Abstract

No broadband amplifying medium has been demonstrated yet for terahertz radiation. We present simulations showing that laser-aligned molecules can amplify broadband terahertz radiation, allowing high-energy amplification of few-cycle pulses at terahertz frequencies.

© 2008 Optical Society of America

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References

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  1. Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
    [CrossRef] [PubMed]
  2. C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955).
  3. H. Harde and D. Grischkowsky, "Coherent transients excited by subpicosecond pulses of terahertz radiation," J. Opt. Soc. Am. B 8, 1642-1651 (1991).
    [CrossRef]
  4. Y. -H. Chen, S. Varma, A. York, and H. M. Milchberg, "Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O," Opt. Express 15, 11341-11357 (2007).
    [CrossRef] [PubMed]
  5. S. Ramakrishna and T. Seideman, "Dissipative dynamics of laser induced nonadiabatic molecular alignment," J. Chem. Phys. 124034101 (2006).
    [CrossRef] [PubMed]
  6. J. O. Hirschfelder and C. F. Curtiss, "Molecular Theory of Gases and Liquids" (John Wiley & Sons, Inc., New York, 1954).
  7. C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13813-829 (1976).
    [CrossRef]
  8. D. V. Kartashov, A. V. Kisrsanov, A. M. Kiselev, A. N. Stepanov, N. N. Bochkarev, Yu. N. Ponomarev, and B. A. Tikhomirov, "Nonlinear absorption of intense femtosecond laser radiation in air," Opt. Express 147552-7558 (2006).
    [CrossRef] [PubMed]
  9. A. G. Smith, W. Gordy, J. W. Simmons, and W. V. Smith "Microwave Spectroscopy in the Region of Three to Five Millimeters," Phys. Rev. 75260-263 (1949).
    [CrossRef]
  10. V. Kumarappan, C. Z. Bisgaard, S. S. Viftrup, L. Holmegaard, and H. Stapelfeldt, "Role of rotational temperature in adiabatic molecular alignment," J. Chem. Phys 125, 194309-1 -194309-7 (2006).
    [CrossRef] [PubMed]
  11. For example, the Coherent SIFIR-50
  12. A. T. Rosenberger, H. K. Chung, and T. A. De Temple "Sub-T2 Optical Pulse Generation: Application to Optically Pumped Far-Infrared Lasers," IEE J. Quantum Electron. QE-20523-532 (1984).
    [CrossRef]

2007 (2)

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

Y. -H. Chen, S. Varma, A. York, and H. M. Milchberg, "Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O," Opt. Express 15, 11341-11357 (2007).
[CrossRef] [PubMed]

2006 (3)

S. Ramakrishna and T. Seideman, "Dissipative dynamics of laser induced nonadiabatic molecular alignment," J. Chem. Phys. 124034101 (2006).
[CrossRef] [PubMed]

V. Kumarappan, C. Z. Bisgaard, S. S. Viftrup, L. Holmegaard, and H. Stapelfeldt, "Role of rotational temperature in adiabatic molecular alignment," J. Chem. Phys 125, 194309-1 -194309-7 (2006).
[CrossRef] [PubMed]

D. V. Kartashov, A. V. Kisrsanov, A. M. Kiselev, A. N. Stepanov, N. N. Bochkarev, Yu. N. Ponomarev, and B. A. Tikhomirov, "Nonlinear absorption of intense femtosecond laser radiation in air," Opt. Express 147552-7558 (2006).
[CrossRef] [PubMed]

1991 (1)

1984 (1)

A. T. Rosenberger, H. K. Chung, and T. A. De Temple "Sub-T2 Optical Pulse Generation: Application to Optically Pumped Far-Infrared Lasers," IEE J. Quantum Electron. QE-20523-532 (1984).
[CrossRef]

1976 (1)

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13813-829 (1976).
[CrossRef]

1949 (1)

A. G. Smith, W. Gordy, J. W. Simmons, and W. V. Smith "Microwave Spectroscopy in the Region of Three to Five Millimeters," Phys. Rev. 75260-263 (1949).
[CrossRef]

Arena, D. A.

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

Bisgaard, C. Z.

V. Kumarappan, C. Z. Bisgaard, S. S. Viftrup, L. Holmegaard, and H. Stapelfeldt, "Role of rotational temperature in adiabatic molecular alignment," J. Chem. Phys 125, 194309-1 -194309-7 (2006).
[CrossRef] [PubMed]

Bochkarev, N. N.

Carr, G. L.

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

Chen, Y. -H.

Chiao, R. Y.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13813-829 (1976).
[CrossRef]

Chung, H. K.

A. T. Rosenberger, H. K. Chung, and T. A. De Temple "Sub-T2 Optical Pulse Generation: Application to Optically Pumped Far-Infrared Lasers," IEE J. Quantum Electron. QE-20523-532 (1984).
[CrossRef]

De Temple, T. A.

A. T. Rosenberger, H. K. Chung, and T. A. De Temple "Sub-T2 Optical Pulse Generation: Application to Optically Pumped Far-Infrared Lasers," IEE J. Quantum Electron. QE-20523-532 (1984).
[CrossRef]

Gordy, W.

A. G. Smith, W. Gordy, J. W. Simmons, and W. V. Smith "Microwave Spectroscopy in the Region of Three to Five Millimeters," Phys. Rev. 75260-263 (1949).
[CrossRef]

Grischkowsky, D.

Gustafson, T. K.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13813-829 (1976).
[CrossRef]

Harde, H.

Heritage, J. P.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13813-829 (1976).
[CrossRef]

Holmegaard, L.

V. Kumarappan, C. Z. Bisgaard, S. S. Viftrup, L. Holmegaard, and H. Stapelfeldt, "Role of rotational temperature in adiabatic molecular alignment," J. Chem. Phys 125, 194309-1 -194309-7 (2006).
[CrossRef] [PubMed]

Kao, C.-C.

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

Kartashov, D. V.

Kiselev, A. M.

Kisrsanov, A. V.

Kumarappan, V.

V. Kumarappan, C. Z. Bisgaard, S. S. Viftrup, L. Holmegaard, and H. Stapelfeldt, "Role of rotational temperature in adiabatic molecular alignment," J. Chem. Phys 125, 194309-1 -194309-7 (2006).
[CrossRef] [PubMed]

Lin, C. H.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13813-829 (1976).
[CrossRef]

McTague, J. P.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13813-829 (1976).
[CrossRef]

Milchberg, H. M.

Murphy, J. B.

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

Ponomarev, Yu. N.

Ramakrishna, S.

S. Ramakrishna and T. Seideman, "Dissipative dynamics of laser induced nonadiabatic molecular alignment," J. Chem. Phys. 124034101 (2006).
[CrossRef] [PubMed]

Rosenberger, A. T.

A. T. Rosenberger, H. K. Chung, and T. A. De Temple "Sub-T2 Optical Pulse Generation: Application to Optically Pumped Far-Infrared Lasers," IEE J. Quantum Electron. QE-20523-532 (1984).
[CrossRef]

Seideman, T.

S. Ramakrishna and T. Seideman, "Dissipative dynamics of laser induced nonadiabatic molecular alignment," J. Chem. Phys. 124034101 (2006).
[CrossRef] [PubMed]

Shen, Y.

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

Simmons, J. W.

A. G. Smith, W. Gordy, J. W. Simmons, and W. V. Smith "Microwave Spectroscopy in the Region of Three to Five Millimeters," Phys. Rev. 75260-263 (1949).
[CrossRef]

Smith, A. G.

A. G. Smith, W. Gordy, J. W. Simmons, and W. V. Smith "Microwave Spectroscopy in the Region of Three to Five Millimeters," Phys. Rev. 75260-263 (1949).
[CrossRef]

Smith, W. V.

A. G. Smith, W. Gordy, J. W. Simmons, and W. V. Smith "Microwave Spectroscopy in the Region of Three to Five Millimeters," Phys. Rev. 75260-263 (1949).
[CrossRef]

Stapelfeldt, H.

V. Kumarappan, C. Z. Bisgaard, S. S. Viftrup, L. Holmegaard, and H. Stapelfeldt, "Role of rotational temperature in adiabatic molecular alignment," J. Chem. Phys 125, 194309-1 -194309-7 (2006).
[CrossRef] [PubMed]

Stepanov, A. N.

Tikhomirov, B. A.

Tsang, T. Y.

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

Varma, S.

Viftrup, S. S.

V. Kumarappan, C. Z. Bisgaard, S. S. Viftrup, L. Holmegaard, and H. Stapelfeldt, "Role of rotational temperature in adiabatic molecular alignment," J. Chem. Phys 125, 194309-1 -194309-7 (2006).
[CrossRef] [PubMed]

Wang, X. J.

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

Watanabe, T.

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

York, A.

IEE J. Quantum Electron. (1)

A. T. Rosenberger, H. K. Chung, and T. A. De Temple "Sub-T2 Optical Pulse Generation: Application to Optically Pumped Far-Infrared Lasers," IEE J. Quantum Electron. QE-20523-532 (1984).
[CrossRef]

J. Chem. Phys (1)

V. Kumarappan, C. Z. Bisgaard, S. S. Viftrup, L. Holmegaard, and H. Stapelfeldt, "Role of rotational temperature in adiabatic molecular alignment," J. Chem. Phys 125, 194309-1 -194309-7 (2006).
[CrossRef] [PubMed]

J. Chem. Phys. (1)

S. Ramakrishna and T. Seideman, "Dissipative dynamics of laser induced nonadiabatic molecular alignment," J. Chem. Phys. 124034101 (2006).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Phys. Rev. (1)

A. G. Smith, W. Gordy, J. W. Simmons, and W. V. Smith "Microwave Spectroscopy in the Region of Three to Five Millimeters," Phys. Rev. 75260-263 (1949).
[CrossRef]

Phys. Rev. A (1)

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13813-829 (1976).
[CrossRef]

Phys. Rev. Lett. (1)

Y. Shen, T. Watanabe, D. A. Arena, C.-C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr "Nonlinear Cross-Phase Modulation with Intense Single-Cycle Terahertz Pulses," Phys. Rev. Lett. 99, 043901 (2007).
[CrossRef] [PubMed]

Other (3)

C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955).

J. O. Hirschfelder and C. F. Curtiss, "Molecular Theory of Gases and Liquids" (John Wiley & Sons, Inc., New York, 1954).

For example, the Coherent SIFIR-50

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Figures (7)

Fig. 1.
Fig. 1.

Proposed broadband terahertz amplification

Fig. 2.
Fig. 2.

Rotational state populations ρm jj vs. j of HCN gas for selected m-values (a) before illumination (thermal population), (b) after illumination by a 15TW/cm2, 100fs, 800nm optical alignment pulse, and (c) after a train of four such pulses separated by 11.49ps (the revival time of HCN). Below are intensity plots of ρm jj vs. j and m for (d) thermal, (e) one-pulse, and (f) four-pulse illumination.

Fig. 3.
Fig. 3.

Energy absorbed/emitted by 200fs-pulse THz-driven jj±1 transitions vs. j and m of the upper state for (a) an initially thermal HCN gas and (b) the optically-excited rotational populations shown in Fig. 2(c, f). Summed over m, this gives energy absorbed/emitted near each resonant frequency 2jf 0 for c thermal and d excited gas. The ~200fs terahertz pulse driving these transitions (e) follows at Tr /2 after the last optical excitation pulse.

Fig. 4.
Fig. 4.

Energy absorbed/emitted by 800fs-pulse terahertz-driven jj±1 transitions vs. j and m of the upper state for (a) an initially thermal HCN gas and (b) the optically-excited rotational populations shown in Fig. 2(c, f). Summed over m, this gives energy absorbed/emitted near each resonant frequency 2jf 0 for c thermal and d excited gas. The ~800fs terahertz pulse driving these transitions the 19 lowest absorptionthe 19 lowest absorption(e) follows at Tr /2 after the last optical excitation pulse.

Fig. 5.
Fig. 5.

A 1TW/cm2 optical pulse weakly aligns HCN and strongly modulates (a) terahertz energy absorbed/emitted per molecule, per m=0,jj-1 transition depending on the optical-terahertz relative delay ΔT. (b) Averaging over delay shows the ‘incoherent’ absorption that a terahertz pulse would experience if it was not collinear with the optical pump pulses. (c) Summing over j gives total absorption vs. ΔT.

Fig. 6.
Fig. 6.

Population ρm j,j for different dissipation rates γ and number of optical pump pulses for (a) m=0 and (b) m=1.

Fig. 7.
Fig. 7.

Population ρm j,j for static gas and gas jet initial temperatures T for (a) m=0 and (b) m=1, neglecting collisions (1/γ≫1ns).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

d d t ρ j , k m ( t ) = i ω j , k ρ j , k m ( t ) ( d ρ j , k m d t ) diss +
i Δ α 4 h ¯ E optical 2 ( t ) q [ O j , q m ρ q , k m ( t ) O q , k m ρ j , q m ( t ) ] +
i μ h ¯ E terahertz ( t ) q [ T j , q m ρ q , k m ( t ) T q , k m ρ j , q m ( t ) ]
ρ j , j m ρ 0,0 0 = exp ( h ¯ ω j k B T )

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