^{2}/\text{mm}$)	${\it\beta}_{3}$ ($\text{fs}^{3}/\text{mm}$)	${\it\beta}_{4}$ ($\text{fs}^{4}/\text{mm}$)	Reference
$\text{Al}_{2}\text{O}_{3}$-(e) (HEM)	800	1.7540	5928.1	49.9	48.3	$-30.0$	[85]
$\text{Al}_{2}\text{O}_{3}$-(o) (HEM)	800	1.7620	5960.6	42.2	48.7	$-36.7$	[85]
$\text{Al}_{2}\text{O}_{3}$-(e) (HEM)	1030	1.7477	5912.4	11.9	81.3	$-127.6$	[85]
$\text{Al}_{2}\text{O}_{3}$-(o) (HEM)	1030	1.7552	5946.7	7.0	87.9	$-146.4$	[85]
LiSAF-(e)	850	1.4054	4709.2	7.9	15.7	$-15.0$	[86]
LiSAF-(o)	850	1.4074	4720.0	9.5	28.4	$-1.2$	[86]
LiCAF-(e)	760	1.3890	4654.6	23.6	13.6	$-3.3$	[87]
LiCAF-(o)	760	1.3899	4659.5	23.1	13.7	$-3.9$	[87]
YAG	1060	1.8243	6148.6	60.9	68.3	$-46.9$	[88]
YAG	1030	1.8153	6121.7	66.6	66.7	$-41.6$	[88]
LuAG	1060	1.8279	6136.5	74.6	45.7	7.3	[89]
LuAG	1030	1.8249	6151.8	64.4	66.1	$-39.3$	[89]
YALO-(a)	1040	1.9341	6502.8	93.4	55.5	7.6	[90]
YALO-(b)	1040	1.9258	6473.2	90.3	53.5	7.2	[90]
YALO-(c)	1040	1.9140	6430.1	84.2	49.7	6.3	[90]
YLF-(e)	1020	1.4705	4927.6	21.7	24.2	$-18.7$	[91]
YLF-(o)	1020	1.4483	4851.8	18.9	23.3	$-21.3$	[91]
YVO4-(e)	1060	2.1661	5947.6	341.1	305.0	69.1	[92]
YVO4-(o)	1060	1.9579	6662.4	191.7	168.5	18.2	[92]
KGW-(Np)	1032	1.9829	6726.0	165.8	129.6	9.1	[93]
KGW-(Nm)	1027	2.0113	6828.7	178.7	139.5	12.6	[93]
KGW-(Ng)	1024	2.0625	7005.8	216.0	141.5	3.5	[93]
KYW-(Np)	1028	1.9690	6673.0	184.4	429.5	21.3	[93]
KYW-(Nm)	1028	2.0073	6814.0	207.2	495.1	26.0	[93]
KYW-(Ng)	1028	2.0514	6972.1	223.8	543.2	28.9	[93]
KYbW-(Np)	1040	1.9932	6772.2	130.5	106.2	$-29.9$	[93]
KYbW-(Nm)	1026	2.0365	6897.3	173.2	421.5	56.3	[93]
KYbW-(Ng)	1024	2.0789	7074.3	179.6	307.7	20.9	[93]
$\text{Y}_{2}\text{O}_{3}$	1030	1.8889	6386.6	113.9	93.2	$-14.0$	[94]
$\text{Sc}_{2}\text{O}_{3}$	1030	1.9654	6659.2	124.8	108.6	$-30.4$	[94]
$\text{Lu}_{2}\text{O}_{3}$	1030	1.9102	5691.4	126.1	100.6	$-15.8$	[94]
$\text{CaF}_{2}$	1030	1.4287	4784.1	18.4	20.2	$-14.7$	[26]
BK-7, N-BK-7	800	1.5108	5088.8	44.6	32.0	$-10.0$	[26]
BK-7, N-BK-7	1030	1.5071	5070.2	25.1	44.7	$-49.8$	[26]
SF10	800	1.7112	5836.7	159.2	102.9	33.4	[47]
SF10	1030	1.7030	5766.4	108.1	97.3	$-15.7$	[47]
SF11	800	1.7648	6036.4	189.4	124.1	48.3	[26]
SF11	1030	1.7553	5952.9	128.9	113.0	$-7.3$	[26]
N-SF14	800	1.7429	5957.1	176.4	117.6	41.6	[26]
N-SF14	1030	1.7337	5879.7	118.3	110.2	$-17.7$	[26]
Crystal $\text{SiO}_{2}$ (e)	1030	1.5282	5189.3	0.4	98.8	$-193.5$	[95]
Crystal $\text{SiO}_{2}$ (o)	1030	1.5342	5162.8	25.8	46.2	$-53.6$	[95]
Crystal $\text{SiO}_{2}$ (e)	800	1.5348	5200.6	38.1	50.4	$-43.9$	[95]
Crystal $\text{SiO}_{2}$ (o)	800	1.5381	5181.9	45.8	32.1	$-12.0$	[95]
Fused silica $(\text{SiO}_{2})$	800	1.4533	4890.5	36.1	27.3	$-11.0$	[96]
Fused silica $(\text{SiO}_{2})$	1030	1.4500	4875.7	19.0	40.4	$-49.8$	[96]

Table 5. Calculated room-temperature values of the linear index and the first-, second-, third- and fourth-order dispersion parameters for legacy and newer laser crystals of length 1 mm. Also shown are the operating laser wavelengths, as well as references to allow readers to know what Sellmeier or alternative index equation was used in the calculations. Table reproduced from Ref. [3].