- Email: [email protected]
Design and verification of the polarization beamsplitter based on photonic crystals
Optics Communications 351 (2015) 40–44
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Design and verification of the polarization beamsplitter based on photonic crystals Ting Wang, Binming Liang n, Qiang Jiang, Lun Gao, Jinbin Hu, Heng Cao, Jiabi Chen, Song-lin Zhuang Optical Electronic Information and Computer Engineering College, University of Shanghai for Science and Technology, Shanghai 200093, China
art ic l e i nf o
a b s t r a c t
Article history: Received 6 January 2015 Received in revised form 13 March 2015 Accepted 17 April 2015 Available online 24 April 2015
Photonic crystals have a great prospect in the field of integrated optics due to their high integration and low transmission loss. In this paper, a beam splitter based on the bandgap of photonic crystal is designed and demonstrated experimentally for polarization-dependent beam splitting. The simulated radiation patterns show excellent polarization purity, with a cross-polarization level above 20 dB. Furthermore, the angle deviation of the incident and the temperature change of device have slight impact on beamsplitting. Larger shifting range of incident wavelength is allowed. What is more, the range of medium radius with good splitting effect is relatively large, which reduces the difficulty of production and processing. & 2015 Elsevier B.V. All rights reserved.
Keywords: Beam splitter Photonic crystal Bandgap
1. Introduction
2. Structure of the two-dimensional photonic crystals
Polarization beamsplitter can separate two orthogonal polarization modes of electromagnetic waves into different directions, which plays an important role in optical communications [1,2], information-recycle [3] and integrated optical circuits [4,5]. Many kinds of beamsplitter have been proposed [6–9]. Conventional ones generally use birefringence effect of natural crystal (e.g. Wollaston prism), either polarization splitter cubes or multi-layer film structure to achieve beams splitting. These polarization beamsplitters cannot meet the development of high-density integrated optical circuits. Now many methods in photonic crystals are used for beam polarization as its high integration, good beam effect, and low transmission loss [10,11]. The one based on directional coupler [12] must insert waveguide bend in the output as a small splitting angle, which increases the size of device; another is based on crystal structure [13], whose design is complex, and the manufacture is difficult. Moreover the polarization splitting depends on structural parameters and operating wavelength. In this paper, we propose a beamsplitter based on photonic crystal band gap. The beam splitting will not be affected by drifting of incident wavelength and changing of device temperature, which has a stable and reliable performance. The range of medium radius with good splitting effect is relatively large, which reduces the difficulty of production and processing, What is more, the structure is simple and easy processing.
Photonic crystal is a material that has been structured to possess a periodic modulation of the refractive index. The rectangular photonic crystal structure applicated in the mathematical simulation experiment is shown in Fig. 1(a). In which, the black dots represent the silica column (refractive index n is 3.42), the cell shape of dielectric rod is cylinder, arranging in a triangle. Lattice period (the distance between two silicon column centers) is represented by a (a=λ*Frequency , Frequency is the normalized frequency, λ is the free space wavelength ), which is shown in Fig. 1 (b). Diameter of dielectric column is 2r, another saying is waveguide width, which is often defined as b*a (b is a constant, which is greater than 0 and less than 1, denotes the waveguide width parameter).
n
Corresponding author. E-mail address: [email protected] (B. Liang).
http://dx.doi.org/10.1016/j.optcom.2015.04.044 0030-4018/& 2015 Elsevier B.V. All rights reserved.
3. Simulation data and result discussion This paper uses the FDTD method to carry on the simulation of the 2D photonic crystal fabricated from a hexagonal array of circular dielectric rods with Si. With the simulation software RSoft, the photonic band structure is shown in Fig. 2. The horizontal coordinate is value b while the vertical coordinate is normalized frequency. The shadow section is called conduction band, where photon can transmit. On the contrary, the blank sections represent forbidden regions. It can be seen from Fig. 2 that the changing of value b will influence the band structure. With the increase of value b, the band gap are all broadening then narrowing and
T. Wang et al. / Optics Communications 351 (2015) 40–44
41
Fig. 1. (a) Structure for 2D photonic crystal and (b) hexagonal structure.
Frequency (ωa/2πc=a/λ)
TE Band Map 2
1
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1. 0
0.6
0.7
0.8
0.9
1. 0
b Frequency (ωa/2πc=a/λ)
TM Band Map 2
1
0 0.0
0.1
0.2
0.3
0.4
0.5 b
Fig. 2. The band structure of photonic crystal polarization influenced by wave guide width parameter b.
falling gradually. When the value b ranging from 0.15 to 0.4 with the normalized frequency is 0.4717, which is just in the conduction band of TM but the forbidden band of TE. Without defects the TM wave can pass through in no loss, however the TE wave will be reflected. Defining incident power as 1, then the output power becomes relative value. Simulating with the Fullwave method of Rsoft, the propagation is presented in Fig. 3. θ is incident angle, TTE and TTM are the transmition RTE and RTM are the reflection of TE and TM respectively. Normally the performance of polarization splitter can be evaluated by splitting ratio or extinction ratio (ER). Therefore the ER of the two cores are defined as
Fig. 4. Relation between the output power and incident angle θ.
ER1 = − 10* lg(TTE /TTM )
(1)
ER2 = − 10* lg(RTM /RTE )
(2)
By setting a suitable incident angle and value b, the photon can fall in conduction band of TM but the forbidden one of TE, so the whole transmission of TM and the whole reflection of TE. When θ = 44° and value b ranging from 0.16 to 0.33, excellent polarization purity can be achieved, with a cross-polarization level above 20 dB. To reduce the difficulty of production and processing, we set b as 0.25 (b = 0.25 ± 0.08 all the value b can achieve excellent polarization). At the same time, If the incident angle has a deviation (θ = 44° ± 2°), efficient separation can also be achieved. The relation between the output power and incident angle is shown in Fig. 4.
Fig. 3. Light propagation (Ey represents TE and Hy represents TM).
42
T. Wang et al. / Optics Communications 351 (2015) 40–44
1.0
1.0
0.8 0.6
0.6
power
power
TTE TTM
0.4
0.4
RTM RTE
0.2 0.0 0.3
0.8
b=0.2
0.4
0.5
0.2
0.6
0.7
Frequency(a/ λ)
0.0 0.3
b=0.25 TTE TTM
RTM RTE 0.4
0.5
0.6
Frequency (a/λ)
0.7
1.0 0.8
b=0.3
0.6
power
TTE
TTM RTM
0.4
RTE
0.2 0.0 0.3
0.4
0.5
0.6
Frequency (a / λ)
0.7
Fig. 5. Relation between the output power and frequency (the horizontal coordinate represents frequency and the vertical coordinate represents the output power).
It can be seen from Fig. 5 that in large range of normalized frequency, the reflection of TE and the transmission of TM are near to 1, moreover the transmission of TE and the reflection of TM are near to 0. The range of normalized frequency with a cross-polarization level above 20 dB can be got by further calculation. b = 0.2, the range is 0.4098–0.521.b = 0.25, the range is 0.362–0.5. b = 0.3, the range is 0.325–0.481. It can be seen from the Frequency range, there are large range of normalized frequency with a cross-polarization level above 20 dB, which demonstrates larger incident light wavelength shiftting range of device is allowed (a = λ*Frequency ). Due to the thermoeffect of photonic crystals (silicon), the change of temperature will occur to the small change of refractive index in the medium column.
Δn = αnΔT
Fig. 6. Relation between the output power and temperature (the horizontal coordinate represents temperature and the vertical coordinate represents the output power).
When θ = 44°, the relation between normalized frequency and transmission as well as reflection of TE and TM are shown in Fig. 5. In which, Frequency is normalized frequency and power is output power.
(3)
In which, α is the thermo-optic coefficient of silicon (α ¼1.86 10 4/°C). The change of the refractive index will have impact on the separation effect and then affects the output power indirectly. When the temperature changes from 50 °C to 200 °C, the relation between the output power and temperature is shown in Fig. 6. The cross-polarization level are calculated all above 22 dB. That is to say, the changing of temperature has little impact on the separation effect. For the wavelength is normalized, different wavelengths just
T. Wang et al. / Optics Communications 351 (2015) 40–44
43
Fig. 7. SEM Photo of a sample by microscope ((a) is overlook and (b) is side-look).
detector
Photonic crystals
lens Half-wave plate polarizer CO2 laser
Fig. 8. Experimental set-up for verification of the beamsplitting effect.
and the theoretical height of column is assumed an infinite amount. Thus, actually the analogous photonic crystal structure can be achieved in manufacture. The experimental platform is setting up. Experimental set-up for verification of the beamsplitting effect is shown in Fig. 8. The beam emitted from laser will become linearly polarized one, which oblique- incidents on the photonic crystals after aggregating by the lenses.The beam refracted out of the photonic crystal will be picked by the detector and the detector is linked with the computer to record the output data. In the platform, the linear-polarizing plate is used to re-polarize the beam emitted from a laser. The polarization can access to 99.9% after being re-polarized of the linear-polarizing plate. The polarization direction of linearly polarized beam can be changed by a half-wave plate, which realizes the mode converse between TE and TM. Analysing with output data, the preliminary result is shown in Fig. 9. The output power for different positions of the TM and TE wave is shown in Fig. 9. As is depicted that the ratio of the optical power output (TM /TE ) can access to 7.5, which demonstrates the beam splitting effect is very good. Because of the unaverage diameter of the column and this experiment works with the devices instead of waveguide devices, which exists some stray light. Waveguide devices will be used to improve the experiment in the next step.
4. Conclusion
Fig. 9. Relation illustration between the output power and position (the horizontal coordinate represents position and the vertical coordinate represents the output power).
need to change the period a, the separation can be achieved. Setting a as 141.51 μm can achieve the separation of Thz (300 μm). Moreover setting a as 0.731 μm, the communication one (1.55 μm) can be realized. The working group has a mature study on the photonic crystal structure incident wavelength of 10.6 μm [14]. The photonic crystal sample processing as incident wavelength 10.6 μm and lattice period 5 μm is shown in Fig. 7. The diameter of column is 1.25 μm, height is 50 μm, as the height of the column is 40 times to the diameter of the column
This paper uses the FDTD method to study the structure and transmitting character of the 2D photonic crystal fabricated from a hexagonal array of circular dielectric rods with Si. Aiming at the application on beamsplitter, the simulating results show that comparing to the traditional polarization device, the one made by 2D photonic crystal is in a small size and can achieve efficient separation between the TE wave TM waves in large angle. What is more, it is simple and with great stable. Large range of normalized frequency can realize efficient separation, which can avoid the interference by shifting of incident wavelength. The changing of temperature has little impact on the separation effect. The device with a stable separation effect, moreover it is easy processing, which is expected to have a great application on integrated optics.
Acknowledgments This work is supported by the National Basic Research Program of China (Grant no. 2011CB707504), the National Natural Science Foundation of China (61177043 and 11104184).
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T. Wang et al. / Optics Communications 351 (2015) 40–44
Reference [1] S.Y. Lin, E. Chow, J. Bur, Low-loss, wide-angle Y splitter at 1.6-mm wavelengths built with a two-dimensional photonic crystal, J. Opt. Lett. 27 (16) (2002) 1400–1402. [2] Tiaoming Niu, Withawat Withayachumnankul, et al., Terahertz reflectarry as a polarizing beam splitter, J. Opt. Express 22 (13) (2014) 16148–16160. [3] S.A. Haine, Information-recycling beam splitters for quantum enhanced atom interferometry, J. Phys. Rev. Lett. 110 (5) (2013) 053002. [4] N. Prtlj, R.J. Coles, et al., Monolithic integration of a quantum emitter with a compact on-chip beam-splitter, J. Appl. Phys. Lett. 104 (23) (2014) 1–3. [5] Jianjun Chen, Chengwei Sun, Hongyun Li, Qihuang Gong, Experimental demonstration of an on-chip polarization splitter in a submicron asymmetric dielectric-coated metal slit, J. Appl. Phys. Lett. 104 (23) (2014) 1–4. [6] Sangsik Kim, Minghao Qi, Copper nanorod array assisted silicon waveguide polarization beam splitter, J. Opt. Express 22 (8) (2014) 9508–9516. [7] Wenjia Yuan, Weidong Shen, Yueguang Zhang, Xu Liu, Dielectric multilayer beam splitter withdifferential phase shift on transmission and reflection for division-of-amplitude photopolarimeter, J. Opt. Express 22 (9) (2014) 11011–11020.
[8] Mao-Wang Lu, Gui-Lian Zhang, Sai-Yan Chen, Spin-electron beam splitters based on magnetic barrier nanostructures, J. Appl. Phys. 112 (1) (2012) 014309–014313. [9] Chuanhong Zhou, Punit Kohli, Ultracompact beam splitters based on plasmonic nanoslits, J. Appl. Phys. 109 (9) (2011) 093114. [10] Pi-Gang Luan, Kao-Der Chang, Periodic dielectric waveguide beamsplitter based on co-directional coupling, J.Opt. Express 15 (8) (2007) 4536–4545. [11] Min Zhang, Radu Malureanu, Asger Christian Krüger, Martin Kristensen, 1 3 Beam splitter for TE polarization based on self-imaging phenomena in photonic crystal waveguides, J.Opt. Express 18 (14) (2010) 14944–14949. [12] Zejun Zhang, Yasuhide Tsuji, et al., Design of polarization splitter with singlepolarized elliptical-hole core circular-hole holey fibers, J. Photonics Technol. Lett. 26 (6) (2014) 541–543. [13] J. Park, S. Lee, H. Park, M. Lee, High-efficiency polarization beamsplitter based on a self-collimating photonic crystal, J. Opt. Soc. Am. B 27 (11) (2010) 2247–2254. [14] Jia-bi Chen, Yan Wang, Bao-hua Jia, et al., Observation of the inverse Doppler effect in negative-index materials at optical frequencies, J. Nat. Photonic 5 (4) (2011) 239–245.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Design and verification of the polarization beamsplitter based on photonic crystals Ting Wang, Binming Liang n, Qiang Jiang, Lun Gao, Jinbin Hu, Heng Cao, Jiabi Chen, Song-lin Zhuang Optical Electronic Information and Computer Engineering College, University of Shanghai for Science and Technology, Shanghai 200093, China
art ic l e i nf o
a b s t r a c t
Article history: Received 6 January 2015 Received in revised form 13 March 2015 Accepted 17 April 2015 Available online 24 April 2015
Photonic crystals have a great prospect in the field of integrated optics due to their high integration and low transmission loss. In this paper, a beam splitter based on the bandgap of photonic crystal is designed and demonstrated experimentally for polarization-dependent beam splitting. The simulated radiation patterns show excellent polarization purity, with a cross-polarization level above 20 dB. Furthermore, the angle deviation of the incident and the temperature change of device have slight impact on beamsplitting. Larger shifting range of incident wavelength is allowed. What is more, the range of medium radius with good splitting effect is relatively large, which reduces the difficulty of production and processing. & 2015 Elsevier B.V. All rights reserved.
Keywords: Beam splitter Photonic crystal Bandgap
1. Introduction
2. Structure of the two-dimensional photonic crystals
Polarization beamsplitter can separate two orthogonal polarization modes of electromagnetic waves into different directions, which plays an important role in optical communications [1,2], information-recycle [3] and integrated optical circuits [4,5]. Many kinds of beamsplitter have been proposed [6–9]. Conventional ones generally use birefringence effect of natural crystal (e.g. Wollaston prism), either polarization splitter cubes or multi-layer film structure to achieve beams splitting. These polarization beamsplitters cannot meet the development of high-density integrated optical circuits. Now many methods in photonic crystals are used for beam polarization as its high integration, good beam effect, and low transmission loss [10,11]. The one based on directional coupler [12] must insert waveguide bend in the output as a small splitting angle, which increases the size of device; another is based on crystal structure [13], whose design is complex, and the manufacture is difficult. Moreover the polarization splitting depends on structural parameters and operating wavelength. In this paper, we propose a beamsplitter based on photonic crystal band gap. The beam splitting will not be affected by drifting of incident wavelength and changing of device temperature, which has a stable and reliable performance. The range of medium radius with good splitting effect is relatively large, which reduces the difficulty of production and processing, What is more, the structure is simple and easy processing.
Photonic crystal is a material that has been structured to possess a periodic modulation of the refractive index. The rectangular photonic crystal structure applicated in the mathematical simulation experiment is shown in Fig. 1(a). In which, the black dots represent the silica column (refractive index n is 3.42), the cell shape of dielectric rod is cylinder, arranging in a triangle. Lattice period (the distance between two silicon column centers) is represented by a (a=λ*Frequency , Frequency is the normalized frequency, λ is the free space wavelength ), which is shown in Fig. 1 (b). Diameter of dielectric column is 2r, another saying is waveguide width, which is often defined as b*a (b is a constant, which is greater than 0 and less than 1, denotes the waveguide width parameter).
n
Corresponding author. E-mail address: [email protected] (B. Liang).
http://dx.doi.org/10.1016/j.optcom.2015.04.044 0030-4018/& 2015 Elsevier B.V. All rights reserved.
3. Simulation data and result discussion This paper uses the FDTD method to carry on the simulation of the 2D photonic crystal fabricated from a hexagonal array of circular dielectric rods with Si. With the simulation software RSoft, the photonic band structure is shown in Fig. 2. The horizontal coordinate is value b while the vertical coordinate is normalized frequency. The shadow section is called conduction band, where photon can transmit. On the contrary, the blank sections represent forbidden regions. It can be seen from Fig. 2 that the changing of value b will influence the band structure. With the increase of value b, the band gap are all broadening then narrowing and
T. Wang et al. / Optics Communications 351 (2015) 40–44
41
Fig. 1. (a) Structure for 2D photonic crystal and (b) hexagonal structure.
Frequency (ωa/2πc=a/λ)
TE Band Map 2
1
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1. 0
0.6
0.7
0.8
0.9
1. 0
b Frequency (ωa/2πc=a/λ)
TM Band Map 2
1
0 0.0
0.1
0.2
0.3
0.4
0.5 b
Fig. 2. The band structure of photonic crystal polarization influenced by wave guide width parameter b.
falling gradually. When the value b ranging from 0.15 to 0.4 with the normalized frequency is 0.4717, which is just in the conduction band of TM but the forbidden band of TE. Without defects the TM wave can pass through in no loss, however the TE wave will be reflected. Defining incident power as 1, then the output power becomes relative value. Simulating with the Fullwave method of Rsoft, the propagation is presented in Fig. 3. θ is incident angle, TTE and TTM are the transmition RTE and RTM are the reflection of TE and TM respectively. Normally the performance of polarization splitter can be evaluated by splitting ratio or extinction ratio (ER). Therefore the ER of the two cores are defined as
Fig. 4. Relation between the output power and incident angle θ.
ER1 = − 10* lg(TTE /TTM )
(1)
ER2 = − 10* lg(RTM /RTE )
(2)
By setting a suitable incident angle and value b, the photon can fall in conduction band of TM but the forbidden one of TE, so the whole transmission of TM and the whole reflection of TE. When θ = 44° and value b ranging from 0.16 to 0.33, excellent polarization purity can be achieved, with a cross-polarization level above 20 dB. To reduce the difficulty of production and processing, we set b as 0.25 (b = 0.25 ± 0.08 all the value b can achieve excellent polarization). At the same time, If the incident angle has a deviation (θ = 44° ± 2°), efficient separation can also be achieved. The relation between the output power and incident angle is shown in Fig. 4.
Fig. 3. Light propagation (Ey represents TE and Hy represents TM).
42
T. Wang et al. / Optics Communications 351 (2015) 40–44
1.0
1.0
0.8 0.6
0.6
power
power
TTE TTM
0.4
0.4
RTM RTE
0.2 0.0 0.3
0.8
b=0.2
0.4
0.5
0.2
0.6
0.7
Frequency(a/ λ)
0.0 0.3
b=0.25 TTE TTM
RTM RTE 0.4
0.5
0.6
Frequency (a/λ)
0.7
1.0 0.8
b=0.3
0.6
power
TTE
TTM RTM
0.4
RTE
0.2 0.0 0.3
0.4
0.5
0.6
Frequency (a / λ)
0.7
Fig. 5. Relation between the output power and frequency (the horizontal coordinate represents frequency and the vertical coordinate represents the output power).
It can be seen from Fig. 5 that in large range of normalized frequency, the reflection of TE and the transmission of TM are near to 1, moreover the transmission of TE and the reflection of TM are near to 0. The range of normalized frequency with a cross-polarization level above 20 dB can be got by further calculation. b = 0.2, the range is 0.4098–0.521.b = 0.25, the range is 0.362–0.5. b = 0.3, the range is 0.325–0.481. It can be seen from the Frequency range, there are large range of normalized frequency with a cross-polarization level above 20 dB, which demonstrates larger incident light wavelength shiftting range of device is allowed (a = λ*Frequency ). Due to the thermoeffect of photonic crystals (silicon), the change of temperature will occur to the small change of refractive index in the medium column.
Δn = αnΔT
Fig. 6. Relation between the output power and temperature (the horizontal coordinate represents temperature and the vertical coordinate represents the output power).
When θ = 44°, the relation between normalized frequency and transmission as well as reflection of TE and TM are shown in Fig. 5. In which, Frequency is normalized frequency and power is output power.
(3)
In which, α is the thermo-optic coefficient of silicon (α ¼1.86 10 4/°C). The change of the refractive index will have impact on the separation effect and then affects the output power indirectly. When the temperature changes from 50 °C to 200 °C, the relation between the output power and temperature is shown in Fig. 6. The cross-polarization level are calculated all above 22 dB. That is to say, the changing of temperature has little impact on the separation effect. For the wavelength is normalized, different wavelengths just
T. Wang et al. / Optics Communications 351 (2015) 40–44
43
Fig. 7. SEM Photo of a sample by microscope ((a) is overlook and (b) is side-look).
detector
Photonic crystals
lens Half-wave plate polarizer CO2 laser
Fig. 8. Experimental set-up for verification of the beamsplitting effect.
and the theoretical height of column is assumed an infinite amount. Thus, actually the analogous photonic crystal structure can be achieved in manufacture. The experimental platform is setting up. Experimental set-up for verification of the beamsplitting effect is shown in Fig. 8. The beam emitted from laser will become linearly polarized one, which oblique- incidents on the photonic crystals after aggregating by the lenses.The beam refracted out of the photonic crystal will be picked by the detector and the detector is linked with the computer to record the output data. In the platform, the linear-polarizing plate is used to re-polarize the beam emitted from a laser. The polarization can access to 99.9% after being re-polarized of the linear-polarizing plate. The polarization direction of linearly polarized beam can be changed by a half-wave plate, which realizes the mode converse between TE and TM. Analysing with output data, the preliminary result is shown in Fig. 9. The output power for different positions of the TM and TE wave is shown in Fig. 9. As is depicted that the ratio of the optical power output (TM /TE ) can access to 7.5, which demonstrates the beam splitting effect is very good. Because of the unaverage diameter of the column and this experiment works with the devices instead of waveguide devices, which exists some stray light. Waveguide devices will be used to improve the experiment in the next step.
4. Conclusion
Fig. 9. Relation illustration between the output power and position (the horizontal coordinate represents position and the vertical coordinate represents the output power).
need to change the period a, the separation can be achieved. Setting a as 141.51 μm can achieve the separation of Thz (300 μm). Moreover setting a as 0.731 μm, the communication one (1.55 μm) can be realized. The working group has a mature study on the photonic crystal structure incident wavelength of 10.6 μm [14]. The photonic crystal sample processing as incident wavelength 10.6 μm and lattice period 5 μm is shown in Fig. 7. The diameter of column is 1.25 μm, height is 50 μm, as the height of the column is 40 times to the diameter of the column
This paper uses the FDTD method to study the structure and transmitting character of the 2D photonic crystal fabricated from a hexagonal array of circular dielectric rods with Si. Aiming at the application on beamsplitter, the simulating results show that comparing to the traditional polarization device, the one made by 2D photonic crystal is in a small size and can achieve efficient separation between the TE wave TM waves in large angle. What is more, it is simple and with great stable. Large range of normalized frequency can realize efficient separation, which can avoid the interference by shifting of incident wavelength. The changing of temperature has little impact on the separation effect. The device with a stable separation effect, moreover it is easy processing, which is expected to have a great application on integrated optics.
Acknowledgments This work is supported by the National Basic Research Program of China (Grant no. 2011CB707504), the National Natural Science Foundation of China (61177043 and 11104184).
44
T. Wang et al. / Optics Communications 351 (2015) 40–44
Reference [1] S.Y. Lin, E. Chow, J. Bur, Low-loss, wide-angle Y splitter at 1.6-mm wavelengths built with a two-dimensional photonic crystal, J. Opt. Lett. 27 (16) (2002) 1400–1402. [2] Tiaoming Niu, Withawat Withayachumnankul, et al., Terahertz reflectarry as a polarizing beam splitter, J. Opt. Express 22 (13) (2014) 16148–16160. [3] S.A. Haine, Information-recycling beam splitters for quantum enhanced atom interferometry, J. Phys. Rev. Lett. 110 (5) (2013) 053002. [4] N. Prtlj, R.J. Coles, et al., Monolithic integration of a quantum emitter with a compact on-chip beam-splitter, J. Appl. Phys. Lett. 104 (23) (2014) 1–3. [5] Jianjun Chen, Chengwei Sun, Hongyun Li, Qihuang Gong, Experimental demonstration of an on-chip polarization splitter in a submicron asymmetric dielectric-coated metal slit, J. Appl. Phys. Lett. 104 (23) (2014) 1–4. [6] Sangsik Kim, Minghao Qi, Copper nanorod array assisted silicon waveguide polarization beam splitter, J. Opt. Express 22 (8) (2014) 9508–9516. [7] Wenjia Yuan, Weidong Shen, Yueguang Zhang, Xu Liu, Dielectric multilayer beam splitter withdifferential phase shift on transmission and reflection for division-of-amplitude photopolarimeter, J. Opt. Express 22 (9) (2014) 11011–11020.
[8] Mao-Wang Lu, Gui-Lian Zhang, Sai-Yan Chen, Spin-electron beam splitters based on magnetic barrier nanostructures, J. Appl. Phys. 112 (1) (2012) 014309–014313. [9] Chuanhong Zhou, Punit Kohli, Ultracompact beam splitters based on plasmonic nanoslits, J. Appl. Phys. 109 (9) (2011) 093114. [10] Pi-Gang Luan, Kao-Der Chang, Periodic dielectric waveguide beamsplitter based on co-directional coupling, J.Opt. Express 15 (8) (2007) 4536–4545. [11] Min Zhang, Radu Malureanu, Asger Christian Krüger, Martin Kristensen, 1 3 Beam splitter for TE polarization based on self-imaging phenomena in photonic crystal waveguides, J.Opt. Express 18 (14) (2010) 14944–14949. [12] Zejun Zhang, Yasuhide Tsuji, et al., Design of polarization splitter with singlepolarized elliptical-hole core circular-hole holey fibers, J. Photonics Technol. Lett. 26 (6) (2014) 541–543. [13] J. Park, S. Lee, H. Park, M. Lee, High-efficiency polarization beamsplitter based on a self-collimating photonic crystal, J. Opt. Soc. Am. B 27 (11) (2010) 2247–2254. [14] Jia-bi Chen, Yan Wang, Bao-hua Jia, et al., Observation of the inverse Doppler effect in negative-index materials at optical frequencies, J. Nat. Photonic 5 (4) (2011) 239–245.