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Large angle acceptance of quasi-phase-matched second harmonic generation in a homocentrically poled LiNbO3
Optics Communications 252 (2005) 397–401 www.elsevier.com/locate/optcom
Large angle acceptance of quasi-phase-matched second harmonic generation in a homocentrically poled LiNbO3 Ting Wang *, Boqin Ma, Yan Sheng, Peigen Ni, Binying Cheng, Daozhong Zhang Optical Physics Laboratory, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, China Received 30 November 2004; received in revised form 26 March 2005; accepted 12 April 2005
Abstract A periodically poled LiNbO3 (PPLN) with homocentric semicircle domain structure is prepared, by which a high efficiency second harmonic generation with large angle acceptance is demonstrated. The angle acceptance and conversion efficiency of this PPLN is compared to the PPLN with a strip pattern. In our case the poling period is 26 lm, and the crystal is 9 mm long. The corresponding angle acceptance is 30°, while that of strip pattern PPLN is 2.36°. The conversion efficiency of PPLN with homocentric semicircle pattern and strip pattern is 36.7% and 33% respectively. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Quasi-phase-matching; Homocentric semicircles domain structure; Large angle acceptance; Second-harmonic generation
1. Introduction The quasi-phase matching (QPM) technique has been extensively used for the frequency conversion [1–7] because of its higher conversion efficiency, no walk-off effect and easy reversion of the ferroelectric crystal domain. For example, PPLN can have a gain enhancement about (2d33/ d31p)2 20 over the birefringence phase matching technique [8]. Free of walk-off effect and single *
Corresponding author. Tel.: +86 1082649341; fax: +86 1082649451. E-mail address: [email protected] (T. Wang).
pass highly efficient second harmonic generation (SHG) in a 53 mm length PPLN was reported [9]. In conventional phase matching method, there is a rigorous requirement for the incident direction of the input laser beam. The intensity of SH output is expressed as [10] 2 2 2 1 I 2x ¼ CL I x sin c DkL ; ð1Þ 2 where C is the coefficient related to the crystal parameters; L is the crystal length; Dk = K2x 2Kx is the wave vector difference; Ix and I2x, Kx and K2x are the intensities and wave vectors of the fundamental and second-harmonic waves
0030-4018/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.04.019
398
T. Wang et al. / Optics Communications 252 (2005) 397–401
respectively. In the QPM method, the Dk should be expressed by
DkðKÞ ¼ ðK K0 Þ
2 oDk 1 2 o Dk þ ðK K 0 Þ þ oK 2 oK2
ð2Þ
ð3Þ
where G ¼ 2pm is the reciprocal vector, and m is K an integer, K is the poled period of the crystal. If there was a misalignment between the fundamental beam and the QPM reciprocal vector, there must be a reduction of the conversion efficiency due to the phase mismatch. The full width at half maximum (FWHM) of the SHG output at the case of quasi-phase-matching is typically less than 5° [11]. In this paper, we introduce a novel domain pattern of PPLN crystal for the SHG in order to increase the FWHM of incident angle. The structure consists of a series of homocentric semicircles of inversed domain pattern. We measure the SH output power at different incident angles of fundamental wave. The experimental results demonstrate that a wide incident angle of 30° can be obtained. The advantage of large angle acceptance can be applied to the compact integrated optical circuit, where the multi-direction transportation is required.
We usually may neglect the higher-order terms in the expansion. Using DkL ¼ 0.4429, the FWHM 2 bandwidth in K, which we denote by dK, can be written as 1 0.8858 oDk . ð4Þ dK ¼ L oK
Dk ¼ K 2x 2K x G;
2. Theoretical analysis When the directions of incident fundamental wave (FW) and QPM grating vector is not completely collinear and there is an angle between them, the actual effecting period of QPM becomes longer, and the reciprocal vector involved in the SHG process becomes smaller, therefore the phase matching condition should be Dk ¼ k 2w 2k x 2pm cos h . Based on this expression and Eq. (1), we K may estimate the dependence of conversion efficiency on the deviation of semicircular patternÕs period. According to (1), the phase matching factor in the expression for the power conversion efficiency is sin c2 ðDkL ), we may use the fact that this factor 2 goes to 12 when DkL ¼ 0.4429 to find the FWHM 2 acceptance handwidths. Dk is a function of the QPM period K, and it can be expanded in a Taylor series about K0 which satisfies phase matching condition Dk = 0:
With Eq. (2), we obtain oDk 2pm p ¼ 2 ¼ . oK K 2ml2c
ð5Þ
Here lc ¼ 4ðn2kn1 Þ is the coherence length. Thus the FWHM acceptance width for the variation of period is, according to (4) and (5), 1 0.8858 p dK ¼ ð6Þ . L 2ml2c And we can calculate the FWHM acceptance width for the incident angle with the relationship 0 dh ¼ arccosðK0KþdK Þ. From Eq. (6), we can also find that with the increasing of the crystal length, the period FWHM acceptance will decrease, and this leads to the decrease of incident angle acceptance. Meanwhile, we calculated the incident angle acceptance for strip pattern PPLN with the FW at 1.34 lm, which we used in the experiment. The calculation result shows that the angle acceptance for the strip pattern PPLN is as small as 2.38°, in order to broaden the angle acceptance, we designed the homocentric semicircle pattern PPLN shown in Fig. 1, the center of the semicircle is located at
Fig. 1. Schematic diagram of the homocentric semicircles structure. The fundamental beam was focused at the center of the semicircles domain patterns. The reciprocal vector would be equal at a wide range of incident beam direction.
T. Wang et al. / Optics Communications 252 (2005) 397–401
399
the middle of the input surface of the PPLN. When the focused beam of fundamental wave is incident into the crystal and the focus locates exactly at the center of the semicircles, the structure of homocentric semicircles can provide equal reciprocal vectors at different incident directions. The phase matching condition can be always satisfied within a large range of the input angle, as well as the focused beam with large divergence.
3. Experiments To fabricate the PPLN, pattern of homocentric semicircles structure was transferred onto the +z surface of a polished LiNbO3 crystal slab by standard photolithography. The poling process of the crystal was carried out in a chamber containing LiCl electrolyte, which was separated by the crystal sample, two O-rings were used to clip the sample tightly [8,12,13]. An external electric pulse was applied onto the sample via two liquid electrodes. The pulse voltage and duration were about 22 kV/ mm and 950 ms respectively. The length, width and thickness of the poled area were 9, 5 and 0.4 mm respectively. The period of semicircle domain of the QPM was 26 lm, which was very convenient for us to fabricate high quality sample, and we could get relatively high laser output at the corresponding FW wavelength of 1.34 lm The radius of the first semicircle was designed to be 500 lm with the consideration that the radius should be larger than the width of incident beam. For comparison, we also polled LN crystal with the same poling period but the domain pattern was straight stripe. Fig. 2(a) and (b) shows the amplified poled pattern of the homocentric semicircles in +z and z surface respectively. We can see that the reversed domains circles are uniform in a fan-like region. The domains overlapped into each other along specific orientations, shown in Fig. 2 and the angle between the orientations was about 60°. There are a lot of hexagonal nucleus formed during the poling process, and corresponding domain walls are parallel to each other [14,15]. We suppose that the domain walls are prefer to grow along the diagonal direction of the hexagonal nucleus which is normal to the tangent of the semicircle electrode
Fig. 2. Optical micrographs of the semicircle pattern QPM device: (a) +z surface; (b) z surface. The interval of radium is 26 lm for second order QPM of fundamental wavelength 1.34 lm. Domains overlapped into each other at black area.
edge, shown in Fig. 3. Thus the angle of the adjacent two overlapped areas is typical 60° in case of poling LiNbO3. The quality of the poled structure was checked by the diffraction of a laser beam. When a He– Ne laser beam was incident onto the +z or z surface, which was pre-treated by putting the poled crystal into an acid cell for about 15 min. The diffraction of the semicircle domains structure is shown in Fig. 4. All bright arcs in the figure have the same center point, and intervals between the adjacent circles are also equal. This implies that the reciprocal vectors of the structure have the
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T. Wang et al. / Optics Communications 252 (2005) 397–401
Fig. 3. The black semicircle indicates the shape of the electrode, hexagons are schematic diagram of nucleus formed during poling LiNbO3, the arrows show the direction at which the domain walls grow fast.
Fig. 4. The diffraction pattern of the semicircle domain structure using He–Ne laser.
same period at different direction. If the input beam travels through the center point, the equal conversion efficiency of the fundamental wave
can be obtained within a wide range of the input directions. A tunable optical parametric oscillator (OPO) pumped by a 1064 nm Nd:YAG laser was used as an incident light source. The pulse duration and repetition rate were 4 ns and 10 Hz respectively. A lens of 30 cm focal length was used to focus the incident beam into the crystal, and the focal spot diameter was about 260 lm. The PPLN sample was put on a stage, which can be rotated around the axis that passed through the center of the semicircles of the reversed domains. An optical filter was put just behind the sample stage so as to filter off the fundamental wave, and a thermoelectric power meter was used to measure the red SH power. In the experiment the incident beam at a wavelength of 1.34 lm was focused at the center of the semicircles reversed domains as shown in Fig. 1. We measured the output power of the second harmonic waves at the wavelength of 0.67 lm for different incident angles. The normalized SH power verses the incident input beam angles for two different domain structures are plotted in Fig. 5. Fig. 5(a) shows the second harmonic output for the stripe domain structure. The dark round points represent the measured value and the solid curve is the numerical simulation. The zero degree represents the normal incidence. The FWHM angle is less than 2.4°. Fig. 5(b) shows the output of the homocentric semicircle domain structure. The dark round points represent the measured results and the solid line is the fit curve. It means that the SH power output is not changed very much within an angle range of 30°, which is more than 12 times wider than that in stripe domains structure. The output decreases as the incident angle become larger, it is probably because of the reflection loss from the incident surface. If the incident surface were polished to form a curve with appropriate curvature, the output power would remain unchanged for a wider incident angle. The conversion efficiency for semicircle pattern in our experiment is 36.7% with an input average power of 1.864 mW, which is close to that of theoretical value 38% and the conversion efficiency of stripe pattern under the same condition is 33%. Both patterns have the same duty cycle of 35%. We
T. Wang et al. / Optics Communications 252 (2005) 397–401
for QPM. SHG at a wavelength of 0.67 lm was obtained in the crystal by using second order QPM technique. The relationship between output SH power and incident angle was studied and compared with a stripe QPM crystal. The homocentric semicircle QPM device allows a fundamental laser beam with large input angle. This would be helpful for the construction of all-optical integrated circuits with multi-channel.
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0.4
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Acknowledgements 0.0 -15
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3
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internal angle (degrees) 1.0
The financial supports of Chinese National Key Basic Research Special Fund and National Natural Science Foundation of China are gratefully acknowledged.
0.9 0.8
References
SH (normalized)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -15
-12
-9
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3
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9
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internal angle (degrees)
Fig. 5. SH output power versus the internal angle for: (a) strip domain pattern, (b) semicircle domain pattern.
can expect a larger output power and wider range of incident angle if the duty cycle reached 50%.
4. Conclusion In conclusion, we fabricated a domain structure of homocentric semicircle lithium niobate crystal
[1] K. Mizuuchi, K. Yamamoto, Appl. Phys. Lett. 60 (1992) 1283. [2] J.P. Meyn, M.M. Fejer, Opt. Lett. 22 (1997) 1214. [3] K.R. Parameswaran, J.R. Kurz, R.V. Roussev, M.M. Fejer, Opt. Lett. 27 (2002) 43. [4] M. Fujimura, A. Shiratsuki, T. Suhara, H. Nishihara, Jpn. J. Appl. Phys 37 (1998) L659. [5] D. Taverner, P. Britton, P.G.R. Smith, D.J. Richandson, G.W. Ross, D.C. Hanna, Opt. Lett. 23 (1998) 162. [6] K. Koch, G.T. Moore, J. Opt. Soc. Am. B 16 (1999) 448. [7] S.N. Zhu, Y.Y. Zhu, N.B. Ming, Science 278 (1997) 843. [8] L.E. Myers, R.C. Eckardt, M.M. Fejer, R.L. Byer, W.R. Bosenberg, J.W. Pierce, J. Opt. Soc. Am. B 12 (1995) 2102. [9] G.D. Miller, R.G. Batchko, W.M. Tulloch, D.R. Weise, M.M. Fejer, R.L. Byer, Opt. Lett. 22 (1997) 1834. [10] M. Belmonte, T. Skettrup, C. Pedersen, J. Opt. A: Pure Appl. Opt. 1 (1999) 60. [11] H. Kim, L. Jankovic, G. Stegeman, M. Katz, S. Carrasco, L. Torner, Appl. Phys. Lett. 81 (2002) 2710. [12] S. Grilli, P. Ferraro, S.D. Nicola, A. finizio, G. Pierattini, P.D. Natale, M. Chiarini, Opt. Express 11 (2003) 392. [13] Hirohashi, K. Yamada, H. Kamio, S. Shichijyo, Jpn. J. Appl. Phys. 43 (2) (2004) 559. [14] V. Gopanlan, Q.X. Jia, T.E. Mitchell, Appl. Phys. Lett. 75 (1999) 2482. [15] T.J. Yang, V. Gopanlan, P. Swart, U. Mohideen, Phys. Rev. Lett. 82 (1999) 4106.
Large angle acceptance of quasi-phase-matched second harmonic generation in a homocentrically poled LiNbO3 Ting Wang *, Boqin Ma, Yan Sheng, Peigen Ni, Binying Cheng, Daozhong Zhang Optical Physics Laboratory, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, China Received 30 November 2004; received in revised form 26 March 2005; accepted 12 April 2005
Abstract A periodically poled LiNbO3 (PPLN) with homocentric semicircle domain structure is prepared, by which a high efficiency second harmonic generation with large angle acceptance is demonstrated. The angle acceptance and conversion efficiency of this PPLN is compared to the PPLN with a strip pattern. In our case the poling period is 26 lm, and the crystal is 9 mm long. The corresponding angle acceptance is 30°, while that of strip pattern PPLN is 2.36°. The conversion efficiency of PPLN with homocentric semicircle pattern and strip pattern is 36.7% and 33% respectively. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Quasi-phase-matching; Homocentric semicircles domain structure; Large angle acceptance; Second-harmonic generation
1. Introduction The quasi-phase matching (QPM) technique has been extensively used for the frequency conversion [1–7] because of its higher conversion efficiency, no walk-off effect and easy reversion of the ferroelectric crystal domain. For example, PPLN can have a gain enhancement about (2d33/ d31p)2 20 over the birefringence phase matching technique [8]. Free of walk-off effect and single *
Corresponding author. Tel.: +86 1082649341; fax: +86 1082649451. E-mail address: [email protected] (T. Wang).
pass highly efficient second harmonic generation (SHG) in a 53 mm length PPLN was reported [9]. In conventional phase matching method, there is a rigorous requirement for the incident direction of the input laser beam. The intensity of SH output is expressed as [10] 2 2 2 1 I 2x ¼ CL I x sin c DkL ; ð1Þ 2 where C is the coefficient related to the crystal parameters; L is the crystal length; Dk = K2x 2Kx is the wave vector difference; Ix and I2x, Kx and K2x are the intensities and wave vectors of the fundamental and second-harmonic waves
0030-4018/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.04.019
398
T. Wang et al. / Optics Communications 252 (2005) 397–401
respectively. In the QPM method, the Dk should be expressed by
DkðKÞ ¼ ðK K0 Þ
2 oDk 1 2 o Dk þ ðK K 0 Þ þ oK 2 oK2
ð2Þ
ð3Þ
where G ¼ 2pm is the reciprocal vector, and m is K an integer, K is the poled period of the crystal. If there was a misalignment between the fundamental beam and the QPM reciprocal vector, there must be a reduction of the conversion efficiency due to the phase mismatch. The full width at half maximum (FWHM) of the SHG output at the case of quasi-phase-matching is typically less than 5° [11]. In this paper, we introduce a novel domain pattern of PPLN crystal for the SHG in order to increase the FWHM of incident angle. The structure consists of a series of homocentric semicircles of inversed domain pattern. We measure the SH output power at different incident angles of fundamental wave. The experimental results demonstrate that a wide incident angle of 30° can be obtained. The advantage of large angle acceptance can be applied to the compact integrated optical circuit, where the multi-direction transportation is required.
We usually may neglect the higher-order terms in the expansion. Using DkL ¼ 0.4429, the FWHM 2 bandwidth in K, which we denote by dK, can be written as 1 0.8858 oDk . ð4Þ dK ¼ L oK
Dk ¼ K 2x 2K x G;
2. Theoretical analysis When the directions of incident fundamental wave (FW) and QPM grating vector is not completely collinear and there is an angle between them, the actual effecting period of QPM becomes longer, and the reciprocal vector involved in the SHG process becomes smaller, therefore the phase matching condition should be Dk ¼ k 2w 2k x 2pm cos h . Based on this expression and Eq. (1), we K may estimate the dependence of conversion efficiency on the deviation of semicircular patternÕs period. According to (1), the phase matching factor in the expression for the power conversion efficiency is sin c2 ðDkL ), we may use the fact that this factor 2 goes to 12 when DkL ¼ 0.4429 to find the FWHM 2 acceptance handwidths. Dk is a function of the QPM period K, and it can be expanded in a Taylor series about K0 which satisfies phase matching condition Dk = 0:
With Eq. (2), we obtain oDk 2pm p ¼ 2 ¼ . oK K 2ml2c
ð5Þ
Here lc ¼ 4ðn2kn1 Þ is the coherence length. Thus the FWHM acceptance width for the variation of period is, according to (4) and (5), 1 0.8858 p dK ¼ ð6Þ . L 2ml2c And we can calculate the FWHM acceptance width for the incident angle with the relationship 0 dh ¼ arccosðK0KþdK Þ. From Eq. (6), we can also find that with the increasing of the crystal length, the period FWHM acceptance will decrease, and this leads to the decrease of incident angle acceptance. Meanwhile, we calculated the incident angle acceptance for strip pattern PPLN with the FW at 1.34 lm, which we used in the experiment. The calculation result shows that the angle acceptance for the strip pattern PPLN is as small as 2.38°, in order to broaden the angle acceptance, we designed the homocentric semicircle pattern PPLN shown in Fig. 1, the center of the semicircle is located at
Fig. 1. Schematic diagram of the homocentric semicircles structure. The fundamental beam was focused at the center of the semicircles domain patterns. The reciprocal vector would be equal at a wide range of incident beam direction.
T. Wang et al. / Optics Communications 252 (2005) 397–401
399
the middle of the input surface of the PPLN. When the focused beam of fundamental wave is incident into the crystal and the focus locates exactly at the center of the semicircles, the structure of homocentric semicircles can provide equal reciprocal vectors at different incident directions. The phase matching condition can be always satisfied within a large range of the input angle, as well as the focused beam with large divergence.
3. Experiments To fabricate the PPLN, pattern of homocentric semicircles structure was transferred onto the +z surface of a polished LiNbO3 crystal slab by standard photolithography. The poling process of the crystal was carried out in a chamber containing LiCl electrolyte, which was separated by the crystal sample, two O-rings were used to clip the sample tightly [8,12,13]. An external electric pulse was applied onto the sample via two liquid electrodes. The pulse voltage and duration were about 22 kV/ mm and 950 ms respectively. The length, width and thickness of the poled area were 9, 5 and 0.4 mm respectively. The period of semicircle domain of the QPM was 26 lm, which was very convenient for us to fabricate high quality sample, and we could get relatively high laser output at the corresponding FW wavelength of 1.34 lm The radius of the first semicircle was designed to be 500 lm with the consideration that the radius should be larger than the width of incident beam. For comparison, we also polled LN crystal with the same poling period but the domain pattern was straight stripe. Fig. 2(a) and (b) shows the amplified poled pattern of the homocentric semicircles in +z and z surface respectively. We can see that the reversed domains circles are uniform in a fan-like region. The domains overlapped into each other along specific orientations, shown in Fig. 2 and the angle between the orientations was about 60°. There are a lot of hexagonal nucleus formed during the poling process, and corresponding domain walls are parallel to each other [14,15]. We suppose that the domain walls are prefer to grow along the diagonal direction of the hexagonal nucleus which is normal to the tangent of the semicircle electrode
Fig. 2. Optical micrographs of the semicircle pattern QPM device: (a) +z surface; (b) z surface. The interval of radium is 26 lm for second order QPM of fundamental wavelength 1.34 lm. Domains overlapped into each other at black area.
edge, shown in Fig. 3. Thus the angle of the adjacent two overlapped areas is typical 60° in case of poling LiNbO3. The quality of the poled structure was checked by the diffraction of a laser beam. When a He– Ne laser beam was incident onto the +z or z surface, which was pre-treated by putting the poled crystal into an acid cell for about 15 min. The diffraction of the semicircle domains structure is shown in Fig. 4. All bright arcs in the figure have the same center point, and intervals between the adjacent circles are also equal. This implies that the reciprocal vectors of the structure have the
400
T. Wang et al. / Optics Communications 252 (2005) 397–401
Fig. 3. The black semicircle indicates the shape of the electrode, hexagons are schematic diagram of nucleus formed during poling LiNbO3, the arrows show the direction at which the domain walls grow fast.
Fig. 4. The diffraction pattern of the semicircle domain structure using He–Ne laser.
same period at different direction. If the input beam travels through the center point, the equal conversion efficiency of the fundamental wave
can be obtained within a wide range of the input directions. A tunable optical parametric oscillator (OPO) pumped by a 1064 nm Nd:YAG laser was used as an incident light source. The pulse duration and repetition rate were 4 ns and 10 Hz respectively. A lens of 30 cm focal length was used to focus the incident beam into the crystal, and the focal spot diameter was about 260 lm. The PPLN sample was put on a stage, which can be rotated around the axis that passed through the center of the semicircles of the reversed domains. An optical filter was put just behind the sample stage so as to filter off the fundamental wave, and a thermoelectric power meter was used to measure the red SH power. In the experiment the incident beam at a wavelength of 1.34 lm was focused at the center of the semicircles reversed domains as shown in Fig. 1. We measured the output power of the second harmonic waves at the wavelength of 0.67 lm for different incident angles. The normalized SH power verses the incident input beam angles for two different domain structures are plotted in Fig. 5. Fig. 5(a) shows the second harmonic output for the stripe domain structure. The dark round points represent the measured value and the solid curve is the numerical simulation. The zero degree represents the normal incidence. The FWHM angle is less than 2.4°. Fig. 5(b) shows the output of the homocentric semicircle domain structure. The dark round points represent the measured results and the solid line is the fit curve. It means that the SH power output is not changed very much within an angle range of 30°, which is more than 12 times wider than that in stripe domains structure. The output decreases as the incident angle become larger, it is probably because of the reflection loss from the incident surface. If the incident surface were polished to form a curve with appropriate curvature, the output power would remain unchanged for a wider incident angle. The conversion efficiency for semicircle pattern in our experiment is 36.7% with an input average power of 1.864 mW, which is close to that of theoretical value 38% and the conversion efficiency of stripe pattern under the same condition is 33%. Both patterns have the same duty cycle of 35%. We
T. Wang et al. / Optics Communications 252 (2005) 397–401
for QPM. SHG at a wavelength of 0.67 lm was obtained in the crystal by using second order QPM technique. The relationship between output SH power and incident angle was studied and compared with a stripe QPM crystal. The homocentric semicircle QPM device allows a fundamental laser beam with large input angle. This would be helpful for the construction of all-optical integrated circuits with multi-channel.
1.0
0.8
SH (normalized)
401
0.6
0.4
0.2
Acknowledgements 0.0 -15
-12
-9
-6
-3
0
3
6
9
12
15
internal angle (degrees) 1.0
The financial supports of Chinese National Key Basic Research Special Fund and National Natural Science Foundation of China are gratefully acknowledged.
0.9 0.8
References
SH (normalized)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -15
-12
-9
-6
-3
0
3
6
9
12
15
internal angle (degrees)
Fig. 5. SH output power versus the internal angle for: (a) strip domain pattern, (b) semicircle domain pattern.
can expect a larger output power and wider range of incident angle if the duty cycle reached 50%.
4. Conclusion In conclusion, we fabricated a domain structure of homocentric semicircle lithium niobate crystal
[1] K. Mizuuchi, K. Yamamoto, Appl. Phys. Lett. 60 (1992) 1283. [2] J.P. Meyn, M.M. Fejer, Opt. Lett. 22 (1997) 1214. [3] K.R. Parameswaran, J.R. Kurz, R.V. Roussev, M.M. Fejer, Opt. Lett. 27 (2002) 43. [4] M. Fujimura, A. Shiratsuki, T. Suhara, H. Nishihara, Jpn. J. Appl. Phys 37 (1998) L659. [5] D. Taverner, P. Britton, P.G.R. Smith, D.J. Richandson, G.W. Ross, D.C. Hanna, Opt. Lett. 23 (1998) 162. [6] K. Koch, G.T. Moore, J. Opt. Soc. Am. B 16 (1999) 448. [7] S.N. Zhu, Y.Y. Zhu, N.B. Ming, Science 278 (1997) 843. [8] L.E. Myers, R.C. Eckardt, M.M. Fejer, R.L. Byer, W.R. Bosenberg, J.W. Pierce, J. Opt. Soc. Am. B 12 (1995) 2102. [9] G.D. Miller, R.G. Batchko, W.M. Tulloch, D.R. Weise, M.M. Fejer, R.L. Byer, Opt. Lett. 22 (1997) 1834. [10] M. Belmonte, T. Skettrup, C. Pedersen, J. Opt. A: Pure Appl. Opt. 1 (1999) 60. [11] H. Kim, L. Jankovic, G. Stegeman, M. Katz, S. Carrasco, L. Torner, Appl. Phys. Lett. 81 (2002) 2710. [12] S. Grilli, P. Ferraro, S.D. Nicola, A. finizio, G. Pierattini, P.D. Natale, M. Chiarini, Opt. Express 11 (2003) 392. [13] Hirohashi, K. Yamada, H. Kamio, S. Shichijyo, Jpn. J. Appl. Phys. 43 (2) (2004) 559. [14] V. Gopanlan, Q.X. Jia, T.E. Mitchell, Appl. Phys. Lett. 75 (1999) 2482. [15] T.J. Yang, V. Gopanlan, P. Swart, U. Mohideen, Phys. Rev. Lett. 82 (1999) 4106.