Nonlinear light conversion involves one or more bound–bound, bound–free, free–free, and free–bound transitions. It is often challenging to interpret the exact conversion mechanisms. Here we use a femtosecond mid-infrared laser to enhance free–free transitions in terahertz and Brunel harmonic generation from air plasma. Microscopically, both THz and harmonics originate from a common source–ionization-induced plasma currents–and are greatly enhanced when driven by intense long-wavelength pulses. We observe 1% laser-to-terahertz conversion efficiency. Using two-color laser fields, we generate coherent radiation from terahertz to petahertz and investigate the interplay among tunneling ionization, terahertz, and harmonic generation with coherent control.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Two-color laser mixing in gas has been widely used as an intense broadband terahertz (THz) source in many applications [1–18]. In this scheme, a femtosecond laser pulse () and its second harmonic () are co-focused to ionize a gas and create a plasma current. Under the right phase difference between the two-color laser fields, a directional current can arise on the time scale of the laser pulse duration, which emits THz radiation in the far field [5–7].
Ionization-induced plasma currents can also produce harmonic radiation as originally proposed by Brunel . This Brunel harmonic radiation (free–free) is emitted from an ensemble of free electrons oscillating nonsinusoidally in time as a result of phase-dependent tunneling ionization . This is also responsible for low-order harmonics typically up to the 9th order , whereas high-order harmonics are largely produced by electron–ion recollision (free–bound) . THz radiation arising from free–free transitions can be considered as the 0th order Brunel radiation since both arise from the same plasma current.
Low-order harmonics can also be produced by nonlinear bound electron polarization. At a single atom level, this bound–bound contribution, however, can be dominated by the plasma current when driven by intense long-wavelength pulses. This happens because the electron quiver velocity (or plasma current) increases with a wavelength () at a constant laser intensity, whereas the third-order nonlinear susceptibility from bound electrons, the dominant lowest-order for centrosymmetric media, exhibits no wavelength-favorable dependence . This trend is confirmed in a recent time-dependent Schrödinger equation (TDSE) simulation  (see Supplement 1 for a semiclassical calculation). Furthermore, the contribution from free-bound recollision dramatically decreases as the driver laser wavelength increases [23,24]. This was observed in theoretical  and experimental  studies, both reporting a high-order harmonic yield scaling of . Thus, a long-wavelength setting provides an ideal testbed to study plasma currents as a main source for both THz and low-order harmonic generation with reduced involvement from other nonlinear mechanisms. With increasing laser wavelength, the nature of ionization also shifts from multiphoton to tunneling regimes, where laser phase-dependent electron dynamics plays a key role in new frequency generation. Previously, simultaneous measurements of THz and harmonics were conducted at near-infrared (0.8 μm) laser wavelengths [15,27,28], and those studies were limited to high-order harmonics (), neither observing nor considering lower-order harmonics.
In two-color laser fields, the plasma current obtains a drift velocity that scales linearly with wavelength () , like the electron quiver velocity. Thus, for fixed laser intensity, both THz and Brunel harmonic energies are expected to scale with . A recent experiment conducted at , however, shows a surprisingly high THz energy scaling as . Although this dependence may be explained by high-order plasma currents , additional experiments at longer laser wavelengths are desirable to better understand wavelength-dependent THz generation [16–18].
Our experiment was performed with an optical parametric chirped pulse amplification (OPCPA) laser capable of delivering 3.9 μm, 30 mJ, 80 fs pulses at a repetition rate of 20 Hz [29–31]. A schematic of our experimental layout is shown in Fig. 1. To generate two-color laser fields, a thin GaSe crystal is used for second harmonic generation (SHG) [32,33]. The crystal shows the azimuthal angle () dependent second harmonic (SH) and THz generation, as shown in Fig. 2. Due to fact that the GaSe crystal has threefold symmetry , both SH and THz signals exhibit a 60° rotational period. We observe both Type 0 and Type 1 SHG with the GaSe crystal (see Supplement 1). Here, THz generation is dominantly governed by Type 0 SHG, in which both the and pulses are linearly polarized along the extraordinary axis of GaSe (, 90°, 150°). This configuration yields much greater THz radiation compared to the case where the two-color fields are perpendicularly polarized (, 60°, 120°, 180°). The resulting THz radiation is also linearly polarized along the laser field direction.
In two-color laser fields, , where is the relative phase between the fundamental () and second harmonic () fields, we can study phase-dependent tunneling ionization and subsequent plasma-current-induced Brunel radiation. In our scheme, the initial relative phase is controlled by using material dispersion inside a thin coverslip glass placed after the GaSe crystal at angle from the laser axis (see Fig. 1 and Supplement 1). In the tunneling regime, the ionization rate is highly nonlinear and strongly enhanced when the two-color wave crests are in phase with , but this results in less THz radiation according to the plasma current model . Note that the optimum phases for peak ionization rate and for THz generation differ by .
This phase-dependent ionization is evident from plasma fluorescence signatures remaining long after rapid tunneling ionization, as shown in Figs. 3(a) and 3(b). Note that the initial relative phase in the plot is arbitrarily defined ( when the coverslip is normal to the laser at ), whereas the relative phase at can be determined from local plasma fluorescence intensities. For instance, the points marked with in Fig. 3(b) yield the lowest local fluorescence yields, thus . Note that a full extraction of is difficult because of spatial (, ) and temporal () variations of the two-color laser pulses with propagation. Here we consider an effective that contributes to the THz signal most as we tilt the coverslip. The fluorescence variation along at , which yields maximal far-field THz radiation, is plotted in Fig. 3(c) with local THz emission intensities determined by an aperture scanning method . As the relative phase varies along due to plasma dispersion and Gouy phase shifts, at where minimal THz radiation emits overall, most THz radiation arises from with . This radiation is much weaker than that at because it originates Rayleigh length away from the laser focus. The corresponding THz radiation profiles are shown in Figs. 3(d) and 3(e). They exhibit characteristic conical emission, consistent with previous observations in near-infrared two-color laser mixing [8,10,12]. Also, the difference in size confirms their phase-dependent origin of emission.
We note that the secondary fluorescence hump observed around in Fig. 3(b) is caused by an uncontrolled aberration in our beam focusing, also observed in the single-color case in Fig. 1(b). Figures 3(f) and 3(g) show phase-dependent plasma fluorescence, THz, and low-order harmonics (up to the 9th order) yields. All exhibit strong phase-dependent modulations. The THz and fluorescence (or ionization rate) signals are clearly anti-correlated as shown in Fig. 3(f), consistent with the plasma current model . Figure 3(g) shows measured radiation from 0th to 9th order, which exhibits coherent radiation from terahertz to petahertz frequencies under phase control (versus ). The emitted THz spectrum is characterized by a Michelson-type Fourier transform infrared (FTIR) spectrometer.
Figure 4(a) shows measured field autocorrelations (inset) and corresponding spectra obtained via Fourier transformation. The radiation peaks at 12 THz with a bandwidth exceeding 30 THz. Also, the THz output rapidly increases with laser energy as shown in Fig. 4(b). The maximum laser-to-THz conversion efficiency reaches even with a relatively low SH energy ratio of (see Supplement 1). Along with other previous measurements [11,12], our experiment shows a wavelength-dependent scaling of for THz conversion efficiency as shown in Fig. 4(c). We note that this scaling is not absolute and largely depends on the energy ratio . Due to our low energy ratio 0.02 compared to at 800 nm  and 0.05 at , our result provides a lower limit of scaling. Nonetheless, our scaling agrees well with some variants, , obtained from 0.8–2 μm [16,18]. Figure 5(a) displays all measured phase-dependent harmonic (2nd–9th) yields. Those agree well with our simulation [Fig. 5(b)] based on a unidirectional pulse propagation equation model (see Supplement 1) [35,36]. Through the simulation, we confirm that the plasma current-induced Brunel mechanism is dominant over bound electron effects for THz generation [see Fig. 5(c)]. The simulation predicts efficiency, consistent with the measurement. However, for harmonic (), the bound electron effect cannot be ignored because the combined ( plus plasma) effects contribute much more than the plasma effect alone. It is possibly due to synergistic effects between those two such as -based cascade mixing of plasma-produced Brunel radiation, -induced beam self-focusing, and enhanced phase-matching of -induced harmonics due to plasma formation (see Supplement 1). All these make it difficult to separate those two contributions in a macroscopic beam propagation setting [37,38].
In conclusion, we report the generation of coherent radiation from THz to ultraviolet via two-color laser mixing at the mid-infrared level. Here we make simultaneous measurements of THz and low-order harmonic radiation under common phase control. In practice, we achieve significant laser-to-THz conversion efficiency (), about times larger than conventional values obtained with 0.8 μm lasers. The efficiency can be enhanced further with more efficient SHG. This type of source can potentially produce single-cycle, broadband, millijoule-level THz radiation, which is useful for studying THz-driven extreme nonlinearities.
Office of Naval Research (N00014-17-1-2705); Air Force Office of Scientific Research (FA9550-16-1-0163); SSGF program (DE-NA0003864).
Daniel Woodbury acknowledges support from SSGF program.
See Supplement 1 for supporting content.
1. D. J. Cook and R. M. Hochstrasser, Opt. Lett. 25, 1210 (2000). [CrossRef]
2. M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, Opt. Lett. 29, 1120 (2004). [CrossRef]
3. T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, Opt. Lett. 30, 2805 (2005). [CrossRef]
4. X. Xie, J. Dai, and X.-C. Zhang, Phys. Rev. Lett. 96, 075005 (2006). [CrossRef]
5. K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, Opt. Express 15, 4577 (2007). [CrossRef]
6. K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, Nat. Photonics 2, 605 (2008). [CrossRef]
7. K. Y. Kim, Phys. Plasmas 16, 056706 (2009). [CrossRef]
8. Y. S. You, T. I. Oh, and K. Y. Kim, Phys. Rev. Lett. 109, 183902 (2012). [CrossRef]
9. T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, Appl. Phys. Lett. 102, 201113 (2013). [CrossRef]
10. L. A. Johnson, J. P. Palastro, T. M. Antonsen, and K. Y. Kim, Phys. Rev. A 88, 063804 (2013). [CrossRef]
11. M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, Phys. Rev. Lett. 110, 253901 (2013). [CrossRef]
12. T. I. Oh, Y. J. Yoo, Y. S. You, and K. Y. Kim, Appl. Phys. Lett. 105, 041103 (2014). [CrossRef]
13. I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Berge, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010). [CrossRef]
14. H. Wen and A. M. Lindenberg, Phys. Rev. Lett. 103, 023902 (2009). [CrossRef]
15. D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, Phys. Rev. Lett. 109, 243002 (2012). [CrossRef]
16. A. Nguyen, P. González de Alaiza Martínez, J. Déchard, I. Thiele, I. Babushkin, S. Skupin, and L. Bergé, Opt. Express 25, 4720 (2017). [CrossRef]
17. A. Nguyen, P. González de Alaiza Martínez, I. Thiele, S. Skupin, and L. Bergé, Phys. Rev. A 97, 063839 (2018). [CrossRef]
18. A. Nguyen, K. J. Kaltenecker, J.-C. Delagnes, B. Zhou, E. Cormier, N. Fedorov, R. Bouillaud, D. Descamps, I. Thiele, S. Skupin, P. U. Jepsen, and L. Bergé, Opt. Lett. 44, 1488 (2019). [CrossRef]
19. F. Brunel, J. Opt. Soc. Am. B 7, 521 (1990). [CrossRef]
20. N. H. Burnett, C. Kan, and P. B. Corkum, Phys. Rev. A 51, R3418 (1995). [CrossRef]
21. P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993). [CrossRef]
22. S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, Opt. Lett. 40, 5794 (2015). [CrossRef]
23. E. E. Serebryannikov and A. M. Zheltikov, Phys. Rev. Lett. 113, 043901 (2014). [CrossRef]
24. A. M. Zheltikov, J. Phys. B 50, 092001 (2017). [CrossRef]
25. J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, Phys. Rev. Lett. 98, 013901 (2007). [CrossRef]
26. A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Phys. Rev. Lett. 103, 073902 (2009). [CrossRef]
27. Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, J. Phys. B 46, 155602 (2013). [CrossRef]
28. A. Gragossian, D. V. Seletskiy, and M. Sheik-Bahae, Sci. Rep. 6, 34973 (2016). [CrossRef]
29. A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, Sci. Rep. 5, 8368 (2015). [CrossRef]
30. T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, Science 336, 1287 (2012). [CrossRef]
31. D. Woodbury, L. Feder, V. Shumakova, C. Gollner, R. Schwartz, B. Miao, F. Salehi, A. Korolov, A. Pugžlys, A. Baltuška, and H. M. Milchberg, Opt. Lett. 43, 1131 (2018). [CrossRef]
32. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1999).
33. K. Kato, F. Tanno, and N. Umemura, Appl. Opt. 52, 2325 (2013). [CrossRef]
34. X. Zhou, J. X. Cheng, Y. B. Zhou, T. Cao, H. Hong, Z. M. Liao, S. W. Wu, H. L. Peng, K. H. Liu, and D. P. Yu, J. Am. Chem. Soc. 137, 7994 (2015). [CrossRef]
35. M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604 (2004). [CrossRef]
36. S. Zahedpour, S. W. Hancock, and H. M. Milchberg, Opt. Lett. 44, 843 (2019). [CrossRef]
37. U. Sapaev, A. Husakou, and J. Herrmann, Opt. Express 21, 25582 (2013). [CrossRef]
38. T. Balciunas, A. J. Verhoef, A. V. Mitrofanov, G. Fan, E. E. Serebryannikov, M. Y. Ivanov, A. M. Zheltikov, and A. Baltuska, Chem. Phys. 414, 92 (2013). [CrossRef]