Symmetry Selection Rules of Electric-Dipole Transitions ofEu3+andSm2+in Crystals: A Solid-State Infrared Quantum Counter-Amplifier

A practical scheme for a 10-μ infrared quantum counter-amplifier is proposed, where the infrared frequency is converted into an easily detectable optical frequency. Detailed analysis of the electric-dipole transitions within the $4f^6$ ground configuration of ${\mathrm{Eu}}^{3+}$ and ${\mathrm{Sm}}^{2+}$ ions in various symmetries reveals that these ions have selection rules in $C_{3h}$, $D_{3h}$, and $D_3$ symmetries which allow for significant amplification. This scheme could provide a means of detecting the 10-μ photons generated by the C${\mathrm{O}}_2$ laser.