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OPTICS LETTERS / Vol. 38, No. 21 / November 1, 2013
Phase difference in modulated signals of two orthogonally polarized outputs of a Nd:YAG microchip laser with anisotropic optical feedback Peng Zhang,1 Yi-Dong Tan,1,* Ning Liu,1,2 Yun Wu,1 and Shu-Lian Zhang1 1
State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China 2 School of Mechanical Engineering, Nantong University, Nantong, Jiangsu 226019, China *Corresponding author: [email protected] Received August 2, 2013; revised September 17, 2013; accepted September 23, 2013; posted September 24, 2013 (Doc. ID 195049); published October 18, 2013 We present an experimental observation of the output responses of a Nd:YAG microchip laser with an anisotropic external cavity under weak optical feedback. The feedback mirror is stationary during the experiments. A pair of acousto-optic modulators is used to produce a frequency shift in the feedback light with respect to the initial light. The laser output is a beat signal with 40 kHz modulation frequency and is separated into two orthogonal directions by a Wollaston prism. Phase differences between the two intensity curves are observed as the laser works in two orthogonal modes, and vary with the external birefringence element and the pump power. Theoretical analyses are given, and the simulated results are consistent with the experimental phenomena. © 2013 Optical Society of America OCIS codes: (120.5060) Phase modulation; (140.3480) Lasers, diode-pumped; (140.3580) Lasers, solid-state. http://dx.doi.org/10.1364/OL.38.004296
Anisotropic laser feedback, in which a birefringence element is placed in the external cavity, has been applied to such kinds of measurement fields as displacement [1,2] and phase retardation [3–5] measurement, and to produce rapid polarization modulation [6–8], which may be used in communications or other fields. In the experiments of [6–8], the feedback target is stationary; on the contrary, the feedback mirror keeps moving in [1–5]. Recently, frequency-shifted optical feedback has attracted attention in laser Doppler velocimetry (LDV) [9,10], vibration measurement [11], laser optical feedback imaging (LOFI) [12,13], and displacement measurement [14,15]. In most of this research, the feedback mirror or the measured target is also in motion. A phenomenon in which the modulated signals of two orthogonally polarized outputs have a phase difference between them, as a laser works with an anisotropic feedback cavity, has been reported [16,17]. In those experiments, the feedback mirror moves along the laser axis to generate a modulation in the laser intensity. In this Letter, we present the phase difference behavior of a Nd:YAG microchip laser with anisotropic weak feedback. The distinctions from the previous experiments are that a pair of acousto-optic modulators (AOMs) is used to generate a frequency shift of 40 kHz and the feedback mirror is not moved. Phase differences between the laser intensities in two orthogonal directions are observed and vary with the birefringence element in the external cavity, and also the laser polarization state and the pump power are changed. This system has better stability and waveform than those in [16,17] because there is no need for a moving feedback mirror. Figure 1 shows the experimental setup. A 1 mm thick and 5 mm diameter Nd:YAG crystal chip with both end faces coated is used to form the resonator. The reflectivity of the two end faces is 99.8% and 99% at 1064 nm. A fiber-coupled LD is used as the pump, and its output is focused on the chip by a self-focusing lens (SFL). The 0146-9592/13/214296-04$15.00/0
laser output is split by a beam splitter (BS). The reflected part goes to a Wollaston prism (W) and is separated into two orthogonal polarization directions, and then impinges on photodetectors (D1 and D2 ) for detection. The transmitted part passes through a pair of AOMs (AOM1 and AOM2 , customized in China; central modulation frequency is 70 MHz∕70.04 MHz) to form optical feedback. AOMs are driven by two radio frequency signal generators (RF1 and RF 2 ). The feedback mirror (MF ) is coated with antireflection film on one end face and is uncoated with the other, so the reflectivity of it is nearly 4%. The feedback light has a 40 kHz frequency shift with respect to the initial light by means of appropriate adjustments of the AOMs and MF . L is a converging lens for focusing the laser onto MF . SI is a scanning interferometer (THORLABS SA200-8B, FSR 1.5 GHz) driven by a spectrum analyzer controller (SID, THORLABS SA201) for monitoring the output state of the laser. A waveplate (WP) is placed between MF and L. The outputs of D1 , D2 , and the synchronization signal of SID are sent to a fourchannel oscilloscope (OS, Tektronix DPO2014). The orientations of W and WP are similar to those in [16,17]. The orientation of the Wollaston prism is unchanged after being adjusted in the beginning. We used two Nd:YAG microchip lasers with the same thickness. The lasers can work in single mode or two modes with different pump powers (for instance, 47.7 mW for a single-mode output and 51.5 mW for a
Fig. 1. Schematic of the experimental setup. © 2013 Optical Society of America
November 1, 2013 / Vol. 38, No. 21 / OPTICS LETTERS
two-mode output), which are shown in Figs. 2(a) and 2(b). In the latter situation, the relationship between the polarization directions of the two modes is parallel for one laser and perpendicular for the other, which can be checked by a polarizer; i.e., the variation tendencies of the two amplitudes are similar for the parallel relationship as the polarizer is rotated; however, the variation tendencies are opposite for the perpendicular relationship, as shown in Figs. 2(c) and 2(d), respectively. It should be noticed that these two modes may be two longitudinal modes, or two components with an oscillation frequency difference that are split from one longitudinal mode by the residual stress existing in the crystal. A 12-order quartz waveplate (corresponding to 22order 86.5° phase retardation for 632.8 nm wavelength) is placed in the feedback cavity and can be rotated around an axis parallel to its surface normal. It is observed that when the laser works in single mode or two parallel-polarized modes, no phase difference appears between the light intensities detected by D1 and D2 , as shown in Fig. 3(a). The phase difference remains absent basically even though the waveplate is rotated or the pump power is varied. Moreover, this phenomenon still remains although the waveplate is changed with different phase retardation, which is quite different from that observed in [16,17]. This phenomenon can be explained as the light beams in the two axis directions of the Wollaston prism are split from the same electric field (single mode) or mixed by the same proportions of the light field (two parallel-polarized modes), so no phase difference appears between the two modulated signals. However, for the laser works in two orthogonally polarized modes, phase differences are clearly observed between the two intensity signals. The phase differences can change with the waveplate being rotated and the pump power being changed, as can be seen in Figs. 3(b)– 3(f). The waveform is a sine (or cosine) type due to the modulation being just a beat signal, which is more convenient than the sine-like type produced by a moving feedback mirror. The phase difference is also related to the change of the pump power. We observed that the phase difference has a maximum when the pump power
Fig. 2. Output modes of the lasers. (a) Single mode. (b) Two modes. (c) and (d) Orthogonally polarized two modes.
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Fig. 3. Experimental results. (a) In phase. (b)–(d) Phase difference appears. (e) Nearly 90° phase difference. (f) Nearly phase inversion.
is 52.35 mW, and it decreases gradually at the both sides of this power. Phase difference disappears when the pump power is up to 54.48 mW, and appears again when the pump power continues to increase, and then repeats the tendency above. The reasons for these phenomena are considered to be attributed to the polarization rotation and frequencydifference variation of the laser outputs induced by the change of the waveplate and the pump power, which are shown in Fig. 4 schematically. In Fig. 4(a), the fast and slow axes of the waveplate (f axis and s axis) are parallel to the optic axes of the Wollaston prism (o axis and e axis), respectively. But in Fig. 4(b), the optic axes of the waveplate and Wollaston prism are relatively rotated to each other and with respect to the laser initial polarization directions. In this case, the optical fields detected by the detectors can be written as
Fig. 4. Schematic of the orientations of optic axes and laser polarization directions. (a) No rotation. (b) Relative rotation.
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OPTICS LETTERS / Vol. 38, No. 21 / November 1, 2013
Eo E1s F sin β E1f F cos β E2s F sin β E2f F cos β;
g12f (1)
Ee E1s F cos β E1f F sin β E2s F cos β E2f
F
sin β;
g12s (2)
where the subscripts f and s indicate the components in the fast-axis and slow-axis directions of the waveplate, respectively. And the superscript F indicates the electric fields induced by the optical feedback. We can get E 1s
F
Ls expjω0 t E 1ms 1 η exp j4πν1 c × sinα β;
(3)
Lf expjω0 t E 1f F E1mf 1 η exp j4πν1 c × cosα β;
(4)
L E 2s F E 2ms 1 η exp j4πν2 s expjω0 t c × cosα β;
(5)
Lf expjω0 t E 2f E2mf 1 η exp j4πν2 c F
× sinα β;
(6)
where η T 2 r 3 ξ∕r 2 ;
(7)
where r 1 ; r 2 , and r 3 are the amplitude reflection coefficients of the two end faces of the Nd:YAG laser and the feedback mirror, respectively. T 2 1 − r 2 × r 2 is the transmittance of the output end of the Nd:YAG laser. L is the length of the external cavity, and its subscripts are defined as the above. ω0 2πΩ0 , in which Ω0 40 kHz is the modulation frequency induced by AOMs. ξ is the coupling efficiency from the external optical field back into the laser cavity [18]. ν is light frequency and c is the light speed in a vacuum. E1msor f and E 2msor f are written as nl E 1msf r 1 r 2 exp j4πν1 2g1sf l E 1 ; c
(8)
nl E 2msf r 1 r 2 exp j4πν2 2g2sf l E 2 ; c
(9)
where l is the length of the laser cavity, n is the effective refractive index of the medium in the laser cavity, and g is the linear gain per unit length of the gain medium with the presence of optical feedback, and can be expressed as [16]
2πLf 1 ; lnr 1 r 2 η cos − λ 2l
4πLf 1 2δ ; lnr 1 r 2 η cos − λ 2l
(10)
(11)
where δ is the phase retardation of the waveplate. Then we can obtain the light intensities as I o E o · E o ;
(12)
I e E e · E e :
(13)
From Eqs. (1)–(13), the light intensities in the two directions can be simulated by setting different values of α, β and the oscillation frequency difference of the two modes; the results are shown in Fig. 5 (the oscillation frequency difference is selected around 500 MHz). It can be seen that various phase differences can be obtained by changing the values of angles α, β and the oscillation frequency difference. These results correspond to those observed in Fig. 3, which means the theoretical analyses are consistent qualitatively with the phenomena in the experiments. The phase differences can change with the oscillation frequency difference, and the included angles, α and β, even almost disappear with some certain values of these three parameters, which is coincident with the phenomenon in which the phase difference is varied with the pump power and has a maximum in some pump powers, and a minimum in others. The phase difference behavior in modulated signals of two orthogonally polarized outputs of a Nd:YAG microchip laser with a frequency-shifted anisotropic weak optical feedback is observed and analyzed preliminarily. Phase differences are found between the two modulated intensity signals of the outputs in orthogonal directions, as the laser works in two orthogonally polarized modes.
Fig. 5. Simulated results. (a) In phase. (b)–(d) Phase difference appears. (e) Nearly 90° phase difference. (f) Nearly phase inversion.
November 1, 2013 / Vol. 38, No. 21 / OPTICS LETTERS
And the phase difference can be changed with variations of the pump power of the laser, and the rotation of the waveplate placed in the external cavity. These phenomena can be used to produce two sinetype laser outputs with a certain phase difference, which may be applied in some measurement and communications techniques. Moreover, they provide the possibility for measuring the phase retardation of a birefringent element or the rotation angle of a target. This work is supported by the Key Program of National Natural Science Foundation of China (grant 61036016). References 1. G. Liu, S. L. Zhang, J. Zhu, and Y. Li, Appl. Opt. 42, 6636 (2003). 2. L. F. Zhou, B. Zhang, S. L. Zhang, Y. D. Tan, and W. X. Liu, Chin. Phys. B 18, 1141 (2009). 3. L. G. Fei, S. L. Zhang, Y. Li, and J. Zhu, Opt. Express 13, 3117 (2005). 4. W. X. Chen, X. W. Long, S. L. Zhang, and G. Z. Xiao, Opt. Laser Technol. 44, 2427 (2012).
4299
5. W. X. Chen, S. L. Zhang, and X. W. Long, Opt. Lett. 37, 2433 (2012). 6. W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990). 7. Y. Mitsuhashi, J. Appl. Phys. 53, 9200 (1982). 8. T. Fujita, A. Schremer, and C. L. Tang, Appl. Phys. Lett. 51, 392 (1987). 9. K. Otsuka, R. Kawai, Y. Asakawa, and T. Fukazawa, Opt. Lett. 24, 1862 (1999). 10. S. Sudo, T. Ohtomo, Y. Takahashi, T. Oishi, and K. Otsuka, Appl. Opt. 48, 4049 (2009). 11. K. Otsuka, K. Abe, and J. Y. Ko, Opt. Lett. 27, 1339 (2002). 12. E. Lacot, R. Day, and F. Stoeckel, Phys. Rev. A 64, 043815 (2001). 13. E. Lacot and O. Hugon, Phys. Rev. A 70, 053824 (2004). 14. X. J. Wan, D. Li, and S. L. Zhang, Opt. Lett. 32, 367 (2007). 15. Z. Ren, D. Li, X. Wan, and S. Zhang, Laser Phys. 18, 939 (2008). 16. Y. D. Tan and S. L. Zhang, Appl. Opt. 46, 6064 (2007). 17. P. Zhang, S. L. Zhang, Y. D. Tan, Z. Q. Zhao, and Z. L. Zeng, Appl. Phys. B 106, 657 (2012). 18. W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, J. Lightwave Technol. 12, 1577 (1994).
OPTICS LETTERS / Vol. 38, No. 21 / November 1, 2013
Phase difference in modulated signals of two orthogonally polarized outputs of a Nd:YAG microchip laser with anisotropic optical feedback Peng Zhang,1 Yi-Dong Tan,1,* Ning Liu,1,2 Yun Wu,1 and Shu-Lian Zhang1 1
State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China 2 School of Mechanical Engineering, Nantong University, Nantong, Jiangsu 226019, China *Corresponding author: [email protected] Received August 2, 2013; revised September 17, 2013; accepted September 23, 2013; posted September 24, 2013 (Doc. ID 195049); published October 18, 2013 We present an experimental observation of the output responses of a Nd:YAG microchip laser with an anisotropic external cavity under weak optical feedback. The feedback mirror is stationary during the experiments. A pair of acousto-optic modulators is used to produce a frequency shift in the feedback light with respect to the initial light. The laser output is a beat signal with 40 kHz modulation frequency and is separated into two orthogonal directions by a Wollaston prism. Phase differences between the two intensity curves are observed as the laser works in two orthogonal modes, and vary with the external birefringence element and the pump power. Theoretical analyses are given, and the simulated results are consistent with the experimental phenomena. © 2013 Optical Society of America OCIS codes: (120.5060) Phase modulation; (140.3480) Lasers, diode-pumped; (140.3580) Lasers, solid-state. http://dx.doi.org/10.1364/OL.38.004296
Anisotropic laser feedback, in which a birefringence element is placed in the external cavity, has been applied to such kinds of measurement fields as displacement [1,2] and phase retardation [3–5] measurement, and to produce rapid polarization modulation [6–8], which may be used in communications or other fields. In the experiments of [6–8], the feedback target is stationary; on the contrary, the feedback mirror keeps moving in [1–5]. Recently, frequency-shifted optical feedback has attracted attention in laser Doppler velocimetry (LDV) [9,10], vibration measurement [11], laser optical feedback imaging (LOFI) [12,13], and displacement measurement [14,15]. In most of this research, the feedback mirror or the measured target is also in motion. A phenomenon in which the modulated signals of two orthogonally polarized outputs have a phase difference between them, as a laser works with an anisotropic feedback cavity, has been reported [16,17]. In those experiments, the feedback mirror moves along the laser axis to generate a modulation in the laser intensity. In this Letter, we present the phase difference behavior of a Nd:YAG microchip laser with anisotropic weak feedback. The distinctions from the previous experiments are that a pair of acousto-optic modulators (AOMs) is used to generate a frequency shift of 40 kHz and the feedback mirror is not moved. Phase differences between the laser intensities in two orthogonal directions are observed and vary with the birefringence element in the external cavity, and also the laser polarization state and the pump power are changed. This system has better stability and waveform than those in [16,17] because there is no need for a moving feedback mirror. Figure 1 shows the experimental setup. A 1 mm thick and 5 mm diameter Nd:YAG crystal chip with both end faces coated is used to form the resonator. The reflectivity of the two end faces is 99.8% and 99% at 1064 nm. A fiber-coupled LD is used as the pump, and its output is focused on the chip by a self-focusing lens (SFL). The 0146-9592/13/214296-04$15.00/0
laser output is split by a beam splitter (BS). The reflected part goes to a Wollaston prism (W) and is separated into two orthogonal polarization directions, and then impinges on photodetectors (D1 and D2 ) for detection. The transmitted part passes through a pair of AOMs (AOM1 and AOM2 , customized in China; central modulation frequency is 70 MHz∕70.04 MHz) to form optical feedback. AOMs are driven by two radio frequency signal generators (RF1 and RF 2 ). The feedback mirror (MF ) is coated with antireflection film on one end face and is uncoated with the other, so the reflectivity of it is nearly 4%. The feedback light has a 40 kHz frequency shift with respect to the initial light by means of appropriate adjustments of the AOMs and MF . L is a converging lens for focusing the laser onto MF . SI is a scanning interferometer (THORLABS SA200-8B, FSR 1.5 GHz) driven by a spectrum analyzer controller (SID, THORLABS SA201) for monitoring the output state of the laser. A waveplate (WP) is placed between MF and L. The outputs of D1 , D2 , and the synchronization signal of SID are sent to a fourchannel oscilloscope (OS, Tektronix DPO2014). The orientations of W and WP are similar to those in [16,17]. The orientation of the Wollaston prism is unchanged after being adjusted in the beginning. We used two Nd:YAG microchip lasers with the same thickness. The lasers can work in single mode or two modes with different pump powers (for instance, 47.7 mW for a single-mode output and 51.5 mW for a
Fig. 1. Schematic of the experimental setup. © 2013 Optical Society of America
November 1, 2013 / Vol. 38, No. 21 / OPTICS LETTERS
two-mode output), which are shown in Figs. 2(a) and 2(b). In the latter situation, the relationship between the polarization directions of the two modes is parallel for one laser and perpendicular for the other, which can be checked by a polarizer; i.e., the variation tendencies of the two amplitudes are similar for the parallel relationship as the polarizer is rotated; however, the variation tendencies are opposite for the perpendicular relationship, as shown in Figs. 2(c) and 2(d), respectively. It should be noticed that these two modes may be two longitudinal modes, or two components with an oscillation frequency difference that are split from one longitudinal mode by the residual stress existing in the crystal. A 12-order quartz waveplate (corresponding to 22order 86.5° phase retardation for 632.8 nm wavelength) is placed in the feedback cavity and can be rotated around an axis parallel to its surface normal. It is observed that when the laser works in single mode or two parallel-polarized modes, no phase difference appears between the light intensities detected by D1 and D2 , as shown in Fig. 3(a). The phase difference remains absent basically even though the waveplate is rotated or the pump power is varied. Moreover, this phenomenon still remains although the waveplate is changed with different phase retardation, which is quite different from that observed in [16,17]. This phenomenon can be explained as the light beams in the two axis directions of the Wollaston prism are split from the same electric field (single mode) or mixed by the same proportions of the light field (two parallel-polarized modes), so no phase difference appears between the two modulated signals. However, for the laser works in two orthogonally polarized modes, phase differences are clearly observed between the two intensity signals. The phase differences can change with the waveplate being rotated and the pump power being changed, as can be seen in Figs. 3(b)– 3(f). The waveform is a sine (or cosine) type due to the modulation being just a beat signal, which is more convenient than the sine-like type produced by a moving feedback mirror. The phase difference is also related to the change of the pump power. We observed that the phase difference has a maximum when the pump power
Fig. 2. Output modes of the lasers. (a) Single mode. (b) Two modes. (c) and (d) Orthogonally polarized two modes.
4297
Fig. 3. Experimental results. (a) In phase. (b)–(d) Phase difference appears. (e) Nearly 90° phase difference. (f) Nearly phase inversion.
is 52.35 mW, and it decreases gradually at the both sides of this power. Phase difference disappears when the pump power is up to 54.48 mW, and appears again when the pump power continues to increase, and then repeats the tendency above. The reasons for these phenomena are considered to be attributed to the polarization rotation and frequencydifference variation of the laser outputs induced by the change of the waveplate and the pump power, which are shown in Fig. 4 schematically. In Fig. 4(a), the fast and slow axes of the waveplate (f axis and s axis) are parallel to the optic axes of the Wollaston prism (o axis and e axis), respectively. But in Fig. 4(b), the optic axes of the waveplate and Wollaston prism are relatively rotated to each other and with respect to the laser initial polarization directions. In this case, the optical fields detected by the detectors can be written as
Fig. 4. Schematic of the orientations of optic axes and laser polarization directions. (a) No rotation. (b) Relative rotation.
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OPTICS LETTERS / Vol. 38, No. 21 / November 1, 2013
Eo E1s F sin β E1f F cos β E2s F sin β E2f F cos β;
g12f (1)
Ee E1s F cos β E1f F sin β E2s F cos β E2f
F
sin β;
g12s (2)
where the subscripts f and s indicate the components in the fast-axis and slow-axis directions of the waveplate, respectively. And the superscript F indicates the electric fields induced by the optical feedback. We can get E 1s
F
Ls expjω0 t E 1ms 1 η exp j4πν1 c × sinα β;
(3)
Lf expjω0 t E 1f F E1mf 1 η exp j4πν1 c × cosα β;
(4)
L E 2s F E 2ms 1 η exp j4πν2 s expjω0 t c × cosα β;
(5)
Lf expjω0 t E 2f E2mf 1 η exp j4πν2 c F
× sinα β;
(6)
where η T 2 r 3 ξ∕r 2 ;
(7)
where r 1 ; r 2 , and r 3 are the amplitude reflection coefficients of the two end faces of the Nd:YAG laser and the feedback mirror, respectively. T 2 1 − r 2 × r 2 is the transmittance of the output end of the Nd:YAG laser. L is the length of the external cavity, and its subscripts are defined as the above. ω0 2πΩ0 , in which Ω0 40 kHz is the modulation frequency induced by AOMs. ξ is the coupling efficiency from the external optical field back into the laser cavity [18]. ν is light frequency and c is the light speed in a vacuum. E1msor f and E 2msor f are written as nl E 1msf r 1 r 2 exp j4πν1 2g1sf l E 1 ; c
(8)
nl E 2msf r 1 r 2 exp j4πν2 2g2sf l E 2 ; c
(9)
where l is the length of the laser cavity, n is the effective refractive index of the medium in the laser cavity, and g is the linear gain per unit length of the gain medium with the presence of optical feedback, and can be expressed as [16]
2πLf 1 ; lnr 1 r 2 η cos − λ 2l
4πLf 1 2δ ; lnr 1 r 2 η cos − λ 2l
(10)
(11)
where δ is the phase retardation of the waveplate. Then we can obtain the light intensities as I o E o · E o ;
(12)
I e E e · E e :
(13)
From Eqs. (1)–(13), the light intensities in the two directions can be simulated by setting different values of α, β and the oscillation frequency difference of the two modes; the results are shown in Fig. 5 (the oscillation frequency difference is selected around 500 MHz). It can be seen that various phase differences can be obtained by changing the values of angles α, β and the oscillation frequency difference. These results correspond to those observed in Fig. 3, which means the theoretical analyses are consistent qualitatively with the phenomena in the experiments. The phase differences can change with the oscillation frequency difference, and the included angles, α and β, even almost disappear with some certain values of these three parameters, which is coincident with the phenomenon in which the phase difference is varied with the pump power and has a maximum in some pump powers, and a minimum in others. The phase difference behavior in modulated signals of two orthogonally polarized outputs of a Nd:YAG microchip laser with a frequency-shifted anisotropic weak optical feedback is observed and analyzed preliminarily. Phase differences are found between the two modulated intensity signals of the outputs in orthogonal directions, as the laser works in two orthogonally polarized modes.
Fig. 5. Simulated results. (a) In phase. (b)–(d) Phase difference appears. (e) Nearly 90° phase difference. (f) Nearly phase inversion.
November 1, 2013 / Vol. 38, No. 21 / OPTICS LETTERS
And the phase difference can be changed with variations of the pump power of the laser, and the rotation of the waveplate placed in the external cavity. These phenomena can be used to produce two sinetype laser outputs with a certain phase difference, which may be applied in some measurement and communications techniques. Moreover, they provide the possibility for measuring the phase retardation of a birefringent element or the rotation angle of a target. This work is supported by the Key Program of National Natural Science Foundation of China (grant 61036016). References 1. G. Liu, S. L. Zhang, J. Zhu, and Y. Li, Appl. Opt. 42, 6636 (2003). 2. L. F. Zhou, B. Zhang, S. L. Zhang, Y. D. Tan, and W. X. Liu, Chin. Phys. B 18, 1141 (2009). 3. L. G. Fei, S. L. Zhang, Y. Li, and J. Zhu, Opt. Express 13, 3117 (2005). 4. W. X. Chen, X. W. Long, S. L. Zhang, and G. Z. Xiao, Opt. Laser Technol. 44, 2427 (2012).
4299
5. W. X. Chen, S. L. Zhang, and X. W. Long, Opt. Lett. 37, 2433 (2012). 6. W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990). 7. Y. Mitsuhashi, J. Appl. Phys. 53, 9200 (1982). 8. T. Fujita, A. Schremer, and C. L. Tang, Appl. Phys. Lett. 51, 392 (1987). 9. K. Otsuka, R. Kawai, Y. Asakawa, and T. Fukazawa, Opt. Lett. 24, 1862 (1999). 10. S. Sudo, T. Ohtomo, Y. Takahashi, T. Oishi, and K. Otsuka, Appl. Opt. 48, 4049 (2009). 11. K. Otsuka, K. Abe, and J. Y. Ko, Opt. Lett. 27, 1339 (2002). 12. E. Lacot, R. Day, and F. Stoeckel, Phys. Rev. A 64, 043815 (2001). 13. E. Lacot and O. Hugon, Phys. Rev. A 70, 053824 (2004). 14. X. J. Wan, D. Li, and S. L. Zhang, Opt. Lett. 32, 367 (2007). 15. Z. Ren, D. Li, X. Wan, and S. Zhang, Laser Phys. 18, 939 (2008). 16. Y. D. Tan and S. L. Zhang, Appl. Opt. 46, 6064 (2007). 17. P. Zhang, S. L. Zhang, Y. D. Tan, Z. Q. Zhao, and Z. L. Zeng, Appl. Phys. B 106, 657 (2012). 18. W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, J. Lightwave Technol. 12, 1577 (1994).
