## Large-mode enhancement cavities |

Optics Express, Vol. 21, Issue 9, pp. 11606-11617 (2013)

http://dx.doi.org/10.1364/OE.21.011606

Acrobat PDF (1053 KB)

### 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/*e*^{2} 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

## 1. Introduction

*enhancement cavity*(EC) and the power circulating in the cavity can be several orders of magnitude larger than the input power. The enhancement is limited by the resonator round trip losses and, in the case of pulsed light, by chromatic dispersion. In general the efficiency of optical frequency conversion processes increases with the driving intensity and thus the EC technique lends itself to the efficient conversion of laser light to short wavelengths in the extreme-ultraviolet (XUV) or the THz spectral region.

## 2. Theoretical models

### 2.1. Misaligned stable resonators

16. H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE **54**, 1312–1329 (1966) [CrossRef] .

*M*, describing a round trip through the (misaligned) resonator, can be obtained by matrix multiplication of the individual elements. The system matrix

*M*reads: The upper left 2×2 sub-matrix is the conventional ABCD matrix and thus allows for the calculation of the eigenmode if the cavity is stable, i.e. if −2 <

*A*+

*D*< 2 holds [16

16. H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE **54**, 1312–1329 (1966) [CrossRef] .

*x*and Δ

*α*. For the system matrix

*M*, these quantities can be interpreted as the offset and angle, respectively, of the optical axis of the unperturbed resonator (0, 0, 1)

^{T}after one round trip through the resonator. Corresponding values for optical elements such as lenses or mirrors can be found e.g. in [17

17. V. Magni, “Multielement stable resonators containing a variable lens,” J. Opt. Soc. Am. A **4**, 1962–1969 (1987) [CrossRef] .

*M*as [15] Here,

*x*

_{0}and

*V*

_{0}denote the offset and the angle of the new optical axis, respectively, in a reference plane with respect to that of the unperturbed resonator. The displacement of the optical axis diverges in general for

*A*+

*D*= +2, i.e. at one of the stability edges, but not for the other edge (

*A*+

*D*= −2). In [18

18. 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] .

*ϕ*

_{Gouy}of the fundamental mode for one round-trip through a stable resonator is given by [19

19. S. Gigan, L. Lopez, N. Treps, A. Maître, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A **72**, 023804 (2005) [CrossRef] .

*A*+

*D*= +2), the Gouy-phase is 0 + 2

*πN*, and at the other edge

*π*+ 2

*πN*, where

*N*is an integer. The accumulated Gouy phase shift upon propagation through a focus (propagation distance much larger than the Rayleigh length) is

*π*. Therefore, if we can subdivide a resonator into

*N*strongly focused arms (corresponding to

*ϕ*

_{Gouy}≈

*π*in each arm) and collimated arms (corresponding to

*ϕ*

_{Gouy}≈ 0) – as it is typical for resonators at a stability edge – the total Gouy-phase is

*Nπ*. In conclusion, for even numbers of strongly focused arms, the alignment sensitivity diverges, while for odd numbers the resonator is robust with respect to misalignment.

### 2.2. Quantification of the alignment sensitivity for enhancement cavities

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

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

_{initial}(

*x*,

*y*) before and Ψ

_{pert}(

*x*,

*y*) after a perturbation. Mathematically, it is given by the overlap integral [22

22. W. B. Joyce and B. C. DeLoach, “Alignment of Gaussian beams,” Appl. Opt. **23**, 4187–4196 (1984) [CrossRef] [PubMed] .

_{inital}(

*x*,

*y*) and Ψ

_{pert}(

*x*,

*y*) are the normalized complex transverse field distributions.

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

*x*

_{0}and a (small) tilt

*V*

_{0}(both in

*x*direction), but equal transverse field distribution, can be written as [22

22. W. B. Joyce and B. C. DeLoach, “Alignment of Gaussian beams,” Appl. Opt. **23**, 4187–4196 (1984) [CrossRef] [PubMed] .

*k*= 2

*π*/

*λ*.

## 3. Cavity designs

### 3.1. Design considerations

*F*=

*P*/(

*cλ*) (optical power

*P*, speed of light

*c*and wavelength

*λ*), this limits. Larger spot sizes on the mirrors and therefore a higher power can only be obtained at a stability edge or in a longer cavity. As the cavity round-trip time must be an integer multiple of the pulse repetition period, the length can be increased even for a fixed repetition rate of the seeding laser, however at the expense of a narrower cavity resonance linewidth. Therefore, operating the EC at a stability edge can be a more robust approach. To improve the ratio of the intensity at the focus to that on the subsequent mirror assuming a given focus size, weaker focusing mirrors with larger separation distance have to be used. This maximum separation is limited by the cavity length, so this ratio might impose a lower bound on the cavity length. Based on these considerations, we discuss cavity designs that allow for an increase on

*all*optics in the cavity simultaneously. In particular for HHG, a larger focus is favorable, as the harmonic yield scales at least quadratically with the focus radius [25

25. 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] .

26. C. M. Heyl, J. Güdde, A. L’Huillier, and U. Höfer, “High-order harmonic generation with *μ*J laser pulses at high repetition rates,” J. Phys. B **45**, 074020 (2012) [CrossRef] .

### 3.2. The standard bow-tie cavity

*L*consists of two identical spherical mirrors (radius of curvature

*R*) separated by a distance

*d*and some folding mirrors as shown in Fig. 1(a). The distance

*d*between the focusing mirrors can be increased up to

*L*/2 for a triangular three-mirror cavity. Provided that

*R*≤

*L*/4 holds, the SBT is stable for

*R*>

*L*/4 the outer stability edge does not exist, so the cavity is stable up to the maximum possible distance

*d*=

*L*/2. For larger separations, the two distances

*d*and

*L*−

*d*are interchanged. Towards the inner stability edge (

*d*=

*R*), the short arm is tightly focused and the long arm gets collimated, i.e. the spot size can be increased on all mirrors simultaneously. As discussed in Section 2.1, the alignment sensitivity does not diverge at this edge, because the round-trip Gouy phase is

*π*. At the outer stability edge, both arms are focused (the Gouy-phase is 2

*π*), so that the alignment sensitivity diverges and the spot size only grows on the curved mirrors, but not necessarily on the folding mirrors in between.

*μ*rad tilt of one curved mirror in an astigmatism-free SBT and calculate the change in overlap over the entire stability zone (by variation of

*d*) for a fixed cavity length and fixed radii of curvature of the focusing mirrors. When using typical kinematic 1” mirror mounts, this small tilt introduces a cavity length change of only about 50 nm. This effect of the misalignment on the absolute angle of incidence on the curved mirrors and on the cavity length is negligible for the range of parameters considered here. The result is shown in Fig. 2(a) where the beam size

*w*(1/

_{m}*e*

^{2}-intensity radius) on the curved mirror indicates the position in the stability zone. Each cavity has a point of minimum sensitivity near, but not exactly at the smallest beam radius

*w*. In general, this point is not the center of the stability zone. By approaching the outer stability edge (upper branch), the alignment sensitivity increases drastically, as the displacement of the optical axis diverges. In this branch, short cavities are more sensitive, as a given beam radius is obtained closer to the stability edge. Two SBT cavities of equal length, but with different focusing geometries, exhibit the same sensitivity towards the outer stability edge, as can be seen in the example of the 10 MHz cavities. By approaching the inner stability edge (lower branch), the sensitivity only increases moderately. Interestingly, the curves for all resonators converge towards the same inner edge, i.e. in this limit the alignment sensitivity depends only on the spot size on the mirrors, but not on the cavity geometry.

_{m}*d*between two opposite curved mirrors (as defined in Fig. 1) is changed by some small value Δ

*d*, see Fig. 2(b). This leads again to two branches, the upper one being that of the inner stability edge. Equivalently, the overlap variation upon a change of the mirror curvature, as induced e.g. by thermal lensing, can be considered. For the example of the 125 MHz cavity, the longitudinal sensitivity increases by 7 orders of magnitude from the stability center to the point where the beam radius on the mirrors reaches 5 mm. This sensitivity will ultimately limit the achievable spot size. The longitudinal sensitivity decreases with increasing cavity length, as large spot sizes can be obtained closer to the stability center. Thus, increasing the cavity length offers a means to overcome limitations induced by the longitudinal sensitivity.

*μ*rad typically results in a cavity lenght change of only about 50 nm, a value much smaller than the considered longitudinal misalignment of 1

*μ*m. Despite the smaller perturbation, the change in overlap is larger in the transverse case for the cavities shown in Fig. 2 at the inner stability edge. Therefore, the impact of mechanical vibrations with a certain amplitude will perturb this cavity mainly due to transverse effects, making the transverse alignment sensitivity the more important one. For the SBT the inner stability edge is expected to be more robust than the outer one, as here the transverse sensitivity is much lower. However, for perturbations that solely affect the cavity longitudinally (e.g. thermal lensing), the operation at the outer stability edge might be advantageous.

### 3.3. All-curved-mirror cavity

*d*. For symmetry reasons, the spot sizes are the same on all mirrors. A particular feature of the ACM are the two crossing foci, which can be used e.g. for non-collinear HHG [27

27. 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. Express **16**, 6233–6239 (2008) [CrossRef] [PubMed] .

28. K. D. Moll, R. J. Jones, and J. Ye, “Output coupling methods for cavity-based high-harmonic generation,” Opt. Express **14**, 8189–8197 (2006) [CrossRef] [PubMed] .

*d*towards the stability edge near 2

*R*, but here the number of strongly focused arms is even (round-trip Gouy phase approaches 4

*π*), i.e. the alignment sensitivity diverges. There is no other stability edge with non-divergent alignment sensitivity for this resonator. Note that the double-bow-tie resonator suggested in [28

28. K. D. Moll, R. J. Jones, and J. Ye, “Output coupling methods for cavity-based high-harmonic generation,” Opt. Express **14**, 8189–8197 (2006) [CrossRef] [PubMed] .

*π*.

*d*= 2

*R*are plotted in Fig. 2. The transverse sensitivity at this edge is the same as for the 125 MHz SBT cavity at its corresponding

*A*+

*D*= +2 edge, i.e. the more sensitive edge. The longitudinal sensitivity is slightly worse than that of an 125 MHz SBT at the inner stability edge. When large spot sizes on all cavity mirrors are desired, this design is disadvantageous in comparison with the SBT design in terms of robustness. However, it should be noted that the ACM cavity might be useful for applications where the effect on the position of the optical axis needs to be maximized for a given perturbation, such as output coupling for cavity-dumping [29

29. T. Heupel, M. Weitz, and T. W. Hänsch, “Phase-coherent light pulses for atom optics and interferometry,” Opt. Lett. **22**, 1719 (1997) [CrossRef] .

30. G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics **7**, 258–261 (2013) [CrossRef] .

### 3.4. Alternative designs

*Quasi-imaging*[31]31. J. Weitenberg, P. Rußbüldt, T. Eidam, and I. Pupeza, “Transverse mode tailoring in a quasi-imaging high-finesse femtosecond enhancement cavity,” Opt. Express

**19**, 9551–9561 (2011) [CrossRef] [PubMed] .*and Bessel-Gauss-beams*[32]: In these concepts, the circulating field can have an on-axis intensity maximum near the focus and avoids an on-axis opening in a mirror for output coupling of the frequency-converted light. As these beams are not diffraction-limited, the ratio of the intensity in (or close to) the focus to the intensity on a mirror is naturally higher for the same propagation distance. However, this is achieved at the cost of a reduced focal volume.32. W. P. Putnam, D. N. Schimpf, G. Abram, and F. X. Kärtner, “Bessel-Gauss beam enhancement cavities for high-intensity applications,” Opt. Express

**20**, 24429–24443 (2012) [CrossRef] [PubMed] .*Imaging resonators*[33]: These are degenerate resonators, where arbitrary field distributions are reproduced after one round-trip. Large spot sizes on the mirrors could be obtained by coupling a large mode into the cavity.33. J. A. Arnaud, “Degenerate optical cavities,” Appl. Opt.

**8**, 189–195 (1969) [CrossRef] [PubMed] .*Oblique incidence*: The illuminated area on a mirror can also be increased by choosing a large angle of incidence (AOI), as the area increases by a factor 1/cos(AOI). This requires the use of toroidal or off-axis parabolic mirrors. Also, dielectric mirrors are in general polarization-discriminating for large AOI.

## 4. Experiments

### 4.1. Setup

*d*= 2

*R*and an SBT (R = 600 mm) operated close to

*d*=

*R*in order to determine whether or not the operation close to the stability edge is constrained by the alignment sensitivity and/or mechanical vibrations in a laboratory environment. The cavities are tested in the setup shown in Fig. 3. We lock a single-frequency

*λ*= 1064 nm non-planar ring oscillator (NPRO) [34

34. T. J. Kane and R. L. Byer, “Monolithic, unidirectional single-mode Nd:YAG ring laser,” Opt. Lett. **10**, 65–67 (1985) [CrossRef] [PubMed] .

35. 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. B **31**, 97–105 (1983) [CrossRef] .

*K*and the second one to obtain an error signal. The incoming beam is mode-matched to each cavity (round beam with spot size 3 mm at the respective input coupler) and is not changed throughout the experiments.

*E*of the incoming power

*P*

_{in}is given by

*P*

_{circ}/

*P*

_{in}where the circulating power

*P*

_{circ}can be measured via the transmission through a cavity mirror with known transmission. The cavity round trip power attenuation factor

*A*that accounts for all losses except for those at the input coupler can be calculated according to

*A*= 1 −

*K/E*. The round trip power loss is given by 1 −

*A*. This analysis allows to distinguish between the overlap and the cavity losses (including diffraction losses at the mirror boundaries) as reasons for a change of the enhancement while the eigenmode is varied and the input field is kept constant. The intensity distribution at the surface of one of the mirrors is imaged to the CCD camera with known magnification (calibrated with an aperture of known size). From the measured beam size we determine the position in the stability zone. The beam ellipticity

*w*/

_{x}*w*provides an independent measurement, as the angles of incidence are known (1.24° for both cavities).

_{y}### 4.2. Results

## 5. Astigmatic compensation

### 5.1. In-plane compensation using astigmatic elements

36. 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] .

- Replacing two plane mirrors by two identical cylindrical mirrors with a weak curvature (either convex in the tangential plane, or concave in the sagittal plane).
- Replacing the two spherical mirrors by two identical toroidal mirrors with a weak curvature difference in the two planes.
- Both methods may be implemented by elastic deformation of the plane or curved mirrors, respectively.

### 5.2. Non-planar cavities

37. D. Sigg and N. Mavalvala, “Principles of calculating the dynamical response of misaligned complex resonant optical interferometers,” J. Opt. Soc. Am. A **17**, 1642–1649 (2000) [CrossRef] .

38. 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] .

## 6. Conclusion

## Acknowledgments

## References and links

1. | A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quant. Electron. |

2. | I. Pupeza, |

3. | 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,” Nature |

4. | 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. |

5. | J. Lee, D. R. Carlson, and R. J. Jones, “Optimizing intracavity high harmonic generation for XUV fs frequency combs,” Opt. Express |

6. | 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,” Nature |

7. | 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. |

8. | T. K. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Extreme nonlinear optics in a femtosecond enhancement cavity,” Phys. Rev. Lett. |

9. | 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. |

10. | 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) |

11. | 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. SPIE |

12. | M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B |

13. | 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. |

14. | 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. |

15. | A. Gerrard and J. M. Burch, |

16. | H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE |

17. | V. Magni, “Multielement stable resonators containing a variable lens,” J. Opt. Soc. Am. A |

18. | S. d. Silvestri, P. Laporta, and V. Magni, “Rod thermal lensing effects in solid-state laser ring resonators,” Opt. Commun. |

19. | S. Gigan, L. Lopez, N. Treps, A. Maître, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A |

20. | N. Hodgson and H. Weber, “Misalignment sensitivity of stable resonators in multimode operation,” J. Mod. Opt. |

21. | R. Hauck, H. P. Kortz, and H. Weber, “Misalignment sensitivity of optical resonators,” Appl. Opt. |

22. | W. B. Joyce and B. C. DeLoach, “Alignment of Gaussian beams,” Appl. Opt. |

23. | F. Kawazoe, R. Schilling, and H. Lück, “Eigenmode changes in a misaligned triangular optical cavity,” J. Opt. |

24. | A. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J |

25. | 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. |

26. | C. M. Heyl, J. Güdde, A. L’Huillier, and U. Höfer, “High-order harmonic generation with |

27. | 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. Express |

28. | K. D. Moll, R. J. Jones, and J. Ye, “Output coupling methods for cavity-based high-harmonic generation,” Opt. Express |

29. | T. Heupel, M. Weitz, and T. W. Hänsch, “Phase-coherent light pulses for atom optics and interferometry,” Opt. Lett. |

30. | G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics |

31. | J. Weitenberg, P. Rußbüldt, T. Eidam, and I. Pupeza, “Transverse mode tailoring in a quasi-imaging high-finesse femtosecond enhancement cavity,” Opt. Express |

32. | W. P. Putnam, D. N. Schimpf, G. Abram, and F. X. Kärtner, “Bessel-Gauss beam enhancement cavities for high-intensity applications,” Opt. Express |

33. | J. A. Arnaud, “Degenerate optical cavities,” Appl. Opt. |

34. | T. J. Kane and R. L. Byer, “Monolithic, unidirectional single-mode Nd:YAG ring laser,” Opt. Lett. |

35. | 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. B |

36. | H. Kogelnik, E. Ippen, A. Dienes, and C. Shank, “Astigmatically compensated cavities for CW dye lasers,” IEEE J. Quant. Electron. |

37. | D. Sigg and N. Mavalvala, “Principles of calculating the dynamical response of misaligned complex resonant optical interferometers,” J. Opt. Soc. Am. A |

38. | F. Zomer, Y. Fedala, N. Pavloff, V. Soskov, and A. Variola, “Polarization induced instabilities in external four-mirror Fabry-Perot cavities,” Appl. Opt. |

**OCIS Codes**

(140.4780) Lasers and laser optics : Optical resonators

(140.7240) Lasers and laser optics : UV, EUV, and X-ray lasers

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: April 3, 2013

Revised Manuscript: April 23, 2013

Manuscript Accepted: April 27, 2013

Published: May 3, 2013

**Citation**

Henning Carstens, Simon Holzberger, Jan Kaster, Johannes Weitenberg, Volodymyr Pervak, Alexander Apolonski, Ernst Fill, Ferenc Krausz, and Ioachim Pupeza, "Large-mode enhancement cavities," Opt. Express **21**, 11606-11617 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11606

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### References

- A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quant. Electron.2, 109–124 (1966). [CrossRef]
- I. Pupeza, Power Scaling of Enhancement Cavities for Nonlinear Optics (Springer, 2012). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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)
- 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]
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