Abstract

A new scheme for quasi-phasematching high harmonic generation (HHG) in gases is proposed. In this, the rapid variation of the axial intensity resulting from excitation of more than one mode of a waveguide is used to achieve quasi phasematching. Numerical modeling demonstrates enhancement of the harmonic signal over that achieved for a single coherence length by factors >104.

© 2007 Optical Society of America

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  1. A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in High-Order Harmonic Generation,” Phys. Rev. Lett. 68, 166–169 (1992). P. B. Corkum “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993).
    [Crossref] [PubMed]
  2. J. Seres, et al., “Generation of coherent keV x-rays with intensefemtosecond laser pulses” NJP 8, 251 (2006).
    [Crossref]
  3. X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751 (1989).
    [Crossref] [PubMed]
  4. C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of High-Order Harmonics in Hollow Waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
    [Crossref]
  5. A. Paul, et al., “Quasi-phase-matched generation of coherent extreme ultraviolet light,” Nature 42, 51–54, (2003).
    [Crossref]
  6. I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Dispersion-controlled hollow core fiber for Phase Matched Harmonic Generation” Opt. Express 3, 360 (1998).
    [Crossref] [PubMed]
  7. S. Voronov “Control of Laser High-Harmonic Generation with Counterpropagating Light,” Phys. Rev. Lett. 87, 133902 (2001).
    [Crossref] [PubMed]
  8. E. A. Gibson, et al. “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95–98 (2003).
    [Crossref] [PubMed]
  9. R. L. Abrams, “Coupling losses in hollow waveguide fiber resonators,”IEEE J. Quantum Electron. 8, 838 (1972).
    [Crossref]
  10. C. Courtois, A. Couairon, B. Cros, J. R. Marques, and G. Matthieussent, “Propagation of in tense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,” Phys. Plasmas 8, 3445 (2001).
    [Crossref]
  11. E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).
  12. B. Cros, et al. “Eigenmodes for capillary tubes with dielectric walls and ultraintense laser pulse guiding,” Phys. Rev. E 65, 026405 (2002).
    [Crossref]
  13. M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).
  14. M. Zepf and B. Dromey, Queens University Belfast, are preparing a manuscript to be called “Bright quasi-phase matched soft x-ray harmonic radiation from Argon ions,” (Feb 2007) - pre-submission access http://arxiv.org/abs/physics/0702117
  15. T. Pfeifer, et al., “Spatial control of high-harmonic generation inhollow fibers,” Opt. Lett. 30, 1497 (2005).
    [Crossref] [PubMed]
  16. D. Walter, et al, “Adaptive spatial control of fiber modes and their excitation for high-harmonic generation” Opt. Exp. 14, 3433 (2006).
    [Crossref]

2006 (2)

J. Seres, et al., “Generation of coherent keV x-rays with intensefemtosecond laser pulses” NJP 8, 251 (2006).
[Crossref]

D. Walter, et al, “Adaptive spatial control of fiber modes and their excitation for high-harmonic generation” Opt. Exp. 14, 3433 (2006).
[Crossref]

2005 (1)

2003 (2)

A. Paul, et al., “Quasi-phase-matched generation of coherent extreme ultraviolet light,” Nature 42, 51–54, (2003).
[Crossref]

E. A. Gibson, et al. “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

2002 (1)

B. Cros, et al. “Eigenmodes for capillary tubes with dielectric walls and ultraintense laser pulse guiding,” Phys. Rev. E 65, 026405 (2002).
[Crossref]

2001 (2)

S. Voronov “Control of Laser High-Harmonic Generation with Counterpropagating Light,” Phys. Rev. Lett. 87, 133902 (2001).
[Crossref] [PubMed]

C. Courtois, A. Couairon, B. Cros, J. R. Marques, and G. Matthieussent, “Propagation of in tense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,” Phys. Plasmas 8, 3445 (2001).
[Crossref]

1999 (1)

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of High-Order Harmonics in Hollow Waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

1998 (1)

1992 (1)

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in High-Order Harmonic Generation,” Phys. Rev. Lett. 68, 166–169 (1992). P. B. Corkum “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993).
[Crossref] [PubMed]

1989 (1)

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751 (1989).
[Crossref] [PubMed]

1986 (1)

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

1972 (1)

R. L. Abrams, “Coupling losses in hollow waveguide fiber resonators,”IEEE J. Quantum Electron. 8, 838 (1972).
[Crossref]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).

Abrams, R. L.

R. L. Abrams, “Coupling losses in hollow waveguide fiber resonators,”IEEE J. Quantum Electron. 8, 838 (1972).
[Crossref]

Ammosov, M.

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Backus, S.

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of High-Order Harmonics in Hollow Waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

Balcou, P.

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in High-Order Harmonic Generation,” Phys. Rev. Lett. 68, 166–169 (1992). P. B. Corkum “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993).
[Crossref] [PubMed]

Christov, I. P.

Couairon, A.

C. Courtois, A. Couairon, B. Cros, J. R. Marques, and G. Matthieussent, “Propagation of in tense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,” Phys. Plasmas 8, 3445 (2001).
[Crossref]

Courtois, C.

C. Courtois, A. Couairon, B. Cros, J. R. Marques, and G. Matthieussent, “Propagation of in tense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,” Phys. Plasmas 8, 3445 (2001).
[Crossref]

Cros, B.

B. Cros, et al. “Eigenmodes for capillary tubes with dielectric walls and ultraintense laser pulse guiding,” Phys. Rev. E 65, 026405 (2002).
[Crossref]

C. Courtois, A. Couairon, B. Cros, J. R. Marques, and G. Matthieussent, “Propagation of in tense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,” Phys. Plasmas 8, 3445 (2001).
[Crossref]

Delone, N.

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Dromey, B.

M. Zepf and B. Dromey, Queens University Belfast, are preparing a manuscript to be called “Bright quasi-phase matched soft x-ray harmonic radiation from Argon ions,” (Feb 2007) - pre-submission access http://arxiv.org/abs/physics/0702117

Durfee, C.

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of High-Order Harmonics in Hollow Waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

Ferray, M.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751 (1989).
[Crossref] [PubMed]

Gibson, E. A.

E. A. Gibson, et al. “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Herne, C.

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of High-Order Harmonics in Hollow Waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

Kapteyn, H. C.

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of High-Order Harmonics in Hollow Waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Dispersion-controlled hollow core fiber for Phase Matched Harmonic Generation” Opt. Express 3, 360 (1998).
[Crossref] [PubMed]

Krainov, V.

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

L’Huillier, A.

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in High-Order Harmonic Generation,” Phys. Rev. Lett. 68, 166–169 (1992). P. B. Corkum “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993).
[Crossref] [PubMed]

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751 (1989).
[Crossref] [PubMed]

Li, X. F.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751 (1989).
[Crossref] [PubMed]

Lompre, L.

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in High-Order Harmonic Generation,” Phys. Rev. Lett. 68, 166–169 (1992). P. B. Corkum “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993).
[Crossref] [PubMed]

Lompré, L. A.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751 (1989).
[Crossref] [PubMed]

Mainfray, G.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751 (1989).
[Crossref] [PubMed]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).

Marques, J. R.

C. Courtois, A. Couairon, B. Cros, J. R. Marques, and G. Matthieussent, “Propagation of in tense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,” Phys. Plasmas 8, 3445 (2001).
[Crossref]

Matthieussent, G.

C. Courtois, A. Couairon, B. Cros, J. R. Marques, and G. Matthieussent, “Propagation of in tense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,” Phys. Plasmas 8, 3445 (2001).
[Crossref]

Murnane, M. M.

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of High-Order Harmonics in Hollow Waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Dispersion-controlled hollow core fiber for Phase Matched Harmonic Generation” Opt. Express 3, 360 (1998).
[Crossref] [PubMed]

Paul, A.

A. Paul, et al., “Quasi-phase-matched generation of coherent extreme ultraviolet light,” Nature 42, 51–54, (2003).
[Crossref]

Pfeifer, T.

Rundquist, A.

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of High-Order Harmonics in Hollow Waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).

Seres, J.

J. Seres, et al., “Generation of coherent keV x-rays with intensefemtosecond laser pulses” NJP 8, 251 (2006).
[Crossref]

Voronov, S.

S. Voronov “Control of Laser High-Harmonic Generation with Counterpropagating Light,” Phys. Rev. Lett. 87, 133902 (2001).
[Crossref] [PubMed]

Walter, D.

D. Walter, et al, “Adaptive spatial control of fiber modes and their excitation for high-harmonic generation” Opt. Exp. 14, 3433 (2006).
[Crossref]

Zepf, M.

M. Zepf and B. Dromey, Queens University Belfast, are preparing a manuscript to be called “Bright quasi-phase matched soft x-ray harmonic radiation from Argon ions,” (Feb 2007) - pre-submission access http://arxiv.org/abs/physics/0702117

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).

IEEE J. Quantum Electron. (1)

R. L. Abrams, “Coupling losses in hollow waveguide fiber resonators,”IEEE J. Quantum Electron. 8, 838 (1972).
[Crossref]

Nature (1)

A. Paul, et al., “Quasi-phase-matched generation of coherent extreme ultraviolet light,” Nature 42, 51–54, (2003).
[Crossref]

NJP (1)

J. Seres, et al., “Generation of coherent keV x-rays with intensefemtosecond laser pulses” NJP 8, 251 (2006).
[Crossref]

Opt. Exp. (1)

D. Walter, et al, “Adaptive spatial control of fiber modes and their excitation for high-harmonic generation” Opt. Exp. 14, 3433 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Plasmas (1)

C. Courtois, A. Couairon, B. Cros, J. R. Marques, and G. Matthieussent, “Propagation of in tense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,” Phys. Plasmas 8, 3445 (2001).
[Crossref]

Phys. Rev. A (1)

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751 (1989).
[Crossref] [PubMed]

Phys. Rev. E (1)

B. Cros, et al. “Eigenmodes for capillary tubes with dielectric walls and ultraintense laser pulse guiding,” Phys. Rev. E 65, 026405 (2002).
[Crossref]

Phys. Rev. Lett. (3)

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in High-Order Harmonic Generation,” Phys. Rev. Lett. 68, 166–169 (1992). P. B. Corkum “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993).
[Crossref] [PubMed]

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of High-Order Harmonics in Hollow Waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[Crossref]

S. Voronov “Control of Laser High-Harmonic Generation with Counterpropagating Light,” Phys. Rev. Lett. 87, 133902 (2001).
[Crossref] [PubMed]

Science (1)

E. A. Gibson, et al. “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Other (1)

M. Zepf and B. Dromey, Queens University Belfast, are preparing a manuscript to be called “Bright quasi-phase matched soft x-ray harmonic radiation from Argon ions,” (Feb 2007) - pre-submission access http://arxiv.org/abs/physics/0702117

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Figures (3)

Fig. 1.
Fig. 1.

Idealised multimode beating assuming two equal intensity modes (j=1 and j=20) excited in a capillary with a~90μm. Figure 1(a) shows the axial intensity as a function of z, I(z), normalised at z=0, over the first 0.2 cm of the capillary while Fig. 1(b) shows corresponding harmonic source term (assumed proportional to the ADK rate for tunnel ionisation [13]).

Fig. 2.
Fig. 2.

Normalised Intensity profiles for coupling to an evacuated capillary with a=90μm. The coupling coefficient for the Gaussian (solid line) and the central maximum of the Airy profile (dashed line) are χ=0.64 and χ=0.2 respectively.

Fig. 3.
Fig. 3.

Multimode quasi phase matching. Calculated axial intensity as a function of distance z into a capillary of radius 90μm for beams with the Gaussian (a) and Airy (b) incident transverse profiles shown in Fig. 2. The corresponding calculated harmonic source terms (normalised at peak intensity) are shown in Figs. 3(c) and 3(d). The resulting harmonic growth for q=201 (solid lines), normalised to the signal expected for one coherence length (dot-dashed line), is shown in Figs. 3(e) and 3(f). The dotted line in both 3(e) and 3(f) corresponds to the expected harmonic growth for the two mode axial intensity profile given in Fig. 1(a), while the dashed line is the signal expected for perfect phase matching. Harmonic growth is calculated using a 1-D code under optimal matching conditions for the normalised harmonic source terms given in Figs. 3(c) and 3(d). Optimal matching conditions were achieved in each case by varying intensity at z=0 and pressure (approx. 20mbar Ar) slightly to adjust Z * such that 2Lc LB over extended interaction regions. It should be noted that the rapid growth of HHG over the first few mm of the capillary for the intensity profiles in Figs. 3(c) and 3(d) in comparison to that for the idealised MMQPM scheme from Fig. 2 is due to the constructive interference of multiple modes leading to increased on-axis intensity and hence greater HHG signal.

Equations (8)

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L c = π Δ k , Δ k = k q qk 0
Δ k Δ k e + Δ k g
L = 2 m L c
Δ K = mK Δ k 0 where K = 2 π L
E L ( r ) = j = 1 C j E 1 , j ( r )
A ( r ) = j = 1 J 0 ( r a . U 0 , j ) C j 2
χ = w 0 a = 0.64
I ( z ) = j = 1 C j E 1, j e i ( Δ k j z ) L z , j 2

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