Laser cooling in Yb<sup>3+</sup>:YAG

Galina Nemova; Raman Kashyap

doi:10.1364/JOSAB.31.000340

Journal of the Optical Society of America B
Vol. 31,
Issue 2,
pp. 340-348
(2014)
•https://doi.org/10.1364/JOSAB.31.000340

Laser cooling in Yb³⁺:YAG

Galina Nemova and Raman Kashyap

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Galina Nemova and Raman Kashyap, "Laser cooling in Yb³⁺:YAG," J. Opt. Soc. Am. B 31, 340-348 (2014)

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Abstract

We develop a detailed theoretical model for laser cooling in ${Yb}^{3 +} : YAG$ . The expressions for the fluorescence power density removed from the system with spontaneous emission, the power density radiated with stimulated emission, as well as the heat power density generated in the system by nonradiative decays on the impurities of the host material have been calculated. The influence of each of these power densities on the cooling process has been analyzed. We show, for the first time to our knowledge, how the temperature dependences of the different parameters of the system as well as the concentration of the impurities in the host influence the final temperature of the cooled sample.

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	Sublevels $(0, i)$
Sublevels $(1, j)$	(0,1) $E_{01} = 0 {cm}^{- 1}$ [17]	(0,2) $E_{02} = 565 {cm}^{- 1}$ [17]	(0,3) $E_{03} = 612 {cm}^{- 1}$ [17]	(0,4) $E_{04} = 785 {cm}^{- 1}$ [17]
(1,1) $E_{11} = 10, 327 {cm}^{- 1}$ [17] $τ_{11} = 0.88 ms$ [18]	$β_{01}^{11} = 0.225$ [18]	$β_{02}^{11} = 0.09$ [18]	$β_{03}^{11} = 0.342$ [18]	$β_{04}^{11} = 0.088$ [18]
(1,2) $E_{12} = 10, 624 {cm}^{- 1}$ [17] $τ_{12} = 3.27 ms$ [18]	$β_{01}^{12} = 0.079$ [18]	$β_{02}^{12} = 0.084$ [18]	$β_{03}^{12} = 0.015$ [18]	$β_{04}^{12} = 0.023$ [18]
(1,3) $E_{13} = 10, 941 {cm}^{- 1}$ [17] or $10, 930 {cm}^{- 1}$ [19] $τ_{13} = 12.2 ms$ [18]	$β_{01}^{13} = 0.009$ [18]	$β_{02}^{13} = 0.010$ [18]	$β_{03}^{13} = 0.010$ [18]	$β_{04}^{13} = 0.025$ [18]
Maximum phonon energy in the YAG [20]				$860 {cm}^{- 1}$
Critical concentration of the ${Yb}^{3 +}$ ions, $N_{Yb}^{0}$ [9]				$2.3 \times 10^{21} {cm}^{- 3}$
Product of the absorption cross section and the average absorption length, $σ l$ [9]				$1.9 \times 10^{- 22} {cm}^{3}$
Intrinsic lifetime without trapping, ${\tilde{τ}}_{1 t}^{r}$ [9]				0.95 ms

Manifold	Energy ( ${cm}^{- 1}$ ) 50 at. % (exp.)	Energy ( ${cm}^{- 1}$ ) 50 at. % (calc.)	Energy ( ${cm}^{- 1}$ ) 1 at. % (exp.)
${{}^{4}I}_{11 / 2}$	10, 414	${\begin{matrix} 10,422 \\ 10,413 \end{matrix}$
	10,375	10,382
	10,364	10,359
	10,285	10,290
	10,256	10,255
${{}^{4}I}_{15 / 2}$	570		574
	518		527
	429		432
	${\begin{matrix} 419 \\ 368 \end{matrix}$		417
	79		80
	57		60
	25		22
	0		0

	Sublevels $(0, i)$
Sublevels $(1, j)$	(0,1) $E_{01} = 0 {cm}^{- 1}$ [17]	(0,2) $E_{02} = 565 {cm}^{- 1}$ [17]	(0,3) $E_{03} = 612 {cm}^{- 1}$ [17]	(0,4) $E_{04} = 785 {cm}^{- 1}$ [17]
(1,1) $E_{11} = 10, 327 {cm}^{- 1}$ [17] $τ_{11} = 0.88 ms$ [18]	$β_{01}^{11} = 0.225$ [18]	$β_{02}^{11} = 0.09$ [18]	$β_{03}^{11} = 0.342$ [18]	$β_{04}^{11} = 0.088$ [18]
(1,2) $E_{12} = 10, 624 {cm}^{- 1}$ [17] $τ_{12} = 3.27 ms$ [18]	$β_{01}^{12} = 0.079$ [18]	$β_{02}^{12} = 0.084$ [18]	$β_{03}^{12} = 0.015$ [18]	$β_{04}^{12} = 0.023$ [18]
(1,3) $E_{13} = 10, 941 {cm}^{- 1}$ [17] or $10, 930 {cm}^{- 1}$ [19] $τ_{13} = 12.2 ms$ [18]	$β_{01}^{13} = 0.009$ [18]	$β_{02}^{13} = 0.010$ [18]	$β_{03}^{13} = 0.010$ [18]	$β_{04}^{13} = 0.025$ [18]
Maximum phonon energy in the YAG [20]				$860 {cm}^{- 1}$
Critical concentration of the ${Yb}^{3 +}$ ions, $N_{Yb}^{0}$ [9]				$2.3 \times 10^{21} {cm}^{- 3}$
Product of the absorption cross section and the average absorption length, $σ l$ [9]				$1.9 \times 10^{- 22} {cm}^{3}$
Intrinsic lifetime without trapping, ${\tilde{τ}}_{1 t}^{r}$ [9]				0.95 ms

Manifold	Energy ( ${cm}^{- 1}$ ) 50 at. % (exp.)	Energy ( ${cm}^{- 1}$ ) 50 at. % (calc.)	Energy ( ${cm}^{- 1}$ ) 1 at. % (exp.)
${{}^{4}I}_{11 / 2}$	10, 414	${\begin{matrix} 10,422 \\ 10,413 \end{matrix}$
	10,375	10,382
	10,364	10,359
	10,285	10,290
	10,256	10,255
${{}^{4}I}_{15 / 2}$	570		574
	518		527
	429		432
	${\begin{matrix} 419 \\ 368 \end{matrix}$		417
	79		80
	57		60
	25		22
	0		0

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Journal of the Optical Society of America B