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Abstract
A highly sensitive method for detecting transient reflection in the extreme ultraviolet (XUV) region was developed on the basis of high-order harmonics for tracking carrier and coherent phonon dynamics. The use of lock-in detection and boxcar integration enables us to observe optical modulation (ΔR/R) as high as 1 × 10−4, and the data acquisition takes only four minutes. XUV transient reflections of bismuth exhibited exponential decay originating from excited carriers and periodic oscillation originating from A1g optical phonons. The linear power dependence of the electronic and phonon amplitudes indicated that one-photon excitation occurred under the experimental conditions. The cosine of the initial phase of the phonon oscillation revealed that a displacive excitation mechanism contributed to phonon generation. The phonon parameters obtained by the XUV and NIR probes were consistent even though their penetration depths were different. The result indicated that the XUV and NIR pulses probe the same excited region, which should be near the surface due to the short penetration depth of the NIR pump pulses. The present highly sensitive means of detecting XUV transient reflections in solid-state materials could be utilized for detecting attosecond dynamics in the future.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
16 January 2020: A typographical correction was made to Fig. 1.
1. Introduction
An understanding of ultrafast carrier and phonon dynamics is crucial for developing optoelectronics, photochemical materials, and other solid based devices. As a tool to probe their dynamics, time-resolved extreme ultraviolet (XUV) spectroscopy based on high-order harmonic generation (HHG) has advantages with respect to temporal coherence over other sources of XUV radiation (e.g., synchrotron radiation, XUV-free electron lasers). XUV pulses generated through HHG track dynamics in the atto- to picosecond time region and provide insight into electronic excitations [1–3], electron and hole decay [4,5], phonon oscillation [6,7], and demagnetization dynamics [8,9]. In particular, when the pump pulse duration is shorter than that of the lattice vibration, coherent oscillations along the vibrational coordinates, that is, coherent phonons are excited [10]. Since the phonons modulate the dielectric function, the coherent lattice oscillations can be probed through time-resolved optical spectroscopy. For example, observation of coherent phonons in XUV spectroscopy reveals motion and displacements of specific nuclei [7]. A variety of ultrafast phenomena have been revealed with attosecond pulses through transient absorption and reflection measurements. Compared to absorption measurements, reflection measurements have been limitedly applied because of technical difficulties, such as the reduction of an already scarce XUV flux at the reflection interface [11]. In absorption measurement, the sample thickness must be less than 100 nm due to high attenuation of XUV by materials. In the creation of thin films, deterioration of crystallinity and introduction of defects and/or dislocations are unavoidable [12], which makes it difficult to consider these thin films relevant as well-defined single crystals. Hence, development of a means of XUV spectroscopy that does not require thin samples is essential step to unraveling ultrafast processes in solids.
In contrast to absorption, reflection measurements can be made on a variety of materials. For example, XUV transient reflections were measured from metallic multilayers [13], sputtered metal oxides on SiO2 substrates [14] and single-crystal Ge [4]. These studies succeeded in tracking the transient dielectric function of the samples and illustrate the applicability of using XUV reflections to study real functional materials regardless of their thickness, substrate, or deposition method. However, instabilities in the XUV probe originating from the high non-linearity of HHG have made it difficult to observe coherent phonons, because the coherent phonons generally produce a ΔR/R of less than 10−3. In order to observe coherent phonons, the signal-to-noise ratio has to be improved. To overcome this problem, we developed a highly sensitive XUV transient reflection system combined with lock-in detection and boxcar integration. The sample we measured was single-crystalline Bi (111) epitaxially grown on Si(111), which required reflection configuration. The setup detected optical modulations (ΔR/R) as high as 1×10−4, and the data acquisition took only a few minutes. The short acquisition time allowed us to measure the power dependence and to study the carrier and coherent phonon dynamics in detail.
2. Experimental setup
The experimental set-up (Fig. 1) consisted of a Ti:sapphire amplifier system, a concave focusing mirror, Bi film on Si(111), a variable time delay line, and an electron multiplier tube to detect the reflected signal from the sample.
Fig. 1. Schematic illustration of XUV transient reflection measurement based on HHG. BS, WP, PL, and CM stand for beam splitter, wave plate, polarizer, and concave mirror with a 250-mm focal length, respectively. EMT and PD stand for electron-multiplier tube and photodiode. The Ag mirror near the sample is inserted in NIR-NIR measurements for confirming temporal and spatial overlap between the pump and probe pulses. Inset graph shows the HH spectrum taken after the Al filter (gray solid line), the SiC reflectivity (dotted blue line), and the HH spectrum multiplied with the SiC reflectivity (black solid line). The scale of the multiplied spectrum is enlarged five times relative to the scale used for the original spectrum.
The Ti:sapphire amplifier system delivered near-infrared (NIR) pulses, which was used to generate high-order harmonics (HH) and excite the sample. The pulse duration was 21.5 ± 0.9 fs, the wavelength was centered at 790 nm (1.57 eV), and the pulse energy was 2.2 mJ/pulse at a repetition rate of 3 kHz (FemtoPower HE/HR CEP4) [15]. The pulse was split with a 5:95 beam splitter. Ninety-five percent of the energy (2.1 mJ/pulse) was used to generate the XUV via HHG. The HH were produced by focusing the pulse into an Ar gas jet with a 60 cm focusing concave lens. Residual NIR was removed from the HH with a 300-nm thick Al filter. After the Al filter, we observed the discrete spectrum up to the 25th HH, as shown by the gray line in the inset of Fig. 1. The XUV pulse was then focused on the sample using a concave SiC mirror whose focal length was 250 mm at an angle of 70° from the normal. Because of the reflectivity of SiC [16], HH lower than the 15 th order (23.6 eV) mainly irradiated the sample (see the black line in the inset of Fig. 1). The reflected XUV probe from the sample was detected with an electron multiplier (Hamamatsu, R595) without spectrally resolving it. The remaining five percent of the energy was used as a pump pulse for exciting the sample. The pump pulse was time delayed with a retroreflector on a piezostage and recombined collinearly with the probe using an annular mirror. The diameter of the pump pulse at the sample was estimated to be 120(10) µm × 360(30) µm. The detailed procedure for determining the spot size will be described later. The polarization and power of the pump and probe pulses were individually controlled with a half-wave plate and a polarizer. The pump laser intensity was varied from 0.33 to 3.3 µJ/pulse, in which measurements could be done repeatedly without damaging sample. The intensity stabilities of the NIR and XUV pulses were ± 1% and ± 2.5% over 15 minutes, respectively. The polarizations of the probe and pump were set to be s- and p- polarized, respectively.
We utilized a boxcar integrator and lock-in detection, which is useful in experiments with low-repetition laser systems [17]. First, the reflected XUV signal detected by the electron multiplier was amplified with a current amplifier (Femto, HSA-Y-1-60), and then it was integrated with a boxcar integrator (Stanford Research Systems, SR250) to improve the duty cycle. The boxcar integration improved the duty cycle from 130 ns/333 µs = 0.04% to ∼1. Here, 130 ns and 333 µs corresponded to the signal duration detected by the electron multiplier and one-cycle period. We could not observe any signal without the boxcar integration. Therefore, the boxcar integration was essential for getting transient reflection signals. Next, the integrated signal was sent to a lock-in amplifier (Stanford Research Systems, SR830) to single out pump-induced components. The lock-in detection should reduce noise originating from the intensity fluctuation of the XUV probe pulses. For the lock-in detection, an optical chopper operated at 1.5 kHz was inserted in the optical path of the pump beam. The frequency was synchronized with the laser system and was used as the reference frequency of the lock-in amplifier. The time constant of the lock-in amplifier was set at 1 sec. The time for a single scan (1.6 ps) was 80 secs, and the total integration time was 240 sec.
To determine spatial and temporal overlaps between the NIR-pump and XUV-probe pulses (NIR-XUV), we used NIR-pump and NIR-probe signals (NIR-NIR). For the NIR-NIR measurement, the Al filter and Ar gas were removed and then the NIR pulses irradiated the sample as the NIR probe. We used a Si p-i-n photodiode (Hamamatsu, S5973) instead of an electron multiplier to detect the NIR probe. The signal detected by the photodiode was integrated with the boxcar integrator and sent to the lock-in amplifier in the same way as the XUV probe. The NIR-NIR signal exhibited a sharp signal originating from excited carrier responses only when the NIR probe and NIR pump pulses overlapped in time and space. Next, we switched to the NIR-XUV measurements by introducing the Al filter and Ar gas. Finally, we could obtain the NIR-XUV signals because group delay induced by the Al filter and Ar gas was significantly small. This alignment method also allowed us to make a direct comparison between NIR- and XUV-transient reflections as discussed later.
The sample was Bi epitaxial film epitaxially grown on Si(111) substrate by molecular beam epitaxy as described in [18]. Bi was evaporated on a Si(111)-7 × 7 surface at 100 °C at a deposition rate of 0.8 Å/sec. The thickness of the sample was 200 nm, as determined by a crystal quartz monitor. The epitaxial orientation relationship was confirmed by reflection high-energy electron diffraction.
3. Results and discussion
The XUV transient reflectivity of Bi is plotted as open circles in Fig. 2(a). For comparison, data that were not lock-in detected are shown in Fig. 2(b); the comparison shows the improvement in the signal-to-noise ratio to be had with the lock-in detection. The data gathered without lock-in detection are useful for evaluating ΔR/R; they indicate that the present experimental set-up can probe ΔR/R∼1 × 10−4.
Fig. 2. (a) XUV transient reflection of Bi detected with lock-in detection. Experimental and fitting results are shown as open blue circles and the solid black line. Dotted green and dashed red lines correspond to the first and second terms of Eq. (2). (b) XUV transient reflection taken without lock-in detection. The data were obtained by subtracting integrated signal with the pump from the integrated signal without the pump.
The signal exhibited an exponential decay and periodical oscillation. To analyze the time-dependent total-reflection signal, we chose the model proposed in the previous coherent-phonon study on opaque samples [19]. According to this model, the pump-induced reflectivity changes (ΔR(t)) can be decomposed into three contributions that affect the sample reflectivity through modulation of the dielectric response: (1) n(t), the excited carrier density, (2) ΔTe(t), the change in electron temperature, which characterized the Fermi-Dirac distribution near the Fermi energy, and (3) Q(t), the coherent phonon amplitude. Consequently, ΔR(t) can be written as follows,
Fig. 3. Power dependence of (a) electronic amplitude (Ae), (b) phonon amplitude (Aph), (c) phonon frequency (ωph), (d) phonon decay rate (Γph), and (e) electronic decay rate (Γe). Blue squares and red circles are results obtained by XUV and NIR probes, respectively.
In Figs. 3(a) and 3(b), the electronic and phonon amplitudes both exhibit linear dependences, which means that one-photon excitation process occurred under the present experimental conditions. As the laser intensity increases (>2.0 µJ/pulse), a deviation from the linear dependence appears, which should originate from saturation, as reported in [21]. Previous time-resolved measurements suggest several possible excitation processes for one-photon excitation in Bi [22–24]. We consider that the excitation from the valence to the conduction bands at the L point should be dominant on the basis of the piezoreflectance measurements [25,26] and time-resolved measurements [22,24,27]. The excitation from the valence to the conduction band causes a nearly instantaneous shift in the lattice potential energy surface, which acts as a generation mechanism for coherent phonons known as displacive excitation of coherent phonons (DECP) [19]. In fact, the XUV transient reflections exhibit a cosine-like oscillation (red broken lines in Fig. 2(a)), which is a typical feature of DECP. The linear power dependence and cosine of the initial phase observed with the XUV probe is consistent with those obtained with the NIR probe, which highlights that XUV transient reflections can quantify dynamics as visible spectroscopy does.
The phonon frequency (ωph) also exhibits a linear power dependence as shown in Fig. 3(c). Extrapolations to the low-fluence limit converge to 2.89(2) THz, which is consistent with the bismuth A1g phonon frequency measured by Raman spectroscopy [28]. From the phonon frequency, the maximum laser fluence (3.3 µJ/pulse) is found to be 7.7 mJ/cm2, which is mostly consistent with the damage threshold of bulk Bi [29]. The power dependence of the phonon frequency and phonon dephasing rate (i.e., redshift frequency and increase in the dephasing rate as the pump fluence increases) are consistent with the previous time-resolved measurements [22,30]. Therefore, the redshift of the phonon frequency would be attributed to electronic softening (i.e., a weakening of the interatomic restoring forces due to excitation of electrons) under the present experimental conditions [30]. The increase in the dephasing rate could be due to the higher density of excited carriers, which should cause carrier-phonon scattering more frequently as the laser intensity increases [22]. It should be noted that the parameters relating to the phonon properties (i.e., Aph, ωph and Γph) are consistent between the XUV and NIR probes, although the penetration depths of the XUV (50 nm at 20 eV) and NIR (16 nm) pulses are different [31]. The present results, therefore, suggest that the pump-excited region is near the sample surface due to the short penetration depth of the NIR pump pulses. As a result, the XUV pulses could probe the excited region near the surface, which should lead to the same results as with the NIR probe.
The observed phonon frequency could be used to estimate the pump spot size on the sample, which is an important experimental parameter. To determine the pump spot size on the sample, we used the linear power dependence of the phonon frequency from the previous time-resolved measurements [22]. In [22], the measurements were done with a similar laser system to ours with respect to the central wavelength and pump fluence. The different angle of incidence in the present study from [22] does not lead to a frequency shift because the observed signal should originate from phonons at the Γ point. Consequently, the linear relationship between the phonon frequency and laser intensity reported by [22] could be used for the conversion from the laser intensity (P [mJ/pulse]) to the laser intensity (I [mJ/cm2]). Since the spot size on the sample (S [cm2]) is given by S = P/I, we could determine the pump spot diameter (d [cm]) on the sample. In the derivation of the diameter, we assumed that S=π(d/2)2/cos70° due to the oblique incidence. Accordingly, the diameter of the pump pulse at the sample was 120(10) µm × 360(30) µm.
Only the electronic decay rate (Γe) exhibited a difference between the NIR and XUV probes (Fig. 3(e)). The electronic decay observed by the XUV probe was faster than that observed by the NIR probe under all excitation conditions. Since Γe originates from n(t), that is, the density of excited-carriers, the present results suggest that the XUV and NIR pulses probe different electronic states. On one hand, the NIR probe would probe the transient dynamics of the excited carriers in the NIR-excited state itself. As the pump intensity increases, the higher density of excited carriers should cause carrier-carrier scattering more frequently, which shortens the decay rate. On the other hand, the XUV pulses would probe the dynamics of other states, for example, unoccupied states near the Fermi level, because the transitions from the 5d core level to these states are allowed through one-photon absorption of 15th HH (24 eV) [32]. A decrease in the dephasing rate appears when the laser intensity is higher than 2.0 µJ/pulse, above which Ae and Aph exhibit saturation. Therefore, the power dependence of the dephasing rate might be involved in the saturation effect, as observed in other semiconductors [33]. To gain a deeper understanding, spectrally resolved measurements will be required, which is beyond the scope of this paper.
In summary, we developed a way of measuring transient reflections in the extreme-ultraviolet region for tracking carriers and coherent phonon dynamics. The lock-in detection combined with the boxcar integrator improves the signal-to-noise ratio. The detection limit of the optical modulation (ΔR/R) is 1 × 10−4, and the data acquisition takes only four minutes. The short measurement time enabled us to study the details of carrier and coherent phonon dynamics in single-crystalline Bi film epitaxially grown on Si (111). The present detection scheme can be applied to transient absorption in the XUV region. The results presented here benchmark the limit of sensitivity of attosecond spectroscopy based on HHG. We expect that this experimental technique will open the door to attosecond spectroscopy of materials and dynamics that have been inaccessible to conventional absorption methods.
Funding
Japan Society for the Promotion of Science (16H02120, 19H02637).
Disclosures
The authors declare no conflicts of interest.
References
1. H. Mashiko, K. Oguri, T. Yamaguchi, A. Suda, and H. Gotoh, “Petahertz optical drive with wide-bandgap semiconductor,” Nat. Phys. 12(8), 741–745 (2016). [CrossRef]
2. M. Schultze, K. Ramasesha, C. D. Pemmaraju, S. A. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Science 346(6215), 1348–1352 (2014). [CrossRef]
3. M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493(7430), 75–78 (2013). [CrossRef]
4. C. J. Kaplan, P. M. Kraus, A. D. Ross, M. Zürch, S. K. Cushing, M. F. Jager, H.-T. Chang, E. M. Gullikson, D. M. Neumark, and S. R. Leone, “Femtosecond tracking of carrier relaxation in germanium with extreme ultraviolet transient reflectivity,” Phys. Rev. B 97(20), 205202 (2018). [CrossRef]
5. K. Oguri, T. Tsunoi, K. Kato, H. Nakano, T. Nishikawa, K. Tateno, T. Sogawa, and H. Gotoh, “Dynamical observation of photo-Dember effect on semi-insulating GaAs using femtosecond core-level photoelectron spectroscopy,” Appl. Phys. Express 8(2), 022401 (2015). [CrossRef]
6. E. Papalazarou, D. Boschetto, J. Gautier, T. Garl, C. Valentin, G. Rey, P. Zeitoun, A. Rousse, P. Balcou, and M. Marsi, “Probing coherently excited optical phonons by extreme ultraviolet radiation with femtosecond time resolution,” Appl. Phys. Lett. 93(4), 041114 (2008). [CrossRef]
7. J. Weisshaupt, A. Rouzée, M. Woerner, M. J. J. Vrakking, T. Elsaesser, E. L. Shirley, and A. Borgschulte, “Ultrafast modulation of electronic structure by coherent phonon excitations,” Phys. Rev. B 95(8), 081101 (2017). [CrossRef]
8. P. Tengdin, W. You, C. Chen, X. Shi, D. Zusin, Y. Zhang, C. Gentry, A. Blonsky, M. Keller, P. M. Oppeneer, H. C. Kapteyn, Z. Tao, and M. M. Murnane, “Critical behavior within 20 fs drives the out-of-equilibrium laser-induced magnetic phase transition in nickel,” Sci. Adv. 4(3), eaap9744 (2018). [CrossRef]
9. S. Mathias, C. La-O-Vorakiat, P. Grychtol, P. Granitzka, E. Turgut, J. M. Shaw, R. Adam, H. T. Nembach, M. E. Siemens, S. Eich, C. M. Schneider, T. J. Silva, M. Aeschlimann, M. M. Murnane, and H. C. Kapteyn, “Probing the timescale of the exchange interaction in a ferromagnetic alloy,” Proc. Natl. Acad. Sci. 109(13), 4792–4797 (2012). [CrossRef]
10. R. Merlin, “Generating coherent THz phonons with light pulses,” Solid State Commun. 102(2-3), 207–220 (1997). [CrossRef]
11. R. Geneaux, H. J. B. Marroux, A. Guggenmos, D. M. Neumark, and S. R. Leone, “Philosophical Transactions of the Royal Society A: Mathematical,” Philos. Trans. R. Soc., A 377(2145), 20170463 (2019). [CrossRef]
12. S. Rubanov and P. R. Munroe, “Damage in III-V Compounds during Focused Ion Beam Milling,” Microsc. Microanal. 11(5), 446–455 (2005). [CrossRef]
13. D. Rudolf, C. La-O-Vorakiat, M. Battiato, R. Adam, J. M. Shaw, E. Turgut, P. Maldonado, S. Mathias, P. Grychtol, H. T. Nembach, T. J. Silva, M. Aeschlimann, H. C. Kapteyn, M. M. Murnane, C. M. Schneider, and P. M. Oppeneer, “Ultrafast magnetization enhancement in metallic multilayers driven by superdiffusive spin current,” Nat. Commun. 3(1), 1037 (2012). [CrossRef]
14. J. Husek, A. Cirri, S. Biswas, and L. R. Baker, “Surface electron dynamics in hematite (α-Fe2O3): correlation between ultrafast surface electron trapping and small polaron formation,” Chem. Sci. 8(12), 8170–8178 (2017). [CrossRef]
15. K. Oguri, H. Mashiko, T. Ogawa, Y. Hanada, H. Nakano, and H. Gotoh, “Sub-50-as isolated extreme ultraviolet continua generated by 1.6-cycle near-infrared pulse combined with double optical gating scheme,” Appl. Phys. Lett. 112(18), 181105 (2018). [CrossRef]
16. D. L. Windt, W. C. Cash, M. Scott, P. Arendt, B. Newnam, R. F. Fisher, A. B. Swartzlander, P. Z. Takacs, and J. M. Pinneo, “Optical constants for thin films of C, diamond, Al, Si, and CVD SiC from 24 Å to 1216 Å,” Appl. Opt. 27(2), 279–295 (1988). [CrossRef]
17. C. S. Gonçalves, A. S. Silva, D. Navas, M. Miranda, F. Silva, H. Crespo, and D. S. Schmool, “A Dual-Colour Architecture for Pump-Probe Spectroscopy of Ultrafast Magnetization Dynamics in the Sub-10-femtosecond Range,” Sci. Rep. 6(1), 22872 (2016). [CrossRef]
18. R. Ohsugi, H. Omi, Y. Krockenberger, and A. Fujiwara, “Spin splitting in EuO(111)/Si(111) spin-filter tunnel junctions with atomically sharp interface,” Jpn. J. Appl. Phys. 57(11), 110304 (2018). [CrossRef]
19. H. J. Zeiger, J. Vidal, T. K. Cheng, E. P. Ippen, G. Dresselhaus, and M. S. Dresselhaus, “Theory for displacive excitation of coherent phonons,” Phys. Rev. B 45(2), 768–778 (1992). [CrossRef]
20. M. Hase, K. Ishioka, J. Demsar, K. Ushida, and M. Kitajima, “Ultrafast dynamics of coherent optical phonons and nonequilibrium electrons in transition metals,” Phys. Rev. B 71(18), 184301 (2005). [CrossRef]
21. O. V. Misochko, M. Hase, K. Ishioka, and M. Kitajima, “Transient Bose-Einstein condensation of phonons,” Phys. Lett. A 321(5-6), 381–387 (2004). [CrossRef]
22. T. Shin, J. W. Wolfson, S. W. Teitelbaum, M. Kandyla, and K. A. Nelson, “Carrier confinement and bond softening in photoexcited bismuth films,” Phys. Rev. B 92(18), 184302 (2015). [CrossRef]
23. A. A. Melnikov, O. V. Misochko, and S. V. Chekalin, “Ultrafast electronic dynamics in laser-excited crystalline bismuth,” J. Appl. Phys. 114(3), 033502 (2013). [CrossRef]
24. I. Timrov, T. Kampfrath, J. Faure, N. Vast, C. R. Ast, C. Frischkorn, M. Wolf, P. Gava, and L. Perfetti, “Thermalization of photoexcited carriers in bismuth investigated by time-resolved terahertz spectroscopy and ab initio calculations,” Phys. Rev. B 85(15), 155139 (2012). [CrossRef]
25. M. Cardona and D. L. Greenaway, “Optical Properties and Band Structure of Group IV-VI and Group V Materials,” Phys. Rev. 133(6A), A1685–A1697 (1964). [CrossRef]
26. P. Y. Wang and A. L. Jain, “Modulated Piezoreflectance in Bismuth,” Phys. Rev. B 2(8), 2978–2983 (1970). [CrossRef]
27. J. Faure, J. Mauchain, E. Papalazarou, M. Marsi, D. Boschetto, I. Timrov, N. Vast, Y. Ohtsubo, B. Arnaud, and L. Perfetti, “Direct observation of electron thermalization and electron-phonon coupling in photoexcited bismuth,” Phys. Rev. B 88(7), 075120 (2013). [CrossRef]
28. M. Hase, K. Mizoguchi, H. Harima, S.-i. Nakashima, and K. Sakai, “Dynamics of coherent phonons in bismuth generated by ultrashort laser pulses,” Phys. Rev. B 58(9), 5448–5452 (1998). [CrossRef]
29. M. Hase, M. Kitajima, S.-i. Nakashima, and K. Mizoguchi, “Dynamics of Coherent Anharmonic Phonons in Bismuth Using High Density Photoexcitation,” Phys. Rev. Lett. 88(6), 067401 (2002). [CrossRef]
30. ÉD Murray, D. M. Fritz, J. K. Wahlstrand, S. Fahy, and D. A. Reis, “Effect of lattice anharmonicity on high-amplitude phonon dynamics in photoexcited bismuth,” Phys. Rev. B 72(6), 060301 (2005). [CrossRef]
31. H. J. Hagemann, W. Gudat, C. Kunz, and J. Opt, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” J. Opt. Soc. Am. 65(6), 742–744 (1975). [CrossRef]
32. A. Ejiri, F. Sugawara, H. Onuki, M. Hirano, and T. Yao, “Absorption Spectra of the Outermost 5d Core-Levels in Lead and Bismuth,” J. Phys. Soc. Jpn. 50(10), 3451–3458 (1981). [CrossRef]
33. V. K. Mag-usara, S. Funkner, G. Niehues, E. A. Prieto, M. H. Balgos, A. Somintac, E. Estacio, A. Salvador, K. Yamamoto, M. Hase, and M. Tani, “Low temperature-grown GaAs carrier lifetime evaluation by double optical pump terahertz time-domain emission spectroscopy,” Opt. Express 24(23), 26175–26185 (2016). [CrossRef]
