April 1, 2014 / Vol. 39, No. 7 / OPTICS LETTERS
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Widely tunable second-harmonic generation in a chalcogenide–tellurite hybrid optical fiber Tonglei Cheng,1,* Weiqing Gao,1 Hiroyasu Kawashima,1 Dinghuan Deng,1 Meisong Liao,1 Morio Matsumoto,2 Takashi Misumi,2 Takenobu Suzuki,1 and Yasutake Ohishi1 1
Research Center for Advanced Photon Technology, Toyota Technological Institute, 2-12-1, Hisakata, Tempaku, Nagoya 468-8511, Japan 2
Furukawa Denshi Co., Ltd., 2-3-2, Marunouchi, Chioda-Ku, Tokyo 100-8370, Japan *Corresponding author: [email protected] Received January 15, 2014; revised February 17, 2014; accepted March 4, 2014; posted March 4, 2014 (Doc. ID 204801); published March 31, 2014
When a chalcogenide–tellurite hybrid optical fiber with a high refractive index difference Δn 0.24 is pumped by an optical parametric oscillator with a pump wavelength from 1700 to 3000 nm, widely tunable second-harmonic generation (SHG) from 850 to 1502 nm is obtained. The observation of SHG is primarily due to the surface nonlinearity polarization at the core–cladding interface and the second-harmonic signal remains stable at the maximal level throughout the laser pulse irradiation. © 2014 Optical Society of America OCIS codes: (190.2620) Harmonic generation and mixing; (060.2270) Fiber characterization; (060.4370) Nonlinear optics, fibers. http://dx.doi.org/10.1364/OL.39.002145
Second-harmonic generation (SHG) in a crystal structure that lacks a center of inversion can be easily obtained and depends mainly on two factors: the second-order nonlinear susceptibility (χ 2 ) and phase matching of the fundamental (ω) to the second-harmonic (SH, 2ω) waves [1–4]. Generally, χ 2 of optical fibers made from glass is zero due to the centrosymmetric and amorphous nature of glass material, and thus SHG in optical fibers should normally not occur. Despite this, some experiments showed that SHG could be observed after pumping such a fiber with intense 1060 nm infrared laser pulses [5,6]. Österberg and Margulis also reported SHG in an optical fiber with power-conversion efficiency as high as ∼3% [7,8]. Then, theories about the SHG mechanism began to evolve and more research was reported by the end of the 1980s [9–13]. More recently, a variety of techniques referred to as thermal poling, corona poling, and electron implantation have been utilized to break the symmetry to introduce a high effective χ 2 [14–16], and an efficient surface SHG in slot micro/nanofiber has been reported in theory [17]. However, the exact nature of SHG in optical fibers is as yet still unclear and some models have been proposed. Some describe the physical mechanism from the microscopic aspects of glass structure. For instance, some reports postulate the generation of a grating of color centers enhances the second-order nonlinear susceptibility χ 2 [9,18], while others assume a photoinduced effect forms the alignment of some dipolebearing molecules and allows SHG in optical fibers [11,19–21]. On the other hand, some researchers have approached the generation mechanism from the nature of optical fibers, and have stated that SHG and sum frequency generation are due to the nonlinear polarization at the core–cladding interface [12]. In this Letter, a chalcogenide–tellurite hybrid optical fiber with a refractive index difference Δn 0.24 was used for SHG. Tunable SHG from 850 to 1502 nm was obtained when the optical fiber was pumped by an optical parametric oscillator (OPO) with a pump wavelength from 1700 to 3000 nm. SHG was primarily due to the 0146-9592/14/072145-03$15.00/0
surface nonlinearity polarization at the core–cladding interface. The chalcogenide–tellurite hybrid optical fiber was fabricated with the rod-in-tube technique, and the core was made of 15Ge–3Ga–12Sb–70S (mol. %, GGSS) glass and the cladding was made of 78TeO2 -5ZnO-12Li2 O-5Bi2 O3 (mol. %, TZLB) glass [22]. This optical fiber with a core diameter of ∼1.38 μm is shown in the inset of Fig. 1(a). The material refractive indices of GGSS core and TZLB cladding were ∼2.240 and ∼2.005 at 1550 nm, and the numerical aperture (NA) was 0.99. The calculated cut-off wavelength for the single mode was shorter than 1780 nm. An 8-m-long fiber was used to measure the loss by the cutback technique, and the loss was ∼2.0 dB∕m at 1550 nm. The effective refractive indices of the fundamental and SH modes as well as the phase mismatch condition (Δβ) were calculated, as shown in Fig. 1(b). The experimental setup for observing SHG in the chalcogenide–tellurite hybrid optical fiber is shown in Fig. 2. The pulse with width of ∼200 fs duration and a repetition rate of ∼80 MHz was coupled into the core of a 2.5-cmlong optical fiber by a lens with focus length of ∼4.5 mm and NA of ∼0.47. The output signal from the fiber was butt-coupled into a large-mode-area (LMA) fluoride fiber with core diameter of ∼105 μm. The LMA fluoride fiber was connected to two optical spectrum analyzers (OSAs,
Fig. 1. (a) Material refractive indices of GGSS core (red line) and TZLB cladding (black line). (b) Calculated effective refractive indices of the fundamental (red line) and SH modes (black line), and the phase mismatch condition (Δβ) (blue line). © 2014 Optical Society of America
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Fig. 2. Experimental setup for observing SHG in the chalcogenide–tellurite hybrid optical fiber.
350–1200 nm and 1200–2400 nm) to measure the fundamental and SH signals, respectively. Tunable SHG from 850 to 1502 nm was obtained in the chalcogenide–tellurite hybrid optical fiber with the pump wavelength adjusting from 1700 to 3000 nm, as shown in Fig. 3. In this experiment, only a 2.5-cm-long optical fiber was used. This is because longer fiber lengths tend to induce phase mismatch and high loss, which lead to a low conversion efficiency of SHG. From Fig. 3 we can see that the SH signal decreases with the decline in the pump average power and the increase of the wavelength, and no SH signal is obtained when the pump wavelength increases over 3000 nm. This is because only part of the pulses were guided into the core, and some of the guided fundamental mode was diffused in the cladding due to the poor confinement in the long wavelength region. Figure 4(a) shows SH signal intensity with the pump average power increasing from 100 to 370 mW at ∼1800 nm. The central wavelength of SH wave was ∼901 nm, and the repeatability of the experimental results was good. Considering the coupling efficiency (about ∼28%), the peak powers launched into the optical fiber were 1.75, 2.63, 3.51, 4.38, 5.25, and 6.48 kW. With
the average power increasing, the spectral intensity increased and the spectral range broadened. The average power of SH waves and output pump signals was ∼0.21 nW and ∼96.4 mW, respectively, at the maximal average power of ∼370 mW, and the conversion efficiency was of the order of 10−8 . Figure 4(b) shows the log–log plot of the SHG output average power and the pump average power. We can see that the slope of the fit line was ∼2.15 and SHG output power follows the expected square dependence on the pump average power. This is consistent with the theoretical square evolution of SHG. To explain the generation mechanism of SHG in the chalcogenide–tellurite hybrid optical fiber, a 5-cm-long GGSS rod with the diameter of ∼0.26 mm and a 5-cmlong preform with GGSS core diameter of ∼0.25 mm were pumped by an 1800 nm pulse with average power of ∼397 mW. The experimental setup was the same as in Fig. 2, except that the lens was changed into one whose focus length was 6 mm (NA 0.25). From Fig. 5 we can see that, under the same experimental conditions, the GGSS rod has no signal but the preform has a weak signal near 900 nm. This observation cannot be properly explained by models that claim that SHG in optical fibers originates from the microscopic aspects of glass structure, such as color centers [9] and photoinduced effects forming the dipole [11]. If these models work for this experiment, SHG should also be obtained from a GGSS rod under the same conditions, which is not the case in the observed result. This phenomenon suggested that the surface nonlinearity polarization at the core–cladding interface of the preform would become the major physical mechanism for SHG in this work. Due to the high loss of the preform and phase mismatch between the fundamental and SH modes, the SH signal was weak in the preform. SHG output average power from the 2.5-cm-long optical fiber was also measured with the time at the pump wavelength at ∼1800 nm to further reveal the generation mechanism of SHG, as shown in Fig. 6. Considering the coupling efficiency, the peak power launched into the fiber corresponding to an average power 397 mW was 6.95 kW. From the beginning of laser pulse irradiation, the SH signal reached the maximal level and kept the power level at ∼0.265 nW. this is different from some
Fig. 3. Tunable SHG from 850 to 1502 nm in the chalcogenide– tellurite hybrid optical fiber with the pump wavelength adjusted from 1700 to 3000 nm.
Fig. 4. (a) SHG output spectrum intensity at the pump wavelength of ∼1800 nm. The pump peak power from bottom to top corresponding to the average powers were 1.75, 2.63, 3.51, 4.38, 5.25, and 6.48 kW. (b) Log–log plot of the SHG output average power versus the average power from 100 to 370 mW.
Fig. 5. (a) GGSS rod with a diameter of 0.26 mm and length of 5 cm pumped by 1800 nm pulses. (b) Fiber preform with GGSS core diameter of 0.25 mm and length of 5 cm pumped by 1800 nm pulses.
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interface was the major physical mechanism for SHG in this work. This work is supported by MEXT, the Support Program for Forming Strategic Research Infrastructure (2011–2015).
Fig. 6. SHG average power measured over 16 min of laser pulse irradiation in a 2.5-cm-long chalcogenide–tellurite hybrid optical fiber.
reports that state that the forming process of SHG requires buildup time and describe the SHG mechanism from the microscopic aspects of the glass structure [10,11]. This property also suggests the chalcogenide– tellurite hybrid optical fiber may have a generation mechanism different from these previous reports [9,11,19–21]. In this work, the conversion efficiency of SHG is of the order of 10−8 while a theoretical maximum value of around 10−5 has been reported by Terhune and Weinberger based on the surface nonlinearity polarization at the core–cladding interface [12]. There were several possible reasons for the low conversion efficiency: the fiber loss due to impurities of glasses, the low pump average power within the damage threshold of the fiber, and the phase mismatch (∼0.34 μm−1 ). The situation may be improved in the future in the following ways: reducing the fiber loss by enhancing the material purities and making the GGSS rod surface smoother, increasing the pump peak power within the damage threshold and improving the phase-matching condition by changing the fiber core size of the, or using a photonic crystal fiber structure. In summary, widely tunable SHG from 850 to 1502 nm in chalcogenide–tellurite hybrid optical fiber was demonstrated in the Letter. SHG can be obtained from the preform but not from the GGSS rod. From the beginning of laser pulse irradiation, the SH signal reached the maximal level. These measured results suggested that the surface nonlinearity polarization at the core–cladding
References 1. D. A. Chestnut, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 88, 071113 (2006). 2. I. N. M. Wijeratne, N. Kejalakshmy, A. Agrawal, B. M. A. Rahman, and K. T. V. Grattan, IEEE Photon. J. 4, 357 (2012). 3. E. Y. Zhu, L. Qian, L. G. Helt, M. Liscidini, J. E. Sipe, C. Corbari, A. Canagasabey, M. Ibsen, and P. G. Kazansky, J. Opt. Soc. Am. B 27, 2410 (2010). 4. S. S. Pal, S. K. Mondal, P. P. Bajpai, and P. Kapur, Opt. Lett. 37, 4017 (2012). 5. Y. Fujii, B. S. Kawasaki, K. O. Hill, and D. C. Johnson, Opt. Lett. 5, 48 (1980). 6. Y. Sasaki and Y. Ohmori, Appl. Phys. Lett. 39, 466 (1981). 7. U. Österberg and W. Margulis, Opt. Lett. 11, 516 (1986). 8. U. Österberg and W. Margulis, Opt. Lett. 12, 57 (1987). 9. M. C. Farries, P. S. J. Russel, M. E. Fermann, and D. N. Payne, Electron. Lett. 23, 322 (1987). 10. B. Valk, E. M. Kim, and M. M. Salour, Appl. Phys. Lett. 51, 722 (1987). 11. R. H. Stolen and H. W. K. Tom, Opt. Lett. 12, 585 (1987). 12. R. W. Terhune and D. A. Weinberger, J. Opt. Soc. Am. B 4, 661 (1987). 13. J. M. Gabriagues and H. Février, Opt. Lett. 12, 720 (1987). 14. S. Richard, J. Opt. Soc. Am. B 27, 1504 (2010). 15. A. Canagasabey, C. Corbari, A. V. Gladyshev, F. Liegeois, S. Guillemet, Y. Hernandez, M. V. Y. A. Kosolapov, E. M. Dianov, M. Ibsen, and P. G. Kazansky, Opt. Lett. 34, 2483 (2009). 16. R. A. Myers, N. Mukherjee, and S. R. J. Brueck, Opt. Lett. 16, 1732 (1991). 17. W. Luo, W. Guo, F. Xu, and Y. Lu, Opt. Express 21, 11554 (2013). 18. M. A. Saifi and M. J. Andrejco, Opt. Lett. 13, 773 (1988). 19. D. Z. Anderson, V. Mizrahi, and J. E. Sipe, Opt. Lett. 16, 796 (1991). 20. T. E. Tsai, M. A. Saifi, E. J. Friebele, D. L. Griscom, and U. Österberg, Opt. Lett. 14, 1023 (1989). 21. V. Dominic and J. Feinberg, Phys. Rev. Lett. 71, 3446 (1993). 22. T. L. Cheng, W. Q. Gao, M. S. Liao, Z. C. Duan, D. H. Deng, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, Opt. Lett. 39, 1005 (2014).
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Widely tunable second-harmonic generation in a chalcogenide–tellurite hybrid optical fiber Tonglei Cheng,1,* Weiqing Gao,1 Hiroyasu Kawashima,1 Dinghuan Deng,1 Meisong Liao,1 Morio Matsumoto,2 Takashi Misumi,2 Takenobu Suzuki,1 and Yasutake Ohishi1 1
Research Center for Advanced Photon Technology, Toyota Technological Institute, 2-12-1, Hisakata, Tempaku, Nagoya 468-8511, Japan 2
Furukawa Denshi Co., Ltd., 2-3-2, Marunouchi, Chioda-Ku, Tokyo 100-8370, Japan *Corresponding author: [email protected] Received January 15, 2014; revised February 17, 2014; accepted March 4, 2014; posted March 4, 2014 (Doc. ID 204801); published March 31, 2014
When a chalcogenide–tellurite hybrid optical fiber with a high refractive index difference Δn 0.24 is pumped by an optical parametric oscillator with a pump wavelength from 1700 to 3000 nm, widely tunable second-harmonic generation (SHG) from 850 to 1502 nm is obtained. The observation of SHG is primarily due to the surface nonlinearity polarization at the core–cladding interface and the second-harmonic signal remains stable at the maximal level throughout the laser pulse irradiation. © 2014 Optical Society of America OCIS codes: (190.2620) Harmonic generation and mixing; (060.2270) Fiber characterization; (060.4370) Nonlinear optics, fibers. http://dx.doi.org/10.1364/OL.39.002145
Second-harmonic generation (SHG) in a crystal structure that lacks a center of inversion can be easily obtained and depends mainly on two factors: the second-order nonlinear susceptibility (χ 2 ) and phase matching of the fundamental (ω) to the second-harmonic (SH, 2ω) waves [1–4]. Generally, χ 2 of optical fibers made from glass is zero due to the centrosymmetric and amorphous nature of glass material, and thus SHG in optical fibers should normally not occur. Despite this, some experiments showed that SHG could be observed after pumping such a fiber with intense 1060 nm infrared laser pulses [5,6]. Österberg and Margulis also reported SHG in an optical fiber with power-conversion efficiency as high as ∼3% [7,8]. Then, theories about the SHG mechanism began to evolve and more research was reported by the end of the 1980s [9–13]. More recently, a variety of techniques referred to as thermal poling, corona poling, and electron implantation have been utilized to break the symmetry to introduce a high effective χ 2 [14–16], and an efficient surface SHG in slot micro/nanofiber has been reported in theory [17]. However, the exact nature of SHG in optical fibers is as yet still unclear and some models have been proposed. Some describe the physical mechanism from the microscopic aspects of glass structure. For instance, some reports postulate the generation of a grating of color centers enhances the second-order nonlinear susceptibility χ 2 [9,18], while others assume a photoinduced effect forms the alignment of some dipolebearing molecules and allows SHG in optical fibers [11,19–21]. On the other hand, some researchers have approached the generation mechanism from the nature of optical fibers, and have stated that SHG and sum frequency generation are due to the nonlinear polarization at the core–cladding interface [12]. In this Letter, a chalcogenide–tellurite hybrid optical fiber with a refractive index difference Δn 0.24 was used for SHG. Tunable SHG from 850 to 1502 nm was obtained when the optical fiber was pumped by an optical parametric oscillator (OPO) with a pump wavelength from 1700 to 3000 nm. SHG was primarily due to the 0146-9592/14/072145-03$15.00/0
surface nonlinearity polarization at the core–cladding interface. The chalcogenide–tellurite hybrid optical fiber was fabricated with the rod-in-tube technique, and the core was made of 15Ge–3Ga–12Sb–70S (mol. %, GGSS) glass and the cladding was made of 78TeO2 -5ZnO-12Li2 O-5Bi2 O3 (mol. %, TZLB) glass [22]. This optical fiber with a core diameter of ∼1.38 μm is shown in the inset of Fig. 1(a). The material refractive indices of GGSS core and TZLB cladding were ∼2.240 and ∼2.005 at 1550 nm, and the numerical aperture (NA) was 0.99. The calculated cut-off wavelength for the single mode was shorter than 1780 nm. An 8-m-long fiber was used to measure the loss by the cutback technique, and the loss was ∼2.0 dB∕m at 1550 nm. The effective refractive indices of the fundamental and SH modes as well as the phase mismatch condition (Δβ) were calculated, as shown in Fig. 1(b). The experimental setup for observing SHG in the chalcogenide–tellurite hybrid optical fiber is shown in Fig. 2. The pulse with width of ∼200 fs duration and a repetition rate of ∼80 MHz was coupled into the core of a 2.5-cmlong optical fiber by a lens with focus length of ∼4.5 mm and NA of ∼0.47. The output signal from the fiber was butt-coupled into a large-mode-area (LMA) fluoride fiber with core diameter of ∼105 μm. The LMA fluoride fiber was connected to two optical spectrum analyzers (OSAs,
Fig. 1. (a) Material refractive indices of GGSS core (red line) and TZLB cladding (black line). (b) Calculated effective refractive indices of the fundamental (red line) and SH modes (black line), and the phase mismatch condition (Δβ) (blue line). © 2014 Optical Society of America
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Fig. 2. Experimental setup for observing SHG in the chalcogenide–tellurite hybrid optical fiber.
350–1200 nm and 1200–2400 nm) to measure the fundamental and SH signals, respectively. Tunable SHG from 850 to 1502 nm was obtained in the chalcogenide–tellurite hybrid optical fiber with the pump wavelength adjusting from 1700 to 3000 nm, as shown in Fig. 3. In this experiment, only a 2.5-cm-long optical fiber was used. This is because longer fiber lengths tend to induce phase mismatch and high loss, which lead to a low conversion efficiency of SHG. From Fig. 3 we can see that the SH signal decreases with the decline in the pump average power and the increase of the wavelength, and no SH signal is obtained when the pump wavelength increases over 3000 nm. This is because only part of the pulses were guided into the core, and some of the guided fundamental mode was diffused in the cladding due to the poor confinement in the long wavelength region. Figure 4(a) shows SH signal intensity with the pump average power increasing from 100 to 370 mW at ∼1800 nm. The central wavelength of SH wave was ∼901 nm, and the repeatability of the experimental results was good. Considering the coupling efficiency (about ∼28%), the peak powers launched into the optical fiber were 1.75, 2.63, 3.51, 4.38, 5.25, and 6.48 kW. With
the average power increasing, the spectral intensity increased and the spectral range broadened. The average power of SH waves and output pump signals was ∼0.21 nW and ∼96.4 mW, respectively, at the maximal average power of ∼370 mW, and the conversion efficiency was of the order of 10−8 . Figure 4(b) shows the log–log plot of the SHG output average power and the pump average power. We can see that the slope of the fit line was ∼2.15 and SHG output power follows the expected square dependence on the pump average power. This is consistent with the theoretical square evolution of SHG. To explain the generation mechanism of SHG in the chalcogenide–tellurite hybrid optical fiber, a 5-cm-long GGSS rod with the diameter of ∼0.26 mm and a 5-cmlong preform with GGSS core diameter of ∼0.25 mm were pumped by an 1800 nm pulse with average power of ∼397 mW. The experimental setup was the same as in Fig. 2, except that the lens was changed into one whose focus length was 6 mm (NA 0.25). From Fig. 5 we can see that, under the same experimental conditions, the GGSS rod has no signal but the preform has a weak signal near 900 nm. This observation cannot be properly explained by models that claim that SHG in optical fibers originates from the microscopic aspects of glass structure, such as color centers [9] and photoinduced effects forming the dipole [11]. If these models work for this experiment, SHG should also be obtained from a GGSS rod under the same conditions, which is not the case in the observed result. This phenomenon suggested that the surface nonlinearity polarization at the core–cladding interface of the preform would become the major physical mechanism for SHG in this work. Due to the high loss of the preform and phase mismatch between the fundamental and SH modes, the SH signal was weak in the preform. SHG output average power from the 2.5-cm-long optical fiber was also measured with the time at the pump wavelength at ∼1800 nm to further reveal the generation mechanism of SHG, as shown in Fig. 6. Considering the coupling efficiency, the peak power launched into the fiber corresponding to an average power 397 mW was 6.95 kW. From the beginning of laser pulse irradiation, the SH signal reached the maximal level and kept the power level at ∼0.265 nW. this is different from some
Fig. 3. Tunable SHG from 850 to 1502 nm in the chalcogenide– tellurite hybrid optical fiber with the pump wavelength adjusted from 1700 to 3000 nm.
Fig. 4. (a) SHG output spectrum intensity at the pump wavelength of ∼1800 nm. The pump peak power from bottom to top corresponding to the average powers were 1.75, 2.63, 3.51, 4.38, 5.25, and 6.48 kW. (b) Log–log plot of the SHG output average power versus the average power from 100 to 370 mW.
Fig. 5. (a) GGSS rod with a diameter of 0.26 mm and length of 5 cm pumped by 1800 nm pulses. (b) Fiber preform with GGSS core diameter of 0.25 mm and length of 5 cm pumped by 1800 nm pulses.
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interface was the major physical mechanism for SHG in this work. This work is supported by MEXT, the Support Program for Forming Strategic Research Infrastructure (2011–2015).
Fig. 6. SHG average power measured over 16 min of laser pulse irradiation in a 2.5-cm-long chalcogenide–tellurite hybrid optical fiber.
reports that state that the forming process of SHG requires buildup time and describe the SHG mechanism from the microscopic aspects of the glass structure [10,11]. This property also suggests the chalcogenide– tellurite hybrid optical fiber may have a generation mechanism different from these previous reports [9,11,19–21]. In this work, the conversion efficiency of SHG is of the order of 10−8 while a theoretical maximum value of around 10−5 has been reported by Terhune and Weinberger based on the surface nonlinearity polarization at the core–cladding interface [12]. There were several possible reasons for the low conversion efficiency: the fiber loss due to impurities of glasses, the low pump average power within the damage threshold of the fiber, and the phase mismatch (∼0.34 μm−1 ). The situation may be improved in the future in the following ways: reducing the fiber loss by enhancing the material purities and making the GGSS rod surface smoother, increasing the pump peak power within the damage threshold and improving the phase-matching condition by changing the fiber core size of the, or using a photonic crystal fiber structure. In summary, widely tunable SHG from 850 to 1502 nm in chalcogenide–tellurite hybrid optical fiber was demonstrated in the Letter. SHG can be obtained from the preform but not from the GGSS rod. From the beginning of laser pulse irradiation, the SH signal reached the maximal level. These measured results suggested that the surface nonlinearity polarization at the core–cladding
References 1. D. A. Chestnut, S. V. Popov, and J. R. Taylor, Appl. Phys. Lett. 88, 071113 (2006). 2. I. N. M. Wijeratne, N. Kejalakshmy, A. Agrawal, B. M. A. Rahman, and K. T. V. Grattan, IEEE Photon. J. 4, 357 (2012). 3. E. Y. Zhu, L. Qian, L. G. Helt, M. Liscidini, J. E. Sipe, C. Corbari, A. Canagasabey, M. Ibsen, and P. G. Kazansky, J. Opt. Soc. Am. B 27, 2410 (2010). 4. S. S. Pal, S. K. Mondal, P. P. Bajpai, and P. Kapur, Opt. Lett. 37, 4017 (2012). 5. Y. Fujii, B. S. Kawasaki, K. O. Hill, and D. C. Johnson, Opt. Lett. 5, 48 (1980). 6. Y. Sasaki and Y. Ohmori, Appl. Phys. Lett. 39, 466 (1981). 7. U. Österberg and W. Margulis, Opt. Lett. 11, 516 (1986). 8. U. Österberg and W. Margulis, Opt. Lett. 12, 57 (1987). 9. M. C. Farries, P. S. J. Russel, M. E. Fermann, and D. N. Payne, Electron. Lett. 23, 322 (1987). 10. B. Valk, E. M. Kim, and M. M. Salour, Appl. Phys. Lett. 51, 722 (1987). 11. R. H. Stolen and H. W. K. Tom, Opt. Lett. 12, 585 (1987). 12. R. W. Terhune and D. A. Weinberger, J. Opt. Soc. Am. B 4, 661 (1987). 13. J. M. Gabriagues and H. Février, Opt. Lett. 12, 720 (1987). 14. S. Richard, J. Opt. Soc. Am. B 27, 1504 (2010). 15. A. Canagasabey, C. Corbari, A. V. Gladyshev, F. Liegeois, S. Guillemet, Y. Hernandez, M. V. Y. A. Kosolapov, E. M. Dianov, M. Ibsen, and P. G. Kazansky, Opt. Lett. 34, 2483 (2009). 16. R. A. Myers, N. Mukherjee, and S. R. J. Brueck, Opt. Lett. 16, 1732 (1991). 17. W. Luo, W. Guo, F. Xu, and Y. Lu, Opt. Express 21, 11554 (2013). 18. M. A. Saifi and M. J. Andrejco, Opt. Lett. 13, 773 (1988). 19. D. Z. Anderson, V. Mizrahi, and J. E. Sipe, Opt. Lett. 16, 796 (1991). 20. T. E. Tsai, M. A. Saifi, E. J. Friebele, D. L. Griscom, and U. Österberg, Opt. Lett. 14, 1023 (1989). 21. V. Dominic and J. Feinberg, Phys. Rev. Lett. 71, 3446 (1993). 22. T. L. Cheng, W. Q. Gao, M. S. Liao, Z. C. Duan, D. H. Deng, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, Opt. Lett. 39, 1005 (2014).
