Abstract

Accurate three-dimensional modelling of nonlinear pulse propagation within a gas-filled capillary is essential for understanding and improving the XUV yield in high harmonic generation. We introduce both a new model based on a multimode generalized nonlinear Schrödinger equation and a novel spatio-spectral measurement technique to which the model can be compared. The theory shows excellent agreement with the measured output spectrum and the spatio-spectral measurement reveals that the model correctly predicts higher order mode contributions to spectral broadening of the pulse. Fluorescence from the excited argon is used to verify the predicted ion distribution along the capillary.

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  1. A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70(6), 774–777 (1993).
    [CrossRef] [PubMed]
  2. I. Christov, H. Kapteyn, and M. Murnane, “Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,” Opt. Express 7(11), 362–367 (2000).
    [CrossRef] [PubMed]
  3. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, ““High-Harmonic Generation of Attosecond Pulses in the “single-cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
    [CrossRef]
  4. I. P. Christov, “Control of high harmonic and attosecond pulse generation in aperiodic modulated waveguides,” J. Opt. Soc. Am. B 18(12), 1877–1881 (2001).
    [CrossRef]
  5. C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, “Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: Simulations and experiments,” Phys. Plasmas 8(7), 3445–3456 (2001).
    [CrossRef]
  6. M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002).
    [CrossRef]
  7. R. K. Nubling and J. A. Harrington, “Launch conditions and mode coupling in hollow-glass waveguides,” Opt. Eng. 37(9), 2454–2458 (1998).
    [CrossRef]
  8. C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
    [CrossRef]
  9. F. Poletti and P. Horak, “Description of ultrashort pulse propagation in multimode optical fibers,” J. Opt. Soc. Am. B 25(10), 1645 (2008).
    [CrossRef]
  10. 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, 1783–1809 (1964).
  11. F. Poletti and P. Horak, “Dynamics of femtosecond supercontinuum generation in multimode fibers,” Opt. Express 17(8), 6134–6147 (2009).
    [CrossRef] [PubMed]
  12. V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Phys.Usp. 47(9), 855–885 (2004).
    [CrossRef]

2009

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

F. Poletti and P. Horak, “Dynamics of femtosecond supercontinuum generation in multimode fibers,” Opt. Express 17(8), 6134–6147 (2009).
[CrossRef] [PubMed]

2008

2004

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Phys.Usp. 47(9), 855–885 (2004).
[CrossRef]

2002

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002).
[CrossRef]

2001

I. P. Christov, “Control of high harmonic and attosecond pulse generation in aperiodic modulated waveguides,” J. Opt. Soc. Am. B 18(12), 1877–1881 (2001).
[CrossRef]

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, “Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: Simulations and experiments,” Phys. Plasmas 8(7), 3445–3456 (2001).
[CrossRef]

2000

1998

R. K. Nubling and J. A. Harrington, “Launch conditions and mode coupling in hollow-glass waveguides,” Opt. Eng. 37(9), 2454–2458 (1998).
[CrossRef]

1997

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, ““High-Harmonic Generation of Attosecond Pulses in the “single-cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

1993

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70(6), 774–777 (1993).
[CrossRef] [PubMed]

1964

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, 1783–1809 (1964).

Balcou, P.

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70(6), 774–777 (1993).
[CrossRef] [PubMed]

Brocklesby, W. S.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Butcher, T. J.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Chapman, R. T.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Christov, I.

Christov, I. P.

I. P. Christov, “Control of high harmonic and attosecond pulse generation in aperiodic modulated waveguides,” J. Opt. Soc. Am. B 18(12), 1877–1881 (2001).
[CrossRef]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, ““High-Harmonic Generation of Attosecond Pulses in the “single-cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

Couairon, A.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, “Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: Simulations and experiments,” Phys. Plasmas 8(7), 3445–3456 (2001).
[CrossRef]

Courtois, C.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, “Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: Simulations and experiments,” Phys. Plasmas 8(7), 3445–3456 (2001).
[CrossRef]

Cros, B.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, “Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: Simulations and experiments,” Phys. Plasmas 8(7), 3445–3456 (2001).
[CrossRef]

de Paula, A. M.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Frey, J. G.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Froud, C. A.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Grant-Jacob, J.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Harrington, J. A.

R. K. Nubling and J. A. Harrington, “Launch conditions and mode coupling in hollow-glass waveguides,” Opt. Eng. 37(9), 2454–2458 (1998).
[CrossRef]

Hatayama, M.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002).
[CrossRef]

Horak, P.

Kapteyn, H.

Kapteyn, H. C.

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, ““High-Harmonic Generation of Attosecond Pulses in the “single-cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

L’Huillier, A.

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70(6), 774–777 (1993).
[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, 1783–1809 (1964).

Marquès, J. R.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, “Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: Simulations and experiments,” Phys. Plasmas 8(7), 3445–3456 (2001).
[CrossRef]

Matthieussent, G.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, “Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: Simulations and experiments,” Phys. Plasmas 8(7), 3445–3456 (2001).
[CrossRef]

Midorikawa, K.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002).
[CrossRef]

Mills, B.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Murnane, M.

Murnane, M. M.

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, ““High-Harmonic Generation of Attosecond Pulses in the “single-cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

Nagasaka, K.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002).
[CrossRef]

Nubling, R. K.

R. K. Nubling and J. A. Harrington, “Launch conditions and mode coupling in hollow-glass waveguides,” Opt. Eng. 37(9), 2454–2458 (1998).
[CrossRef]

Nurhuda, M.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002).
[CrossRef]

Poletti, F.

Popov, V. S.

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Phys.Usp. 47(9), 855–885 (2004).
[CrossRef]

Praeger, M.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Rogers, E. T. F.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[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, 1783–1809 (1964).

Stebbings, S. L.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

Suda, A.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002).
[CrossRef]

Bell Syst. Tech. 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, 1783–1809 (1964).

J. Opt. A, Pure Appl. Opt.

C. A. Froud, R. T. Chapman, E. T. F. Rogers, M. Praeger, B. Mills, J. Grant-Jacob, T. J. Butcher, S. L. Stebbings, A. M. de Paula, J. G. Frey, and W. S. Brocklesby, “Spatially resolved Ar * and Ar + * imaging as a diagnostic for capillary-based high harmonic generation,” J. Opt. A, Pure Appl. Opt. 11(5), 054011 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Eng.

R. K. Nubling and J. A. Harrington, “Launch conditions and mode coupling in hollow-glass waveguides,” Opt. Eng. 37(9), 2454–2458 (1998).
[CrossRef]

Opt. Express

Phys. Plasmas

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, “Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: Simulations and experiments,” Phys. Plasmas 8(7), 3445–3456 (2001).
[CrossRef]

Phys. Rev. A

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002).
[CrossRef]

Phys. Rev. Lett.

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, ““High-Harmonic Generation of Attosecond Pulses in the “single-cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70(6), 774–777 (1993).
[CrossRef] [PubMed]

Phys.Usp.

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Phys.Usp. 47(9), 855–885 (2004).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic for measuring the spatio-spectral output and argon ion fluorescence from a capillary running in a HHG regime.

Fig. 2
Fig. 2

Predicted (a) and experimental (b) output spectra measured for three input powers, shown. The predicted data shows the total spectrum (solid), as well as those for the EH11 (dashed) and EH12 (dot dashed) modes. At each laser power, the summed spectral intensity of the modes is normalised to a peak level of 1, as is the experimental data.

Fig. 3
Fig. 3

Predicted (a) and experimental (b) spectral intensity plots in the lambda-r-plane. The solid and dashed white lines show the far-field profiles of the EH11 and EH12 modes respectively.

Fig. 4
Fig. 4

Comparison of the summed radial ionisation (a) and the imaged argon ion fluorescence (b) along the length of the capillary. The vertical dashed lines show the beat positions for linear mode beating between the EH11 and EH12 modes.

Equations (2)

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E ( r , z , t ) = 2 Z 0 2 π n 1 2 F n ( r ) A n ( z , t ) e i ( k 0 z ω 0 t ) + c . c .
A n z =i D n +i n 2 (z) k 0 k,l,m Q nklm A k A l A l * + i 2 k 0 rdr F n (r)S(r,z,t) n pl 2 (r,z,t) 1 2 rdr F n (r)S(r,z,t) ρ 0 (r,z,t)W(r,z,t)U | S(r,z,t) | 2 /(2π)

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