Competing Inversion-Based Lasing and Raman Lasing in Doped Silicon

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Competing Inversion-Based Lasing and Raman Lasing in Doped Silicon

S. G. Pavlov, N. Deßmann, B. Redlich, A. F. G. van der Meer, N. V. Abrosimov, H. Riemann, R. Kh. Zhukavin, V. N. Shastin, and H.-W. Hübers

Phys. Rev. X 8, 041003 – Published 5 October 2018

Abstract

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 [ $| 1 ⟩$ : $1 s (A_{1})$ in $Si ∶ Bi$ ], upper [ $| 3 ⟩$ : $2 p_{\pm}$ ] and lower [ $| 2 ⟩$ : $1 s (E)$ ] laser levels. The $| 1 ⟩ \leftrightarrow | 3 ⟩$ and $| 2 ⟩ \leftrightarrow | 3 ⟩$ transitions are optically allowed and the $| 1 ⟩ \leftrightarrow | 2 ⟩$ 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 $| 3 ⟩ \to | 2 ⟩$ 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.

Received 8 January 2018
Revised 20 July 2018

DOI:https://doi.org/10.1103/PhysRevX.8.041003

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Laser dynamics Semiconductors Stimulated Raman scattering Ultrashort pulses

Condensed Matter, Materials & Applied PhysicsNonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

S. G. Pavlov^1,*, N. Deßmann², B. Redlich³, A. F. G. van der Meer³, N. V. Abrosimov⁴, H. Riemann⁴, R. Kh. Zhukavin⁵, V. N. Shastin^5,6, and H.-W. Hübers^1,2

¹Institute of Optical Sensor Systems, German Aerospace Center (DLR), Berlin 12489, Germany
²Department of Physics, Humboldt-Universität zu Berlin, Berlin 12489, Germany
³Radboud University Nijmegen, Institute for Molecules and Materials, FELIX Laboratory, Nijmegen 6525 ED, Netherlands
⁴Leibniz-Institut für Kristallzüchtung (IKZ), 12489 Berlin, Germany
⁵Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod 603950, Russia
⁶Lobachevsky State University, Nizhny Novgorod 603950, Russia

^*sergeij.pavlov@dlr.de

Popular Summary

Optically pumped lasers can create intense, coherent beams of light using two different mechanisms: inversion based and inversionless. The difference between the two lies in whether electrons fall from an overpopulated excited energy state to a lower one (inversion based) or whether they transition from a low state to a higher one (inversionless). Typically, only one of these mechanisms works at any one time. However, we show that both mechanisms can operate simultaneously and at the same emission frequency.

Our lasing medium is crystalline silicon doped with bismuth. We utilize three of the available electronic levels in this system to create an energy cascade for laser pumping. Inversion-based photons originate from electrons dropping from the highest to the middle levels, while transitions from the lowest to the middle mediate Raman scattering that, in turn, emits inversionless photons.

Time-resolved spectroscopy reveals that the system rapidly alternates between the two lasing mechanisms. Theoretical modeling shows that this behavior arises from the ultrafast evolution of electron populations among all three energy levels. The change in the contribution to the total laser output from a particular mechanism occurs within just a few picoseconds.

We hope that this research will stimulate searches for similar simultaneous lasing mechanisms in other media.

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Vol. 8, Iss. 4 — October - December 2018

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Figure 1
Different lasing schemes in $Si ∶ Bi$ lasers. The transition between these schemes depends on the pump frequency, pump intensity, and time that has elapsed after the start of the pump pulse. The horizontal gray and black lines indicate the discrete energy levels of the Bi donor. The straight blue arrows up indicate the optical pump process. The straight arrows down are for PIL (filled yellow) and SRS (filled purple) lasing, the curved arrows down are the dominating nonradiative relaxation paths of an excited electron. $1 s (E)$ and $1 s (T_{2})$ are split-off ground states, $1 s (E) \to 1 s (A_{1})$ is a Raman-active intracenter transition in $n$ -Si with an energy $Δ_{S}$ . (a) PIL: four-level laser scheme based on population inversion between the long-lived $2 p_{\pm}$ and the short-lived $1 s (E)$ , $1 s (T_{2})$ states; depletion of the lower laser states into the ground state is due to intervalley phonons. (b)–(d) merged PIL and SRS lasing processes under resonant pumping into the long-lived $2 p_{\pm}$ state. In this particular case the virtual state coincides with the $2 p_{\pm}$ state of the Bi donor. At pump start (b) PIL dominates, the laser scheme is reduced to the three levels; later on (c) SRS develops and balances PIL; in the end (d) SRS prevails, and the elecrons are scattered directly into the $1 s (E)$ state, the upper $2 p_{\pm}$ level becomes essentially unpopulated. (e) SRS lasing occurs at off-resonant pumping to any of the higher impurity states.
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Figure 2
(a) $Si ∶ Bi$ laser scheme under resonant pumping in the upper laser level. Labels are the ground and excited states of a Bi center. Bold straight arrows indicate optical pump and lasing transitions, wavy arrows show nonradiative phonon-assisted relaxations. Note that energy spacings below the $2 p_{0}$ state are for clarity not to scale. (b) Integrated intensity of the $Si ∶ Bi$ laser as a function of the pump photon energy (spectral resolution: $0.05 μ m$ ). The laser spectra were measured at different FEL power (the attenuation from maximum FEL power is given in the legend). For comparison the $Si ∶ Bi$ absorption spectrum measured with a spectral resolution of $0.1 {cm}^{- 1}$ ( $12.5 μ eV$ ) is plotted as well. Note that at lower pump intensities the integrated intensity is resolved into a discrete spectrum which is similar to the impurity absorption spectrum.
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Figure 3
(a) Integrated intensity of the $Si ∶ Bi$ laser vs FEL pump photon energy at different times elapsed from the front of the pump pulse and compared with the $Si ∶ Bi$ absorption spectrum. Note that the $Si ∶ Bi$ lasing starts on the $1 s (A_{1}) \to 2 p_{\pm}$ transition where pumping is most effective for the PIL transition $1 s (A_{1}) \to 2 p_{\pm}$ (at about $64.6 meV$ , $19.2 μ m$ ). With a delay of a few microseconds the SRS-typical, broad lasing spectrum sets on and dominates towards the end of the pump macropulse (see also complementary file Si_Integrated_Emission.gif for full reconstructed dynamics [18]). The spectral resolution of pump spectra is $0.05 μ m$ and of absorption spectrum is $0.1 {cm}^{- 1}$ . (b) Dependence of the photon energy and intensity of the SRS and PIL emission on the pump photon energy. The $Si ∶ Bi$ absorption spectrum is given for orientation. The circles show the pump photon energies where $Si ∶ Bi$ emission spectar were taken. Note the linearity of the SRS lasing frequency with the pump photon energy and the Stokes shift of about 40.8 meV. The SRS lasing (dashed line) spans the pump photon range from below the $2 p_{0}$ excited state up to the $3 p_{0}$ excited state. Pumping in the $2 p_{\pm}$ Bi state results in joint PIL and SRS lasing. Pumping in the $3 p_{0}$ Bi state and above results in PIL only.
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Figure 4
Lasing thresholds, dynamics, and emission spectra for different laser mechanisms in $Si ∶ Bi$ . (a) Typical four-level population inversion scheme (PIL): The pump photon energy corresponds to the excitation of bound electrons into a higher excited state. The laser transitions are $2 p_{\pm} \to 1 s (E)$ and $2 p_{\pm} \to 1 s (T_{2})$ at 5.75 and 6.16 THz, correspondingly. The FEL pump wavelength is $18.25 μ m$ (16.43 THz or 67.95 meV) and the photon flux is $4 \times 10^{25} {cm}^{- 2} s^{- 1}$ . (b) Simultaneous operation of Raman and population inversion lasing (PIL and SRS): The pump photon energy corresponds to excitation in the $2 p_{\pm}$ Bi state. The previously distinct laser lines merge into one emission line which corresponds to the energy of the $2 p_{\pm} \to 1 s (E)$ Bi transition. The FEL pump wavelength is $19.26 μ m$ (15.57 THz or 64.4 meV) and the photon flux is $4 \times 10^{25} {cm}^{- 2} s^{- 1}$ . (c) Raman lasing scheme (SRS): The pump photon energy corresponds to excitation into a virtual state. The Stokes emission line is from the virtual state into the $1 s (E)$ state (5.04 THz or 20.84 meV). The FEL pump wavelength is $20.06 μ m$ (14.95 THz or 61.81 meV) and the photon flux is $5 \times 10^{25} {cm}^{- 2} s^{- 1}$ .
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Figure 5
Simulated laser pulse dynamics of a three-level system under pulsed FEL excitation at the front of the macropulse: (a) Evolution of the PIL gain; (b) separate outputs of the PIL and SRS lasing. Evolution on the micropulse timescale: (c) relative populations of the states, (d) SRS gain, (e) PIL gain. The parameters of the model: pump rate $R_{13}$ is $10^{11} s^{- 1}$ ; the relaxation rate $W_{32}$ between the upper $2 p_{\pm}$ state and the intermediate $1 s (E)$ state is $2 \times 10^{10} s^{- 1}$ and $W_{21}$ between the $1 s (E)$ and the $1 s (A_{1})$ ground state is $10^{11} s^{- 1}$ ; direct relaxation from the upper into the ground state ( $| 3 ⟩ \to | 1 ⟩$ ) is neglected; losses at the $Si ∶ Bi$ emission frequency are $10^{10} s^{- 1}$ . Note that developing Raman emission competes with the PIL and causes a specific step in the output power (for details see the Supplemental Material [18]).
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Figure 6
(See also the complementary files with reconstructed dynamics [18].) Temporal and spectral evolution of the $Si ∶ Bi$ laser emission when pumped at $19.02 μ m$ (65.2 meV) which is 0.6 meV above the long-lived $2 p_{\pm}$ state (color map with projections to time and photon energy axis). The emission lines at approximately $23.8 meV$ (5.78 THz) and at 24.5 meV (5.92 THz) correspond to the PIL $2 p_{\pm} \to 1 s (E)$ transition and to the Raman emission from a virtual state into the $1 s (E)$ state, respectively. The ${FWHM}_{FEL}$ is about $0.25 meV$ and the spectral resolution of the Fourier-transform infrared spectrometer is $37 μ eV$ ( $0.3 {cm}^{- 1}$ ). The right upper graph shows the $Si ∶ Bi$ absorption spectrum compared with the FEL pump spectrum.
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