Competing Inversion-Based Lasing and Raman Lasing in Doped Silicon

We report on an optically pumped laser where photons are simultaneously generated by Population inversion and by stimulated Raman scattering in the same active medium, namely crystalline silicon doped by bismuth (Si∶Bi). The medium utilizes three electronic levels: ground state [1], upper [3] and lower [2] laser levels. The 1 ↔ 3 and 2 ↔ 3 transitions are optically allowed and the 1 ↔ 2 transition is Raman active. Lasing based on population inversion occurs between the states 3 and 2, while Raman scattering benefits from the Raman-active transition. At high pump power the inversion-based stimulated emission 3 → 2 disappears, because electronic scattering from 1 to 2
via a virtual state dominates and the electrons are excited into 2 rather than into 3. Starting as population
inversion-based lasing, it ends as stimulated Raman scattering. Our model shows that such a competition
occurs on the timescale of the 10-ps-long pump pulse.

We report on an optically pumped laser where photons are simultaneously generated by population inversion and by stimulated Raman scattering in the same active medium, namely crystalline silicon doped by bismuth (Si∶Bi). The medium utilizes three electronic levels: ground state [j1i: 1sðA 1 Þ in Si∶Bi], upper [j3i: 2p AE ] and lower [j2i: 1sðEÞ] laser levels. The j1i ↔ j3i and j2i ↔ j3i transitions are optically allowed and the j1i ↔ j2i transition is Raman active. Lasing based on population inversion occurs between the states j3i and j2i, while Raman scattering benefits from the Raman-active transition. At high pump power the inversion-based stimulated emission j3i → j2i disappears, because electronic scattering from j1i to j2i via a virtual state dominates and the electrons are excited into j2i rather than into j3i. Starting as population inversion-based lasing, it ends as stimulated Raman scattering. Our model shows that such a competition occurs on the timescale of the 10-ps-long pump pulse. DOI Optically pumped lasers are examples of active media where two alternative lasing schemes can be realized: inversion based and inversionless. Population inversion lasing (PIL) is based on inversion between particular states, an upper long-lived electronic state j3i and a lower shortlived electronic state j2i. The transition between these states is usually optically allowed. Two lasing mechanisms without population inversion are known. These are light amplification by quantum interference between electronic states [1] or by stimulated Raman scattering (SRS) [2][3][4]. When an optically allowed PIL transition, j3i → j2i, and a SRS transition, j1i → j2i via a virtual state, are combined in a three-level cascade j3i → j2i → j1i, alternative lasing schemes can occur.
Such schemes have been first considered in optically pumped, low-dimensional semiconductor structures with intersubband j3i → j2i → j1i cascades. Theoretical models of the total gain in a three-level system, including methods based on the density matrix theory, show that at certain conditions, such as fast resonant scattering and large pump powers, the Raman gain can exceed the gain on transitions between the same levels with population inversion [5][6][7]. Both PIL and SRS lasing mechanisms have been experimentally achieved in different active media having three electronic subbands as laser levels [8][9][10]. PIL and SRS lasing mechanisms can be distinguished since the emission frequency of the Raman laser changes linearly with the pump laser frequency while it is independent of the pump laser frequency for PIL. Raman lasing at infrared wavelengths has been obtained from artificial three-level quantum-well structures, e.g., in GaAs=ðAl; GaÞAs and ðGa; InÞAs=ðAl; InÞAs [8,10]. SRS lasing occurs on the j1i → j2i transition by optical excitation on the j1i → j3i transition while the spacing between states j1i and j2i corresponds to a phonon energy or an electronic resonance. Similar structures were used for quantum fountain lasers [9]. In these lasers PIL on the j3i → j2i transition dominates. An electrically excited infrared Raman laser has been claimed by embedding a three-level structure in the active medium of an infrared quantum-cascade laser which serves as the optical pump [3]. It should be noted that simultaneous inversion and Raman lasing has not been obtained in these devices with electronic subbands. However, for an accurate description electron scattering with a broad kinetic energy spectrum and the formation of hot electrons in the subbands should be taken into account [8]. Separate PIL and Raman lasing have been demonstrated using atomiclike discrete levels of shallow donor centers in silicon [11,12].
In a three-level active medium, strong competition between PIL and SRS lasing mechanisms can occur since the lasing gains of both mechanisms are dominantly determined by population differences between the states in the cascade j3i → j2i → j1i, namely, n 3 vs n 2 for PIL and n 1 vs n 2 for SRS. As a result, saturation occurs at different optical pump powers and the pump intensity is the parameter which controls the relative contributions of PIL and SRS to the stimulated emission. In this paper, we show that such a three-level system is formed by the electronic states of the bismuth donor in silicon (Si∶Bi). This active medium supports the simultaneous operation of terahertz (THz) PIL and SRS lasing under specific optical pump conditions with the infrared radiation from a free-electron laser (FEL). Low pump rates and resonant pumping into the upper level favor the PIL mechanism while the SRS lasing benefits from high optical pump intensities and slightly detuned off-resonant pumping (Fig. 1). The high-Q factor of the Si∶Bi laser resonator supports lasing photons between pump micropulses and enables thus the observation of the competing laser processes despite the short (approximately 10 ps) pump pulses and the large pulse separation (1 ns).
As an active medium, several n-type silicon crystals grown by the float-zone technique in the f100g direction have been used. The dopant concentration in the crystals is in the range of N D ∼ ð3-5Þ×10 15 cm −3 . Samples with dimensions of ð7 × 7Þ × 5 mm 3 were cut from the ingot and optically polished to form a high-Q resonator operating on total internal reflection modes. The Si∶Bi samples were first characterized by measuring their impurity absorption spectra at low temperature (about 5 K) with a Fourier transform infrared spectrometer (Bruker Vertex 80v) and a spectral resolution of 0.1 cm −1 (12.5 μeV). The lasing experiments were carried out with the infrared free-electron laser FELIX at Radboud University, Nijmegen, The Netherlands. Its pump pulses consist of 6-μs-long macropulses at a repetition rate of 5 Hz. Each macropulse consists of approximately 10 -ps-long micropulses with a peak power of about 10 MW separated by 1 ns. The spectral width of each micropulse is approximately 0.5 meV (full width at half maximum, FWHM). The Si samples were mounted in a cryogenic dipstick, which was immersed in a liquid-helium transport vessel. The dependence of the spectrally integrated Si∶Bi laser intensity on the FEL pump photon energy has been measured in the entire impurity absorption band up to the transition into the bottom of conduction band [spectral resolution of 0.05 μm (FWHM) as determined by a grating spectrometer in the FEL diagnostic station]. The lasing emission from Si was analyzed by a Fourier transform infrared spectrometer operating in step-scan mode with a spectral resolution of 0.3 cm −1 (37 μeV) equipped with a Ge∶Ga photoconductive detector, which is sensitive from 40 to 120 μm. The interferograms were measured with a time resolution of 50 ns. This time gating has reduced significantly the integrated laser intensity reaching the detector, so that only stimulated emission at pump powers well above the lasing threshold could be measured. Spectra were calculated from the interferograms applying a Blackman-Harris filter for apodization. Combinations of infrared filters mounted in the dipstick at liquid-helium temperature and outside at room temperature prevented that pump radiation from reaching the detector. The hydrogenlike Bi centers in Si form localized electronic states in the band gap. The degenerate 1s electronic ground state, whose orbit is closest to the nucleus, is affected by the so-called chemical splitting which leads to a splitting and shifting: the singlet 1sðA 1 Þ state (laser level j1i) is most strongly downshifted from the position predicted by the effective mass theory while the triplet 1sðT 2 Þ and doublet 1sðEÞ (laser level j2i) components are less downshifted [ Fig. 2(a)]. Optical transitions between these states are dipole forbidden while the transition between the 1sðA 1 Þ ground state and the excited 1sðEÞ state j1i ↔ j2i is Raman active [13]. In thermal equilibrium at low temperature, typically less than 10 K, virtually all extrinsic electrons are bound to the donor ground state.
An optically pumped intracenter n-Si∶Bi laser [Figs. 1 and 2(a)] utilizes population inversion formed by the accumulation of electrons, photoexcited from the donor ground state (j1i → j3i) and accumulated in the long-lived 2p AE state (laser level j3i, lifetime about 50 ps [14]). The 2p 0 and 2s excited states in Si∶Bi are resonantly coupled to the ground state via intervalley f-TO and g-TO optical phonons [ Fig. 2(a)]. These states remain unpopulated [15] and can therefore be neglected when considering the PIL scheme. Therefore, the Si∶Bi laser emits on the 2p AE → 1sðEÞ transition (j3i → j2i) with the corresponding photon energy hω PIL ¼ jE 2pAE − E 1sðEÞ j (23.8 meV) and, when pumped above the upper laser state [j1i → j4i, Figs. 1(a), 3(b), 4(a)], additionally on the 2p AE → 1sðT 2 Þ transition with hω 2 ¼ jE 2pAE − E 1sðT2Þ j (25.5 meV) [15]. This modification of the Si∶Bi lasing spectrum occurs due to specific coherent excitation of the upper laser state. Under resonant pumping in the 2p AE state (which has the irreducible representation 2T 1 þ 2T 2 of T d symmetry group) only two asymmetric from four components of the 2p AE state are selectively excited that results in dominating dipole-allowed laser emission on 2p AE → 1sðEÞ transition. When pumped above the 2p AE state, this pumping induced "selectivity" gets lost due to electron scattering during relaxation towards the 2p AE state (also including processes between equivalent conduction band valleys). Therefore, all components of the 2p AE Bi state become equally populated and both dipole-allowed 2p AE ð2T 1 þ 2T 2 Þ→ 1sðEÞ; 1sðT 2 Þ laser transitions occur. Depletion of the lower laser state is dominated by an interaction with intervalley phonons [16]. In general, a four-level laser scheme is realized [ Figs. 1(a) and 4(a)]. This laser scheme involves the donor ground state j1i, the pumped state j4i, and the upper j3i and lower j2i laser states. A particular situation occurs when the pumped state and the upper laser state are identical j4i ≡ j3i [ Figs. 1(b),1(c),1(d), 4(b)]. This is a degenerate four-level scheme with three electronic states involved in the laser mechanism. The lower 1sðEÞ → 1sðA 1 Þ intracenter transition in the three-level system provides resonant inelastic light scattering and by this enhances SRS in n-Si, in particular in Si∶Bi [12]. Under nonresonant excitation a virtual state is formally ascribed to an optically excited electron. In Raman Stokes lasers the energy of the emitted photon hω SRS equals the pump photon energy hω pump reduced by the Stokes shift We have analyzed Si∶Bi emission by tuning the FEL pump frequency across the absorption spectrum of the Bi donors and measuring the integrated intensity of the Si∶Bi laser [ Fig. 2(b)]. At the highest pump power there is almost continuous Si∶Bi laser emission for FEL pump photon energy from 58 to 66 meV, as expected for SRS. When attenuating the pump power, laser emission remains observed only when pumped resonantly into the 2p 0 and 2p AE states (at 10 dB FEL attenuation) and only in the 2p AE state (at 18 dB FEL attenuation) [ Fig. 2(b)]. In Fig. 3(a) the integrated intensity of the Si∶Bi laser is shown when measured in the time gates set at 1.5 and 4.8 μs after the onset of the pump pulse. Early lasing appears only when pumped at around 64.6 meV, which corresponds to the 1sðA 1 Þ → 2p AE Bi transition. At 4.8 μs laser emission occurs not only when pumped resonantly into a bound state but also between the states. This is an indication of SRS lasing. Figure 3(b) summarizes these findings. The Si∶Bi laser photon energy increases linearly with the pump photon energy up to about 24.5 meV at 65.5 meV pump photon energy. Above that pump photon energy, emission occurs only when Si∶Bi is directly excited into one of the Bi states. The emission frequency corresponds either to the 2p AE →1sðT 2 Þ transition or to the 2p AE → 1sðEÞ transition. In this case PIL prevails.
The distinction between PIL and SRS becomes possible by analyzing the Si∶Bi lasing thresholds, output power, and emission dynamics if compared with the borderline cases, i.e., resonant pumping in other electronic states around the 2p AE state (pure PIL, pumping j1i → j4i) or off-resonance pumping (SRS, pumping j1i → jvirtual statei). PIL has a lower lasing threshold and remains at strongly reduced FEL pump powers where SRS has ceased [ Fig. 2(b)]. Pure PIL [ Fig. 4(a)] differs from the merged case [ Fig. 4 Fig. 4(a) and 4(c), middle row], the lasing threshold is larger, and the slope efficiency is different. Such a delay in the SRS pulse is often reflected in a steplike dynamic transition from spontaneous to stimulated mode, more pronounced at pump wavelengths with a larger SRS lasing threshold. Within the macropulse   pump time, the merged case [ Fig. 4(b)] combines features of both lasing mechanisms resulting in a single 2p AE → 1sðEÞ emission line, low lasing threshold and little delay of the emission pulse as for PIL. However, the emission pulse has a characteristic step in the first part, which becomes more pronounced at low FEL pump power, indicating changes of the laser dynamics. We explain the observed lasing dynamics by evolution of the intracavity stimulated emission due to fast changes in level populations, which we have modeled on the basis of balanced equations for a three-level system (see Supplemental Material [18]). The PIL gain g PIL is proportional to the pump-induced population difference n 3 − n 2 . It saturates when the absorption on the 1sðA 1 Þ → 2p AE (j1i → j3i) transition saturates, i.e., when n 3 approaches n 1 . The laser emission on the 2p AE → 1sðEÞ (j3i → j2i) transition saturates when n 2 approaches n 3 in the PIL mode. The Raman gain is proportional to the population difference n 1 − n 2 and to the pump power [5]. Saturation of the SRS emission occurs by stimulated electron scattering into the 1sðEÞ state when n 2 approaches n 1 . Under pulsed pumping the decay of the PIL gain is determined by the lifetime of level j3i (about 50 ps), while the SRS gain exists only during the pump micropulse. The Q factor of the Si.Bi laser resonator plays a key role, because it enables us to sustain stimulated emission between the approximately 10-ps-long pump micropulses which have an interpulse period of 1 ns. The typical photon lifetime in the Si resonator under intracenter pumping is about 10 −8 s. It is limited mainly by lattice absorption and radiative losses. Thus, averaging over a 1-ns period yields relatively lower Raman gain and causes the delayed onset of the SRS emission [ Fig. 4(c)] as compared to PIL [ Fig. 4(a)]. The model shows that at certain pump rates into the upper level 2p AE and typical optical cross sections for transitions in Si∶Bi, SRS can block the initial absorption of pump light from the lowest level j1i into level j3i and dominate over PIL (Fig. 5). The timescale of the process is similar to the pump micropulse duration. The upper long-lived level j3i, populated in the PIL scheme by optical absorption, becomes a virtual state in the SRS process where electrons from the ground state j1i scatter directly in the lower laser state j2i leaving level j3i unpopulated. The growing gain for SRS emission leads to a decay of the PIL gain and emission. This causes the characteristic step in the Si∶Bi laser output power under resonant pumping [ Fig. 5(b)].
A slight detuning of the pump wavelength from the resonance with the 1sðA 1 Þ → 2p AE transition allows distinguishing between the two lasing mechanisms by timeresolved emission spectroscopy. Figure 6 demonstrates the  lasing dynamics under almost resonant pumping into the 3p 0 Bi state at about 1 meV off the resonance with the 2p AE Bi state. In this case PIL and SRS lasing have different frequencies and can be spectrally resolved (Fig. 6). At the start of the pump macropulse excited electrons relax from the 3p 0 state into the 2p AE state and form population inversion. As a result, PIL on the 2p AE → 1sðEÞ transition ) 23.8 meV, 5.75 THz) sets on first. With about 1 μs delay, SRS lasing appears at 24.5 meV (5.92 THz). This can be clearly seen in the dynamics of the integrated intensity of the Si∶Bi laser as a function of the FEL pump photon energy and by the Si∶Bi lasing emission spectra reconstructed from their time-resolved interferogram maps (see complementary files Si_Integrated_Emission.gif and Si_Emission_Spectrum.gif in the Supplemental Material [18]).
In conclusion, we have observed simultaneous lasing by two principally different and competing mechanisms operating in a degenerate four-level system in Si∶Bi: conventional lasing, which requires population inversion between particular electronic levels, and inversion-less Raman lasing on the same levels. The interplay between SRS and conventional inversion-based lasing depends on the pump frequency and power. The high-Q factor of the laser resonator enables the competition of both processes, because the photon lifetime in the resonator exceeds the ns intervals between two pump pulses. Under resonant pump conditions into the upper laser level the PIL mechanism starts earlier since its gain sustains over the approximately 50-ps lifetime of the laser upper level while the SRS gain acts only during the approximately 10-pslong pump pulse. Later on, the accumulation of the photons in the resonator leads to an increase of the SRS gain within the pump micropulse of the FEL and transition from population-inversion-based lasing to Raman lasing occurs so that for some time both lasing mechanisms exist simultaneously. This is caused by changes of the populations of the involved levels and thus the gain of both processes. At slight detuning of the pump wavelength from the resonance the lasing mechanisms can be distinguished by time-resolved spectroscopy. The observed lasing dynamics has been described by a rate equation model for a three-level system.