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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 28 — Dec. 31, 2012
  • pp: 29659–29664
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Triple-wavelength Nd-laser system by cascaded electro-optic periodically poled lithium niobate Bragg modulator

Shou-Tai Lin and Chuan-Sheng Hsieh  »View Author Affiliations


Optics Express, Vol. 20, Issue 28, pp. 29659-29664 (2012)
http://dx.doi.org/10.1364/OE.20.029659


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Abstract

This study presents a diode-pumped cw triple-wavelength Nd:GdVO4 laser system using an electro-optic periodically poled lithium niobate (PPLN) Bragg modulator. The PPLN consists of two cascaded sections, 20.3 μm and 25.7 μm, functioning as loss modulators for 1063 and 1342 nm at the same Bragg incident angle. When switching the dc voltages on PPLN and applying 25 W pump power, the output wavelength can be selected among 912, 1063, and 1342 nm with output power of 2, 5, and 1.4 W, respectively. The device is capable of triple-wavelength generation simultaneous when applied voltages are 180 (Λ = 20.3 μm) and −50 V (Λ = 25.7 μm) at a 25 W pump power. Gain competition induced power instability was also observed.

© 2012 OSA

1. Introduction

Diode-pumped Nd-laser systems have been widely used because of the compactness and high conversion efficiency. Three fundamental wavelengths, 0.9, 1 and 1.3 μm, from the transition of 4F3/24I9/2, 4F3/24I11/2, and 4F3/24I13/2, have unique applications in laser spectroscopy, medical treatment, and two-photon microscopy. Through the frequency-doubling process into the visible region, the blue, green, and red lasers are useful for display, hologram, and fluorescence spectroscopy. However, the huge emission cross-section differences between each transition increase the difficulty of simultaneously generating multi wavelengths. For an Nd:GdVO4 laser crystal, the ratio of the emission cross section between the 4F3/24I9/2, 4F3/24I11/2, and 4F3/24I13/2 is approximately 1:18.9:5.1 [1

1. C. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981. [CrossRef]

]. To balance the line competition of resonated waves, adjusted cavity-mode matching [2

2. Y. F. Chen, “cw dual-wavelength operation of a diode-end-pumped Nd:YVO4 laser,” Appl. Phys. B 70(4), 475–478 (2000), http://www.springerlink.com/content/lepeuct3fen8ab4l/. [CrossRef]

], varied output coupler [3

3. L. Chen, Z. Wang, H. Liu, S. Zhuang, H. Yu, L. Guo, R. Lan, J. Wang, and X. Xu, “Continuous-wave tri-wavelength operation at 1064, 1319 and 1338 nm of LD end-pumped Nd:YAG ceramic laser,” Opt. Express 18(21), 22167–22173 (2010). [CrossRef] [PubMed]

], and multiple gain medium [4

4. E. Herault, F. Balembois, and P. Georges, “491 nm generation by sum-frequency mixing of diode pumped neodymium lasers,” Opt. Express 13(15), 5653–5661 (2005). [CrossRef] [PubMed]

] are adopted. Herault [4

4. E. Herault, F. Balembois, and P. Georges, “491 nm generation by sum-frequency mixing of diode pumped neodymium lasers,” Opt. Express 13(15), 5653–5661 (2005). [CrossRef] [PubMed]

] reported dual-wavelength laser operation between 4F3/24I9/2 and 4F3/24I11/2. The 912 nm only existed when the intracavity power of 1063 nm remained below a few watts. The current study reports a novel configuration to actively modulate the loss of 4F3/24I11/2 (1 μm) and 4F3/24I13/2 (1.3 μm). The following discussion shows a first wavelength-switchable Nd-laser among three fundamental wavelengths by a cascaded electro-optic periodic poled lithium niobate Bragg modulators (EPBM). Dual or triple-wavelength emission can be also achieved by manipulating the loss of 1 and 1.3 μm.

Periodically poled lithium niobate (PPLN) crystals [5

5. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12(11), 2102–2116 (1995), http://www.opticsinfobase.org/josab/abstract.cfm?id=33615. [CrossRef]

] have attracted considerable attention because their collinear process uses the largest nonlinear coefficient, and changes the phase-matching condition by the lithography process. In addition to using the PPLN crystal as a frequency converter, Lin et al. [6

6. Y. Y. Lin, S. T. Lin, G. W. Chang, A. C. Chiang, Y. C. Huang, and Y. H. Chen, “Electro-optic periodically poled lithium niobate Bragg modulator as a laser Q-switch,” Opt. Lett. 32, 545–547 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?id=125673. [CrossRef] [PubMed]

] demonstrated the Q-switching process in an EPBM. When a laser passes through the EPBM at Bragg incident angle θB,m = sin−1(mλ0/(2nΛ)), the laser is deflected to a certain angle matching momentum conservation, where m is the diffraction order, λ0 is the laser wavelength, n is the average refractive index of the grating, and Λ is the grating period. Because the Bragg angle condition means another phase-matching condition for deflecting the certain wavelength, cascaded PPLN gratings can be designed for several wavelengths at the same Bragg angle in a single device. Table 1

Table 1. Calculated PPLN grating periods for matching the same Bragg incident angle (0.7°) at 1.063 and 1.342 μm.

table-icon
View This Table
shows the design of PPLN grating periods for diffracting 1.063 and 1.342 μm at the same Bragg incident angle (0.7 degree). Since the EPBM is insensitive to the temperature [6

6. Y. Y. Lin, S. T. Lin, G. W. Chang, A. C. Chiang, Y. C. Huang, and Y. H. Chen, “Electro-optic periodically poled lithium niobate Bragg modulator as a laser Q-switch,” Opt. Lett. 32, 545–547 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?id=125673. [CrossRef] [PubMed]

], multi-function device including frequency converter, Bragg deflector and phase modulator can be integrated monolithically [7

7. S. T. Lin, G. W. Chang, Y. Y. Lin, Y. C. Huang, A. C. Chiang, and Y. H. Chen, “Monolithically integrated laser Bragg Q-switch and wavelength converter in a PPLN crystal,” Opt. Express 15(25), 17093–17098 (2007). [CrossRef] [PubMed]

]. In the current design, the grating period of 20.3 μm is also matched the 3rd order second harmonic generation (SHG) for 1/1063 + 1/1063 →1/531.5.

2. Experimental setup

Figure 1
Fig. 1 Schematic of the wavelength switchable Nd:GdVO4 laser pumped by a 808 nm diode laser. The EPBM1 and EPBM2 function as a loss modulator for 1063 and 1342 nm, respectively. The 912 nm laser cavity was formed by the M1 and output coupler M2. The 1063 and 1342 laser cavity were formed by M1, M3, M4, and output coupler M5.
shows a schematic of a wavelength switchable through EPBM in a diode-pumped Nd:GdVO4 laser. The PPLN adopted in this paper was a 2-mm-thick 5 mol.% MgO:PPLN (made by HC Photonics, Taiwan). The dimensions of EPBM were 10 mm (width in x) x 15.5 mm (length in y) x 2 mm (thickness in z) and were separated in two sections, EPBM1 and EPBM2, for diffracting 1064 and 1342 nm at the same Bragg angle θB,1(1064 nm) = θB,1(1342 nm) = 0.7°. The grating period of EPBM1 was 20.3 μm, and the dimensions were 10 mm (width in x) x 8 mm (length in y). The grating period of EPBM2 was 25.7 μm, and the dimensions were 10 mm (width in x) x 5.5 mm (length in y). Using a cw laser with approximately 200 mW at 1063 nm, the half-wave voltages of the 20.3 and 25.74 μm gratings were measured at 740 and 1020 V, respectively. The input faces of the EPBM are optically polished and have anti-reflection coating at 1063 and 1342 nm (R<1%). The NiCr electrodes were coated on ± z surfaces. To independently apply the electric field, an uncoated electrode of 2 mm was placed between EPBM1 and EPBM2. This study used a 25 W fiber-pigtailed diode laser at 808 nm pumped an a-cut 0.1-at.% 5-mm-long Nd-doped GdVO4 crystal through a set of 1 to 2 coupling lenses. The diameter of the fiber core was 200 μm. The reduced Nd doping level helped diminish the reabsorption loss in a 912 nm cavity [9

9. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423 (1988), http://www.opticsinfobase.org/josab/abstract.cfm?id=5205. [CrossRef]

] and absorbed only 55% diode power. The Nd:GdVO4 crystal was wrapped by indium foil and kept in a copper housing for water cooling at 18 °C. The two end surfaces of the Nd:GdVO4 crystal are optically polished and have anti-reflection coating (R<1%) at 808, 912, 1063, and 1342 nm. The 912 nm laser cavity was formed by a flat high reflection (HR) (R>99.8%) coated mirror M1 and mirror M2 with 300 mm radical of curvature (ROC). Mirror M2 has a 3% output coupling at 912 nm and a high transmission coating (HT) (T>99%) at 1063 and 1342 nm. The 1063 and 1342 nm lasers share the same z-folded cavity constructed by M1, M3, M4, and M5. M3 and M4 are concave mirrors with ROC 300 and 100 mm, respectively, and both have an HR coating (R>99.8%) at 1063 and 1342 nm. To efficiently couple out the 912 nm, M3 was also coated with HT coating (T>95%) at 912 nm. The 1063 and 1342 nm lasers were coupled out through the flat end mirror M5 with 35 and 7% output coupling, respectively. The distance between M1 and M3 is 130 mm, and that between M1 and M4 was 420 mm. The total z-folded cavity length was approximately 500 mm. The thermal focal length in the gain medium was estimated to be 30-40 cm at a pump power of 25 W. When the thermal focal length of the Nd:GdVO4 crystal varied, the beam radius inside the EPBM was calculated between 280 and 300 μm at 1063 nm, contributing to more than a 70% loss of modulation at a half-wave voltage [7

7. S. T. Lin, G. W. Chang, Y. Y. Lin, Y. C. Huang, A. C. Chiang, and Y. H. Chen, “Monolithically integrated laser Bragg Q-switch and wavelength converter in a PPLN crystal,” Opt. Express 15(25), 17093–17098 (2007). [CrossRef] [PubMed]

].

The performance of the 1063 nm laser was first characterized. At a pump power of 10 W, Fig. 2
Fig. 2 Output power of 1063 nm versus applied voltage on EPBM sections at 10 W pump power. The filled and open circles represent the output power when the EPBM2 and EPBM1 are fixed at 0 and −300 V, respectively.
shows the output power of 1063 nm through applied voltages of EPBM1 and EPBM2. We first turned off the applied voltage on EPBM2 and recorded the output power as a function of applied voltage on EPBM1 (filled circle). Because of the strong stress-induced refractive index change [10

10. Y. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett. 93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1. [CrossRef]

] in MgO:PPLN, the highest output power (approximately 0.83 W) of the 1063 nm laser was measured at −300 V, and the modulated loss was higher than the gain at 300 V. Then we fixed the EPBM1 = −300 V and varied the applied voltage of EPBM2 (open circle). The maximum output power of 1063 nm was also appeared at EPBM2 = −300 V. Although EPBM2 (Λ = 25.74 μm) did not match the Bragg angle at 1063 nm, the high order Bragg grating and side-band coupling effects still affected the performance at 1063 nm. When both EPBM sections were operated at 300 V, the 1063 nm did not lase until reaching the maximum diode power. The stress-induced refractive index change was calculated as 2x10−5, and then found that it can be eliminated through an annealing process. In this study, we still adopted EPBM chips without the annealing process.

3. Experimental result

After characterizing the performances of EPBM, Fig. 3
Fig. 3 Measured output power of 912, 1063, and 1342 nm when switching dc voltages on EPBM sections. 912 nm: EPBM1 = EPBM2 = 300 V, 1063 nm: EPBM1 = EPBM2 = −300 V, 1342 nm: EPBM1 = 20 V, EPBM2 = −300 V
shows the measured output power of three wavelengths at different applied voltages. To ensure the lasing of 912 nm cavity, a 300 dc voltage was applied at both EPBM1 and EPBM2 to provide high loss at 1063, and 1342 nm cavity. The open triangle shows the measured 912 nm output power versus pump power. After overcoming the threshold at 10.5 W, the 912 nm output power reached 2 W at a 25 W pump power. The slope efficiency was calculated at approximately 13.25%. Until the pump power reached 25 W, there was no measured output of 1063 or 1342 nm. The generation of 1342 nm was realized when EPBM1 and EPBM2 were operated at 20 V and −300 V, respectively. The threshold was found at 5 W, and the maximum output power was measured ~1.4 W at 21 W pump power. Moderate loss on EPBM1 (1063 nm) was applied because the output power of 1342 nm was found to decrease effectively while the applied loss of 1063 nm was increased. Dual-wavelength lasing between 1063 and 1342 nm occurred when the pump power exceeded 21 W. This dual-wavelength laser provides the possibility to use in the application of two-color spectroscopy, to process sum-frequency mixing into the sodium region and to utilize in the pump-probe system. The generation of 1063 nm was achieved by removing the stress-induced refractive index change through the applied −300 V on both EPBM sections. The threshold appeared at 2.3 W and reached a 5 W output at a 25 W pump power. The 912 and 1342 nm were completely suppressed during the line competition. Therefore, the laser wavelength was switchable by applying the voltage on EPBM. This is the first demonstration of a triple-wavelength switchable laser system.

Figure 4
Fig. 4 Far-field beam profiles at maximum output power: (a)912 nm, (b) 1063 nm, (c)1342 nm.
shows the spacial profile of three wavelengths at the maximum output power. The transverse mode with Gaussian distribution shows the beam quality of this switchable laser system. Further beam quality characterization was conducted by the standard knife-edge measurement. The M2 values of 912, 1063 and 1342 nm are measured to be 1.3, 1.8, and 1.4, respectively.

Because EPBM has the ability to actively control the loss of 1063 and 1342 nm, we were searching for a balanced point to generate three wavelengths simultaneously. When the pump power was 25 W, triple-wavelength lasing among 912, 1063, and 1342 nm was produced at biased voltages of EPBM1 = 180 and EPBM2 = −50 V. The output power of all three wavelengths was approximately 100 mW. Two dichroic mirrors were used to combine 912 and 1063/1342 nm into an optical spectrum analyzer, as shown in Fig. 5
Fig. 5 Measured optical spectrum at triple-wavelength lasing scheme. At 25 W pump power, three fundamental wavelengths of Nd:GdVO4 laser can be generated simultaneously with output power ~100 mW for each wavelength. The applied voltages on EPBM1 and EPBM2 are 180 and −50 V, respectively.
. This is the first report of triple-wavelength lasing at a single-laser cavity. Because of the strong line competition among three wavelengths at the 4F3/2 energy level, the power fluctuation was increased effectively. To trace the short term stability, three photodiodes were used to monitor each wavelength, as shown in Fig. 6
Fig. 6 10 seconds power fluctuation of three wavelengths at single and triple wavelength scheme: (a)912 nm, (b)1063 nm, (c)1342 nm.
. At the full pump power and single-wavelength lasing scheme, the 10 second rms power variation of 912, 1063, and 1342 nm was 1%, 1.6%, and 6.2%, respectively. However the 10 second rms power variation of 912, 1063, and 1342 nm was increased to 14%, 20.2%, and 10.5%, respectively, in the triple-wavelength scheme. The power fluctuation of 912 and 1063 nm was severe because of the huge cross section difference. During the gain competition, 912 nm was in a disadvantage position compared with 1063 nm, as shown in Fig. 6(a) and 6(b). Since the triple-wavelength scheme belongs to the critical equilibrium, any perturbations including pump power variation, thermal issue or vibration will unbalance the equilibrium. Without any feedback control, triple-wavelength scheme can only sustain in 10 minutes and switch to the single-wavelength scheme. Because 4F3/24I11/2 has the largest emission cross section, 1063 nm was usually survived.

4. Conclusion

In conclusion, we have demonstrated for the first time a cw triple-wavelength-selectable scheme involving cascaded electro-optic periodically poled lithium niobate Bragg modulator in a diode-pumped Nd:GdVO4 laser. At 25 W pump power, the wavelength can be switched among 912, 1063, and 1342 nm with output power of 2, 5, and 1.4 W, respectively. Simultaneously triple fundamental wavelengths generation can be also realized by controlling the loss of 4F3/24I11/2 (EPBM1 = 180 V), and 4F3/24I13/2 (EPBM2 = −50 V). The performance of the EPBM allows to choose the output wavelength of Nd:GdVO4 laser by switching the dc voltages and integrate monolithically with frequency conversion process which is useful in practical applications.

Acknowledgments

This work was supported by National Science Council under Contract NSC 100-2221-E-035-063-MY3. The authors thank HC Photonics for providing high quality 2-mm-thick MgO:PPLN.

References and links

1.

C. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981. [CrossRef]

2.

Y. F. Chen, “cw dual-wavelength operation of a diode-end-pumped Nd:YVO4 laser,” Appl. Phys. B 70(4), 475–478 (2000), http://www.springerlink.com/content/lepeuct3fen8ab4l/. [CrossRef]

3.

L. Chen, Z. Wang, H. Liu, S. Zhuang, H. Yu, L. Guo, R. Lan, J. Wang, and X. Xu, “Continuous-wave tri-wavelength operation at 1064, 1319 and 1338 nm of LD end-pumped Nd:YAG ceramic laser,” Opt. Express 18(21), 22167–22173 (2010). [CrossRef] [PubMed]

4.

E. Herault, F. Balembois, and P. Georges, “491 nm generation by sum-frequency mixing of diode pumped neodymium lasers,” Opt. Express 13(15), 5653–5661 (2005). [CrossRef] [PubMed]

5.

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12(11), 2102–2116 (1995), http://www.opticsinfobase.org/josab/abstract.cfm?id=33615. [CrossRef]

6.

Y. Y. Lin, S. T. Lin, G. W. Chang, A. C. Chiang, Y. C. Huang, and Y. H. Chen, “Electro-optic periodically poled lithium niobate Bragg modulator as a laser Q-switch,” Opt. Lett. 32, 545–547 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?id=125673. [CrossRef] [PubMed]

7.

S. T. Lin, G. W. Chang, Y. Y. Lin, Y. C. Huang, A. C. Chiang, and Y. H. Chen, “Monolithically integrated laser Bragg Q-switch and wavelength converter in a PPLN crystal,” Opt. Express 15(25), 17093–17098 (2007). [CrossRef] [PubMed]

8.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/. [CrossRef]

9.

W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423 (1988), http://www.opticsinfobase.org/josab/abstract.cfm?id=5205. [CrossRef]

10.

Y. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett. 93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1. [CrossRef]

OCIS Codes
(140.3480) Lasers and laser optics : Lasers, diode-pumped
(190.4360) Nonlinear optics : Nonlinear optics, devices
(230.2090) Optical devices : Electro-optical devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: October 31, 2012
Revised Manuscript: December 8, 2012
Manuscript Accepted: December 10, 2012
Published: December 20, 2012

Citation
Shou-Tai Lin and Chuan-Sheng Hsieh, "Triple-wavelength Nd-laser system by cascaded electro-optic periodically poled lithium niobate Bragg modulator," Opt. Express 20, 29659-29664 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-28-29659


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References

  1. C. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun.205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 . [CrossRef]
  2. Y. F. Chen, “cw dual-wavelength operation of a diode-end-pumped Nd:YVO4 laser,” Appl. Phys. B70(4), 475–478 (2000), http://www.springerlink.com/content/lepeuct3fen8ab4l/ . [CrossRef]
  3. L. Chen, Z. Wang, H. Liu, S. Zhuang, H. Yu, L. Guo, R. Lan, J. Wang, and X. Xu, “Continuous-wave tri-wavelength operation at 1064, 1319 and 1338 nm of LD end-pumped Nd:YAG ceramic laser,” Opt. Express18(21), 22167–22173 (2010). [CrossRef] [PubMed]
  4. E. Herault, F. Balembois, and P. Georges, “491 nm generation by sum-frequency mixing of diode pumped neodymium lasers,” Opt. Express13(15), 5653–5661 (2005). [CrossRef] [PubMed]
  5. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B12(11), 2102–2116 (1995), http://www.opticsinfobase.org/josab/abstract.cfm?id=33615 . [CrossRef]
  6. Y. Y. Lin, S. T. Lin, G. W. Chang, A. C. Chiang, Y. C. Huang, and Y. H. Chen, “Electro-optic periodically poled lithium niobate Bragg modulator as a laser Q-switch,” Opt. Lett.32, 545–547 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?id=125673 . [CrossRef] [PubMed]
  7. S. T. Lin, G. W. Chang, Y. Y. Lin, Y. C. Huang, A. C. Chiang, and Y. H. Chen, “Monolithically integrated laser Bragg Q-switch and wavelength converter in a PPLN crystal,” Opt. Express15(25), 17093–17098 (2007). [CrossRef] [PubMed]
  8. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/ . [CrossRef]
  9. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B5(7), 1412–1423 (1988), http://www.opticsinfobase.org/josab/abstract.cfm?id=5205 . [CrossRef]
  10. Y. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett.93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1 . [CrossRef]

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