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Polarization-independent electro-optic modulator based on PMNT electrically-controlled birefringence effect and Sagnac interferometer
Optics & Laser Technology 57 (2014) 5–8
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Polarization-independent electro-optic modulator based on PMNT electrically-controlled birefringence effect and Sagnac interferometer Xuejiao Zhang, Qing Ye n, Haiwen Cai, Ronghui Qu nn Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
art ic l e i nf o
a b s t r a c t
Article history: Received 30 June 2013 Received in revised form 26 August 2013 Accepted 19 September 2013 Available online 12 October 2013
A novel polarization-independent electro-optic modulator is proposed and investigated by using the electrically-controlled birefringence effect of transparent lead magnesium niobate titanate (PMNT) electro-optic ceramic and a Sagnac interferometer structure. The PMNT electro-optic ceramic is used as a phase retarder for two counter-propagating waves in which their polarization directions are adjusted to parallel and vertical to the electrical-field vector respectively. Then the output light intensity from the Sagnac interferometer will be modulated completely with the driven electrical signal and it is independent with the polarization direction of incident light. The extinction ratio is more than 21 dB. This modulated device will be very appropriate as a Q-switch or optical attenuator in the high power laser system. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Electro-optic modulator Polarization-independent characteristic Electrically-controlled birefringence effect
1. Introduction Electro-optic modulator (EOM) [1,2] is an optical device in which the amplitude, phase, frequency or polarization of the beam can be modulated by the electro-optic effect of a nonlinear optical material. Over the past decade, lithium niobate (LiNbO3) waveguide EOM [3–6] have been applied widely in the fiber-optic communication systems. It can provide very wide modulated bandwidth, fast time response, stable operation, very low biasvoltage drift rates and so on. Different from the general direct modulation of laser diode, LiNbO3 EOM can also be designed for zero-chirp or adjustable-chirp operation. Zero-chirp and negativechirp modulators help to minimize the system degradation associated with fiber dispersion. These advances in device and material technology have been accompanied by significant investments in guided-wave device manufacturing. However, small waveguide size and low laser damage threshold for LiNbO3 modulator will be unfit for the applications in high power laser systems, such as electro-optic Q-switch and optical attenuator. Otherwise, the polarization-dependent characteristic of LiNbO3 crystal is also a limit factor which induces the instability of the performance. In order to develop a novel polarization-independent EOM for high-power laser systems, the newly developed transparent PMNT (PbMg1/3Nb2/3 xPbTiO3) electro-optic ceramic [7–9] is one of very ideal candidates. This ceramic belongs to the class of materials possessing relaxor properties, which is easily to produce
n
Corresponding author. Tel.: þ 86 216 991 8363. Corresponding author. E-mail addresses: [email protected] (Q. Ye), [email protected] (R. Qu).
nn
0030-3992/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2013.09.027
birefringence and exhibits a large electro-optic effect. Generally, its attractive features include high electro-optic coefficient (2–5 times that of the PLZT ceramic and equivalent to approximately 100 times that of LiNbO3 under the same voltage at the room temperature) [9–11], good optical transparency (larger than 95% with anti-reflection film), fast response time, low electric hysteresis (noticeably narrower in the range of 0–70 1C), large size (by the mature hot-pressing technique) and high laser damage threshold ( 4 GW/cm2 ) and so on. Therefore it has a very wide application foreground in the ultrafast photoelectron devices [7–10], especially for the high-power laser systems. In this paper, it is the first time to our knowledge that a novel polarization-independent electro-optic modulator is proposed and investigated theoretically and experimentally by using the electrically-controlled birefringence effect of transparent PMNT electro-optic ceramic and a Sagnac interferometer structure. The PMNT electro-optic ceramic is used as a phase retarder for two counter-propagating waves in which their polarization directions are adjusted to parallel and vertical to the electrical-field vector respectively. Then the output light intensity from the Sagnac loop will be modulated completely and the extinction ratio is more than 21 dB. It is believed that this modulated device will be very appropriate as a Q-switch in the high power laser system.
2. Theoretical analysis and experimental setup PMNT electro-optic ceramic is a polycrystalline ceramic for the normal condition and it exhibits an isotropic characteristic. When a bias electrical field E is applied in a specific direction (Ex ¼Ey¼0;
X. Zhang et al. / Optics & Laser Technology 57 (2014) 5–8
Ez ¼E), the ceramic wafer will show a characteristic of single crystal and a birefringence effect will be apparent. The electrooptic coefficients for different electrical field vectors will have a very large distinction. Then the corresponding perturbed index ellipsoid can be written following the methodology as [12,13] ! ! ! 1 1 1 2 2 2 2 2 þ γ E þ þ γ E þ þ γ E ð1Þ x y z2 ¼ 1 12 12 11 n20 n20 n20 where E is the applied electrical field, γ11 and γ12 are the quadratic electro-optic coefficients for transverse electric modes (i.e. optical field P parallel to electrical field E) and transverse magnetic modes (i.e. optical field P perpendicular to electrical field E), n0 (E 2.45) is the refractive index of PMNT. Only the quadratic terms are used since the unpoled quadratic PMNT ceramics have a symmetric, random structure and exhibit nonlinear electro-optic effect. Using the perturbed index ellipsoid of PMNT electro-optic ceramic, the average induced birefringence Δn for two polarization light vectors with the applied electric field across it can be written as Δn ¼ n== n ? ¼ 1=2n0 3 γ ef f jEj2
ð2Þ
where γeff ¼(γ11 γ12) is the total effective quadratic electro-optic coefficient. For our PMNT electro-optic ceramic, Fabry-Perot resonant technique has been used to measure the electro-optic coefficients for transverse electric (TE) and transverse magnetic (TM) modes, and their values are about γ11 ¼21.06 10 16 m2/V2 and γ12 ¼ 1.76 10 16 m2/V2 respectively [10]. Based on the above analysis for the birefringence characteristic of PMNT ceramic, the schematic diagram of the proposed polarization-independent electro-optic modulator is shown in Fig. 1. The key component in the system is a PMNT electro-optic phase retarder with the size of 3 mm 5 mm 1 mm (the gap between electrodes is 3 mm and the light path is 1 mm). The PMNT electro-optic ceramic has a large refractive index n0 ¼2.45. It is also noticed that the ceramic should be polished with highquality in order to add light transmission before developed to a modulator. An Al2O3 anti-reflection film should be also used to reduce the Fresnel reflection. A narrow-linewidth 785 nm polarized incident beam from external cavity diode laser (ECDL) is incident onto a polarization beam splitter (PBS) to obtain a linear polarization light. The direction of linear polarization light can be changed by adjusting a half-wave plate (HWP1). The Sagnac interferometer is composed of a beam splitter (BS), three total reflective mirrors, two half-wave plates (HWP2 and HWP3) and the PMNT phase retarder in which the Ti/Au electrodes is sputtered on the top and bottom surfaces. BS with the split ratio of 50:50 is used for input and interference output. Both the incident light orientation is perpendicular to the PMNT ceramic surface. However, HWP2 and HWP3 are used to adjust the polarization directions of the counter-clockwise (CCW) and clockwise (CW) beams to parallel and perpendicular to the electric field E, as shown in Fig. 1, which may obtain the maximal phase difference. We set the light vector P of incident beam in the y–z plane and the light propagation direction is along the x axis. The Jones matrix method is used to describe the light propagation process in Sagnac interferometer. Usually, the matrix of the linear polarization can be written as cos θ JP ¼ ; sin θ where θ is the angle between the polarized direction and the z axis. The HWP2 and HWP3 have the matrices of cos 2θ J HWP2 ¼ j sin 2θ
sin 2θ cos 2θ θ ¼ 0
and cos 2θ J HWP3 ¼ j sin 2θ
cos 2θ θ ¼ π=4 sin 2θ
since they are parallel and vertical to z axis respectively. The reflection beams on the BS and mirrors will have an additional π phase shift and the corresponding matrix of " # 1 0 J BS;M ¼ ; 0 expðjπÞ the transmission beams in the BS have single unit matrix. The PMNT is considered as a birefringence phase retarder and the electrical field direction is z axis, then the corresponding matrix may be rewritten as " # j sin φ2 sin 2θ cos φ2 þ j sin φ2 cos 2θ ð3Þ J PMNT ¼ cos φ2 j sin φ2 cos 2θ j sin φ2 sin 2θ θ¼0
where φ is the phase difference for the CW and CCW beams due to the quadratic electro-optic birefringence effect in PMNT ceramic. Calculating the propagation matrices for the CW and CCW beams in the Sagnac interferometer respectively and their field vectors may be obtained " # expð jφ2Þ sin θ Ax ¼ J J J J J J J J J ¼ φ BS M3 HWP3 M2 PMNT M1 HWP2 BS P Ay expðj2Þ cos θ CW ð4aÞ
Fig. 1. Schematic diagram of the experimental setup for polarization-independent electro-optic modulator.
1.0
Normalized intensity (a.u.)
6
0.8 0.6 0.4 0.2 0.0 0
200
400
600 800 Voltage (V)
1000
1200
Fig. 2. Variation of light intensity with the driven voltage where L ¼1 mm, d¼ 3 mm, and n0 ¼2.45.
X. Zhang et al. / Optics & Laser Technology 57 (2014) 5–8
"
Ax Ay
¼ J HWP3 J M1 J PMNT J M2 J HWP3 J M3 J P ¼ CCW
expðjφ2Þ cos θ
expð jφ2Þ sin θ
# ð4bÞ
Then the interference output in BS is Ax I out ¼ A y
CW
# 2 2 " expðjðφ=2ÞÞ þ expð jðφ=2ÞÞ sin θ ¼ expðjðφ=2ÞÞ þ expð jðφ=2ÞÞ cos θ CCW
þ
Ax Ay
p cos 2 ðφ=2Þ
ð5Þ
It is easy to see that the output intensity from Sagnac interferometer is only associated with the phase difference φ p 2πn03L (γ11 γ12)|V/d|2/λ (L and d is the length for light transmission and the gap of the electrodes in the PMNT ceramic) and it is independent with the polarization angle θ of incident light. This is a unique characteristic for this proposed EOM structure. Fig. 2 shows the relation of the light intensity and the driven voltage by the Eq. (5). When L¼1 mm and d ¼ 3 mm, the first On–Off voltage is about 780 V.
7
In the following analysis, some experimental results are given to verify the above analysis and the experimental setup is shown in Fig. 1. The direction of incident linear polarization beam from ECDL is adjusted by rotating the HWP1. Firstly, rotating HWP1 to make the polarization direction of the beam be according with z axis (i.e. θ¼ 0), the variation of output light intensity from the interferometer with the driven voltage executed on PMNT is shown in Fig. 3(a). With the driven voltage increases, the intensity will be reduced which will exhibit a quadratic linear relation. When the applied voltage is added to 780 V, the output intensity reaches the minimal value and the corresponding extinction ratio of the PMNT EOM is about 21.5 dB which is similar with that of LiNbO3 EOM [11]. Adding the driven voltage sequentially, then the output intensity will increase again and this is coincident with the above theoretical analysis in Fig. 2. The characteristic of an amplitude modulator is very obvious. Rotating the HWP1 to change the polarization direction of incident beam for θ¼π/4, π/3 and π/2, the corresponding results are shown in Fig. 3(b), (c) and (d). They have the similar variation rule with the driven
Fig. 3. Intensity variation of modulator with the applied voltage for orthogonal electro-optical effect.
8
X. Zhang et al. / Optics & Laser Technology 57 (2014) 5–8
8
θ =0ο θ =90ο
Intensity (mV)
6
4
structure. The PMNT electro-optic ceramic was used as a phase retarder for two counter-propagating waves in which their polarization vectors are adjusted to parallel and vertical to the electrical-field direction respectively. Then the output light intensity from the Sagnac loop will be modulated completely and it is independent of the incident angle of polarization beam.
Acknowledgments
2
0
0
200
400
600
800
1000
1200
The authors want to acknowledge Prof. Aili Ding, Prof. Gourong Li and Dr. Jiangtao Zeng from Shanghai Institute of Ceramics, CAS for providing the good performance PMNT ceramic sample. The work was supported by the National Natural Science Foundation of China (Grant no. 61137004) and the Natural Science Foundation of STCSM (Grant no. 11JC1413500).
Voltage (V) Fig. 4. Intensity variation of modulator with the applied voltage for same electrooptic effect.
voltage increases and the extinction ratios are 22.6 dB, 22.9 dB and 21.7 dB, respectively. The intensity modulated characteristic for this proposed modulator is independent of the incident angle of polarization beam. Small intensity fluctuation for different polarization directions is induced due to the reflectivity difference on the BS and mirrors. Removing HWP2 and HWP3 from the Sagnac interferometer, then the polarization directions for the CW and CCW beam through PMNT phase retarder will be accordant and they have the same electro-optic phase modulated characteristic. The phase difference for the CW and CCW beam will be zero and the interference effect will be not happened in output port of the Sagnac interferometer. Fig. 4 shows the intensity variation with the applied voltage increase for different polarization direction. Rotating the polarization angle by the HWP1 to θ¼ 0 and π/2, the interference effect will be not happened and they are only the intensity addition. Finally, it should be noticed that this modulator has a about 180 ns response speed which is decided by the characteristic of PMNT [14]. This is lower obviously than that of LiNbO3 EOM and it needs be improved in the design of PMNT ceramic structure. 3. Conclusions In summary, a novel polarization-independent electro-optic modulator has been proposed and investigated experimentally by using transparent PMNT electro-optic ceramic and Sagnac interferometer
References [1] Karna Shashi, Yeates Alan, editors. Nonlinear Optical Materials: Theory and Modeling, Washington, DC, American Chemical Society; 1996.p.2-3. 0-84123401-9. [2] Saleh Teich. Fundamentals of Photonics. first ed. . New York: WileyInterscience Publications; 1991 p. 697; 0-471-83965-5697. [3] Wooten EL, Kissa KM, Alfredo Y, Murphy EJ, Lafaw DA, Hallemeier PF, et al. A review of lithium niobate modulators for fiber-optic communications systems. IEEE Journal of Selected topics in Quantun Electronics 2000;6:69–82. [4] Haxha S, Rahman B, Grattan K. Bandwidth estimation for ultra-high-speed lithium niobate modulators. Applied Optics 2003;42:2674–82. [5] Twu RC, Hong HY, Lee HH. An optical homodyne technique to measure photorefractive-induced phase drifts in lithium niobate phase modulators. Optics Express 2008;16:4366–74. [6] García-Granda Miguel, Hu Hui, Rodríguez-García J, Sohler W. Design and fabrication of novel ridge guide modulators in lithium niobate. Journal of Lightwave Technology 2009;27:5690–7. [7] Lei Qiao Qing, Ye Junlin, Gan Haiwen, Cai, Qu Ronghui. Optical characteristics of transparent PMNT ceramic and its application at high speed electro-optic switch. Optics Communications 2011;284:3886–90. [8] Li K.K.. Electro-optic ceramics and devices, PMNT, US Patent Application. 10/139857, 5/6/2002. [9] Kamzina LS, Ruan Wei Li GR, Zeng JT, Ding AL. Electro-optical properties of PMN-xPT compounds: single crystrals and transparent ferroelectric ceramic. Magnetism and Ferroelectricity 2010;52:2142–6. [10] Zhang Xuejiao, Ye Qing, Cai Haiwen, Qu Ronghui. Fabry-Perot resonant technique for measuring the electro-optic coefficients of PMNT ceramic and its application in diffraction grating. Chinese Journal of Lasers 2013;40(7):0708004. [11] Wooten EL, Kissa KM, Yi-Yan A, Murphy KM, Lafaw DA, Hallemeier PF, et al. A review of lithium niobate modulators for fiber-optic communications systems. IEEE Journal on Selected Topics in Quantum Eletronics 2000;6(1):69–82. [12] Jiang H, Zou Y, Ming H, Zhang X, Chen MY. Transparent electro-optic ceramics and devices. Proceedings of SPIE 2004;5644:380–94. [13] James A. Thomas. Optical phased array beam deflection using lead lanthanum zirconate titanate [Ph.D. thesis]. San Diego: University of California; 1998: pp. 59–65 [chapter 5]. [14] Qing Ye Lei, Qiao Haiwen, Cai, Qu Ronghui. High-efficiency electrically tunable phase diffraction grating based on a transparent lead magnesium niobate-lead titanite electro-optic ceramic. Optics Letters 2011;36:2453–5.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Polarization-independent electro-optic modulator based on PMNT electrically-controlled birefringence effect and Sagnac interferometer Xuejiao Zhang, Qing Ye n, Haiwen Cai, Ronghui Qu nn Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
art ic l e i nf o
a b s t r a c t
Article history: Received 30 June 2013 Received in revised form 26 August 2013 Accepted 19 September 2013 Available online 12 October 2013
A novel polarization-independent electro-optic modulator is proposed and investigated by using the electrically-controlled birefringence effect of transparent lead magnesium niobate titanate (PMNT) electro-optic ceramic and a Sagnac interferometer structure. The PMNT electro-optic ceramic is used as a phase retarder for two counter-propagating waves in which their polarization directions are adjusted to parallel and vertical to the electrical-field vector respectively. Then the output light intensity from the Sagnac interferometer will be modulated completely with the driven electrical signal and it is independent with the polarization direction of incident light. The extinction ratio is more than 21 dB. This modulated device will be very appropriate as a Q-switch or optical attenuator in the high power laser system. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Electro-optic modulator Polarization-independent characteristic Electrically-controlled birefringence effect
1. Introduction Electro-optic modulator (EOM) [1,2] is an optical device in which the amplitude, phase, frequency or polarization of the beam can be modulated by the electro-optic effect of a nonlinear optical material. Over the past decade, lithium niobate (LiNbO3) waveguide EOM [3–6] have been applied widely in the fiber-optic communication systems. It can provide very wide modulated bandwidth, fast time response, stable operation, very low biasvoltage drift rates and so on. Different from the general direct modulation of laser diode, LiNbO3 EOM can also be designed for zero-chirp or adjustable-chirp operation. Zero-chirp and negativechirp modulators help to minimize the system degradation associated with fiber dispersion. These advances in device and material technology have been accompanied by significant investments in guided-wave device manufacturing. However, small waveguide size and low laser damage threshold for LiNbO3 modulator will be unfit for the applications in high power laser systems, such as electro-optic Q-switch and optical attenuator. Otherwise, the polarization-dependent characteristic of LiNbO3 crystal is also a limit factor which induces the instability of the performance. In order to develop a novel polarization-independent EOM for high-power laser systems, the newly developed transparent PMNT (PbMg1/3Nb2/3 xPbTiO3) electro-optic ceramic [7–9] is one of very ideal candidates. This ceramic belongs to the class of materials possessing relaxor properties, which is easily to produce
n
Corresponding author. Tel.: þ 86 216 991 8363. Corresponding author. E-mail addresses: [email protected] (Q. Ye), [email protected] (R. Qu).
nn
0030-3992/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2013.09.027
birefringence and exhibits a large electro-optic effect. Generally, its attractive features include high electro-optic coefficient (2–5 times that of the PLZT ceramic and equivalent to approximately 100 times that of LiNbO3 under the same voltage at the room temperature) [9–11], good optical transparency (larger than 95% with anti-reflection film), fast response time, low electric hysteresis (noticeably narrower in the range of 0–70 1C), large size (by the mature hot-pressing technique) and high laser damage threshold ( 4 GW/cm2 ) and so on. Therefore it has a very wide application foreground in the ultrafast photoelectron devices [7–10], especially for the high-power laser systems. In this paper, it is the first time to our knowledge that a novel polarization-independent electro-optic modulator is proposed and investigated theoretically and experimentally by using the electrically-controlled birefringence effect of transparent PMNT electro-optic ceramic and a Sagnac interferometer structure. The PMNT electro-optic ceramic is used as a phase retarder for two counter-propagating waves in which their polarization directions are adjusted to parallel and vertical to the electrical-field vector respectively. Then the output light intensity from the Sagnac loop will be modulated completely and the extinction ratio is more than 21 dB. It is believed that this modulated device will be very appropriate as a Q-switch in the high power laser system.
2. Theoretical analysis and experimental setup PMNT electro-optic ceramic is a polycrystalline ceramic for the normal condition and it exhibits an isotropic characteristic. When a bias electrical field E is applied in a specific direction (Ex ¼Ey¼0;
X. Zhang et al. / Optics & Laser Technology 57 (2014) 5–8
Ez ¼E), the ceramic wafer will show a characteristic of single crystal and a birefringence effect will be apparent. The electrooptic coefficients for different electrical field vectors will have a very large distinction. Then the corresponding perturbed index ellipsoid can be written following the methodology as [12,13] ! ! ! 1 1 1 2 2 2 2 2 þ γ E þ þ γ E þ þ γ E ð1Þ x y z2 ¼ 1 12 12 11 n20 n20 n20 where E is the applied electrical field, γ11 and γ12 are the quadratic electro-optic coefficients for transverse electric modes (i.e. optical field P parallel to electrical field E) and transverse magnetic modes (i.e. optical field P perpendicular to electrical field E), n0 (E 2.45) is the refractive index of PMNT. Only the quadratic terms are used since the unpoled quadratic PMNT ceramics have a symmetric, random structure and exhibit nonlinear electro-optic effect. Using the perturbed index ellipsoid of PMNT electro-optic ceramic, the average induced birefringence Δn for two polarization light vectors with the applied electric field across it can be written as Δn ¼ n== n ? ¼ 1=2n0 3 γ ef f jEj2
ð2Þ
where γeff ¼(γ11 γ12) is the total effective quadratic electro-optic coefficient. For our PMNT electro-optic ceramic, Fabry-Perot resonant technique has been used to measure the electro-optic coefficients for transverse electric (TE) and transverse magnetic (TM) modes, and their values are about γ11 ¼21.06 10 16 m2/V2 and γ12 ¼ 1.76 10 16 m2/V2 respectively [10]. Based on the above analysis for the birefringence characteristic of PMNT ceramic, the schematic diagram of the proposed polarization-independent electro-optic modulator is shown in Fig. 1. The key component in the system is a PMNT electro-optic phase retarder with the size of 3 mm 5 mm 1 mm (the gap between electrodes is 3 mm and the light path is 1 mm). The PMNT electro-optic ceramic has a large refractive index n0 ¼2.45. It is also noticed that the ceramic should be polished with highquality in order to add light transmission before developed to a modulator. An Al2O3 anti-reflection film should be also used to reduce the Fresnel reflection. A narrow-linewidth 785 nm polarized incident beam from external cavity diode laser (ECDL) is incident onto a polarization beam splitter (PBS) to obtain a linear polarization light. The direction of linear polarization light can be changed by adjusting a half-wave plate (HWP1). The Sagnac interferometer is composed of a beam splitter (BS), three total reflective mirrors, two half-wave plates (HWP2 and HWP3) and the PMNT phase retarder in which the Ti/Au electrodes is sputtered on the top and bottom surfaces. BS with the split ratio of 50:50 is used for input and interference output. Both the incident light orientation is perpendicular to the PMNT ceramic surface. However, HWP2 and HWP3 are used to adjust the polarization directions of the counter-clockwise (CCW) and clockwise (CW) beams to parallel and perpendicular to the electric field E, as shown in Fig. 1, which may obtain the maximal phase difference. We set the light vector P of incident beam in the y–z plane and the light propagation direction is along the x axis. The Jones matrix method is used to describe the light propagation process in Sagnac interferometer. Usually, the matrix of the linear polarization can be written as cos θ JP ¼ ; sin θ where θ is the angle between the polarized direction and the z axis. The HWP2 and HWP3 have the matrices of cos 2θ J HWP2 ¼ j sin 2θ
sin 2θ cos 2θ θ ¼ 0
and cos 2θ J HWP3 ¼ j sin 2θ
cos 2θ θ ¼ π=4 sin 2θ
since they are parallel and vertical to z axis respectively. The reflection beams on the BS and mirrors will have an additional π phase shift and the corresponding matrix of " # 1 0 J BS;M ¼ ; 0 expðjπÞ the transmission beams in the BS have single unit matrix. The PMNT is considered as a birefringence phase retarder and the electrical field direction is z axis, then the corresponding matrix may be rewritten as " # j sin φ2 sin 2θ cos φ2 þ j sin φ2 cos 2θ ð3Þ J PMNT ¼ cos φ2 j sin φ2 cos 2θ j sin φ2 sin 2θ θ¼0
where φ is the phase difference for the CW and CCW beams due to the quadratic electro-optic birefringence effect in PMNT ceramic. Calculating the propagation matrices for the CW and CCW beams in the Sagnac interferometer respectively and their field vectors may be obtained " # expð jφ2Þ sin θ Ax ¼ J J J J J J J J J ¼ φ BS M3 HWP3 M2 PMNT M1 HWP2 BS P Ay expðj2Þ cos θ CW ð4aÞ
Fig. 1. Schematic diagram of the experimental setup for polarization-independent electro-optic modulator.
1.0
Normalized intensity (a.u.)
6
0.8 0.6 0.4 0.2 0.0 0
200
400
600 800 Voltage (V)
1000
1200
Fig. 2. Variation of light intensity with the driven voltage where L ¼1 mm, d¼ 3 mm, and n0 ¼2.45.
X. Zhang et al. / Optics & Laser Technology 57 (2014) 5–8
"
Ax Ay
¼ J HWP3 J M1 J PMNT J M2 J HWP3 J M3 J P ¼ CCW
expðjφ2Þ cos θ
expð jφ2Þ sin θ
# ð4bÞ
Then the interference output in BS is Ax I out ¼ A y
CW
# 2 2 " expðjðφ=2ÞÞ þ expð jðφ=2ÞÞ sin θ ¼ expðjðφ=2ÞÞ þ expð jðφ=2ÞÞ cos θ CCW
þ
Ax Ay
p cos 2 ðφ=2Þ
ð5Þ
It is easy to see that the output intensity from Sagnac interferometer is only associated with the phase difference φ p 2πn03L (γ11 γ12)|V/d|2/λ (L and d is the length for light transmission and the gap of the electrodes in the PMNT ceramic) and it is independent with the polarization angle θ of incident light. This is a unique characteristic for this proposed EOM structure. Fig. 2 shows the relation of the light intensity and the driven voltage by the Eq. (5). When L¼1 mm and d ¼ 3 mm, the first On–Off voltage is about 780 V.
7
In the following analysis, some experimental results are given to verify the above analysis and the experimental setup is shown in Fig. 1. The direction of incident linear polarization beam from ECDL is adjusted by rotating the HWP1. Firstly, rotating HWP1 to make the polarization direction of the beam be according with z axis (i.e. θ¼ 0), the variation of output light intensity from the interferometer with the driven voltage executed on PMNT is shown in Fig. 3(a). With the driven voltage increases, the intensity will be reduced which will exhibit a quadratic linear relation. When the applied voltage is added to 780 V, the output intensity reaches the minimal value and the corresponding extinction ratio of the PMNT EOM is about 21.5 dB which is similar with that of LiNbO3 EOM [11]. Adding the driven voltage sequentially, then the output intensity will increase again and this is coincident with the above theoretical analysis in Fig. 2. The characteristic of an amplitude modulator is very obvious. Rotating the HWP1 to change the polarization direction of incident beam for θ¼π/4, π/3 and π/2, the corresponding results are shown in Fig. 3(b), (c) and (d). They have the similar variation rule with the driven
Fig. 3. Intensity variation of modulator with the applied voltage for orthogonal electro-optical effect.
8
X. Zhang et al. / Optics & Laser Technology 57 (2014) 5–8
8
θ =0ο θ =90ο
Intensity (mV)
6
4
structure. The PMNT electro-optic ceramic was used as a phase retarder for two counter-propagating waves in which their polarization vectors are adjusted to parallel and vertical to the electrical-field direction respectively. Then the output light intensity from the Sagnac loop will be modulated completely and it is independent of the incident angle of polarization beam.
Acknowledgments
2
0
0
200
400
600
800
1000
1200
The authors want to acknowledge Prof. Aili Ding, Prof. Gourong Li and Dr. Jiangtao Zeng from Shanghai Institute of Ceramics, CAS for providing the good performance PMNT ceramic sample. The work was supported by the National Natural Science Foundation of China (Grant no. 61137004) and the Natural Science Foundation of STCSM (Grant no. 11JC1413500).
Voltage (V) Fig. 4. Intensity variation of modulator with the applied voltage for same electrooptic effect.
voltage increases and the extinction ratios are 22.6 dB, 22.9 dB and 21.7 dB, respectively. The intensity modulated characteristic for this proposed modulator is independent of the incident angle of polarization beam. Small intensity fluctuation for different polarization directions is induced due to the reflectivity difference on the BS and mirrors. Removing HWP2 and HWP3 from the Sagnac interferometer, then the polarization directions for the CW and CCW beam through PMNT phase retarder will be accordant and they have the same electro-optic phase modulated characteristic. The phase difference for the CW and CCW beam will be zero and the interference effect will be not happened in output port of the Sagnac interferometer. Fig. 4 shows the intensity variation with the applied voltage increase for different polarization direction. Rotating the polarization angle by the HWP1 to θ¼ 0 and π/2, the interference effect will be not happened and they are only the intensity addition. Finally, it should be noticed that this modulator has a about 180 ns response speed which is decided by the characteristic of PMNT [14]. This is lower obviously than that of LiNbO3 EOM and it needs be improved in the design of PMNT ceramic structure. 3. Conclusions In summary, a novel polarization-independent electro-optic modulator has been proposed and investigated experimentally by using transparent PMNT electro-optic ceramic and Sagnac interferometer
References [1] Karna Shashi, Yeates Alan, editors. Nonlinear Optical Materials: Theory and Modeling, Washington, DC, American Chemical Society; 1996.p.2-3. 0-84123401-9. [2] Saleh Teich. Fundamentals of Photonics. first ed. . New York: WileyInterscience Publications; 1991 p. 697; 0-471-83965-5697. [3] Wooten EL, Kissa KM, Alfredo Y, Murphy EJ, Lafaw DA, Hallemeier PF, et al. A review of lithium niobate modulators for fiber-optic communications systems. IEEE Journal of Selected topics in Quantun Electronics 2000;6:69–82. [4] Haxha S, Rahman B, Grattan K. Bandwidth estimation for ultra-high-speed lithium niobate modulators. Applied Optics 2003;42:2674–82. [5] Twu RC, Hong HY, Lee HH. An optical homodyne technique to measure photorefractive-induced phase drifts in lithium niobate phase modulators. Optics Express 2008;16:4366–74. [6] García-Granda Miguel, Hu Hui, Rodríguez-García J, Sohler W. Design and fabrication of novel ridge guide modulators in lithium niobate. Journal of Lightwave Technology 2009;27:5690–7. [7] Lei Qiao Qing, Ye Junlin, Gan Haiwen, Cai, Qu Ronghui. Optical characteristics of transparent PMNT ceramic and its application at high speed electro-optic switch. Optics Communications 2011;284:3886–90. [8] Li K.K.. Electro-optic ceramics and devices, PMNT, US Patent Application. 10/139857, 5/6/2002. [9] Kamzina LS, Ruan Wei Li GR, Zeng JT, Ding AL. Electro-optical properties of PMN-xPT compounds: single crystrals and transparent ferroelectric ceramic. Magnetism and Ferroelectricity 2010;52:2142–6. [10] Zhang Xuejiao, Ye Qing, Cai Haiwen, Qu Ronghui. Fabry-Perot resonant technique for measuring the electro-optic coefficients of PMNT ceramic and its application in diffraction grating. Chinese Journal of Lasers 2013;40(7):0708004. [11] Wooten EL, Kissa KM, Yi-Yan A, Murphy KM, Lafaw DA, Hallemeier PF, et al. A review of lithium niobate modulators for fiber-optic communications systems. IEEE Journal on Selected Topics in Quantum Eletronics 2000;6(1):69–82. [12] Jiang H, Zou Y, Ming H, Zhang X, Chen MY. Transparent electro-optic ceramics and devices. Proceedings of SPIE 2004;5644:380–94. [13] James A. Thomas. Optical phased array beam deflection using lead lanthanum zirconate titanate [Ph.D. thesis]. San Diego: University of California; 1998: pp. 59–65 [chapter 5]. [14] Qing Ye Lei, Qiao Haiwen, Cai, Qu Ronghui. High-efficiency electrically tunable phase diffraction grating based on a transparent lead magnesium niobate-lead titanite electro-optic ceramic. Optics Letters 2011;36:2453–5.