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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 7046–7051
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Variable-wavelength second harmonic generation of CW Yb-fibre laser in partially coupled enhancement cavity

Sergey Khripunov, Daba Radnatarov, Sergey Kobtsev, and Aleksey Skorkin  »View Author Affiliations


Optics Express, Vol. 22, Issue 6, pp. 7046-7051 (2014)
http://dx.doi.org/10.1364/OE.22.007046


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Abstract

This work for the first time proposes and studies a method of frequency doubling of CW non-single-frequency fibre lasers with a high-Q resonator partially coupled to the fibre laser cavity. The proposed new approach resulted in the following parameters: laser’s maximal output power 880 mW at 536 nm when pumped with 6.2 W at 976 nm, wavelength tuneability range 521–545 nm with the output power at the extreme ends of this range 420 and 220 mW correspondingly. The proposed configuration allows efficient non-linear transformation of both CW and pulsed radiation in a partially coupled enhancement cavity.

© 2014 Optical Society of America

1. Introduction

The method of efficient second harmonic generation in external high-finesse optical resonators containing non-linear crystals or other non-linear media is well known [1

1. A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2(6), 109–124 (1966). [CrossRef]

] and until recently has been predominantly applied to non-linear transformation of radiation of single-frequency CW lasers [2

2. W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Second-harmonic generation of a continuous-wave diode-pumped Nd:YAG laser using an externally resonant cavity,” Opt. Lett. 12(12), 1014–1016 (1987). [CrossRef] [PubMed]

5

5. J. I. Kim and D. Meschede, “Continuous-wave coherent ultraviolet source at 326 nm based on frequency trippling of fiber amplifiers,” Opt. Express 16(14), 10803–10808 (2008). [CrossRef] [PubMed]

] or of ultra-short pulses [6

6. M. A. Persaud, J. M. Tolchard, and A. I. Ferguson, “Efficient generation of picosecond pulses at 243 nm,” IEEE J. Quantum Electron. 26(7), 1253–1258 (1990). [CrossRef]

10

10. A. Börzsönyi, R. Chiche, E. Cormier, R. Flaminio, P. Jojart, C. Michel, K. Osvay, L. Pinard, V. Soskov, A. Variola, and F. Zomer, “External cavity enhancement of picosecond pulses with 28,000 cavity finesse,” Appl. Opt. 52(34), 8376–8380 (2013). [CrossRef] [PubMed]

]. In both cases, to achieve efficient frequency doubling it is necessary to match the frequency (or pulse repetition frequency) of the input radiation to the modes of the external cavity. This is done with the help of various methods to automatically adjust the length of the external cavity to match the frequency of the input radiation (or the repetition rate, in case of ultra-short pulses). The most widely used ones are the Hänsch–Couillaud [11

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

] and Pound–Drever–Hall [12

12. 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(2), 97–105 (1983). [CrossRef]

] techniques.

Some recent publications demonstrate the possibility of efficient frequency doubling of non-single-frequency CW radiation of fibre lasers in an enhancement cavity without automatic length adjustment. In [13

13. J. W. Kim, J. Jeong, K. Lee, and S. B. Lee, “Efficient second-harmonic generation of continuous-wave Yb fiber laser coupled with an external resonant cavity,” Appl. Phys. B 108(3), 539–543 (2012). [CrossRef]

], the enhancement cavity was external to the resonator of the fibre laser (Fig. 1(a)
Fig. 1 Schematic diagrams of different configurations of frequency doubling of non-single-frequency CW radiation of fibre lasers in an enhancement cavity without automatic length adjustment.
), while in [14

14. R. Cieslak and W. A. Clarkson, “Internal resonantly enhanced frequency doubling of continuous-wave fiber lasers,” Opt. Lett. 36(10), 1896–1898 (2011). [CrossRef] [PubMed]

] it was inside and effectively acted as a “resonator within resonator” (Fig. 1(b)). In the former configuration of the laser and enhancement cavity, the output mirror was located before, and in the latter configuration, after the enhancement cavity. Both approaches demonstrated feasibility of their configurations and their good efficiency.

The subject of the present study is a new approach to frequency doubling, in which the enhancement cavity is neither external nor internal to the pump laser resonator but is only partially coupled to it (Fig. 1(c)). In this approach, the output mirror of the laser resonator is placed inside the enhancement cavity and, correspondingly, a portion of the enhancement cavity is shared by the enhancement cavity and the laser resonator. This technique also demonstrated good frequency doubling efficiency combined with a possibility of tuning of the second harmonic radiation wavelength within a broad spectral range.

2. Experimental set-up and results

The experimental installation is schematically shown in Fig. 2
Fig. 2 Experimental set-up of the Yb-doped fibre laser with a partially coupled enhancement cavity: M1–M4 – mirrors of the enhancement cavity; M5, M6 – end mirrors of the fibre laser linear resonator.
. The pump radiation at 976 nm is guided through a fibre beam combiner into a 3-m long active double-clad ytterbium fibre with a 10-µm core (NA = 0.08). Yb-doped fibre laser has free-space optical elements on both ends of its linear cavity. The laser radiation is directed onto them through the fibre ends cleaved at 8 degrees and collimators. One of the ends of the fibre laser cavity is terminated with a discrete polariser and a spectrally selective reflector consisting of a prism and a mirror. The polariser combined with the polarisation-maintaining fibre used in the cavity ensures linearly polarised laser radiation. Spectrally selective reflector allows tuning of the laser radiation wavelength within the spectral gain band of the active medium.

At the other end of the fibre laser’s linear cavity, free-space elements include a high-Q four-mirror resonator with a non-linear LBO crystal inside, as well as a focusing element and a polarisation element for mode and polarisation matching of the input radiation to the parameters of the four-mirror resonator. Three of the high-Q resonator mirrors are totally reflective to the fundamental laser harmonics, while the resonator input mirror has transmittance of several per cent, which depends on the radiation wavelength. The 20-mm long non-linear LBO crystal with anti-reflection-coated working surfaces orthogonal to the beam is positioned between two spherical mirrors with equal radii of 75 mm. The crystal is placed inside a high-temperature thermostat to ensure type I non-critical phase-matched second harmonic generation at the temperature of around 150 °С stable to ± 0.05 °С. The anti-reflection coatings of the non-linear crystal cover wavelengths within ranges 1030–1100 nm and 515–550 nm. Spherical mirror M4 of the four-mirror resonator is dichroic: it reflects radiation with wavelengths within 1030–1100 nm and transmits radiation at wavelengths between 515 and 550 nm.

The anti-reflection-coated surface of the non-linear crystal closest to the input mirror of the enhancement cavity plays the role of the fibre laser output coupler (mirror M6, Fig. 2). As it turned out, reflection (0.2%) from this surface is sufficient to establish feed-back in the fibre laser resonator. All other flat surfaces of laser resonator elements (fibre ends, polariser faces, etc.) are inclined relative to the resonator axis so that radiation reflected from them cannot enter the fibre laser resonator. Location of the fibre laser output coupler within the enhancement cavity poses natural limits on the reflectivity of this mirror: the more reflective it is, the lower will be the Q-factor of the four-mirror cavity. Therefore, to maximise the enhancement cavity’s Q-factor, reflectivity of this mirror must be minimal. At the same time, too low reflectivity of the fibre laser output coupler may reduce the output power of the fibre laser. It is necessary to note that for some models of CW fibre lasers [15

15. X. Liao and C. Huang, “Optimization of Yb3+-doped double-clad fiber lasers using a new approximate analytical solution,” Opt. Laser Technol. 43(1), 55–61 (2011). [CrossRef]

] it is indicated that the optimal reflectivity of the output coupler for them should be below 1%. To confirm this indication, a separate special study would be required. Nevertheless, the results of the present work demonstrate that in the proposed optical layout, an output coupler with reflectivity 0.2% effectively increases the power of laser radiation in the partially coupled enhancement cavity.

The high-Q four-mirror cavity in a bow-tie configuration provides enhancement of the fundamental radiation power to the level of over 30 W when pumped with 6.2 W at 976 nm. The radius of the beam waist within which the non-linear crystal is positioned is close to the optimum given by the Boyd-Kleinman theory [16

16. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39(8), 3597–3639 (1968). [CrossRef]

] for the used crystal and amounts to approximately 30 µm. The laser radiation spectrum is narrowed down by the prism to 0.5 nm, which is within the spectral width of the non-linear crystal phase matching, equal to 1.8 nm. In analogy to [14

14. R. Cieslak and W. A. Clarkson, “Internal resonantly enhanced frequency doubling of continuous-wave fiber lasers,” Opt. Lett. 36(10), 1896–1898 (2011). [CrossRef] [PubMed]

], the fibre laser operates in those longitudinal modes of the fibre laser cavity, which are also resonant for the enhancement cavity. To fulfil this condition, it is sufficient for the fibre laser resonator to be much longer than the enhancement cavity. In this study, the fibre laser resonator is more than 6 times as long as the enhancement cavity.

The second harmonic radiation is predominantly generated in one direction, towards mirror M4. The power of the second harmonics generated in the opposite direction (towards mirror M3) is comparatively low and does not exceed several mW. This effectively means that the fundamental radiation inside the partially coupled enhancement cavity is present as a unidirectional running wave.

The maximal achieved power of the second harmonic radiation at 536 nm is 880 mW in TEM00 mode (Fig. 3
Fig. 3 Second harmonic output power dependence on pump power (976 nm). The inset picture shows the beam profile of the second harmonic radiation.
). The corresponding overall power conversion efficiency from pump power (976 nm) to green power (536 nm) is more than 14%. The wavelength of the fundamental harmonics is tuned within the 1042–1090 nm range by rotating mirror M5. The wavelength of the second harmonics is synchronously tuned by adjustment of the temperature of the non-linear crystal. The dependence of the second harmonic power upon wavelength is shown in Fig. 4
Fig. 4 Dependence of the second harmonic output power and transmission of the input mirror of the enhancement cavity on wavelength.
. The same Fig. 4 also demonstrates the dependence of transmittance of input mirror M1 of the four-mirror cavity upon wavelength. Within the generation range of 1042–1090 nm, this transmittance varies from 2% to 16%, and the maximum of the second harmonic output power is reached at the wavelength of 1072 nm, for which the transmittance of input mirror M1 is equal to 5%. The demonstrated tuning range of the second harmonic wavelength was 521–545 nm, and the output power of the green radiation at the extremes of this spectral range was 420 and 220 mW respectively. Significant reduction of the second harmonic output away from the central wavelength corresponding to the maximum (536 nm) occurs because of non-optimal transmission of input mirror M1 at other wavelengths. Without the enhancement cavity (an output mirror with transmission of 4% was used in its stead), power excursion of the fundamental radiation did not exceed 40% of the maximum as the generation wavelength of the fibre laser was tuned within the 1035–1100 nm.

At green output power level of up to ~500 mW, instability of the output radiation power did not exceed 2–3%/s and was in our opinion primarily caused by imperfections of the experimental set-up (open layout, air movements, mechanical instability of unconnectorized fibre ends, etc.). At the output power level over 500 mW, the output spectrum of the laser became increasingly unstable and the fundamental wavelength could jump by as much as 0.4–0.6 nm, indicating insufficient spectral selectivity of the prism at higher power levels. Fundamental wavelength hops led to greater second harmonic power instability, which could be as high as 15–20%. A more spectrally selective element (for example, a diffraction grating) will be able to suppress fundamental wavelength hops at higher powers and reduce the green output power instability at least to within several per cent.

It is pertinent to note that in the studied configuration, coupling of the enhancement cavity to the laser resonator is comparatively strong, since generation occurs at those laser frequencies, which are also resonant for the enhancement cavity. Otherwise, the laser radiation would not reach the non-linear crystal, being almost totally reflected from the input mirror of the enhancement cavity.

In the studied configuration, transmission of the output mirror of the laser resonator remains constant (0.2%). However, the power of radiation reflected from it increases as the radiation power inside the enhancement cavity grows. Correspondingly, effective reflectivity of the output mirror placed inside the cavity is also variable and depends on the intra-cavity power, which in its turn depends on the relative amount of energy exiting the cavity because of second harmonic generation. Therefore, effective transmittance of the output mirror in the studied configuration depends on the relative energy coupled out of the cavity as the second harmonic radiation. This is the key feature of an output mirror contained within an enhancement cavity.

The essential difference of the proposed configuration from the one described in [14

14. R. Cieslak and W. A. Clarkson, “Internal resonantly enhanced frequency doubling of continuous-wave fiber lasers,” Opt. Lett. 36(10), 1896–1898 (2011). [CrossRef] [PubMed]

] is that no fundamental radiation must be coupled out of the enhancement cavity in order to provide feed-back. When this is necessary (as it is in [14

14. R. Cieslak and W. A. Clarkson, “Internal resonantly enhanced frequency doubling of continuous-wave fiber lasers,” Opt. Lett. 36(10), 1896–1898 (2011). [CrossRef] [PubMed]

]), two mirrors of the enhancement cavity cannot be totally reflective, thus reducing finesse of the cavity in the configuration “resonator within resonator”.

Among other differences of the proposed approach from the one discussed in [14

14. R. Cieslak and W. A. Clarkson, “Internal resonantly enhanced frequency doubling of continuous-wave fiber lasers,” Opt. Lett. 36(10), 1896–1898 (2011). [CrossRef] [PubMed]

], one can mention a substantially lower second harmonic generation threshold relative to the pump radiation power. In the proposed configuration it amounts to 2.4 W, whereas in [14

14. R. Cieslak and W. A. Clarkson, “Internal resonantly enhanced frequency doubling of continuous-wave fiber lasers,” Opt. Lett. 36(10), 1896–1898 (2011). [CrossRef] [PubMed]

] it was as high as 6 W. Furthermore, a non-linear crystal with Brewster faces used in [14

14. R. Cieslak and W. A. Clarkson, “Internal resonantly enhanced frequency doubling of continuous-wave fiber lasers,” Opt. Lett. 36(10), 1896–1898 (2011). [CrossRef] [PubMed]

] creates additional losses (~19%) for the s-polarised second harmonic radiation because of its reflection from Brewster faces.

3. Conclusion

The proposed technique of fibre laser radiation frequency doubling in a partially coupled enhancement four-mirror cavity offers relatively high efficiency of variable-wavelength second harmonic generation combined with a comparatively simple set of required components. Among the major advantages of the proposed technique are relatively low second harmonic generation threshold and comparatively high efficiency of the second harmonic generation at relatively low pump power. Tuning of the radiation wavelength is done by rotating a quartz prism, and an anti-reflection-coated face of the non-linear crystal serves as the output coupler of the fibre laser resonator. The proposed approach may be used not only for second harmonic generation of non-single-frequency CW radiation in a enhancement cavity, but also for other types of non-linear conversion of CW and pulsed radiation in a high-Q cavity, such as parametric oscillation, Raman conversion, etc. The proposed method does not require automatic adjustment of the enhancement cavity length. Laser generation occurs at frequencies, which are common for the fibre laser resonator and the enhancement cavity. The developed configuration may be also used for non-linear conversion of pulsed radiation in an enhancement cavity, and the duration of input pulses may be as short as 1 ps (spectral width of such pulses does not exceed the spectral width of phase matching in the employed non-linear crystal). This configuration also allows easy automatic tuning of the second harmonic wavelength within a broad spectral range by synchronous tilting of the resonator’s end mirror and adjustment of the non-linear crystal temperature.

Feeding the fibre laser radiation into an enhancement cavity through a low-reflectivity output coupler located inside this cavity represents a new promising approach to non-linear transformation of radiation in a partially coupled enhancement cavity.

Acknowledgments

This work was supported by the Marie-Curie International Exchange Scheme, Research Executive Agency Grant “TelaSens” No 269271; Grants of Ministry of Education and Science of the Russian Federation (agreement No. 14.B25.31.0003, basic research order); Russian President Grant MK-4683.2013.2; Council of the Russian President for the Leading Research Groups (project No. NSh-4447.2014.2).

References and links

1.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2(6), 109–124 (1966). [CrossRef]

2.

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Second-harmonic generation of a continuous-wave diode-pumped Nd:YAG laser using an externally resonant cavity,” Opt. Lett. 12(12), 1014–1016 (1987). [CrossRef] [PubMed]

3.

C. S. Adams and A. I. Ferguson, “Frequency doubling of a single frequency Ti:Al2O3 laser using an external enhancement cavity,” Opt. Commun. 79(3-4), 219–223 (1990). [CrossRef]

4.

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, and F. Biraben, “Efficient frequency doubling of a continuous wave titanium: sapphire laser in an external enhancement cavity,” Opt. Commun. 99(1-2), 89–94 (1993). [CrossRef]

5.

J. I. Kim and D. Meschede, “Continuous-wave coherent ultraviolet source at 326 nm based on frequency trippling of fiber amplifiers,” Opt. Express 16(14), 10803–10808 (2008). [CrossRef] [PubMed]

6.

M. A. Persaud, J. M. Tolchard, and A. I. Ferguson, “Efficient generation of picosecond pulses at 243 nm,” IEEE J. Quantum Electron. 26(7), 1253–1258 (1990). [CrossRef]

7.

R. J. Jones and J. Ye, “High-repetition-rate coherent femtosecond pulse amplification with an external passive optical cavity,” Opt. Lett. 29(23), 2812–2814 (2004). [CrossRef] [PubMed]

8.

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 436(7048), 234–237 (2005). [CrossRef] [PubMed]

9.

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4(3), 170–173 (2010). [CrossRef]

10.

A. Börzsönyi, R. Chiche, E. Cormier, R. Flaminio, P. Jojart, C. Michel, K. Osvay, L. Pinard, V. Soskov, A. Variola, and F. Zomer, “External cavity enhancement of picosecond pulses with 28,000 cavity finesse,” Appl. Opt. 52(34), 8376–8380 (2013). [CrossRef] [PubMed]

11.

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

12.

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(2), 97–105 (1983). [CrossRef]

13.

J. W. Kim, J. Jeong, K. Lee, and S. B. Lee, “Efficient second-harmonic generation of continuous-wave Yb fiber laser coupled with an external resonant cavity,” Appl. Phys. B 108(3), 539–543 (2012). [CrossRef]

14.

R. Cieslak and W. A. Clarkson, “Internal resonantly enhanced frequency doubling of continuous-wave fiber lasers,” Opt. Lett. 36(10), 1896–1898 (2011). [CrossRef] [PubMed]

15.

X. Liao and C. Huang, “Optimization of Yb3+-doped double-clad fiber lasers using a new approximate analytical solution,” Opt. Laser Technol. 43(1), 55–61 (2011). [CrossRef]

16.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39(8), 3597–3639 (1968). [CrossRef]

17.

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

OCIS Codes
(140.3410) Lasers and laser optics : Laser resonators
(140.3510) Lasers and laser optics : Lasers, fiber
(140.3600) Lasers and laser optics : Lasers, tunable
(140.3515) Lasers and laser optics : Lasers, frequency doubled
(230.4555) Optical devices : Coupled resonators

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 24, 2014
Revised Manuscript: March 4, 2014
Manuscript Accepted: March 4, 2014
Published: March 18, 2014

Citation
Sergey Khripunov, Daba Radnatarov, Sergey Kobtsev, and Aleksey Skorkin, "Variable-wavelength second harmonic generation of CW Yb-fibre laser in partially coupled enhancement cavity," Opt. Express 22, 7046-7051 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-7046


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References

  1. A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2(6), 109–124 (1966). [CrossRef]
  2. W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Second-harmonic generation of a continuous-wave diode-pumped Nd:YAG laser using an externally resonant cavity,” Opt. Lett. 12(12), 1014–1016 (1987). [CrossRef] [PubMed]
  3. C. S. Adams, A. I. Ferguson, “Frequency doubling of a single frequency Ti:Al2O3 laser using an external enhancement cavity,” Opt. Commun. 79(3-4), 219–223 (1990). [CrossRef]
  4. S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben, “Efficient frequency doubling of a continuous wave titanium: sapphire laser in an external enhancement cavity,” Opt. Commun. 99(1-2), 89–94 (1993). [CrossRef]
  5. J. I. Kim, D. Meschede, “Continuous-wave coherent ultraviolet source at 326 nm based on frequency trippling of fiber amplifiers,” Opt. Express 16(14), 10803–10808 (2008). [CrossRef] [PubMed]
  6. M. A. Persaud, J. M. Tolchard, A. I. Ferguson, “Efficient generation of picosecond pulses at 243 nm,” IEEE J. Quantum Electron. 26(7), 1253–1258 (1990). [CrossRef]
  7. R. J. Jones, J. Ye, “High-repetition-rate coherent femtosecond pulse amplification with an external passive optical cavity,” Opt. Lett. 29(23), 2812–2814 (2004). [CrossRef] [PubMed]
  8. C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436(7048), 234–237 (2005). [CrossRef] [PubMed]
  9. R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4(3), 170–173 (2010). [CrossRef]
  10. A. Börzsönyi, R. Chiche, E. Cormier, R. Flaminio, P. Jojart, C. Michel, K. Osvay, L. Pinard, V. Soskov, A. Variola, F. Zomer, “External cavity enhancement of picosecond pulses with 28,000 cavity finesse,” Appl. Opt. 52(34), 8376–8380 (2013). [CrossRef] [PubMed]
  11. T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35(3), 441–444 (1980). [CrossRef]
  12. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983). [CrossRef]
  13. J. W. Kim, J. Jeong, K. Lee, S. B. Lee, “Efficient second-harmonic generation of continuous-wave Yb fiber laser coupled with an external resonant cavity,” Appl. Phys. B 108(3), 539–543 (2012). [CrossRef]
  14. R. Cieslak, W. A. Clarkson, “Internal resonantly enhanced frequency doubling of continuous-wave fiber lasers,” Opt. Lett. 36(10), 1896–1898 (2011). [CrossRef] [PubMed]
  15. X. Liao, C. Huang, “Optimization of Yb3+-doped double-clad fiber lasers using a new approximate analytical solution,” Opt. Laser Technol. 43(1), 55–61 (2011). [CrossRef]
  16. G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39(8), 3597–3639 (1968). [CrossRef]
  17. I. Pupeza, Power Scaling of Enhancement Cavities for Nonlinear Optics (Springer, 2012).

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