OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 21349–21356
« Show journal navigation

Terahertz wave generation from hyper-Raman lines in two-level quantum systems driven by two-color lasers

Wei Zhang, Shi-Fang Guo, Su-Qing Duan, and Xian-Geng Zhao  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 21349-21356 (2013)
http://dx.doi.org/10.1364/OE.21.021349


View Full Text Article

Acrobat PDF (1019 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Based on spatial-temporal symmetry breaking mechanism, we propose a novel scheme for terahertz (THz) wave generation from hyper-Raman lines associated with the 0th harmonic (a particular even harmonic) in a two-level quantum system driven by two-color laser fields. With the help of analysis of quasi-energy, the frequency of THz wave can be tuned by changing the field amplitude of the driving laser. By optimizing the parameters of the laser fields, we are able to obtain arbitrary frequency radiation in the THz regime with appreciable strength (as strong as the typical harmonics). Our proposal can be realized in experiment in view of the recent experimental progress of even-harmonics generation by two-color laser fields.

© 2013 OSA

1. Introduction

One challenge of THz wave generation in optical approach in usual atomic/semiconductor system is to generate low frequency radiation from a quantum system with a large energy gap. Usually, in the emission spectrum of a quantum system, there are harmonics, as well as the associated hyper-Raman lines. Hyper-Raman lines are caused by the transitions between the dressed bound states. Nth hyper-Raman lines are defined as those associated with the nth harmonics (they appear with the corresponding harmonics simultaneously due to the same symmetry reason, and locate near 0, where ω0 is the fundamental frequency of the incident laser) [23

23. T. Millack and A. Maquet, “Hyper-Raman lines produced during high harmonic generation,” J. Mod. Opt. 40(11), 2161–2171 (1993). [CrossRef]

]. Here is one observation that the shift of the hyper-Raman line to the associated harmonic could be small and could be tuned by the external field, even though the fundamental frequency is large. Then one may use the 0th hyper-Raman line (that associated with the 0th harmonic) to generate the low-frequency (THz) wave. There have been some studies on the harmonics and hyper-Raman lines. In many cases, there are only odd harmonics due to the particular symmetry and the associated hyper-Raman line is of high frequency and/or weak intensity. Therefore one has to solve these two problems to generate THz wave by using the hyper-Raman lines in the nonlinear optical processes.

In this article, we adopt an effective optical method to obtain THz wave in typical two-level quantum systems, which solves the two problems mentioned above. Based on the generalized spatial-temporal symmetry principle we developed recently [24

24. S. F. Guo, S. Q. Duan, Y. Xie, W. D. Chu, and W. Zhang, “Tailoring the photon emission patterns in nanostructures,” New J. Phys. 13(5), 053005 (2011). [CrossRef]

], we propose a novel mechanism to obtain the 0th hyper-Raman lines in THz regime by introducing additional laser with frequency 20 (k = 1, 2, 3,...). Using analysis of quasienergy and optimization of laser fields, we are able to obtain considerably intense THz radiation with desired frequency. With the help of our optimization method, it is quite likely that our proposal can be realized in experiment considering the recent experimental progress of even-harmonics generation by two-color laser.

2. Theoretical formulism

Our two-level quantum system driven by laser fields [see the schematic diagram Fig. 1(a)] is described by the Hamiltonian
H=i2Ei|ii|+G(t)(|12|+|21|),
(1)
where G(t) = F(t)e · μ12, the laser field E = F(t)e, F(t) = F(t + T), T the period of the lasers, e a unit vector. μ12 = 〈1|er|2〉 is the dipole between state |1〉 and state |2〉. The energy spacing between the two states [with energies Ei(i = 1, 2)] is set as ΔE = E1E2.

Fig. 1 (a) The schematic diagram of our two-level system driven by an incident laser. The emission spectrum contains the higher-order harmonics and the accompanied hyper-Raman lines; (b)–(f) Emission spectra in the presence of various driving fields F(t). (b) F(t) = F1 cos(ω0t); (c) F(t) = F2 cos(2ω0t); (d) F(t) = F1 cos(ω0t) + F2 cos(2ω0t); (e) F(t) = F1 cos(ω0t) + F2 cos(3ω0t); (f) F(t) = F1 cos(ω0t) + F2 cos(4ω0t). F1 = 4.4 × 109V/m, F2 = 2.2 × 109V/m.

The dynamics of our system is described by the equation of motion of the density matrix [25

25. L. M. Narducci, M. O. Scully, G.-L. Oppo, P. Ru, and J. R. Tredicce, “Spontaneous emission and absorption properties of a driven three-level system,” Phys. Rev. A 42(3), 1630–1649 (1990). [CrossRef] [PubMed]

]
ρt=ih¯[H,ρ]Γρ,
(2)
where H is the Hamiltonian, the last term describes possible dissipative effects (such as spontaneous phonon emission) and we set = 1 in the following. We numerically calculate the photon emission spectra of the two-level quantum systems by solving the density matrix in Eq. (2) through Runge-Kutta method with the time step of 0.002/ω0, total steps of 1200000 and the electron initially setting at the lower level. The average dipole can be calculated as D(t) = ∑ij μijρij(t). We use Fourier transformation to obtain the emission spectrum S(ν) = |∫dtexp(−iνt)D(t)|2. In the calculation we set h̄ω0 (ω0 the driving field frequency) as the unit of energy. We choose ω0 = 100THz as an example, yet in general one can also use other frequency (much larger than THz) laser as will be discussed later. The two-level quantum systems can be realized in many systems, such as atoms, molecules, and semiconductor quantum dots. To demonstrate the basic physical mechanism, we study the optical process of the system with the typical parameters of a quantum dot: the energy spacing ΔE = 10h̄ω0, the dipole moment μ12 = 0.5 e ·nm, phonon emission coefficient Γij = 3.4 × 10−3ω0.

Here we give some analysis on the hyper-Raman lines and their relation to the harmonic components. In our systems driven by a periodic field, the quasienergy state has the form |ψα(t)〉 = eαt |ϕα(t)〉, where the Floquet state |ϕα(t)〉 = |ϕα(t + T)〉 can be written in the form |ϕα(t)=meimω0t|ϕαm. We consider a state |ψ(t)〉 = a1|ψ1〉 + a2|ψ2〉 = a1e1t |ϕ1〉 + a2e2t|ϕ2〉. Then we have
ψ|P^|ψ=m,nei(nm)ω0t[|a1|2ϕ1m|P^|ϕ^1n+|a2|2ϕ2m|P^|ϕ2n]+m,nei[(ε2ε1)+(nm)ω0]ta2a1*ϕ1m|P^|ϕ2n+m,nei[(ε1ε2)+(nm)ω0]ta1a2*ϕ2m|P^|ϕ1n.
(3)
In the emission spectrum, there may be harmonics with frequency (nm)ω0 and hyper-Raman lines with frequency (nm)ω0 ± (ε1ε2).

If the system posses a symmetry generated by the operator Q = Ω · θ and the Floquet state |ϕα(t)〉 has a definite parity under Q, i.e., Q|ϕα(t)〉 = ±|ϕα(t)〉, then we have Ω|ϕαm=±(1)m|ϕαm. Then we have ϕαm|P^|ϕβn=0 (α, β = 1, 2) for nm even/odd number and states α, β of same/different parity. Quite often the harmonics and the associated hyper-Raman lines appear simultaneously due to the same symmetry properties of the Floquet states. In the case with a monochromatic laser, we have odd harmonics and the associated hyper-Raman lines. While in other cases with symmetry broken, more harmonics and the associated hyper-Raman lines are generated.

3. Emission patterns

Let’s first look at the emission spectrum of a system driven by a monochromatic incident laser with frequency ω0. As seen in Fig. 1(b), there are odd harmonics as well as the associated hyper-Raman lines due to the spatial-temporal symmetry properties of the Floquet states as analyzed above. It is natural that, for the incident laser with frequency 2ω0, the emission spectrum contains components with frequencies of 2ω0, 6ω0 and 10ω0...(odd orders of incident frequency 2ω0) as shown in Fig. 1(c). One notices that there is no 0th hyper-Raman line in this case. If we use two-color lasers with frequencies ω0 and 2ω0, interesting phenomena appear. As seen from Fig. 1(d), even harmonics and the associated hyper-Raman lines are generated by introducing the second laser field. Especially a low frequency radiation, 0th hyper-Raman radiation is generated. We would like to point out that the emission spectrum for the case with driving field F(t) = F1 cos(ω0t) + F2 cos(2ω0t) is not the supposition of those driven by F1 cos(ω0t) and F2 cos(2ω0t). For example, the harmonic 4ω0 in Fig. 1(d) neither appears in Fig. 1(b) nor in Fig. 1(c). It is also not the frequency summation or difference of the harmonics of systems driven by monochromatic incident laser with frequency ω0 and 2ω0. In fact, the appearance of all even components (and the associated hyper-Raman lines) in Fig. 1(d) is the consequence of symmetry breaking.

According to our theory, the symmetry of the quantum system generated by Q1 is broken by introducing the second laser with frequency 20 (k = 1, 2, 3...), and it is not broken by introducing the second laser with frequency (2k − 1)ω0 (k = 1, 2, 3...). These predictions are verified by our numerical results shown in Fig. 1(e) (the second laser of frequency 3ω0) and Fig. 1(f) (the second laser of frequency 4ω0). It is clear that the 0th hyper-Raman line does not appear in the cases with symmetry (see Figs. 1(b), 1(c), 1(e)). Interestingly, the second laser field with frequency 4ω0 leads to the appearance of 2nth harmonics (even for n = 1) and the associated hyper-Raman line (in particular the 0th hyper-Raman line) as predicted by our theory, since the second laser with frequency 4ω0 breaks the spatial-temporal symmetry generated by Q1. Using this mechanism, we can explain the experimental results of observing even harmonics in helium or plasma plumes (containing nanoparticles, carbon nanotubes, etc) driven by a two-color laser [26

26. R. A. Ganeev, H. Singhal, P. A. Naik, J. A. Chakera, H. S. Vora, R. A. Khan, and P. D. Gupta, “Systematic studies of two-color pump-induced high-order harmonic generation in plasma plumes,” Phys. Rev. A 82(5), 053831 (2010). [CrossRef]

, 27

27. R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using a two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009). [CrossRef]

], where the second-harmonic driving term, despite being very small, breaks the symmetry and thus allows additional strong even harmonic components. Our general theory [24

24. S. F. Guo, S. Q. Duan, Y. Xie, W. D. Chu, and W. Zhang, “Tailoring the photon emission patterns in nanostructures,” New J. Phys. 13(5), 053005 (2011). [CrossRef]

] also reveals the mechanism of the generation of even harmonics and associated hyper-Raman lines in system with spatial symmetry break [28

28. O. V. Kibis, G. Ya. Slepyan, S. A. Maksimenko, and A. Hoffmann, “Matter Coupling to Strong Electromagnetic Fields in Two-Level Quantum Systems with Broken Inversion Symmetry,” Phys. Rev. Lett. 102(2), 023601 (2009). [CrossRef] [PubMed]

].

As seen from Eq. (3), the frequency of hyper-Raman line is determined by the quasienergy, which is tunable. One may ask whether one can use the hyper-Raman line associated with 1th harmonic to generate the low frequency/THz wave? Actually, as seen from Fig. 2(a) the intensity of the hyper-Raman line associated with the 1th harmonic decreases dramatically as the frequency decreasing. To make this point clearer, we compare the low frequency components associated the 1th harmonic and 0th harmonic for the case with two-color laser shown in Fig. 2(b). One sees that in the every low frequency regime, the intensity of the 0th hyper-Raman line (associated with the 0th harmonic) is much larger than that of the 1th hyper-Raman line. Therefore one should use the 0th hyper-Raman line to generate the THz radiation effectively.

Fig. 2 (a) The intensity of hyper-Raman line associated with 1th harmonic for F(t) = F1 cos(ω0t), F1 is related to ν, the frequency of the hyper-Raman line; (b) The intensities of hyper-Raman lines associated with 0th (peak 1) and 1th (peak 2) harmonics for F(t) = F1 cos(ω0t) + F2 cos(2ω0t), F1 = 4.4 × 109V/m, F2 is related to ν.

4. Tuning of the frequency and intensity of THz wave

Fig. 3 The quasienergy difference (solid line) between two quasi-eigenstates and the frequency (dots) of the 0th hyper-Raman line versus the magnitude of external field F1. F2 = 2.2 × 109V/m.
Fig. 4 (a) The parameters of F1 and F2 for the 0th hyper-Raman line with frequency 2THz= 0.02ω0. The triangle indicates the optimal parameter for the maximal intensity of 0th hyper-Raman line. (b) The corresponding emission spectrum for the case with optimized external field.

In our approach, the typical driving field intensity is in the order of 1012 ∼ 1013W/cm2, which is lower than the typical driving field intensity (in the order of 1014W/cm2 ∼ 1015W/cm2) used in other methods for THz generation and/or HHG by two-color laser [8

8. X. Xie, J. Dai, and X.C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. 96(7), 075005 (2006). [CrossRef] [PubMed]

11

11. J. Penano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E 81(2), 026407 (2010). [CrossRef]

,26

26. R. A. Ganeev, H. Singhal, P. A. Naik, J. A. Chakera, H. S. Vora, R. A. Khan, and P. D. Gupta, “Systematic studies of two-color pump-induced high-order harmonic generation in plasma plumes,” Phys. Rev. A 82(5), 053831 (2010). [CrossRef]

,27

27. R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using a two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009). [CrossRef]

,29

29. I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005). [CrossRef]

31

31. N. Ishii, A. Kosuge, T. Hayashi, T. Kanai, J. Itatani, S. Adachi, and S. Watanabe, “Quantum path selection in high-harmonic generation by a phase-locked two-color field,” Opt. express 16(25), 20876–20883 (2008). [CrossRef] [PubMed]

]. One should also use a long driving laser pulse [much longer than its period (2π/ω0)] as that used in Ref. [26

26. R. A. Ganeev, H. Singhal, P. A. Naik, J. A. Chakera, H. S. Vora, R. A. Khan, and P. D. Gupta, “Systematic studies of two-color pump-induced high-order harmonic generation in plasma plumes,” Phys. Rev. A 82(5), 053831 (2010). [CrossRef]

,27

27. R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using a two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009). [CrossRef]

]. The emitted hyper-Raman line frequency can not only be tuned by the driving field intensity as seen in Fig. 3, but also by the frequency of the incident laser. If we use the incident laser with frequency in the regime ω0 ∼ 50THz – 500THz, we may obtain the 0th hyper-Raman line with frequency 150ω0 ∼ 1THz – 10THz. As shown in Fig. 1, the hyper-Raman lines are usually weaker than high order harmonics and are hard to be observed in experiment. Appropriate optimization may increase the possibility of observing hyper-Raman lines [23

23. T. Millack and A. Maquet, “Hyper-Raman lines produced during high harmonic generation,” J. Mod. Opt. 40(11), 2161–2171 (1993). [CrossRef]

,32

32. N. Moiseyev and M. Lein, “Non-Hermitian Quantum mechanics for high-order harmonic generation spectra,” J. Phys. Chem. A 107(37), 7181–7188 (2003). [CrossRef]

]. In our systems, hyper-Raman lines with suitable frequency and appreciable intensity can be obtained by using our optimization scheme as shown in Fig. 4. The intensity of hyper-Raman lines can be further increased by using appropriate initial state and the relative phase difference between two incident lasers. For effective hyper-Raman line generation, one also needs to keep the Γ/ω0 small to suppress the damping (of hyper-Raman lines) effect.

5. Conclusion

A novel mechanism based on spatial-temporal symmetry breaking is proposed to obtain THz wave from 0th hyper-Raman line in two-color pumped two-level quantum system. Quasienergy is calculated to determine the parameters of the incident laser to obtain radiation of arbitrary frequency from 0.1THz to 10THz. Upon optimization of the driving fields, we are able to obtain THz wave with desired frequency and appreciable intensity (as large as that of the typical harmonics).

Acknowledgments

This work was partially supported by the National Science Foundation of China under Grants No. 11174042, 10874020, 11247245 and by the National Basic Research Program of China (973 Program) under Grants No. 2011CB922204, 2013CB632805, CAEP under Grant No. 2011B0102024, and the Project-sponsored by SRF for ROCS, SEM.

References and links

1.

M. Tonouchi, “Cutting-edge terahertz technology,” Nature Photon. 1(2), 97–105 (2007). [CrossRef]

2.

T. Otsuji, M. Hanabe, T. Nishimura, and E. Sano, “A grating-bicoupled plasma- wave photomixer with resonant-cavity enhanced structure,” Opt. Express 14(11), 4815–4825 (2006). [CrossRef] [PubMed]

3.

N. Sekine and K. Hirakawa, “Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices,” Phys. Rev. Lett. 94(5), 057408 (2005). [CrossRef] [PubMed]

4.

N. Orihashi, S. Suzuki, and M. Asada, “One THz harmonic oscillation of resonant tunneling diodes,” Appl. Phys. Lett. 87(23), 233501 (2005). [CrossRef]

5.

T. W. Crowe, W. L. Bishop, D. W. Perterfield, J. L. Hesler, and R. M. Weikle, “Opening the Terahertz Window With Integrated Diode Circuits,” IEEE J. Solid-State Circuits 40(10), 2104–2110 (2005). [CrossRef]

6.

H. Ito, F. Nakajima, T. Furuta, and T. Ishibashi, “Continuous THz-wave generation using antenna-integrated uni-travelling-carrier photodiodes,” Semicond. Sci. Technol. 20(7), S191–S198 (2005). [CrossRef]

7.

K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D 34(1), R1–R14 (2001).

8.

X. Xie, J. Dai, and X.C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. 96(7), 075005 (2006). [CrossRef] [PubMed]

9.

T. J. Wang, J.F. Daigle, S. Yuan, F. Theberge, M. Chateauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83(5), 053801 (2011). [CrossRef]

10.

T. J. Wang, C. Marceau, Y. Chen, S. Yuan, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “Terahertz emission from a dc-biased two-color femtosecond laser-induced filament in air,” Appl. Phys. Lett. 96(21), 211113 (2010). [CrossRef]

11.

J. Penano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E 81(2), 026407 (2010). [CrossRef]

12.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264(5158), 553–556 (1994). [CrossRef] [PubMed]

13.

R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfeld, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor heterostructure laser,” Nature 417(6885), 156–159 (2002). [CrossRef] [PubMed]

14.

B. S. Williams, “Terahertz quantum-cascade lasers,” Nature Photonics 1(9), 517–525 (2007). [CrossRef]

15.

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Resonant-phonon terahertz quantum-cascade laser operating at 2.1 THz,” Electron. Lett. 40(7), 431–432 (2004). [CrossRef]

16.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference- frequency generation,” Nature Photon. 1(5), 288–292 (2007). [CrossRef]

17.

G. P. Williams, “Far-IR/THz radiation from the Jefferson Laboratory, energy recovered linac, free electron laser,” Rev. Sci.Instr. 73(3), 1461–1463 (2002). [CrossRef]

18.

K. Miyamoto, S. Ohno, M. Fujiwara, H. Minamide 1, H. Hashimoto, and H. Ito, “Optimized terahertz-wave generation using BNA-DFG,” Opt. Express 17(17), 18832–14838 (2009). [CrossRef]

19.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “High performance terahertz quantum cascade laser sources based on intracavity difference frequency generation,” Opt. Express 21(1), 968–973 (2013). [CrossRef] [PubMed]

20.

K. J. Ahn, F. Milde, and A. Knorr, “Phonon-Wave-Induced Resonance Fluorescence in Semiconductor Nanostructures: Acoustoluminescence in the Terahertz Range,” Phys. Rev. Lett. 98(2), 027401 (2007). [CrossRef] [PubMed]

21.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature (London) 457(7226), 174–178 (2009). [CrossRef]

22.

S. Q. Duan, W. Zhang, Y. Xie, W. D. Chu, and X. G. Zhao, “Terahertz radiation in semiconductor quantum dots driven by gigahertz waves: The role of tailoring the quasienergy spectrum,” Phys. Rev. B 80(16), 161304(R) (2009). [CrossRef]

23.

T. Millack and A. Maquet, “Hyper-Raman lines produced during high harmonic generation,” J. Mod. Opt. 40(11), 2161–2171 (1993). [CrossRef]

24.

S. F. Guo, S. Q. Duan, Y. Xie, W. D. Chu, and W. Zhang, “Tailoring the photon emission patterns in nanostructures,” New J. Phys. 13(5), 053005 (2011). [CrossRef]

25.

L. M. Narducci, M. O. Scully, G.-L. Oppo, P. Ru, and J. R. Tredicce, “Spontaneous emission and absorption properties of a driven three-level system,” Phys. Rev. A 42(3), 1630–1649 (1990). [CrossRef] [PubMed]

26.

R. A. Ganeev, H. Singhal, P. A. Naik, J. A. Chakera, H. S. Vora, R. A. Khan, and P. D. Gupta, “Systematic studies of two-color pump-induced high-order harmonic generation in plasma plumes,” Phys. Rev. A 82(5), 053831 (2010). [CrossRef]

27.

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using a two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009). [CrossRef]

28.

O. V. Kibis, G. Ya. Slepyan, S. A. Maksimenko, and A. Hoffmann, “Matter Coupling to Strong Electromagnetic Fields in Two-Level Quantum Systems with Broken Inversion Symmetry,” Phys. Rev. Lett. 102(2), 023601 (2009). [CrossRef] [PubMed]

29.

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005). [CrossRef]

30.

I. J. Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Namb, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92(2), 021125 (2008). [CrossRef]

31.

N. Ishii, A. Kosuge, T. Hayashi, T. Kanai, J. Itatani, S. Adachi, and S. Watanabe, “Quantum path selection in high-harmonic generation by a phase-locked two-color field,” Opt. express 16(25), 20876–20883 (2008). [CrossRef] [PubMed]

32.

N. Moiseyev and M. Lein, “Non-Hermitian Quantum mechanics for high-order harmonic generation spectra,” J. Phys. Chem. A 107(37), 7181–7188 (2003). [CrossRef]

33.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A.-P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81(2), 457–460 (1998). [CrossRef]

34.

L. Plaja and L. Roso, “High-order harmonic generation in a two-level atom: effect of the multiphoton resonances tuned by the light shift,” J. Mod. Opt. 40(5), 793–807 (1993). [CrossRef]

35.

A. D. Piazza and E. Fiordilino, “Why hyper-Raman lines are absent in high-order harmonic generation,” Phys. Rev. A 64(1), 013802 (2001). [CrossRef]

36.

Z. Y. Zhou and J. M. Yuan, “Fine structures of the harmonic and hyper-Raman spectrum of the hydrogen atom in an intense high-frequency laser pulse,” Phys. Rev. A 77(6), 063411 (2008). [CrossRef]

37.

Y. Dakhnovskii and H. Metiu, “Conditions leading to intense low-frequency generation and strong localization in two-level systems,” Phys. Rev. A 48(3), 2342–2345 (1993). [CrossRef] [PubMed]

38.

C. Liu, S. Gong, R. Li, and Z. Xu, “Coherent control in the generation of harmonics and hyper-Raman lines from a strongly driven two-level atom,” Phys. Rev. A 69(2), 023406 (2004). [CrossRef]

39.

F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A 52(1), 525–540 (1995). [CrossRef] [PubMed]

40.

M. Frasca, “Theory of dressed states in quantum optics,” Phys. Rev. A 60(1), 573–581 (1999). [CrossRef]

41.

A. D. Piazza, E. Fiordilino, and M. H. Mittleman, “Analytical study of the spectrum emitted by a two-level atom driven by a strong laser pulse,” Phys. Rev. A 64(1), 013414 (2001). [CrossRef]

42.

M. L. Pons, R. Taieb, and A. Maquet, “Importance of population transfers in high-order harmonic-generation spectra,” Phys. Rev. A 54(4), 3634–3641 (1996). [CrossRef] [PubMed]

43.

H. Wang and X.G. Zhao, “Emission properties of electrons in two-level systems driven by DC - AC fields,” J. Phys.: Condens.Matter 8(18), L285–L289 (1996). [CrossRef]

44.

P. Huang, X.-T. Xie, X. Lu, J. Li, and X. Yang, “Carrier-envelope-phase-dependent effects of high-order harmonic generation in a strongly driven two-level atom,” Phys. Rev. A 79(4), 043806 (2009). [CrossRef]

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4180) Nonlinear optics : Multiphoton processes
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 11, 2013
Revised Manuscript: August 23, 2013
Manuscript Accepted: August 24, 2013
Published: September 4, 2013

Citation
Wei Zhang, Shi-Fang Guo, Su-Qing Duan, and Xian-Geng Zhao, "Terahertz wave generation from hyper-Raman lines in two-level quantum systems driven by two-color lasers," Opt. Express 21, 21349-21356 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-21349


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Tonouchi, “Cutting-edge terahertz technology,” Nature Photon.1(2), 97–105 (2007). [CrossRef]
  2. T. Otsuji, M. Hanabe, T. Nishimura, and E. Sano, “A grating-bicoupled plasma- wave photomixer with resonant-cavity enhanced structure,” Opt. Express14(11), 4815–4825 (2006). [CrossRef] [PubMed]
  3. N. Sekine and K. Hirakawa, “Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices,” Phys. Rev. Lett.94(5), 057408 (2005). [CrossRef] [PubMed]
  4. N. Orihashi, S. Suzuki, and M. Asada, “One THz harmonic oscillation of resonant tunneling diodes,” Appl. Phys. Lett.87(23), 233501 (2005). [CrossRef]
  5. T. W. Crowe, W. L. Bishop, D. W. Perterfield, J. L. Hesler, and R. M. Weikle, “Opening the Terahertz Window With Integrated Diode Circuits,” IEEE J. Solid-State Circuits40(10), 2104–2110 (2005). [CrossRef]
  6. H. Ito, F. Nakajima, T. Furuta, and T. Ishibashi, “Continuous THz-wave generation using antenna-integrated uni-travelling-carrier photodiodes,” Semicond. Sci. Technol.20(7), S191–S198 (2005). [CrossRef]
  7. K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D34(1), R1–R14 (2001).
  8. X. Xie, J. Dai, and X.C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett.96(7), 075005 (2006). [CrossRef] [PubMed]
  9. T. J. Wang, J.F. Daigle, S. Yuan, F. Theberge, M. Chateauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A83(5), 053801 (2011). [CrossRef]
  10. T. J. Wang, C. Marceau, Y. Chen, S. Yuan, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “Terahertz emission from a dc-biased two-color femtosecond laser-induced filament in air,” Appl. Phys. Lett.96(21), 211113 (2010). [CrossRef]
  11. J. Penano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E81(2), 026407 (2010). [CrossRef]
  12. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science264(5158), 553–556 (1994). [CrossRef] [PubMed]
  13. R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfeld, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor heterostructure laser,” Nature417(6885), 156–159 (2002). [CrossRef] [PubMed]
  14. B. S. Williams, “Terahertz quantum-cascade lasers,” Nature Photonics1(9), 517–525 (2007). [CrossRef]
  15. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Resonant-phonon terahertz quantum-cascade laser operating at 2.1 THz,” Electron. Lett.40(7), 431–432 (2004). [CrossRef]
  16. M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference- frequency generation,” Nature Photon.1(5), 288–292 (2007). [CrossRef]
  17. G. P. Williams, “Far-IR/THz radiation from the Jefferson Laboratory, energy recovered linac, free electron laser,” Rev. Sci.Instr.73(3), 1461–1463 (2002). [CrossRef]
  18. K. Miyamoto, S. Ohno, M. Fujiwara, H. Minamide, H. Hashimoto, and H. Ito, “Optimized terahertz-wave generation using BNA-DFG,” Opt. Express17(17), 18832–14838 (2009). [CrossRef]
  19. Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “High performance terahertz quantum cascade laser sources based on intracavity difference frequency generation,” Opt. Express21(1), 968–973 (2013). [CrossRef] [PubMed]
  20. K. J. Ahn, F. Milde, and A. Knorr, “Phonon-Wave-Induced Resonance Fluorescence in Semiconductor Nanostructures: Acoustoluminescence in the Terahertz Range,” Phys. Rev. Lett.98(2), 027401 (2007). [CrossRef] [PubMed]
  21. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature (London)457(7226), 174–178 (2009). [CrossRef]
  22. S. Q. Duan, W. Zhang, Y. Xie, W. D. Chu, and X. G. Zhao, “Terahertz radiation in semiconductor quantum dots driven by gigahertz waves: The role of tailoring the quasienergy spectrum,” Phys. Rev. B80(16), 161304(R) (2009). [CrossRef]
  23. T. Millack and A. Maquet, “Hyper-Raman lines produced during high harmonic generation,” J. Mod. Opt.40(11), 2161–2171 (1993). [CrossRef]
  24. S. F. Guo, S. Q. Duan, Y. Xie, W. D. Chu, and W. Zhang, “Tailoring the photon emission patterns in nanostructures,” New J. Phys.13(5), 053005 (2011). [CrossRef]
  25. L. M. Narducci, M. O. Scully, G.-L. Oppo, P. Ru, and J. R. Tredicce, “Spontaneous emission and absorption properties of a driven three-level system,” Phys. Rev. A42(3), 1630–1649 (1990). [CrossRef] [PubMed]
  26. R. A. Ganeev, H. Singhal, P. A. Naik, J. A. Chakera, H. S. Vora, R. A. Khan, and P. D. Gupta, “Systematic studies of two-color pump-induced high-order harmonic generation in plasma plumes,” Phys. Rev. A82(5), 053831 (2010). [CrossRef]
  27. R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using a two-color pump in plasma plumes,” Phys. Rev. A80(3), 033845 (2009). [CrossRef]
  28. O. V. Kibis, G. Ya. Slepyan, S. A. Maksimenko, and A. Hoffmann, “Matter Coupling to Strong Electromagnetic Fields in Two-Level Quantum Systems with Broken Inversion Symmetry,” Phys. Rev. Lett.102(2), 023601 (2009). [CrossRef] [PubMed]
  29. I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett.94(24), 243901 (2005). [CrossRef]
  30. I. J. Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Namb, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett.92(2), 021125 (2008). [CrossRef]
  31. N. Ishii, A. Kosuge, T. Hayashi, T. Kanai, J. Itatani, S. Adachi, and S. Watanabe, “Quantum path selection in high-harmonic generation by a phase-locked two-color field,” Opt. express16(25), 20876–20883 (2008). [CrossRef] [PubMed]
  32. N. Moiseyev and M. Lein, “Non-Hermitian Quantum mechanics for high-order harmonic generation spectra,” J. Phys. Chem. A107(37), 7181–7188 (2003). [CrossRef]
  33. K. B. Nordstrom, K. Johnsen, S. J. Allen, A.-P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic dynamical Franz-Keldysh Effect,” Phys. Rev. Lett.81(2), 457–460 (1998). [CrossRef]
  34. L. Plaja and L. Roso, “High-order harmonic generation in a two-level atom: effect of the multiphoton resonances tuned by the light shift,” J. Mod. Opt.40(5), 793–807 (1993). [CrossRef]
  35. A. D. Piazza and E. Fiordilino, “Why hyper-Raman lines are absent in high-order harmonic generation,” Phys. Rev. A64(1), 013802 (2001). [CrossRef]
  36. Z. Y. Zhou and J. M. Yuan, “Fine structures of the harmonic and hyper-Raman spectrum of the hydrogen atom in an intense high-frequency laser pulse,” Phys. Rev. A77(6), 063411 (2008). [CrossRef]
  37. Y. Dakhnovskii and H. Metiu, “Conditions leading to intense low-frequency generation and strong localization in two-level systems,” Phys. Rev. A48(3), 2342–2345 (1993). [CrossRef] [PubMed]
  38. C. Liu, S. Gong, R. Li, and Z. Xu, “Coherent control in the generation of harmonics and hyper-Raman lines from a strongly driven two-level atom,” Phys. Rev. A69(2), 023406 (2004). [CrossRef]
  39. F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A52(1), 525–540 (1995). [CrossRef] [PubMed]
  40. M. Frasca, “Theory of dressed states in quantum optics,” Phys. Rev. A60(1), 573–581 (1999). [CrossRef]
  41. A. D. Piazza, E. Fiordilino, and M. H. Mittleman, “Analytical study of the spectrum emitted by a two-level atom driven by a strong laser pulse,” Phys. Rev. A64(1), 013414 (2001). [CrossRef]
  42. M. L. Pons, R. Taieb, and A. Maquet, “Importance of population transfers in high-order harmonic-generation spectra,” Phys. Rev. A54(4), 3634–3641 (1996). [CrossRef] [PubMed]
  43. H. Wang and X.G. Zhao, “Emission properties of electrons in two-level systems driven by DC - AC fields,” J. Phys.: Condens.Matter8(18), L285–L289 (1996). [CrossRef]
  44. P. Huang, X.-T. Xie, X. Lu, J. Li, and X. Yang, “Carrier-envelope-phase-dependent effects of high-order harmonic generation in a strongly driven two-level atom,” Phys. Rev. A79(4), 043806 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited