We have found several errors in our recently published paper [1]. The appearance of $P_v$ in Eq. (15) is redundant, as the corresponding heat loads have been included in $P_{\text{abs}}$. Equation (15) in paper [1] should be replaced by

There is a clerical error in Eq. (18): a minus sign should be added at the right-hand side of the equation.

The simulation results alter with the change of Eq. (15). Figures 4 and 5 in paper [1] should be replaced by the following Figs. 1 and 2, respectively. Figure 1 shows that the copumping scheme for cooling enhancement only works when sample temperature is above 210 K. Figure 2 shows that a maximum cooling power density (MCPD) of $7.5\times {10}^7\mathrm{W}·{\mathrm{m}}^{-3}$ could be achieved in the 1.2% ${\mathrm{Ho}}^{3+}\text{:}{\mathrm{YLiF}}_4$ crystal. The corresponding cooling efficiency is about 4.2%.

 

Fig. 1. Temperature-dependent critical background absorption coefficient of the 1% ${\mathrm{Ho}}^{3+}\text{:}{\mathrm{YLiF}}_4$ crystal ($I_1={10}^6\mathrm{W}·{\mathrm{m}}^{-2}$). The dashed line indicates the background absorption ${\alpha }_b=4.0\times {10}^{-4}{\mathrm{cm}}^{-1}$. The solid point indicates the critical condition of whether cooling enhancement occurs.

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Fig. 2. At temperature of 300 K. (a) The MCPD as a function of dopant concentration. (b) The corresponding optimum pumping intensities (OPI). The solid curve is for ground state absorption, and the dashed curve is for excited state absorption. (c) The corresponding cooling efficiency.

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These changes do not affect the qualitative conclusions of paper [1].