## Transverse mode tailoring in a quasi-imaging high-finesse femtosecond enhancement cavity |

Optics Express, Vol. 19, Issue 10, pp. 9551-9561 (2011)

http://dx.doi.org/10.1364/OE.19.009551

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### Abstract

We demonstrate a high-finesse femtosecond enhancement cavity with an on-axis obstacle. By inserting a wire with a width of 5% of the fundamental mode diameter, the finesse of F = 3400 is only slightly reduced to F = 3000. The low loss is due to the degeneracy of transverse modes, which allows for exciting a circulating field distribution avoiding the obstacle. We call this condition quasi-imaging. The concept could be used for output coupling of intracavity-generated higher-order harmonics through an on-axis opening in one of the cavity mirrors.

© 2011 OSA

## 1. Introduction

*GH*

_{0,0}, G

*H*

_{4,0}and

*GH*

_{8,0}can be excited simultaneously. If an obstacle, e.g. a wire or a slit in a resonator mirror, is introduced into the beam path, these modes arrange to avoid the obstacle. We call this quasi-imaging, because only a subset of the transverse modes is involved, whereas in an imaging resonator all transverse modes are simultaneously resonant.

## 2. Quasi-imaging

### 2.1 Definition of a quasi-imaging resonator

*GH*modes can contribute to the field distribution. This can change the spatial overlap with the incident field, the width of the on-axis region of small intensity, and loss at apertures limiting the transverse extent of the field distribution. Such apertures can be used to suppress the contribution of higher-order

*GH*modes.

*ψ*=

_{x}*ψ*, and the Gauss-Laguerre modes

_{y}*GL*with radial and azimuth mode index

^{l}_{p}*p*and

*l*can be used instead of the

*GH*modes as an orthonormal basis of eigen-modes. Various mode number differences and mode combinations can be chosen. A detailed theoretical description exceeds the scope of this paper and will be provided in [13].

### 2.2 Geometrical on-axis access to a bow-tie ring resonator by quasi-imaging

*R*and resonator length

_{C}*L*(see Fig. 2 ). The distance

*d*of the focusing mirrors determines the Gouy parameters

*ψ*and

_{x}*ψ*in the transverse directions. The angle of incidence

_{y}*α*on the curved mirrors causes different Gouy parameters in the transverse directions, i.e.

*ψ*≠

_{x}*ψ*. Therefore, the condition for quasi-imaging can be achieved only in one transverse direction. In the middle of the stability range, for

_{y}*ψ*= 3π/2, the modes

_{y}*GH*

_{0,0}and

*GH*

_{0,4}are simultaneously resonant and can be combined to a “slit mode” avoiding an on-axis slit in the output coupling mirror. The on-axis intensity oscillates along the propagation direction, with zero on the optical axis in the focal plane and an intensity maximum one Rayleigh length from the focus (see Fig. 2).

### 2.3 Adjustment of transverse mode degeneracy

*GH*

_{0,0}) appear with a period of 2π, corresponding to a change in cavity length by one wavelength λ. Because higher-order transverse modes acquire an additional phase (Eq. (1)), they are resonant at smaller frequencies than the fundamental mode, i.e. at longer oscillator cavity lengths. As can be easily seen, the Gouy parameter in tangential direction

*ψ*is larger than in sagittal direction

_{x}*ψ*for a bow-tie ring resonator. This difference between the Gouy parameters becomes visible in a resonator with finesse

_{y}*F*, if the resonance width 2π/

*F*is smaller than the Gouy parameter difference

*ψ*−

_{x}*ψ*. The position in the stability range can be read from the position of the resonances, the Gouy parameter being the distance between the 0-resonance and 1-resonance. In practice, the transverse modes can be easily identified by the number of adjacent resonances and by tilting of the incident beam and thereby changing its spatial overlap with the cavity transverse modes. Mode

_{y}*GH*

_{4,0}acquires an additional phase compared to the fundamental mode, which is four times the Gouy parameter

*ψ*. Therefore, the two modes are simultaneously resonant if

_{x}*ψ*= 3π/2 holds. In the situation shown in Fig. 3,

_{x}*ψ*has to be increased (by increasing the distance

_{x}*d*between the curved mirrors) in order to achieve the degeneracy.

## 3. Experimental realization

### 3.1 Experimental setup

1. I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, Th. 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**(12), 2052–2054 (2010). [CrossRef] [PubMed]

14. T. Eidam, F. Röser, O. Schmidt, J. Limpert, and A. Tünnermann, “57 W, 27 fs pulses from a fiber laser system using nonlinear compression,” Appl. Phys. B **92**(1), 9–12 (2008). [CrossRef]

*= 78 MHz. Throughout the experiments presented in this paper we used an incident average power of*

_{rep}*P*= 1.4 W. Two spherical lenses were used to match the laser output mode to the enhancement cavity fundamental mode. The passive cavity of length

_{in}*L*= 3.84 m consists of eight mirrors. Mirrors M2-M8 are highly reflective (

*R*= 0.99995) over the entire laser bandwidth and M1 is the input coupler (

_{M}*R*= 0.9986). Mirrors M5 and M6 are spherically curved (radius of curvature

_{IC}*R*= 150 mm), all other mirrors are plane. This yields a Gaussian waist radius of

_{C}*w*

_{0}= 22 µm in the middle of the stability range. All cavity mirrors exhibit low dispersion. In order to minimize round-trip dispersion, as well as to avoid nonlinearities in air, the cavity is placed in a vacuum chamber.

3. I. Pupeza, T. Eidam, J. Kaster, B. Bernhardt, J. Rauschenberger, A. Ozawa, E. Fill, Th. Udem, M. F. Kling, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, Th. W. Hänsch, and F. Krausz, “Power scaling of femtosecond enhancement cavities and high-power applications,” Proc. SPIE **7914**, 79141I, 79141I-13 (2011). [CrossRef]

15. Th. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. **35**(3), 441–444 (1980). [CrossRef]

1. I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, Th. 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**(12), 2052–2054 (2010). [CrossRef] [PubMed]

^{−6}is characterized using a power meter and an optical spectrum analyzer. The circulating power

*P*is calculated from the power

_{circ}*P*leaking through this mirror according to

_{leak}*P*=

_{circ}*P*/1.65·10

_{leak}^{−6}.

*ψ*= 3π/2 acquired at one round trip starting at the wire is independent of its position. Therefore, the convenient implementation of the wire (400 mm before mirror M5) as well as the vertical orientation is chosen for good accessibility. The plane of the wire is imaged 1:1 with a lens (

*f*= 400 mm) on a CCD camera (see Fig. 4(b)). This allows for adjusting the wire to the optical axis and observing the beam profile at that position. To record the beam profile at different positions in the cavity the camera can be moved on a rail. The 100 µm width of the wire equals 5% of the Gaussian beam diameter of 2

*w*= 2·0.99 mm at that position. An additional vertical aperture is placed in the cavity at the same longitudinal position and with a distance from the optical axis of roughly three times the Gaussian beam radius. This aperture serves as a spatial filter, i.e. it suppresses contributions of higher-order transverse modes other than

*GH*

_{0,0}and

*GH*

_{4,0}to the circulating field.

*R*= 0.99. With the resulting finesse

_{M}*F*= 100π and with a scan time

*t*= 7 ms for one free spectral range, the scan time over one resonance width

_{fsr}*t*=

_{res}*t*/

_{fsr}*F*= 22 µs is about 17 times larger than the cavity build-up time

*t*= (

_{bu}*F*/π)/ν

*= 1.3 µs. This is long enough to allow for a full build-up of the intracavity radiation for each transverse mode, and short enough to avoid distortions by mechanical vibrations. We assume a linear behavior of the scanning PZT. Then the intracavity power integrated over the illumination time of a transverse mode or a group of transverse modes is proportional to the spatial overlap of the incident beam with the respective mode or group of modes. Transverse modes with mode order higher than 4 were not measurable and therefore not considered. In this manner, the spatial overlap of the incident beam with the fundamental mode was estimated to be*

_{rep}*U*= 0.94.

### 3.2 Enhancement of the cavity modes GH_{0,0} and GH_{1,0}

*GH*

_{0,0}) and, subsequently, to the

*GH*

_{1,0}mode. The purpose of these experiments was to characterize the empty cavity, in particular the round-trip loss and impedance matching. Also, the elaborate evaluation of finesse and overlap from enhancement and coupling was tested for consistency.

*P*= 1950 W. This corresponds to a power enhancement of

_{circ}*P*/

_{circ}*P*= 1400. The circulating power fluctuates in time and repeatedly drops to ~0.8 of the maximal value. We attribute this strong fluctuation to the relatively slow PZT used for locking (measured mechanical bandwidth <20 kHz) in conjunction with the high cavity finesse. This was confirmed by decreasing the cavity finesse, which led to a significant decrease of the fluctuations. Furthermore, this is not a fundamental limitation of cavity enhancement, since a larger locking bandwidth can be achieved by advanced design of PZT-actuated mirrors [16

_{in}16. T. C. Briles, D. C. Yost, A. Cingöz, J. Ye, and T. R. Schibli, “Simple piezoelectric-actuated mirror with 180 kHz servo bandwidth,” Opt. Express **18**(10), 9739–9746 (2010). [CrossRef] [PubMed]

*P*was measured with a power meter. We assume that the maximal power level

_{circ}*P*is determined by the loss and overlap, and the dropping is due to a deviation from resonance. This maximum value is

_{circ}^{max}*P*= 1.1·

_{circ}^{max}*P*(compare Fig. 5(a) ). The corresponding maximum level of the enhancement, which was used to calculate the loss and the overlap, is

_{circ}*E*=

*P*/

_{circ}^{max}*P*= 1540. The coupling ratio

_{in}*K*of the power coupled into the cavity to the incident power was determined from the drop of the signal reflected from the input coupler compared to the unlocked case. This signal was measured with a photodiode. The maximum level of the coupling was determined to be

*K*= 0.70. From these values the round trip loss factor is calculated to be

*R*= 1 −

*K*/

*E*= 0.99955. It follows for the cavity finesse

*F*= 2π/(1 −

*R*) = 3400. The difference between the measured enhancement

_{IC}R*E*= 1540 and the enhancement expected from the loss

*E*= (1 −

_{R}*R*)/(1 − (

_{IC}*R*)

_{IC}R^{1/2})

^{2}= 1630 can be attributed to an incomplete spatial overlap of

*U*=

*E*/

*E*= 0.94, since a complete spectral overlap was confirmed by measuring the incident and circulating spectra. This spatial overlap matches the value estimated from the scan. The pulse duration was measured to be τ = 200 fs.

_{R}*GH*

_{1,0}mode. Because the

*GH*modes form an orthogonal set of modes, the spatial overlap of an incident

*GH*

_{0,0}mode with the circulating

*GH*

_{1,0}mode vanishes, unless the incident beam has a tilt or transverse offset with respect to the cavity optical axis. In the experiment, the q-parameter was left the same as before and the beam was tilted horizontally to optimize the spatial overlap. The maximum spatial overlap for an incident Gaussian beam with eigen-q-parameter is easily calculated to be

*U*= 1/

*e*= 0.37 for a tilt angle of γ = 2/(

*k*·

*w*) or an offset of Δ

*x*=

*w*with the wave number

*k*and Gaussian beam radius

*w*. The pinhole in the locking scheme was used to select one of the two lobes in the reflected signal. The CEO phase of the incident pulse train had to be adjusted for maximum spectral overlap of the frequency comb modes with the cavity resonances corresponding to the

*GH*

_{1,0}mode. This is due to the fact that the cavity resonances for mode order

*n*= 1 are shifted by the Gouy parameter

*ψ*compared to the fundamental mode (see Fig. 3). A power enhancement of

_{x}*P*/

_{circ}*P*= 550,

_{in}*P*= 1.1·

_{circ}^{max}*P*and a coupling of

_{circ}*K*= 0.28 were measured. The finesse is determined to be

*F*= 3400, which is the same as for the fundamental mode. The spatial overlap is

*U*= 0.37, which matches the value calculated for an incident Gaussian beam. The smaller power enhancement compared to the fundamental mode is due to the reduced spatial overlap alone, the resonator loss and therefore the finesse is identical in both cases. As in the case of the fundamental mode, the entire spectrum was coupled to the

*GH*

_{1,0}mode and evenly enhanced.

### 3.3 Quasi-imaging: enhancement of slit modes with an on-axis obstacle

*d*between the curved mirrors by displacing mirror M5 and compensating the change in the resonator length by displacing mirror M7. The position in the stability range can be read from the scan pattern of the cavity with the wire removed from the beam path, as is discussed in Section 2.3. Figure 5(b) shows a recorded scan pattern.

*GH*

_{8,0}and

*GH*

_{12,0}). In order to suppress these contributions, a vertical aperture was placed in the cavity and moved towards the optical axis until additional lobes besides the four were suppressed. This was the case for a distance from the optical axis of about three times the Gaussian beam radius (see Fig. 7(a) ).

*d*by some tens of µm. Figure 8(a) shows the enhancement as a function of the detuning from the quasi-imaging condition in terms of the Gouy parameter

*ψ*and of the distance

_{x}*d*between the curved mirrors. We have derived a theoretical model for the detuning curve. However, the model exceeds the scope of this paper and will be described in [13]. The experimentally measured width (FWHM) of the detuning curve is Δ

*δ*= 17 µm. On the one hand, this is a small fraction of the entire stability range of 3.2 mm. On the other hand, it is so broad that the quasi-imaging can be easily adjusted manually and does not demand for an active control of the distance

*d*.

*P*/

_{circ}*P*= 330 at circulating power

_{in}*P*= 460 W, a maximum level of the circulating power

_{circ}*P*= 1.08·

_{circ}^{max}*P*(see Fig. 5(a)) and a coupling of

_{circ}*K*= 0.24 were measured. The finesse is determined to be

*F*= 3000, which represents only a small decrease compared to the cavity without the wire

*F*= 3400. The additional round-trip loss at the wire amounts to 2.3·10

^{−4}. With the wire the enhancement expected from the loss is

*E*= 1290. This represents a reduction by 0.79 compared to the cavity without the wire. However, the smaller power enhancement compared to the fundamental mode is mainly due to the reduced spatial overlap. Figure 7 shows the measured intensity distribution of the enhanced field at the position of the wire and at a position of maximum intensity on the optical axis. A fit of a mode combination of

_{R}*GH*

_{0,0},

*GH*

_{4,0}and

*GH*

_{8,0}with complex coefficients to the intensity distribution yields a power fraction of |

*c*

_{0}|

^{2}= 0.25 in the fundamental mode. The power fraction in the

*GH*

_{8,0}mode is only |

*c*

_{8}|

^{2}= 0.03, because it is suppressed by the aperture. The power fraction of |

*c*

_{0}|

^{2}= 0.25 defines the expected spatial overlap with an incident Gaussian beam with the eigen-q-parameter. The spatial overlap calculated from enhancement and coupling is

*U*= 0.27, which is in good agreement with the value of |

*c*

_{0}|

^{2}. The entire spectrum was coupled to the slit mode in the cavity and evenly enhanced (see Fig. 8(b)).

*P*/

_{circ}*P*> 300. Table 1 summarizes the results for the different resonator modes.

_{in}*U*= 0.27 for the simple slit mode. The spatial overlap is expected to reach 0.44 for an incident Gaussian beam with an adapted q-parameter [13]. A cylindrical telescope has to be used then for mode matching. Theoretically, the spatial overlap can reach unity if the incident field is adequately shaped. Beam shaping can e.g. be achieved with free form optics. The increase of the spatial overlap is a problem which can be solved outside the enhancement cavity.

## 4. Further discussion

17. J. A. Arnaud, “Degenerate optical cavities,” Appl. Opt. **8**(1), 189–195 (1969). [CrossRef] [PubMed]

*GH*

_{0,0}and

*GH*

_{4,0}alone. Contributions of higher-order transverse modes can change the shape of the field. This can be manipulated by apertures, by the shape of the incident field and by the position in the stability range. The interaction region for HHG could be limited to one of these two regions. The lobes in the focal plane are in phase, which means that the harmonic signal will exhibit a maximum on the optical axis in the far field. In contrast, the

*GH*

_{1,0}mode, as well as other

*GH*or

*GL*modes with vanishing intensity on the optical axis, are unfavourable for HHG, because the lobes oscillate with opposite phase and the harmonic signal vanishes on the optical axis [8

8. K. D. Moll, R. J. Jones, and J. Ye, “Output coupling methods for cavity-based high-harmonic generation,” Opt. Express **14**(18), 8189–8197 (2006). [CrossRef] [PubMed]

19. F. V. Hartemann, W. J. Brown, D. J. Gibson, S. G. Anderson, A. M. Tremaine, P. T. Springer, A. J. Wootton, E. P. Hartouni, and C. P. J. Barty, “High-energy scaling of Compton scattering light sources,” Phys. Rev. ST Accel. Beams **8**(10), 100702 (2005). [CrossRef]

*GL*modes, an intensity minimum in the focus can be formed, which is strongly localized in radial as well as in axial direction. Such a field distribution, possibly enhanced in a cavity, can serve as a dipole trap for neutral atoms [20

20. R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. At. Mol. Opt. Phys. **42**, 95–170 (2000). [CrossRef]

## 5. Conclusion

*F*= 3400, the cavity finesse was only slightly reduced to

*F*= 3000 by the insertion of the wire with a width equal to 5% of the Gaussian beam diameter. This corresponds to an additional round-trip loss of 2.3·10

^{−4}. The decrease of the power enhancement from

*P*/

_{circ}*P*= 1400 to

_{in}*P*/

_{circ}*P*= 330 is mainly due to the imperfect spatial overlap, which could be increased by shaping the incident beam.

_{in}## Acknowledgments

## References and links

1. | I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, Th. 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. |

2. | A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and Th. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. |

3. | I. Pupeza, T. Eidam, J. Kaster, B. Bernhardt, J. Rauschenberger, A. Ozawa, E. Fill, Th. Udem, M. F. Kling, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, Th. W. Hänsch, and F. Krausz, “Power scaling of femtosecond enhancement cavities and high-power applications,” Proc. SPIE |

4. | 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. |

5. | Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature |

6. | D. C. Yost, T. R. Schibli, and J. Ye, “Efficient output coupling of intracavity high-harmonic generation,” Opt. Lett. |

7. | Y.-Y. Yang, F. Süßmann, S. Zherebtsov, I. Pupeza, J. Kaster, D. Lehr, H.-J. Fuchs, E.-B. Kley, E. Fill, X.-M. Duan, Z.-S. Zhao, F. Krausz, S. L. Stebbings, and M. F. Kling, “Optimization and characterization of a highly-efficient diffraction nanograting for MHz XUV pulses,” Opt. Express |

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

9. | W. P. Putnam, G. Abram, E. L. Falcão-Filho, J. R. Birge, and F. X. Kärtner, “High-intensity Bessel-Gauss beam enhancement cavities,” in |

10. | A. Ozawa, A. Vernaleken, W. Schneider, I. Gotlibovych, Th. Udem, and T. W. Hänsch, “Non-collinear high harmonic generation: a promising outcoupling method for cavity-assisted XUV generation,” Opt. Express |

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

12. | R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions,” Opt. Express |

13. | J. Weitenberg, P. Rußbüldt, I. Pupeza, Th. Udem, H.-D. Hoffmann, and R. Poprawe, “Geometrical on-axis access to high-finesse resonators by quasi-imaging,” (manuscript in preparation). |

14. | T. Eidam, F. Röser, O. Schmidt, J. Limpert, and A. Tünnermann, “57 W, 27 fs pulses from a fiber laser system using nonlinear compression,” Appl. Phys. B |

15. | Th. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. |

16. | T. C. Briles, D. C. Yost, A. Cingöz, J. Ye, and T. R. Schibli, “Simple piezoelectric-actuated mirror with 180 kHz servo bandwidth,” Opt. Express |

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

18. | D. Esser, W. Bröring, J. Weitenberg, and H.-D. Hoffmann, “Laser-manufactured mirrors for geometrical output coupling of intracavity-generated high harmonics,” (manuscript in preparation). |

19. | F. V. Hartemann, W. J. Brown, D. J. Gibson, S. G. Anderson, A. M. Tremaine, P. T. Springer, A. J. Wootton, E. P. Hartouni, and C. P. J. Barty, “High-energy scaling of Compton scattering light sources,” Phys. Rev. ST Accel. Beams |

20. | R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. At. Mol. Opt. Phys. |

**OCIS Codes**

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

(190.4160) Nonlinear optics : Multiharmonic generation

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

(070.5753) Fourier optics and signal processing : Resonators

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: March 4, 2011

Revised Manuscript: April 27, 2011

Manuscript Accepted: April 27, 2011

Published: May 2, 2011

**Citation**

Johannes Weitenberg, Peter Rußbüldt, Tino Eidam, and Ioachim Pupeza, "Transverse mode tailoring in a quasi-imaging high-finesse femtosecond enhancement cavity," Opt. Express **19**, 9551-9561 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9551

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### References

- I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, Th. 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(12), 2052–2054 (2010). [CrossRef] [PubMed]
- A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and Th. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100(25), 253901 (2008). [CrossRef] [PubMed]
- I. Pupeza, T. Eidam, J. Kaster, B. Bernhardt, J. Rauschenberger, A. Ozawa, E. Fill, Th. Udem, M. F. Kling, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, Th. W. Hänsch, and F. Krausz, “Power scaling of femtosecond enhancement cavities and high-power applications,” Proc. SPIE 7914, 79141I, 79141I-13 (2011). [CrossRef]
- 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(19), 193201 (2005). [CrossRef] [PubMed]
- Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436(7048), 234–237 (2005). [CrossRef] [PubMed]
- D. C. Yost, T. R. Schibli, and J. Ye, “Efficient output coupling of intracavity high-harmonic generation,” Opt. Lett. 33(10), 1099–1101 (2008). [CrossRef] [PubMed]
- Y.-Y. Yang, F. Süßmann, S. Zherebtsov, I. Pupeza, J. Kaster, D. Lehr, H.-J. Fuchs, E.-B. Kley, E. Fill, X.-M. Duan, Z.-S. Zhao, F. Krausz, S. L. Stebbings, and M. F. Kling, “Optimization and characterization of a highly-efficient diffraction nanograting for MHz XUV pulses,” Opt. Express 19(3), 1954–1962 (2011). [CrossRef] [PubMed]
- K. D. Moll, R. J. Jones, and J. Ye, “Output coupling methods for cavity-based high-harmonic generation,” Opt. Express 14(18), 8189–8197 (2006). [CrossRef] [PubMed]
- W. P. Putnam, G. Abram, E. L. Falcão-Filho, J. R. Birge, and F. X. Kärtner, “High-intensity Bessel-Gauss beam enhancement cavities,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMD1 (2010).
- A. Ozawa, A. Vernaleken, W. Schneider, I. Gotlibovych, Th. Udem, and T. W. Hänsch, “Non-collinear high harmonic generation: a promising outcoupling method for cavity-assisted XUV generation,” Opt. Express 16(9), 6233–6239 (2008). [CrossRef] [PubMed]
- S. Gigan, L. Lopez, N. Treps, A. Maître, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A 72(2), 023804 (2005). [CrossRef]
- R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions,” Opt. Express 14(13), 6069–6074 (2006). [CrossRef] [PubMed]
- J. Weitenberg, P. Rußbüldt, I. Pupeza, Th. Udem, H.-D. Hoffmann, and R. Poprawe, “Geometrical on-axis access to high-finesse resonators by quasi-imaging,” (manuscript in preparation).
- T. Eidam, F. Röser, O. Schmidt, J. Limpert, and A. Tünnermann, “57 W, 27 fs pulses from a fiber laser system using nonlinear compression,” Appl. Phys. B 92(1), 9–12 (2008). [CrossRef]
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