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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 17 — Aug. 13, 2012
  • pp: 18659–18664

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1.3-mW tunable and narrow-band continuous-wave light source at 191 nm

Matthias Scholz, Dmitrijs Opalevs, Patrick Leisching, Wilhelm Kaenders, Guiling Wang, Xiaoyang Wang, Rukang Li, and Chuangtian Chen  »View Author Affiliations


Optics Express, Vol. 20, Issue 17, pp. 18659-18664 (2012)
http://dx.doi.org/10.1364/OE.20.018659


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Abstract

We report on the realization of a continuous-wave light source based on nonlinear interaction in KBBF at a wavelength of 191 nm. More than 1.3 mW of deep-ultraviolet power was generated in a mechanically robust setup pumped by an amplified grating stabilized diode laser. Mode hop-free tuning over 40 GHz at 191 nm could be demonstrated.

© 2012 OSA

1. Introduction

For long, coherent light generation below 200 nm has not been accessible by direct second-harmonic processes. There is a number of excimers that allow laser emission in the deep-ultraviolet (DUV) spectral range, namely Ar2* (126 nm), Kr2* (146 nm), Xe2* (172/175 nm), and ArF 193 nm [1

D. Basting, Excimer Laser Technology (Springer, 2005). [CrossRef]

], but excimer lasers operate in the pulsed regime with a typical pulse duration of 10 ns and a repetition rate of around 100 Hz. However, many tasks in the DUV require continuous-wave (cw) emission or even prefer the generated light to be narrow-band, but tunable in frequency. Application areas range from wafer inspection in the semiconductor industry to photoemission spectroscopy as a basic research analysis method. Moreover, the excimer laser community itself is looking for a cw laser at 193 nm that can act as a seed source in order to replace lossy intra-cavity spectral filtering and to achieve even narrower emission.

In the ultraviolet, cw radiation is commonly produced by second-harmonic (SHG) or sum-frequency generation (SFG) of visible or near-infrared light sources. Approaching 200 nm, the number of suitable crystals that can mediate the nonlinear interaction is limited, and demonstrations have been mostly done in the pulsed regime. Of all commercially available crystals, β-Barium-Borate (BBO) can produce the lowest wavelength by a direct SHG process, reaching down to 205 nm. However, operation of BBO below 215 nm becomes challenging since the proximity to its absorption edge around 190 nm leads to enhanced absorption and degradation of the crystal due to the creation of color centers [2

W. Köchner, Solid-State Laser Engineerung (Springer, 2006).

]. In order to restrict the complexity of the laser setup to only one fundamental source, second-harmonic schemes are preferred over sum-frequency mixing processes. If costs for an elaborate SFG setup are tolerable, BBO can produce wavelengths down to its absorption edge. By cooling the nonlinear crystal, this edge can even be blue-shifted, and the generation of pulsed 186 nm light from a BBO crystal could be demonstrated [3

H. Kouta and Y. Kuwano, “Attaining 186-nm light generation in cooled β-BaB2O4 crystal,” Opt. Lett. 24, 1230–1232 (1999). [CrossRef]

]. Lithium Triborate and Cesium Lithium Borate also allow SFG below 200 nm which has been shown for the pulsed regime in [4

F. Seifert, J. Ringling, F. Noack, V. Petrov, and O. Kittelmann, “Generation of tunable femtosecond pulses to as low as 172.7 nm by sum-frequency mixing in lithium triborate,” Opt. Lett. 19, 1538–1540 (1994). [CrossRef] [PubMed]

] and [5

C. Qu, M. Yoshimura, J. Tsunoda, Y. Kaneda, M. Imade, T. Sasaki, and Y. Mori, “189-nm wavelength generation with borate crystals,” Conference Proceedings CLEO: Science and Innovations, Nonlinear Materials and Devices, CF3A (2012).

], respectively. These two materials also take advantage from their lower absorption edges compared to BBO.

While these efforts continuously, but slowly move the DUV barrier towards shorter wavelengths, the engineering of Potassium Fluoroboratoberyllate (KBBF) and other crystals from the Berylloborate family marked a major breakthrough in the DUV generation by direct SHG [6

C. Chen, Y. Wang, Y. Xia, B. Wu, D. Tang, K. Wu, Z. Wenrong, L. Yu, and L. Mei, “New development of nonlinear optical crystals for the ultraviolet region with molecule engineering approach,” J. Appl. Phys. 77, 2268–2272 (1994). [CrossRef]

]. A comprehensive review can be found in [7

C. Chen, G. Wang, X. Wang, and Z. Xu, “Deep-UV nonlinear optical crystal KBe2BO3F2 - discovery, growth, optical properties and applications,” Appl. Phys. B 97, 9–25 (2009). [CrossRef]

]. Their superior properties in the DUV have been explained by the contribution of the (BO3)3− groups to the nonlinear coefficient. KBBF is the most thoroughly investigated member of the Berylloborates, but was only studied under pulsed operation, so far. With KBBF’s absorption edge at around 153 nm, the lowest obtained wavelength to date is 156 nm [8

T. Kanai, T. Kanda, T. Sekikawa, S. Watanabe, T. Togashi, C. Chen, C. Zhang, Z. Xu, and J. Wang, “Generation of vacuum-ultraviolet light below 160 nm in a KBBF crystal by the fifth harmonic of a single-mode Ti:sapphire laser,” J. Opt. Soc. Am. B 21, 370–375 (2004). [CrossRef]

], and an output of 120 mW average power was achieved at 177 nm, the sixth harmonic of the 1064 nm Nd:YAG transition [9

X. Zhang, L. Wang, X. Wang, G. Wang, Y. Zhu, and C. Chen, “High-power sixth-harmonic generation of an Nd:YAG laser with KBe2BO3F2 prism-coupled devices,” accepted by Opt. Commun. [PubMed]

].

The demonstration of true cw light generation from KBBF, however, is still pending. This paper is intended to fill this gap and reports on the generation of narrow-band coherent light around a wavelength of 191 nm. In section 2, the reader is introduced to KBBF as a key nonlinear crystal for DUV light generation. Section 3 describes the setup that allows the realization of this 191 nm-light source by two consecutive intra-cavity conversion stages. The major results of our experiments are presented in section 4, followed by a discussion and conclusions in section 5.

2. The nonlinear crystal

The growth method and nonlinear parameters of KBBF have been described elsewhere in detail [10

D. Tang, Y. Xia, B. Wu, and C. Chen, “Growth of a new UV nonlinear optical crystal: KBe2(BO3)F2,” J. Cryst. Growth 222, 125–129 (2001). [CrossRef]

–12

G. Wang, C. Zhang, C. Chen, Z. Xu, and J. Wang, “Determination of nonlinear optical coefficients of KBe2BO3F2 crystals,” Chin. Phys. Lett. 20, 243–245 (2003). [CrossRef]

]. To date, the largest crystal extension in z achieved with the method of spontaneous crystallization is around 2 – 3 mm due to the layer structure of KBBF. For fundamental wavelengths shorter than ≈ 470 nm, the crystal slab must be embedded between an index matching material to avoid total internal reflection of fundamental and DUV waves at the crystal facets due to its large refractive index. This sandwich structure is usually referred to as a prism-coupled device (PCD) [13

C. Chen, J. Lü, G. Wang, Z. Xu, J. Wang, C. Zhang, and Y. Liu, “Deep ultraviolet harmonic generation with KBe2BO3F2 crystal,” Chin. Phys. Lett. 18, 1081 (2001). [CrossRef]

]. As an application example in the pulsed regime, angle-resolved photo-emission spectroscopy (ARPES) at around 177 nm with such a KBBF device has been demonstrated in [14

Y. Zhou, G. Wang, C. Li, Q. Peng, D. Cui, Z. Xu, X. Wang, Y. Zhu, C. Chen, G. Liu, X. Dong, and X. Zhou, “Sixth harmonic of a Nd:YVO4 laser generation in KBBF for ARPES,” Chin. Phys. Lett. 25, 963–965 (2008). [CrossRef]

].

For wavelength conversion from 382 nm to 191 nm, the wave vector k of the fundamental beam and z span a phase-matching angle of θPM = 56.5 deg with a walk-off angle for the second-harmonic of about γ = 63 mrad. In this work, the particular wavelength of 191 nm was chosen since it is close to the wavelength needed for photoemission spectroscopy on silicon while the experimental setup does not need to consider the absorption by oxygen. In order to avoid the chance of DUV damage at the crystal facets, the prism angles are Brewster-cut for the fundamental wavelength with an angle of 55.8 deg. Since KBBF belongs to point group 32, the nonlinear coeffcient under study is dooe = d11 cos(θPM) cos(3ϕ) which maximizes for ϕ = 0. A detailed discussion of the nonlinear conversion efficiency will follow in the next sections.

3. Experimental setup

We generate the 191 nm radiation in a two-stage SHG setup. A general treatment of nonlinear optical processes can be found in [15

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1997).

]. The first conversion process from the initial wavelength of 764 nm to the intermediate wavelength of 382 nm is performed in a commercially available TA-SHG pro by Toptica Photonics (Fig. 1(a)). A narrow linewidth of the 764 nm emission is ensured by starting from a DL pro extended-cavity diode laser (ECDL) in Littrow configuration with a typical short-term linewidth of < 50 kHz due to its passive stability against acoustic noise. The laser head can be tuned mode hop-free over a range of 20 GHz by a piezo element (PZT) behind its grating. Coarse tuning by a macroscopic movement of the grating is possible over a bandwidth of several nanometers. This DL pro diode laser seeds a tapered amplifier (TA) with an output power of 2 W that maintains the spectral properties of the ECDL. The 1.6 W of usable TA power behind a −60 dB Faraday isolator and mode-matching optics are fed into a bow-tie cavity in order to enhance the efficiency of the first nonlinear conversion stage. Around 75% of the TA power is coupled into the cavity which proves that a large fraction of the TA emission is in the TEM00 mode. The cavity is locked to the incident wavelength by the Pound-Drever-Hall technique, and up to 700 mW of blue light at 382 nm are generated. Since the spectral bandwidth of light increases by a factor of 2 during an SHG process, we estimate the linewidth of the second-harmonic at 382 nm to be < 70 kHz.

Fig. 1 (a) Photograph of the TA-SHG pro that provides the 700-mW pump beam for the DUV nonlinear conversion process. (b) Bow-tie cavity with the Brewster-cut KBBF prism-coupled device (PCD). In this top view, the two parallel lines at the PCD indicate the vertically tilted KBBF slab between the SiO2 prisms. For details see text.

Figure 1(b) depicts a sketch of the DUV cavity stage. The 382-nm beam acts as the fundamental wave for the nonlinear frequency conversion into the DUV. This second frequency doubling stage is also realized as a cavity in bow-tie configuration, with the SiO2 prisms around the KBBF crystal Brewster-cut in the tangential plane while phase-matching was adjusted in the sagittal plane as described in section 2. In this scheme, the p-polarized 382-nm light from the TA-SHG pro module can be used directly to pump the second cavity, without the need of an additional retardation plate. A three-lens telescope matches the lateral profile of the 382-nm pump beam to the cavity mode. The length of the intra-cavity path is stabilized to a multiple of 191 nm by the Pound-Drever-Hall technique where a PZT on the second cavity mirror serves as the actuator. The light leaking through cavity mirror M3 is detected by a UV-enhanced photodiode (PD) to provide a monitor signal for the circulating power. The KBBF PCD is mounted to a two-axes tilt aligner that controls both the Brewster and the phase-matching angle. The temperature of the KBBF slab can be stabilized within an accuracy of 50 mK.

The length of the KBBF crystal slab under study was around 1.5 mm. Considering the slab tilt by the phase-matching angle θPM, the beam path through the KBBF crystal is thus L = 2.7 mm. According to the generalized Boyd-Kleinman theory for elliptical Gaussian beams, the optimum waists for the fundamental beam can be calculated from the birefringence parameter B=γ/2 kL [16

T. Freegarde, J. Coutts, J. Walz, D. Leibfried, and T. W. Hänsch, “General analysis of type I second-harmonic generation with elliptical Gaussian beams,” J. Opt. Soc. Am. B 14, 2010–2016 (1997). [CrossRef]

,17

M. Scholz, “General treatment of sum-frequency mixing with elliptical Gaussian beams,” J. Opt. Soc. Am. B 29, 1655–1660 (2012). [CrossRef]

]. Since B ≈ 8, the optimum focussing parameters ξt/s = L/bt/s for the tangential and sagittal planes would be ξt opt≈3.3 and ξs opt≈0.35 with bt/s denoting the confocal parameters in the two planes. However, the corresponding tangential and sagittal beam waists wt opt≈6μm and ws opt≈18μm, respectively would result in a relatively large DUV power density on the KBBF and prism facets and also in a highly diverging and elliptical second-harmonic beam. The fundamental beam waists were therefore chosen larger than these optimum values, and the DUV power load on the facets could be reduced by a factor of 10 while the conversion efficiency suffers a drop by a factor of only 2.5. The resulting theoretical nonlinear conversion efficiency is κNL ≈ 3 × 10−6/W.

4. Results

Even though the mode-matching setup contains only spherical lenses, it allows for a theoretical coupling efficiency to the fundamental cavity mode of > 98%. With proper impedance matching due to scattering, absorption, and conversion losses inside the cavity, an overall incoupling efficiency of > 75% was achieved. We attribute the residual < 25% to contributions of higher transversal modes in the 382-nm beam. Applying a triangular voltage to the cavity PZT, a cavity finesse of 104 for the circulating beam was measured with the photodiode signal leaking through M3. Thereby, absorption at the interfaces of the KBBF PCD mainly governs the intra-cavity losses.

For further characterization, the dependance of the 191-nm power on the fundamental 382-nm power was measured. The 382-nm power was changed by adjusting the TA current in order to leave the lateral beam profile of the 382-nm emission and thus the incoupling efficiency to the second cavity unchanged. The results are shown in Fig. 2(a). The solid line shows a simulation that takes into account the calculated nonlinear conversion efficiency κNL, the measured incoupling efficiency, and an overall PCD absorption of ≈ 2% that was derived from the finesse measurement. No free fit parameters were used to reproduce the measured data. The absence of significant 382-nm power in the DUV beam could be proven by a 10-nm wide bandpass filter centered on 193 nm. Figure 2(b) depicts a measurement of the TA, the 382-nm, and the DUV power over a time interval of 8 h. No degradation of the DUV power level was observed, and the two cavities stayed in lock at all times. Analogously to the previous arguments, the bandwidth of the 191-nm emission can be estimated to be < 100 kHz.

Fig. 2 (a) Dependance of the DUV power at 191 nm on the pump power. The solid line represents a simulation of the generated DUV power. (b) Long-term measurement of the TA, SHG, and DUV power over a interval of 8 hours. None of the signals shows a degradation over time.

For applications that need frequency tuning, we investigated the DUV emission under variations of the seed laser wavelength. For spectrocopic application, the mode hop-free (MHF) tuning range is of particular interest where the seed remains on the same longitudinal ECDL mode.

For these MHF tuning measurements, a triangular voltage was applied to the grating PZT of the ECDL, and the frequency of its emission was measured by a wavemeter (HighFinesse, WSU-30). During this scan, the output power of the TA, the first doubling stage, and the DUV emission were monitored simultaneously. The measured data are summarized in Fig. 3. Aside from the center frequency, the power drops since phase-matching was not readjusted during this continuous scan. There is no jump visible in the recorded signals which means that the seed ECDL did not exhibit any mode hops. This result also proves that the feedback loops of the two consecutive cavities followed the change in frequency in lock. DUV power of more than 1 mW could be obtained over a scan range of 40 GHz at 191 nm. This frequency span is solely limited by the seed’s tuning range.

Fig. 3 Measurement results of the MHF tuning experiments. The graph depicts the output power levels of the TA, the 382-nm beam, and the DUV light during a frequency scan of the ECDL. The achieved MHF scan range of the DUV frequency was 40 GHz.

5. Summary and outlook

We realized a coherent source of cw radiation at 191 nm. More than 1.3 mW of DUV power have be generated, and the system passed a first test of its robustness in an 8-h measurement. By using an extended-cavity diode laser as the fundamental source, a narrow linewidth and tunability of the DUV emission could be ensured. We demonstrated a mode hop-free tuning range of 40 GHz around 191 nm which proves the applicability of this cw light source to multiple tasks in spectroscopy. It should be noted that the demonstated wavelength of 191 nm was only chosen as one of the lowest wavelengths that does not require an elaborate vacuum system. In principle, with the current variety of available tapared amplifiers or an additional single-pass conversion stage pumped by a fiber amplifier, the presented scheme can cover the wavelength range between 160 nm and the visible. Due to its coherence properties, this light source is thus very promising for multiple applications in both basic research and industry like ARPES, DUV metrology, or seeding of excimer lasers.

Acknowledgments

G. L. Wang acknowledged funding by the National Natural Science Foundation of China (grant no. 50972149). M. Scholz would like to thank Jürgen Stuhler for valuable discussions.

References and links

1.

D. Basting, Excimer Laser Technology (Springer, 2005). [CrossRef]

2.

W. Köchner, Solid-State Laser Engineerung (Springer, 2006).

3.

H. Kouta and Y. Kuwano, “Attaining 186-nm light generation in cooled β-BaB2O4 crystal,” Opt. Lett. 24, 1230–1232 (1999). [CrossRef]

4.

F. Seifert, J. Ringling, F. Noack, V. Petrov, and O. Kittelmann, “Generation of tunable femtosecond pulses to as low as 172.7 nm by sum-frequency mixing in lithium triborate,” Opt. Lett. 19, 1538–1540 (1994). [CrossRef] [PubMed]

5.

C. Qu, M. Yoshimura, J. Tsunoda, Y. Kaneda, M. Imade, T. Sasaki, and Y. Mori, “189-nm wavelength generation with borate crystals,” Conference Proceedings CLEO: Science and Innovations, Nonlinear Materials and Devices, CF3A (2012).

6.

C. Chen, Y. Wang, Y. Xia, B. Wu, D. Tang, K. Wu, Z. Wenrong, L. Yu, and L. Mei, “New development of nonlinear optical crystals for the ultraviolet region with molecule engineering approach,” J. Appl. Phys. 77, 2268–2272 (1994). [CrossRef]

7.

C. Chen, G. Wang, X. Wang, and Z. Xu, “Deep-UV nonlinear optical crystal KBe2BO3F2 - discovery, growth, optical properties and applications,” Appl. Phys. B 97, 9–25 (2009). [CrossRef]

8.

T. Kanai, T. Kanda, T. Sekikawa, S. Watanabe, T. Togashi, C. Chen, C. Zhang, Z. Xu, and J. Wang, “Generation of vacuum-ultraviolet light below 160 nm in a KBBF crystal by the fifth harmonic of a single-mode Ti:sapphire laser,” J. Opt. Soc. Am. B 21, 370–375 (2004). [CrossRef]

9.

X. Zhang, L. Wang, X. Wang, G. Wang, Y. Zhu, and C. Chen, “High-power sixth-harmonic generation of an Nd:YAG laser with KBe2BO3F2 prism-coupled devices,” accepted by Opt. Commun. [PubMed]

10.

D. Tang, Y. Xia, B. Wu, and C. Chen, “Growth of a new UV nonlinear optical crystal: KBe2(BO3)F2,” J. Cryst. Growth 222, 125–129 (2001). [CrossRef]

11.

Z. Lin, Z. Wang, C. Chen, S. Chen, and M.-H. Lee, “Mechanism for linear and nonlinear optical effects in KBe2BO3F2 (KBBF) crystal,” Chem. Phys. Lett. 367, 523–527 (2003). [CrossRef]

12.

G. Wang, C. Zhang, C. Chen, Z. Xu, and J. Wang, “Determination of nonlinear optical coefficients of KBe2BO3F2 crystals,” Chin. Phys. Lett. 20, 243–245 (2003). [CrossRef]

13.

C. Chen, J. Lü, G. Wang, Z. Xu, J. Wang, C. Zhang, and Y. Liu, “Deep ultraviolet harmonic generation with KBe2BO3F2 crystal,” Chin. Phys. Lett. 18, 1081 (2001). [CrossRef]

14.

Y. Zhou, G. Wang, C. Li, Q. Peng, D. Cui, Z. Xu, X. Wang, Y. Zhu, C. Chen, G. Liu, X. Dong, and X. Zhou, “Sixth harmonic of a Nd:YVO4 laser generation in KBBF for ARPES,” Chin. Phys. Lett. 25, 963–965 (2008). [CrossRef]

15.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1997).

16.

T. Freegarde, J. Coutts, J. Walz, D. Leibfried, and T. W. Hänsch, “General analysis of type I second-harmonic generation with elliptical Gaussian beams,” J. Opt. Soc. Am. B 14, 2010–2016 (1997). [CrossRef]

17.

M. Scholz, “General treatment of sum-frequency mixing with elliptical Gaussian beams,” J. Opt. Soc. Am. B 29, 1655–1660 (2012). [CrossRef]

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4360) Nonlinear optics : Nonlinear optics, devices

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 27, 2012
Revised Manuscript: July 26, 2012
Manuscript Accepted: July 26, 2012
Published: July 31, 2012

Citation
Matthias Scholz, Dmitrijs Opalevs, Patrick Leisching, Wilhelm Kaenders, Guiling Wang, Xiaoyang Wang, Rukang Li, and Chuangtian Chen, "1.3-mW tunable and narrow-band continuous-wave light source at 191 nm," Opt. Express 20, 18659-18664 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-18659


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References

  1. D. Basting, Excimer Laser Technology (Springer, 2005). [CrossRef]
  2. W. Köchner, Solid-State Laser Engineerung (Springer, 2006).
  3. H. Kouta and Y. Kuwano, “Attaining 186-nm light generation in cooled β-BaB2O4 crystal,” Opt. Lett.24, 1230–1232 (1999). [CrossRef]
  4. F. Seifert, J. Ringling, F. Noack, V. Petrov, and O. Kittelmann, “Generation of tunable femtosecond pulses to as low as 172.7 nm by sum-frequency mixing in lithium triborate,” Opt. Lett.19, 1538–1540 (1994). [CrossRef] [PubMed]
  5. C. Qu, M. Yoshimura, J. Tsunoda, Y. Kaneda, M. Imade, T. Sasaki, and Y. Mori, “189-nm wavelength generation with borate crystals,” Conference Proceedings CLEO: Science and Innovations, Nonlinear Materials and Devices, CF3A (2012).
  6. C. Chen, Y. Wang, Y. Xia, B. Wu, D. Tang, K. Wu, Z. Wenrong, L. Yu, and L. Mei, “New development of nonlinear optical crystals for the ultraviolet region with molecule engineering approach,” J. Appl. Phys.77, 2268–2272 (1994). [CrossRef]
  7. C. Chen, G. Wang, X. Wang, and Z. Xu, “Deep-UV nonlinear optical crystal KBe2BO3F2 - discovery, growth, optical properties and applications,” Appl. Phys. B97, 9–25 (2009). [CrossRef]
  8. T. Kanai, T. Kanda, T. Sekikawa, S. Watanabe, T. Togashi, C. Chen, C. Zhang, Z. Xu, and J. Wang, “Generation of vacuum-ultraviolet light below 160 nm in a KBBF crystal by the fifth harmonic of a single-mode Ti:sapphire laser,” J. Opt. Soc. Am. B21, 370–375 (2004). [CrossRef]
  9. X. Zhang, L. Wang, X. Wang, G. Wang, Y. Zhu, and C. Chen, “High-power sixth-harmonic generation of an Nd:YAG laser with KBe2BO3F2 prism-coupled devices,” accepted by Opt. Commun. [PubMed]
  10. D. Tang, Y. Xia, B. Wu, and C. Chen, “Growth of a new UV nonlinear optical crystal: KBe2(BO3)F2,” J. Cryst. Growth222, 125–129 (2001). [CrossRef]
  11. Z. Lin, Z. Wang, C. Chen, S. Chen, and M.-H. Lee, “Mechanism for linear and nonlinear optical effects in KBe2BO3F2 (KBBF) crystal,” Chem. Phys. Lett.367, 523–527 (2003). [CrossRef]
  12. G. Wang, C. Zhang, C. Chen, Z. Xu, and J. Wang, “Determination of nonlinear optical coefficients of KBe2BO3F2 crystals,” Chin. Phys. Lett.20, 243–245 (2003). [CrossRef]
  13. C. Chen, J. Lü, G. Wang, Z. Xu, J. Wang, C. Zhang, and Y. Liu, “Deep ultraviolet harmonic generation with KBe2BO3F2 crystal,” Chin. Phys. Lett.18, 1081 (2001). [CrossRef]
  14. Y. Zhou, G. Wang, C. Li, Q. Peng, D. Cui, Z. Xu, X. Wang, Y. Zhu, C. Chen, G. Liu, X. Dong, and X. Zhou, “Sixth harmonic of a Nd:YVO4 laser generation in KBBF for ARPES,” Chin. Phys. Lett.25, 963–965 (2008). [CrossRef]
  15. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1997).
  16. T. Freegarde, J. Coutts, J. Walz, D. Leibfried, and T. W. Hänsch, “General analysis of type I second-harmonic generation with elliptical Gaussian beams,” J. Opt. Soc. Am. B14, 2010–2016 (1997). [CrossRef]
  17. M. Scholz, “General treatment of sum-frequency mixing with elliptical Gaussian beams,” J. Opt. Soc. Am. B29, 1655–1660 (2012). [CrossRef]

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