Abstract

In passive enhancement cavities the achievable power level is limited by mirror damage. Here, we address the design of robust optical resonators with large spot sizes on all mirrors, a measure that promises to mitigate this limitation by decreasing both the intensity and the thermal gradient on the mirror surfaces. We introduce a misalignment sensitivity metric to evaluate the robustness of resonator designs. We identify the standard bow-tie resonator operated close to the inner stability edge as the most robust large-mode cavity and implement this cavity with two spherical mirrors with 600 mm radius of curvature, two plane mirrors and a roundtrip length of 1.2 m, demonstrating a stable power enhancement of near-infrared laser light by a factor of 2000. Beam radii of 5.7 mm × 2.6 mm (sagittal × tangential 1/e2 intensity radius) on all mirrors are obtained. We propose a simple all-reflective ellipticity compensation scheme. This will enable a significant increase of the attainable power and intensity levels in enhancement cavities.

© 2013 OSA

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    [CrossRef]
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2013

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics7, 258–261 (2013).
[CrossRef]

2012

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature482, 68–71 (2012).
[CrossRef] [PubMed]

C. M. Heyl, J. Güdde, A. L’Huillier, and U. Höfer, “High-order harmonic generation with μJ laser pulses at high repetition rates,” J. Phys. B45, 074020 (2012).
[CrossRef]

W. P. Putnam, D. N. Schimpf, G. Abram, and F. X. Kärtner, “Bessel-Gauss beam enhancement cavities for high-intensity applications,” Opt. Express20, 24429–24443 (2012).
[CrossRef] [PubMed]

2011

J. Weitenberg, P. Rußbüldt, T. Eidam, and I. Pupeza, “Transverse mode tailoring in a quasi-imaging high-finesse femtosecond enhancement cavity,” Opt. Express19, 9551–9561 (2011).
[CrossRef] [PubMed]

D. R. Carlson, J. Lee, J. Mongelli, E. M. Wright, and R. J. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Opt. Lett.36, 2991–2993 (2011).
[CrossRef] [PubMed]

J. Lee, D. R. Carlson, and R. J. Jones, “Optimizing intracavity high harmonic generation for XUV fs frequency combs,” Opt. Express19, 23315–23326 (2011).
[CrossRef] [PubMed]

T. K. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Extreme nonlinear optics in a femtosecond enhancement cavity,” Phys. Rev. Lett.107, 183903 (2011).
[CrossRef] [PubMed]

I. B. Angelov, A. v. Conta, S. A. Trushin, Z. Major, S. Karsch, F. Krausz, and V. Pervak, “Investigation of the laser-induced damage of dispersive coatings,” Proc. SPIE8190, 81900B (2011).
[CrossRef]

F. Kawazoe, R. Schilling, and H. Lück, “Eigenmode changes in a misaligned triangular optical cavity,” J. Opt.13, 055504 (2011).
[CrossRef]

2010

2009

F. Zomer, Y. Fedala, N. Pavloff, V. Soskov, and A. Variola, “Polarization induced instabilities in external four-mirror Fabry-Perot cavities,” Appl. Opt.48, 6651–6661 (2009).
[CrossRef] [PubMed]

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

2008

M. Theuer, D. Molter, K. Maki, C. Otani, J. A. L’huillier, and R. Beigang, “Terahertz generation in an actively controlled femtosecond enhancement cavity,” Appl. Phys. Lett.93, 041119–3 (2008).
[CrossRef]

A. Ozawa, A. Vernaleken, W. Schneider, I. Gotlibovych, T. Udem, and T. W. Hänsch, “Non-collinear high harmonic generation: a promising outcoupling method for cavity-assisted XUV generation,” Opt. Express16, 6233–6239 (2008).
[CrossRef] [PubMed]

2006

2005

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B71(2005).
[CrossRef]

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature436, 234–237 (2005).
[CrossRef] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett.94, 193201 (2005).
[CrossRef] [PubMed]

S. Gigan, L. Lopez, N. Treps, A. Maître, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A72, 023804 (2005).
[CrossRef]

2000

1999

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett.82, 1668–1671 (1999).
[CrossRef]

1997

1992

N. Hodgson and H. Weber, “Misalignment sensitivity of stable resonators in multimode operation,” J. Mod. Opt.39, 1873–1882 (1992).
[CrossRef]

1988

S. d. Silvestri, P. Laporta, and V. Magni, “Rod thermal lensing effects in solid-state laser ring resonators,” Opt. Commun.65, 373–376 (1988).
[CrossRef]

1987

1985

1984

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983).
[CrossRef]

1980

1972

H. Kogelnik, E. Ippen, A. Dienes, and C. Shank, “Astigmatically compensated cavities for CW dye lasers,” IEEE J. Quant. Electron.8, 373–379 (1972).
[CrossRef]

1969

1966

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quant. Electron.2, 109–124 (1966).
[CrossRef]

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE54, 1312–1329 (1966).
[CrossRef]

1961

A. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J40, 453–488 (1961).

Abram, G.

Agostini, P.

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett.82, 1668–1671 (1999).
[CrossRef]

Alahmed, Z. A.

Allison, T. K.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature482, 68–71 (2012).
[CrossRef] [PubMed]

T. K. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Extreme nonlinear optics in a femtosecond enhancement cavity,” Phys. Rev. Lett.107, 183903 (2011).
[CrossRef] [PubMed]

Angelov, I. B.

I. B. Angelov, A. v. Conta, S. A. Trushin, Z. Major, S. Karsch, F. Krausz, and V. Pervak, “Investigation of the laser-induced damage of dispersive coatings,” Proc. SPIE8190, 81900B (2011).
[CrossRef]

Apolonski, A.

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35, 2052–2054 (2010).
[CrossRef] [PubMed]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Araki, S.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Arnaud, J. A.

Ashkin, A.

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quant. Electron.2, 109–124 (1966).
[CrossRef]

Azzeer, A. M.

Beigang, R.

M. Theuer, D. Molter, K. Maki, C. Otani, J. A. L’huillier, and R. Beigang, “Terahertz generation in an actively controlled femtosecond enhancement cavity,” Appl. Phys. Lett.93, 041119–3 (2008).
[CrossRef]

Bernhardt, B.

Boyd, G.

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quant. Electron.2, 109–124 (1966).
[CrossRef]

Breger, P.

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett.82, 1668–1671 (1999).
[CrossRef]

Brocklesby, B.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics7, 258–261 (2013).
[CrossRef]

Burch, J. M.

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, 1975).

Byer, R. L.

Carlson, D. R.

Carstens, H.

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Cingöz, A.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature482, 68–71 (2012).
[CrossRef] [PubMed]

T. K. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Extreme nonlinear optics in a femtosecond enhancement cavity,” Phys. Rev. Lett.107, 183903 (2011).
[CrossRef] [PubMed]

Constant, E.

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett.82, 1668–1671 (1999).
[CrossRef]

Conta, A. v.

I. B. Angelov, A. v. Conta, S. A. Trushin, Z. Major, S. Karsch, F. Krausz, and V. Pervak, “Investigation of the laser-induced damage of dispersive coatings,” Proc. SPIE8190, 81900B (2011).
[CrossRef]

DeLoach, B. C.

Dienes, A.

H. Kogelnik, E. Ippen, A. Dienes, and C. Shank, “Astigmatically compensated cavities for CW dye lasers,” IEEE J. Quant. Electron.8, 373–379 (1972).
[CrossRef]

Dorrer, C.

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett.82, 1668–1671 (1999).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983).
[CrossRef]

Dziedzic, J.

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quant. Electron.2, 109–124 (1966).
[CrossRef]

Eidam, T.

Esser, D.

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Fabre, C.

S. Gigan, L. Lopez, N. Treps, A. Maître, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A72, 023804 (2005).
[CrossRef]

Fedala, Y.

Fermann, M. E.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature482, 68–71 (2012).
[CrossRef] [PubMed]

Fill, E.

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35, 2052–2054 (2010).
[CrossRef] [PubMed]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983).
[CrossRef]

Fox, A.

A. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J40, 453–488 (1961).

Fukuda, M.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Garzella, D.

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett.82, 1668–1671 (1999).
[CrossRef]

Gerrard, A.

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, 1975).

Gigan, S.

S. Gigan, L. Lopez, N. Treps, A. Maître, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A72, 023804 (2005).
[CrossRef]

Gohle, C.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature436, 234–237 (2005).
[CrossRef] [PubMed]

Gotlibovych, I.

Güdde, J.

C. M. Heyl, J. Güdde, A. L’Huillier, and U. Höfer, “High-order harmonic generation with μJ laser pulses at high repetition rates,” J. Phys. B45, 074020 (2012).
[CrossRef]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983).
[CrossRef]

Hänsch, T.

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Hänsch, T. W.

Hartl, I.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature482, 68–71 (2012).
[CrossRef] [PubMed]

Hauck, R.

Herrmann, M.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature436, 234–237 (2005).
[CrossRef] [PubMed]

Heupel, T.

Heyl, C. M.

C. M. Heyl, J. Güdde, A. L’Huillier, and U. Höfer, “High-order harmonic generation with μJ laser pulses at high repetition rates,” J. Phys. B45, 074020 (2012).
[CrossRef]

Higashi, Y.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Hodgson, N.

N. Hodgson and H. Weber, “Misalignment sensitivity of stable resonators in multimode operation,” J. Mod. Opt.39, 1873–1882 (1992).
[CrossRef]

Höfer, U.

C. M. Heyl, J. Güdde, A. L’Huillier, and U. Höfer, “High-order harmonic generation with μJ laser pulses at high repetition rates,” J. Phys. B45, 074020 (2012).
[CrossRef]

Holzberger, S.

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Holzwarth, R.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature436, 234–237 (2005).
[CrossRef] [PubMed]

Honda, Y.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983).
[CrossRef]

Ippen, E.

H. Kogelnik, E. Ippen, A. Dienes, and C. Shank, “Astigmatically compensated cavities for CW dye lasers,” IEEE J. Quant. Electron.8, 373–379 (1972).
[CrossRef]

Jones, R. J.

Joyce, W. B.

Kane, T. J.

Karsch, S.

I. B. Angelov, A. v. Conta, S. A. Trushin, Z. Major, S. Karsch, F. Krausz, and V. Pervak, “Investigation of the laser-induced damage of dispersive coatings,” Proc. SPIE8190, 81900B (2011).
[CrossRef]

Kärtner, F. X.

Kawazoe, F.

F. Kawazoe, R. Schilling, and H. Lück, “Eigenmode changes in a misaligned triangular optical cavity,” J. Opt.13, 055504 (2011).
[CrossRef]

Kogelnik, H.

H. Kogelnik, E. Ippen, A. Dienes, and C. Shank, “Astigmatically compensated cavities for CW dye lasers,” IEEE J. Quant. Electron.8, 373–379 (1972).
[CrossRef]

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE54, 1312–1329 (1966).
[CrossRef]

Kortz, H. P.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983).
[CrossRef]

Krausz, F.

I. B. Angelov, A. v. Conta, S. A. Trushin, Z. Major, S. Karsch, F. Krausz, and V. Pervak, “Investigation of the laser-induced damage of dispersive coatings,” Proc. SPIE8190, 81900B (2011).
[CrossRef]

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35, 2052–2054 (2010).
[CrossRef] [PubMed]

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature436, 234–237 (2005).
[CrossRef] [PubMed]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

L’Huillier, A.

C. M. Heyl, J. Güdde, A. L’Huillier, and U. Höfer, “High-order harmonic generation with μJ laser pulses at high repetition rates,” J. Phys. B45, 074020 (2012).
[CrossRef]

L’huillier, J. A.

M. Theuer, D. Molter, K. Maki, C. Otani, J. A. L’huillier, and R. Beigang, “Terahertz generation in an actively controlled femtosecond enhancement cavity,” Appl. Phys. Lett.93, 041119–3 (2008).
[CrossRef]

Laporta, P.

S. d. Silvestri, P. Laporta, and V. Magni, “Rod thermal lensing effects in solid-state laser ring resonators,” Opt. Commun.65, 373–376 (1988).
[CrossRef]

Le Blanc, C.

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett.82, 1668–1671 (1999).
[CrossRef]

Lee, J.

Li, T.

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE54, 1312–1329 (1966).
[CrossRef]

A. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J40, 453–488 (1961).

Limpert, J.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics7, 258–261 (2013).
[CrossRef]

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35, 2052–2054 (2010).
[CrossRef] [PubMed]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Liu, J.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B71(2005).
[CrossRef]

Lopez, L.

S. Gigan, L. Lopez, N. Treps, A. Maître, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A72, 023804 (2005).
[CrossRef]

Lück, H.

F. Kawazoe, R. Schilling, and H. Lück, “Eigenmode changes in a misaligned triangular optical cavity,” J. Opt.13, 055504 (2011).
[CrossRef]

Magni, V.

S. d. Silvestri, P. Laporta, and V. Magni, “Rod thermal lensing effects in solid-state laser ring resonators,” Opt. Commun.65, 373–376 (1988).
[CrossRef]

V. Magni, “Multielement stable resonators containing a variable lens,” J. Opt. Soc. Am. A4, 1962–1969 (1987).
[CrossRef]

Maître, A.

S. Gigan, L. Lopez, N. Treps, A. Maître, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A72, 023804 (2005).
[CrossRef]

Major, Z.

I. B. Angelov, A. v. Conta, S. A. Trushin, Z. Major, S. Karsch, F. Krausz, and V. Pervak, “Investigation of the laser-induced damage of dispersive coatings,” Proc. SPIE8190, 81900B (2011).
[CrossRef]

Maki, K.

M. Theuer, D. Molter, K. Maki, C. Otani, J. A. L’huillier, and R. Beigang, “Terahertz generation in an actively controlled femtosecond enhancement cavity,” Appl. Phys. Lett.93, 041119–3 (2008).
[CrossRef]

Mavalvala, N.

Mero, M.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B71(2005).
[CrossRef]

Mével, E.

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett.82, 1668–1671 (1999).
[CrossRef]

Moll, K. D.

K. D. Moll, R. J. Jones, and J. Ye, “Output coupling methods for cavity-based high-harmonic generation,” Opt. Express14, 8189–8197 (2006).
[CrossRef] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett.94, 193201 (2005).
[CrossRef] [PubMed]

Molter, D.

M. Theuer, D. Molter, K. Maki, C. Otani, J. A. L’huillier, and R. Beigang, “Terahertz generation in an actively controlled femtosecond enhancement cavity,” Appl. Phys. Lett.93, 041119–3 (2008).
[CrossRef]

Mongelli, J.

Mourou, G.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics7, 258–261 (2013).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983).
[CrossRef]

Omori, T.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Otani, C.

M. Theuer, D. Molter, K. Maki, C. Otani, J. A. L’huillier, and R. Beigang, “Terahertz generation in an actively controlled femtosecond enhancement cavity,” Appl. Phys. Lett.93, 041119–3 (2008).
[CrossRef]

Ozawa, A.

Pavloff, N.

Pervak, V.

I. B. Angelov, A. v. Conta, S. A. Trushin, Z. Major, S. Karsch, F. Krausz, and V. Pervak, “Investigation of the laser-induced damage of dispersive coatings,” Proc. SPIE8190, 81900B (2011).
[CrossRef]

Pupeza, I.

J. Weitenberg, P. Rußbüldt, T. Eidam, and I. Pupeza, “Transverse mode tailoring in a quasi-imaging high-finesse femtosecond enhancement cavity,” Opt. Express19, 9551–9561 (2011).
[CrossRef] [PubMed]

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35, 2052–2054 (2010).
[CrossRef] [PubMed]

I. Pupeza, Power Scaling of Enhancement Cavities for Nonlinear Optics (Springer, 2012).
[CrossRef]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Putnam, W. P.

Rauschenberger, J.

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35, 2052–2054 (2010).
[CrossRef] [PubMed]

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature436, 234–237 (2005).
[CrossRef] [PubMed]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Ristau, D.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B71(2005).
[CrossRef]

Rudolph, W.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B71(2005).
[CrossRef]

Ruehl, A.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature482, 68–71 (2012).
[CrossRef] [PubMed]

Rußbüldt, P.

J. Weitenberg, P. Rußbüldt, T. Eidam, and I. Pupeza, “Transverse mode tailoring in a quasi-imaging high-finesse femtosecond enhancement cavity,” Opt. Express19, 9551–9561 (2011).
[CrossRef] [PubMed]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Sakaue, K.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Salin, F.

E. Constant, D. Garzella, P. Breger, E. Mével, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett.82, 1668–1671 (1999).
[CrossRef]

Sasao, N.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Schilling, R.

F. Kawazoe, R. Schilling, and H. Lück, “Eigenmode changes in a misaligned triangular optical cavity,” J. Opt.13, 055504 (2011).
[CrossRef]

Schimpf, D. N.

Schneider, W.

Schuessler, H. A.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature436, 234–237 (2005).
[CrossRef] [PubMed]

Shank, C.

H. Kogelnik, E. Ippen, A. Dienes, and C. Shank, “Astigmatically compensated cavities for CW dye lasers,” IEEE J. Quant. Electron.8, 373–379 (1972).
[CrossRef]

Sigg, D.

Silvestri, S. d.

S. d. Silvestri, P. Laporta, and V. Magni, “Rod thermal lensing effects in solid-state laser ring resonators,” Opt. Commun.65, 373–376 (1988).
[CrossRef]

Soskov, V.

Starke, K.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B71(2005).
[CrossRef]

Tajima, T.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics7, 258–261 (2013).
[CrossRef]

Taniguchi, T.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Terunuma, N.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Theuer, M.

M. Theuer, D. Molter, K. Maki, C. Otani, J. A. L’huillier, and R. Beigang, “Terahertz generation in an actively controlled femtosecond enhancement cavity,” Appl. Phys. Lett.93, 041119–3 (2008).
[CrossRef]

Thorpe, M. J.

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett.94, 193201 (2005).
[CrossRef] [PubMed]

Treps, N.

S. Gigan, L. Lopez, N. Treps, A. Maître, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A72, 023804 (2005).
[CrossRef]

Trushin, S. A.

I. B. Angelov, A. v. Conta, S. A. Trushin, Z. Major, S. Karsch, F. Krausz, and V. Pervak, “Investigation of the laser-induced damage of dispersive coatings,” Proc. SPIE8190, 81900B (2011).
[CrossRef]

Tünnermann, A.

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35, 2052–2054 (2010).
[CrossRef] [PubMed]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Udem, T.

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35, 2052–2054 (2010).
[CrossRef] [PubMed]

A. Ozawa, A. Vernaleken, W. Schneider, I. Gotlibovych, T. Udem, and T. W. Hänsch, “Non-collinear high harmonic generation: a promising outcoupling method for cavity-assisted XUV generation,” Opt. Express16, 6233–6239 (2008).
[CrossRef] [PubMed]

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature436, 234–237 (2005).
[CrossRef] [PubMed]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Urakawa, J.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Variola, A.

Vernaleken, A.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983).
[CrossRef]

Washio, M.

K. Sakaue, M. Washio, S. Araki, M. Fukuda, Y. Higashi, Y. Honda, T. Omori, T. Taniguchi, N. Terunuma, J. Urakawa, and N. Sasao, “Observation of pulsed x-ray trains produced by laser-electron Compton scatterings,” Rev. Sci. Instrum.80, 123304–123304–7 (2009).
[CrossRef]

Weber, H.

N. Hodgson and H. Weber, “Misalignment sensitivity of stable resonators in multimode operation,” J. Mod. Opt.39, 1873–1882 (1992).
[CrossRef]

R. Hauck, H. P. Kortz, and H. Weber, “Misalignment sensitivity of optical resonators,” Appl. Opt.19, 598–601 (1980).
[CrossRef] [PubMed]

Weitenberg, J.

J. Weitenberg, P. Rußbüldt, T. Eidam, and I. Pupeza, “Transverse mode tailoring in a quasi-imaging high-finesse femtosecond enhancement cavity,” Opt. Express19, 9551–9561 (2011).
[CrossRef] [PubMed]

I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100-electronvolt radiation,” accepted for publication in Nat. Photonics (2013)

Weitz, M.

Wright, E. M.

Ye, J.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature482, 68–71 (2012).
[CrossRef] [PubMed]

T. K. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Extreme nonlinear optics in a femtosecond enhancement cavity,” Phys. Rev. Lett.107, 183903 (2011).
[CrossRef] [PubMed]

K. D. Moll, R. J. Jones, and J. Ye, “Output coupling methods for cavity-based high-harmonic generation,” Opt. Express14, 8189–8197 (2006).
[CrossRef] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett.94, 193201 (2005).
[CrossRef] [PubMed]

Yost, D. C.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature482, 68–71 (2012).
[CrossRef] [PubMed]

T. K. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Extreme nonlinear optics in a femtosecond enhancement cavity,” Phys. Rev. Lett.107, 183903 (2011).
[CrossRef] [PubMed]

Zomer, F.

Appl. Opt.

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983).
[CrossRef]

Appl. Phys. Lett.

M. Theuer, D. Molter, K. Maki, C. Otani, J. A. L’huillier, and R. Beigang, “Terahertz generation in an actively controlled femtosecond enhancement cavity,” Appl. Phys. Lett.93, 041119–3 (2008).
[CrossRef]

Bell Syst. Tech. J

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Figures (5)

Fig. 1
Fig. 1

(a) Standard bow-tie (SBT) cavity consisting of two focusing mirrors and two plane mirrors, operated close to the inner stability edge. (b) All-curved-mirror (ACM) cavity with four equal focusing mirrors and two overlapping foci. The distance d denotes the geometric separation between opposite curved mirrors. For the ACM cavity, an increase of d also increases the cavity length, while for the SBT the distance d can be chosen in a certain range.

Fig. 2
Fig. 2

The figures show the alignment sensitivity of several cavities by means of the change in overlap ΔU = 1 −U after a perturbation as a function of the beam radius on a curved mirror. (a) A curved mirror is tilted by an angle of 1μ rad, (b) The distance d is changed by Δd = 1μm.

Fig. 3
Fig. 3

Schematic of the experimental setup. NPRO: non-planar ring oscillator, EOM: electro-optical modulator, PD: photodiode, PM: power meter, CCD: CCD camera, VCO: voltage controlled oscillator.

Fig. 4
Fig. 4

Measured beam radii in both planes for the SBT and the ACM cavities while the stability edge was approached. The theoretical values are obtained with the ABCD-matrix formalism. For the SBT the long axis lies in the sagittal plane and for the ACM it lies in the tangential plane.

Fig. 5
Fig. 5

(a) Beam radius of a 125 MHz SBT cavity as described in the text with and without astigmatic compensation. The dotted red lines indicate the positions of the mirrors. (b) Beam ellipticity wx/wy at the mirrors as a function of the distance Δ as defined in Fig. 1 for different spot sizes.

Equations (6)

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M = ( A B Δ x C D Δ α 0 0 1 ) .
x 0 = ( 1 D ) Δ x + B Δ α 2 A D ,
V 0 = ( 1 A ) Δ α + C Δ x 2 A D .
ϕ Gouy = arccos ( A + D 2 ) .
U = | Ψ initial ( x , y ) Ψ pert * ( x , y ) d x d y | 2 ,
Ψ pert ( x , y ) = Ψ initial ( x x 0 , y ) e i k V 0 x ,

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