May 15, 2014 / Vol. 39, No. 10 / OPTICS LETTERS
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High-power and highly efficient amplification of a radially polarized beam using an Yb-doped double-clad fiber Shinya Kanazawa, Yuichi Kozawa,* and Shunichi Sato Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan *Corresponding author: [email protected] Received March 6, 2014; revised April 13, 2014; accepted April 14, 2014; posted April 14, 2014 (Doc. ID 207796); published May 6, 2014 We demonstrated the amplification of a radially polarized beam by using an Yb-doped double-clad fiber. The output power of the amplified beam reached 21 W at pump power of 30 W. The generation of amplified spontaneous emission was suppressed by applying a seed beam with sufficient power. Although the intensity distribution of the seed beam was well maintained after the amplification, partial transformation of radial polarization to azimuthal polarization was observed. © 2014 Optical Society of America OCIS codes: (260.5430) Polarization; (140.4480) Optical amplifiers; (060.2320) Fiber optics amplifiers and oscillators. http://dx.doi.org/10.1364/OL.39.002857
Laser beams with an inhomogeneous polarization distribution in the beam cross section, so-called vector beams, have attracted much attention because of their unique optical properties yet unexplored, such as smaller spot formation and no energy flow on the beam axis. In particular, radially and azimuthally polarized beams are well known as typical vector beams, and have remarkable focusing features [1]. Because of their unconventional optical properties, the vector beams are expected to be used for many applications [2–4]. The polarization characteristics of vector beams on a material surface are also attractive for laser processing [5]. For example, a radially polarized beam had higher efficiency for laser cutting than linearly and circularly polarized beams [5,6]. By contrast, an azimuthally polarized beam was highly efficient for laser drilling [7,8]. To apply vector beams for laser processing, a laser source with sufficient laser power is required. Fiber is one of the promising laser materials for obtaining highpower laser beams. While the output power of fiber lasers is increasing year by year [9], the polarization of most of output beams has been limited to linear or random. There are some reports on the oscillation of vector beams directly from fiber oscillators [10–13]. However, the maximum output power reported has been less than a few watts, which is unsatisfactory for laser processing. Fiber amplification is one of the well-established approaches to increasing output power. The amplification of vector beams by optically active fiber has been reported. The amplification of a radially polarized beam up to 1.1 W with sufficiently suppressed amplified spontaneous emission (ASE) was demonstrated by using a two-mode Yb-doped double-clad fiber (YDDCF) [14]. Similar amplification was reported for both radially and azimuthally polarized beams with output power of 400 mW [15]. A single crystal fiber rod was used for amplification, achieving output power of 100 W [16]. However, the efficiency was less than 20%. Accordingly, high-power and highly efficient amplification of vector beams utilizing the advantages of fiber amplifiers is expected for application to laser processing. 0146-9592/14/102857-03$15.00/0
In this Letter, we demonstrate high-power and highly efficient amplification of a radially polarized beam by using an YDDCF with a seed beam with output power of 1 W to sufficiently suppress the ASE. Figure 1 shows the schematic of the YDDCF amplifier for a radially polarized beam. A commercial 4-m-long YDDCF was used as a gain medium. The diameters of the active core and inner cladding were 30 and 250 μm, respectively. The corresponding NAs were 0.06 and 0.46, respectively. The V parameter of the YDDCF at 1064 nm was 5.31, which is large enough to transmit not only a radially polarized beam (TM01 mode) but also higher order transverse modes. To suppress the higher order modes, the transmission loss of the higher order modes was increased by coiling the fiber at a diameter of 170 mm. The absorption coefficient of the fiber core at 975 nm was 6.3 dB∕m. Both ends of the YDDCF were cut at an angle of 8 deg to avoid by a parasitic oscillation and related damage. First, a seed beam, whose diameter was adjusted by using a lens pair, was coupled to the YDDCF core by a focusing lens. The output power and beam profile were measured by a power meter and a CCD camera, respectively. A laser diode (LD) with maximum output power of 30 W around 976 nm was used as a pump source. The pump beam was coupled to the inner cladding of the YDDCF from the opposite direction to the seed beam. Dichroic mirrors (DMs) were used to separate the seed and amplified beams from the pump beam.
Fig. 1. Setup for the amplification of a radially polarized beam using an YDDCF. © 2014 Optical Society of America
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Fig. 2. Intensity distributions of the seed beam (top row), the transmitted beam through the YDDCF (second row), and the amplified beam pumped at 30 W (bottom row). (a), (f), and (k) Total intensity distributions. (b)–(e), (g)–(j), and (l)–(o) Intensity distributions after passage through a linear polarizer. Each arrow indicates the direction of the polarizer.
A seed beam with radial polarization was generated from a Nd:YAG laser oscillator with a photonic crystal mirror [17]. The output power of the radially polarized beam at a wavelength of 1064 nm was 1 W. Figures 2(a)– 2(e) show the intensity distributions of the seed beam. The total intensity distribution is shown in Fig. 2(a). It is clearly shown that the beam shape is a doughnut with a dark center. The intensity distributions after passage through a linear polarizer are shown in Figs. 2(b)–2(e). Each arrow indicates the transmission direction of the polarizer. Two-lobe-shaped intensity patterns along the polarizer were obtained, indicating that the generated beam was radially polarized. The fraction of radial polarization is estimated to be 93% from Figs. 2(b)–2(e). Figures 3(a) and 3(b) show the intensity profiles of the seed beam across the beam center. The horizontal and vertical axes correspond to the x and y axes in Fig. 2, respectively. In Figs. 3(a) and 3(b), the intensity on the beam center is not zero, meaning that a small fraction of Gaussian beam was generated in the laser oscillator. However, this slight Gaussian component did not affect the amplification of radially polarized beam, as will be mentioned later. The intensity distributions of the seed beam transmitted through the YDDCF without pumping is shown in Figs. 2(f)–2(j). The coupling efficiency is 55%. Figure 2(f) shows the total intensity distribution. The transmitted beam kept the doughnut shape. Small modification of the transmitted beam was probably caused by the birefringence in the fiber core, which was weakly coiled. The intensity distributions after passage through a linear polarizer are shown in Figs. 2(g)–2(j). A slight rotation of the polarization distributions around the beam axis compared to the seed beam itself [Figs. 2(b)–2(e)] was observed. Here the fraction of radial polarization is estimated to be 82%. However, this rotation, which is also attributed to the birefringence of the fiber core, can be compensated by a pair of half-wavelength (λ∕2) plates if necessary. Figures 3(c) and 3(d) show the intensity profiles across the beam center of the transmitted beam. Since there is no significant difference between the intensity profiles of the seed and transmitted beams, it is clear that the radially polarized beam transmitted
Fig. 3. Intensity profiles across the beam center of the seed beam (top row), the transmitted beam (second row), and the amplified beam (bottom row). The horizontal and vertical axes correspond to the x and y directions in Fig. 2, respectively. Solid and dashed lines are the experimental data and the fitting, respectively.
through the YDDCF maintains the intensity and polarization distributions. Figures 2(k)–2(o) show the intensity distributions of the amplified beam at the maximum output power of 21 W. The total intensity distribution is shown in Fig. 2(k). The beam center is still dark and the beam shape is much closer to the doughnut shape than the transmitted beam without amplification [Fig. 2(f)]. Figures 2(l)–2(o) show the intensity distribution after passage through a linear polarizer. The rotation angle of the polarization distribution around the beam axis increases compared to the transmitted beam without amplification [Figs. 2(g)–2(j)]. This additional rotation is thermally enhanced because the rotation angle increases with increasing the pump power (data are not shown). In general, cylindrical vector beams such as radially and azimuthally polarized beams are expected to be free from the depolarization effect. However, the cylindrical symmetry of the fiber is no longer maintained because the coiling and twisting of the fiber probably results in the depolarization shown in Figs. 2(l)–2(o). The fractions of radial and azimuthal polarizations are 65% and 35%, respectively. Figures 3(e) and 3(f) show the intensity profiles of the amplified beam across the beam center. When the ASE was generated, the increase of the intensity on the beam center has been observed because of the Gaussian shape of the ASE [14]. However, the intensity on the beam center showed no significant difference even after the amplification, implying that the generation of the ASE in the fiber was negligible in the experiment.
May 15, 2014 / Vol. 39, No. 10 / OPTICS LETTERS
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of 1 W. The amplified beam obtained in the experiment can be a seed beam for further amplification of a radially polarized beam with suppression of the ASE. In conclusion, the amplification of a radially polarized beam by an YDDCF was demonstrated. The output power reached 21 W, which may be sufficient for some kinds of laser processing, such as cutting of thin materials. The ASE was sufficiently suppressed by using a seed beam with proper power. This technique will be also applicable to the amplification of an azimuthally polarized beam. By using this high-power laser source, we will be able to experimentally evaluate the processing performance of a radially polarized beam as a future work.
-2 -4 -6 -8
W
1080
1100 3.1 W
pu ed
1060
ch
1040
Wavelength (nm)
un
1020
La
1000
2W
W
m
16. 9.4
p
23.
we
30 3W
po
-10
r
0
Relative intensity (dB)
Fig. 4. Output power of the amplified beam as a function of the pump power.
Fig. 5. Emission spectra of the amplified beams at different pump power.
Figure 4 depicts the output power of the amplified beam as a function of the pump power. The maximum output power reached 21 W. The slope efficiency was approximately 70%, which is much higher than the previous reports of the amplification of the vector beams [14,15], and close to the values reported for high-power amplification of scalar beams [18–20]. The saturation of the output power was observed when the pump power was above 26 W. This was attributed to the wavelength shift of the pump beam, which results in the decrease of absorption efficiency, due to the temperature rise of the pump LD. Therefore, further amplification of the radially polarized beam will be possible by using a higher power or frequency-stabilized pump source. Figure 5 shows the emission spectra of the amplified beam at different pump power. The ASE component, which has a peak around 1030 nm, was not observed. This result implies that the ASE was effectively suppressed by injecting the seed beam with sufficient power
This work was supported in part by Core Research for Evolutional Science and Technology (CREST) and the Japan Science and Technology Agency (JST). References 1. Q. Zhan and J. R. Leger, Opt. Express 10, 324 (2002). 2. K. Youngworth and T. Brown, Opt. Express 7, 77 (2000). 3. Q. Zhan, Opt. Express 12, 3377 (2004). 4. W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995). 5. V. G. Niziev and A. V. Nesterov, J. Phys. D 32, 1455 (1999). 6. V. Onuseit, M. A. Ahmed, R. Weber, and T. Graf, Phys. Procedia 12, 584 (2011). 7. M. Meier, V. Romano, and T. Feurer, Appl. Phys. A 86, 329 (2007). 8. M. Kraus, M. A. Ahmed, A. Michalowski, A. Voss, R. Weber, and T. Graf, Opt. Express 18, 22305 (2010). 9. D. J. Richardson, J. Nilsson, and W. A. Clarkson, J. Opt. Soc. Am. B 27, B63 (2010). 10. J. Li, K. Ueda, M. Musha, and A. Shirakawa, Opt. Lett. 31, 2969 (2006). 11. J. Li, K. Ueda, A. Sirakawa, M. Musha, L. X. Zhong, and Z. M. Zhang, Laser Phys. Lett. 4, 814 (2007). 12. R. Zhou, B. Ibarra-Escamilla, J. W. Haus, P. E. Powers, and Q. Zhan, Appl. Phys. Lett. 95, 191111 (2009). 13. D. Lin, K. Xia, J. Li, R. Li, K. Ueda, G. Li, and X. Li, Opt. Lett. 35, 2290 (2010). 14. T. Chubachi, Y. Kozawa, and S. Sato, Opt. Lett. 34, 716 (2009). 15. M. Fridman, M. Nixon, M. Dubinskii, A. A. Friesem, and N. Davidson, Opt. Lett. 35, 1332 (2010). 16. S. Piehler, X. Delen, M. Rumpel, J. Didierjean, N. Aubry, T. Graf, F. Balembois, P. Georges, and M. A. Ahmed, Opt. Express 21, 11376 (2013). 17. Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, Appl. Phys. Express 1, 022008 (2008). 18. A. Liem, J. Limpert, H. Zellmer, and A. Tünnermann, Opt. Lett. 28, 1537 (2003). 19. Y. Jeong, J. Nilsson, J. K. Sahu, D. B. S. Soh, C. Alegria, P. Dupriez, C. A. Codemard, D. N. Payne, R. Horley, L. M. B. Hickey, L. Wanzcyk, C. E. Chryssou, J. A. Alvarez-Chavez, and P. W. Turner, Opt. Lett. 30, 459 (2005). 20. M. Hildebrandt, M. Frede, and D. Kracht, Opt. Lett. 32, 2345 (2007).
2857
High-power and highly efficient amplification of a radially polarized beam using an Yb-doped double-clad fiber Shinya Kanazawa, Yuichi Kozawa,* and Shunichi Sato Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan *Corresponding author: [email protected] Received March 6, 2014; revised April 13, 2014; accepted April 14, 2014; posted April 14, 2014 (Doc. ID 207796); published May 6, 2014 We demonstrated the amplification of a radially polarized beam by using an Yb-doped double-clad fiber. The output power of the amplified beam reached 21 W at pump power of 30 W. The generation of amplified spontaneous emission was suppressed by applying a seed beam with sufficient power. Although the intensity distribution of the seed beam was well maintained after the amplification, partial transformation of radial polarization to azimuthal polarization was observed. © 2014 Optical Society of America OCIS codes: (260.5430) Polarization; (140.4480) Optical amplifiers; (060.2320) Fiber optics amplifiers and oscillators. http://dx.doi.org/10.1364/OL.39.002857
Laser beams with an inhomogeneous polarization distribution in the beam cross section, so-called vector beams, have attracted much attention because of their unique optical properties yet unexplored, such as smaller spot formation and no energy flow on the beam axis. In particular, radially and azimuthally polarized beams are well known as typical vector beams, and have remarkable focusing features [1]. Because of their unconventional optical properties, the vector beams are expected to be used for many applications [2–4]. The polarization characteristics of vector beams on a material surface are also attractive for laser processing [5]. For example, a radially polarized beam had higher efficiency for laser cutting than linearly and circularly polarized beams [5,6]. By contrast, an azimuthally polarized beam was highly efficient for laser drilling [7,8]. To apply vector beams for laser processing, a laser source with sufficient laser power is required. Fiber is one of the promising laser materials for obtaining highpower laser beams. While the output power of fiber lasers is increasing year by year [9], the polarization of most of output beams has been limited to linear or random. There are some reports on the oscillation of vector beams directly from fiber oscillators [10–13]. However, the maximum output power reported has been less than a few watts, which is unsatisfactory for laser processing. Fiber amplification is one of the well-established approaches to increasing output power. The amplification of vector beams by optically active fiber has been reported. The amplification of a radially polarized beam up to 1.1 W with sufficiently suppressed amplified spontaneous emission (ASE) was demonstrated by using a two-mode Yb-doped double-clad fiber (YDDCF) [14]. Similar amplification was reported for both radially and azimuthally polarized beams with output power of 400 mW [15]. A single crystal fiber rod was used for amplification, achieving output power of 100 W [16]. However, the efficiency was less than 20%. Accordingly, high-power and highly efficient amplification of vector beams utilizing the advantages of fiber amplifiers is expected for application to laser processing. 0146-9592/14/102857-03$15.00/0
In this Letter, we demonstrate high-power and highly efficient amplification of a radially polarized beam by using an YDDCF with a seed beam with output power of 1 W to sufficiently suppress the ASE. Figure 1 shows the schematic of the YDDCF amplifier for a radially polarized beam. A commercial 4-m-long YDDCF was used as a gain medium. The diameters of the active core and inner cladding were 30 and 250 μm, respectively. The corresponding NAs were 0.06 and 0.46, respectively. The V parameter of the YDDCF at 1064 nm was 5.31, which is large enough to transmit not only a radially polarized beam (TM01 mode) but also higher order transverse modes. To suppress the higher order modes, the transmission loss of the higher order modes was increased by coiling the fiber at a diameter of 170 mm. The absorption coefficient of the fiber core at 975 nm was 6.3 dB∕m. Both ends of the YDDCF were cut at an angle of 8 deg to avoid by a parasitic oscillation and related damage. First, a seed beam, whose diameter was adjusted by using a lens pair, was coupled to the YDDCF core by a focusing lens. The output power and beam profile were measured by a power meter and a CCD camera, respectively. A laser diode (LD) with maximum output power of 30 W around 976 nm was used as a pump source. The pump beam was coupled to the inner cladding of the YDDCF from the opposite direction to the seed beam. Dichroic mirrors (DMs) were used to separate the seed and amplified beams from the pump beam.
Fig. 1. Setup for the amplification of a radially polarized beam using an YDDCF. © 2014 Optical Society of America
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OPTICS LETTERS / Vol. 39, No. 10 / May 15, 2014
Fig. 2. Intensity distributions of the seed beam (top row), the transmitted beam through the YDDCF (second row), and the amplified beam pumped at 30 W (bottom row). (a), (f), and (k) Total intensity distributions. (b)–(e), (g)–(j), and (l)–(o) Intensity distributions after passage through a linear polarizer. Each arrow indicates the direction of the polarizer.
A seed beam with radial polarization was generated from a Nd:YAG laser oscillator with a photonic crystal mirror [17]. The output power of the radially polarized beam at a wavelength of 1064 nm was 1 W. Figures 2(a)– 2(e) show the intensity distributions of the seed beam. The total intensity distribution is shown in Fig. 2(a). It is clearly shown that the beam shape is a doughnut with a dark center. The intensity distributions after passage through a linear polarizer are shown in Figs. 2(b)–2(e). Each arrow indicates the transmission direction of the polarizer. Two-lobe-shaped intensity patterns along the polarizer were obtained, indicating that the generated beam was radially polarized. The fraction of radial polarization is estimated to be 93% from Figs. 2(b)–2(e). Figures 3(a) and 3(b) show the intensity profiles of the seed beam across the beam center. The horizontal and vertical axes correspond to the x and y axes in Fig. 2, respectively. In Figs. 3(a) and 3(b), the intensity on the beam center is not zero, meaning that a small fraction of Gaussian beam was generated in the laser oscillator. However, this slight Gaussian component did not affect the amplification of radially polarized beam, as will be mentioned later. The intensity distributions of the seed beam transmitted through the YDDCF without pumping is shown in Figs. 2(f)–2(j). The coupling efficiency is 55%. Figure 2(f) shows the total intensity distribution. The transmitted beam kept the doughnut shape. Small modification of the transmitted beam was probably caused by the birefringence in the fiber core, which was weakly coiled. The intensity distributions after passage through a linear polarizer are shown in Figs. 2(g)–2(j). A slight rotation of the polarization distributions around the beam axis compared to the seed beam itself [Figs. 2(b)–2(e)] was observed. Here the fraction of radial polarization is estimated to be 82%. However, this rotation, which is also attributed to the birefringence of the fiber core, can be compensated by a pair of half-wavelength (λ∕2) plates if necessary. Figures 3(c) and 3(d) show the intensity profiles across the beam center of the transmitted beam. Since there is no significant difference between the intensity profiles of the seed and transmitted beams, it is clear that the radially polarized beam transmitted
Fig. 3. Intensity profiles across the beam center of the seed beam (top row), the transmitted beam (second row), and the amplified beam (bottom row). The horizontal and vertical axes correspond to the x and y directions in Fig. 2, respectively. Solid and dashed lines are the experimental data and the fitting, respectively.
through the YDDCF maintains the intensity and polarization distributions. Figures 2(k)–2(o) show the intensity distributions of the amplified beam at the maximum output power of 21 W. The total intensity distribution is shown in Fig. 2(k). The beam center is still dark and the beam shape is much closer to the doughnut shape than the transmitted beam without amplification [Fig. 2(f)]. Figures 2(l)–2(o) show the intensity distribution after passage through a linear polarizer. The rotation angle of the polarization distribution around the beam axis increases compared to the transmitted beam without amplification [Figs. 2(g)–2(j)]. This additional rotation is thermally enhanced because the rotation angle increases with increasing the pump power (data are not shown). In general, cylindrical vector beams such as radially and azimuthally polarized beams are expected to be free from the depolarization effect. However, the cylindrical symmetry of the fiber is no longer maintained because the coiling and twisting of the fiber probably results in the depolarization shown in Figs. 2(l)–2(o). The fractions of radial and azimuthal polarizations are 65% and 35%, respectively. Figures 3(e) and 3(f) show the intensity profiles of the amplified beam across the beam center. When the ASE was generated, the increase of the intensity on the beam center has been observed because of the Gaussian shape of the ASE [14]. However, the intensity on the beam center showed no significant difference even after the amplification, implying that the generation of the ASE in the fiber was negligible in the experiment.
May 15, 2014 / Vol. 39, No. 10 / OPTICS LETTERS
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of 1 W. The amplified beam obtained in the experiment can be a seed beam for further amplification of a radially polarized beam with suppression of the ASE. In conclusion, the amplification of a radially polarized beam by an YDDCF was demonstrated. The output power reached 21 W, which may be sufficient for some kinds of laser processing, such as cutting of thin materials. The ASE was sufficiently suppressed by using a seed beam with proper power. This technique will be also applicable to the amplification of an azimuthally polarized beam. By using this high-power laser source, we will be able to experimentally evaluate the processing performance of a radially polarized beam as a future work.
-2 -4 -6 -8
W
1080
1100 3.1 W
pu ed
1060
ch
1040
Wavelength (nm)
un
1020
La
1000
2W
W
m
16. 9.4
p
23.
we
30 3W
po
-10
r
0
Relative intensity (dB)
Fig. 4. Output power of the amplified beam as a function of the pump power.
Fig. 5. Emission spectra of the amplified beams at different pump power.
Figure 4 depicts the output power of the amplified beam as a function of the pump power. The maximum output power reached 21 W. The slope efficiency was approximately 70%, which is much higher than the previous reports of the amplification of the vector beams [14,15], and close to the values reported for high-power amplification of scalar beams [18–20]. The saturation of the output power was observed when the pump power was above 26 W. This was attributed to the wavelength shift of the pump beam, which results in the decrease of absorption efficiency, due to the temperature rise of the pump LD. Therefore, further amplification of the radially polarized beam will be possible by using a higher power or frequency-stabilized pump source. Figure 5 shows the emission spectra of the amplified beam at different pump power. The ASE component, which has a peak around 1030 nm, was not observed. This result implies that the ASE was effectively suppressed by injecting the seed beam with sufficient power
This work was supported in part by Core Research for Evolutional Science and Technology (CREST) and the Japan Science and Technology Agency (JST). References 1. Q. Zhan and J. R. Leger, Opt. Express 10, 324 (2002). 2. K. Youngworth and T. Brown, Opt. Express 7, 77 (2000). 3. Q. Zhan, Opt. Express 12, 3377 (2004). 4. W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995). 5. V. G. Niziev and A. V. Nesterov, J. Phys. D 32, 1455 (1999). 6. V. Onuseit, M. A. Ahmed, R. Weber, and T. Graf, Phys. Procedia 12, 584 (2011). 7. M. Meier, V. Romano, and T. Feurer, Appl. Phys. A 86, 329 (2007). 8. M. Kraus, M. A. Ahmed, A. Michalowski, A. Voss, R. Weber, and T. Graf, Opt. Express 18, 22305 (2010). 9. D. J. Richardson, J. Nilsson, and W. A. Clarkson, J. Opt. Soc. Am. B 27, B63 (2010). 10. J. Li, K. Ueda, M. Musha, and A. Shirakawa, Opt. Lett. 31, 2969 (2006). 11. J. Li, K. Ueda, A. Sirakawa, M. Musha, L. X. Zhong, and Z. M. Zhang, Laser Phys. Lett. 4, 814 (2007). 12. R. Zhou, B. Ibarra-Escamilla, J. W. Haus, P. E. Powers, and Q. Zhan, Appl. Phys. Lett. 95, 191111 (2009). 13. D. Lin, K. Xia, J. Li, R. Li, K. Ueda, G. Li, and X. Li, Opt. Lett. 35, 2290 (2010). 14. T. Chubachi, Y. Kozawa, and S. Sato, Opt. Lett. 34, 716 (2009). 15. M. Fridman, M. Nixon, M. Dubinskii, A. A. Friesem, and N. Davidson, Opt. Lett. 35, 1332 (2010). 16. S. Piehler, X. Delen, M. Rumpel, J. Didierjean, N. Aubry, T. Graf, F. Balembois, P. Georges, and M. A. Ahmed, Opt. Express 21, 11376 (2013). 17. Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, Appl. Phys. Express 1, 022008 (2008). 18. A. Liem, J. Limpert, H. Zellmer, and A. Tünnermann, Opt. Lett. 28, 1537 (2003). 19. Y. Jeong, J. Nilsson, J. K. Sahu, D. B. S. Soh, C. Alegria, P. Dupriez, C. A. Codemard, D. N. Payne, R. Horley, L. M. B. Hickey, L. Wanzcyk, C. E. Chryssou, J. A. Alvarez-Chavez, and P. W. Turner, Opt. Lett. 30, 459 (2005). 20. M. Hildebrandt, M. Frede, and D. Kracht, Opt. Lett. 32, 2345 (2007).
