Photon-phonon collaboratively pumped laser

Abstract

In 1917, Einstein considered stimulated photon emission of electron radiation, offering the theoretical foundation for laser, technically achieved in 1960. However, thermal phonons along with heat creation of non-radiative transition, are ineffective, even playing a detrimental role in lasing efficiency. Here, we realize a photon-phonon collaboratively pumped laser enhanced by heat in a counterintuitive way. We observe a laser transition from phonon-free 1064 nm lasing to phonon-pumped 1176 nm lasing in Nd:YVO₄ crystal, associated with the phonon-pumped population inversion under high temperatures. Moreover, an additional temperature threshold (T_th) appears besides the photon-pump power threshold (P_th), and a two-dimensional lasing phase diagram is verified with a general relation ruled by P_th = C/T_th (constant C upon loss for a given crystal), similar to Curie's Law. Our strategy will promote the study of laser physics via dimension extension, searching for highly efficient and low-threshold laser devices via this temperature degree of freedom.

Fig. 1. Photon-phonon collaboratively pumped mechanism.

a Configurational coordination model for phonon-pumped lasing. GS ground state, LS laser low-level state, ES excited state, US laser up-level state. The relaxation processes represent the non-radiative transitions. The red dash arrow is a photon-pumping process, and the blue arrow represents a phonon-pumping process. ZPL laser is a phonon-free laser at the zero-phonon line wavelength. PPCP laser is a photon-phonon collaboratively pumped laser. $\hslash \omega$ is the phonon energy. The dash lines are phonon energy levels coupled to a given electronic state. In conventional Nd³⁺-lasers, ①→⑤ transition at 1064 nm is natural at a finite temperature. It represents a phonon-free laser oscillation. If we suppress the ①→⑤ laser oscillation by specific coating cavity, and amplify another transition channel ②→④, photon-phonon collaboratively pumped lasing at 1176 nm become available. At this time, a population inversion happens between ② and ④ states ₍n_② > n_④ for lasing), when there are enough active ions at ① state and sufficient thermal phonons to support ①→② up-moving. b 2D (P, T) lasing phase diagram spanned by temperature and pump power. The color scale represents output power (the color white represents no lasing). The general threshold curve (dashed orange line) satisfies P_th × T_th = Constant. Vertical (horizontal) slice is plotted in the right (bottom) panel.

Fig. 2. Electron-phonon coupling in fluorescence.

a Fluorescence spectra (π-polarization) at various temperatures. The shadow region is the phonon-triggered emission window. A similar σ-polarization emission is plotted in Fig. S2. b Emission cross sections in 1140–1240 nm window. The fluorescence lifetimes of various emission are fitted in Supplementary Fig. S3-S4. c Configuration coordinate model. The forced electronic transition by phonon is represented by the orange arrow, the horizontal dashed lines represent the phonon states, and the vibrational wave functions were plotted as shadow area in the case of quasi-harmonic oscillators. d The emission cross-section at 1176 nm and the calculated Huang-Rhys S factors at various temperatures.

Fig. 3. Symmetry requirement of phonons.

a Hyperfine energy levels of Nd:YVO₄. Solid lines represent electronic states marked with wavenumber (cm^-1) and group irreducible representation Г₆ or Г₇. ZPL represents 1064 nm emission. b Raman spectrum marked with phonon modes. c Phonon modes allowed in different electron radiation conditions. Insets are phonon wavenumbers. The color scale represents the electron-phonon-coupling intensity.

Fig. 4. Laser phase transition diagram and tunable wavelengths of PPCP laser.

a Power-temperature diagram of 1064 and 1176 nm laser. T_th is a temperature threshold for phonon-pumped lasing. Experimental data are presented as mean values±SD with five samples. b The wavelengths of tunable phonon-pumped laser in one-phonon process. Via rotating the birefringent filter (BF) plate, we can obtain the strongest 1176 nm laser coupled to A_1g mode, and the second-strongest 1168 nm laser coupled to E_g mode. In addition, these two laser wavelengths can be existed at a special angle of BF plate.

Fig. 5. Photon-phonon collaboratively pumped lasing phase diagram.

a 1176 nm laser output power at various cooling temperatures (upper panel) and without cooling (lower panel). b Thermal-field distribution inside laser crystal, where the highest value denotes crystal temperature. c Crystal temperature-dependent 1176 nm laser output power at a fixed pump power 7.7 W. d, e 2D lasing phase diagram and general threshold relation P_th×T_th = C. The dots are measured results. Experimental data in Fig. 5d are presented as mean values±SD with five samples.