Abstract

We have previously shown through simulation that an optical beam deflector based on the Pancharatnam (geometric) phase can provide high efficiency with up to 80° deflection using a dual-twist structure for polarization-state control [Appl. Opt. 54, 10035 (2015)]. In this report, we demonstrate that its optical performance is as predicted and far beyond what could be expected for a conventional diffractive optical device. We provide details about construction and characterization of a ± 40° beam-steering device with 90% diffraction efficiency based on our dual-twist design at a 633nm wavelength.

© 2017 Optical Society of America

1. Introduction

Pancharatnam made clear the concept of a phase-only device based on changes in the polarization state of light [1]. It was later shown that this concept could be used to make an optical device that could simulate a prism. A device of this type is sometimes called a circular polarization grating because of the polarization states of interfering light beams that are used to fabricate it by polarization holography [2]. Here, we will call it a Pancharatnam phase device to emphasize the fact that the phase of diffracted light does not have a discontinuous periodic profile but changes continuously. As opposed to Pancharatnam phase devices, Bragg gratings can provide large-angle beam deflection and reflection; however, the angle of incidence and wavelength are restricted by the Bragg condition [3]. Optical phased arrays that have a sawtooth phase profile with an optical depth of one optical wave have been shown to also provide high efficiency, but their efficiency drops if the deflection angle is larger than about 15° [4]. Devices based on the Pancharatnam phase have been proposed by Crawford et al., who have shown a practical way to produce them using technology that is liquid crystal (LC) based [5]. Since then, the optical community has taken an increasing interest in the phenomenon, and researchers have developed numerous excellent applications from this method [6–11]. However, previous approaches to providing large-angle, optical beam-steering devices have not been able to provide the high efficiency for a deflection angle of greater than about 30° for typical materials available [12–15].

Figure 1(a) shows the schematics of a thin-film beam deflector based on the Pancharatnam phase. It can deflect the incident wave of light (λ) to a certain diffraction angle (θdiff), determined by the diffraction grating equation sin(θdiff) = λ/Λ. Here, Λ is called the half-pitch, which is defined as the distance over which liquid crystal molecules are rotated by π radians about the y axis. The LC orientation does not change along the y direction. We will call this basic type of device a conventional Pancharatnam phase deflector (c-PPD).

 figure: Fig. 1

Fig. 1 Concept of Pancharatnam phase deflector. (a) A c-PPD in its side-view and top-view. The inset shows a molecular alignment of reactive mesogen (RM). (b) A revolutionary dual-twist design in its side view with two combined DTPPDs, in which the twist angle is mirror symmetric. S/M/E correspond to the position of simulation in Fig. 11.

Download Full Size | PPT Slide | PDF

From paraxial analysis [16], the relation between input light and output light at one position in the aperture of a c-PPD can be expressed as,

[Eout]=[M(Γ,φ)][Ein],with[M(Γ,φ)]=[R(φ)][eiΓ/200eiΓ/2][R(φ)].

Here, φ is the angle between the optical axis and the z axis, and [R(φ)] is a rotation matrix. If considering a circularly polarized light input [EzinExin]=[1±i], the output is

[EzoutExout]=cosΓ2[1±i]isinΓ2ei(2φ(x))[1i],
where phase retardation Γ=2πΔndλ,and Δn is birefringence. When the phase retardation meets with the half-wave condition (Γ = π), the output will be simplified to

[EzoutExout]=iei(2φ(x))[1i].

This equation makes it clear that light of the opposite-handed circular polarization from the input light achieves a phase shift determined by the angle φ, which is the angle through which the director (the local average orientation of the liquid crystal molecules) is rotated about the axis normal to the plane of the device [the y axis in Fig. 1(a)]. In a beam deflector, φ(x) is a linear function of x, namely φ(x) = 180°·x ∕ Λ, as shown in Fig. 1(a). It has been shown that a c-PPD with a small deflection angle can have ∼100% diffraction efficiency. Unfortunately, when the diffraction angle becomes large, the efficiency goes down quickly, especially for low birefringence materials [17].

We propose the use of a dual-twist structure to improve the steering efficiency, as shown in Fig. 1(b). The phrase “dual twist” refers to the fact that the LC director spirals about the y axis both in-plane (dependent on the x position) and out-of-plane (dependent on the y position). Our design consists of two such dual-twist Pancharatnam phase deflectors (DTPPDs), with equal in-plane periodicity and equal but opposite out-of-plane twist angles. The twist angle in these two DTPPDs is mirror symmetric. Each DTPPD has the thickness of the half-wave plate (d) at the designed wavelength. Such a dual-twist structure has been proposed earlier by Escuti et al. for achromatic application as a broadband beam deflector [18–20]; Li et al. also proposed a high-efficiency broadband device with a wide incident angle range [16]. However, these earlier applications are limited to small diffraction angles. Here, we demonstrate a dual-twist structure that provides the predicted large angles of deflection with high efficiency by experimentally pushing the limit of the half-pitch Λ to ~1 µm, allowing fabrication and characterization of a device with a 40° diffraction angle. With this device, we show a high-efficiency beam steering with 80° field of view (FOV), which is controlled only by changing the handedness of circularly polarized input light.

2. Simulation method

Yee’s grid for finite-difference time-domain (FDTD) simulation is an effective method of computing electromagnetic problems [21]. By directly solving coupled Maxwell’s curl equations with a few approximations, FDTD is also a robust method for dealing with light propagation problems in birefringent media [22,23]. It has been shown that FDTD can provide precise simulation results for Pancharatnam phase devices [17,24]. Therefore, we have chosen the FDTD method as our simulation tool to study the efficiency of large-deflection-angle devices. The simulation scheme and program can be referred to in our previous publications [25,26].

To quantify the performance of the Pancharatnam phase device, we firstly define the intrinsic diffraction efficiency, ηimth. The intrinsic diffraction efficiency is equal to

ηmthi=ImthITotaldiff,withITotaldiff=mImth.

Imth is the light intensity of the transverse magnetic (TM) mode at the mth diffraction order, and ITotal diff is the total diffraction intensity of the TM mode. ηimth is used to compare light intensity at different diffraction orders, not taking into account the effect of back reflections.

To verify our FDTD simulation, we simulate the intrinsic diffraction efficiency of a c-PPD with different half-pitches Λ and birefringence values Δn for normally incident light. All simulations are set up to match the half-wave condition. These results are summarized in Fig. 2. It can be seen that when the device is made with a higher birefringence material, the diffraction efficiency is higher, and the device has a lower efficiency when the diffraction angle of the device becomes larger. Our simulation results are comparable to results that have been reported by Escuti et al. [13].

 figure: Fig. 2

Fig. 2 Simulation of the 1st-order intrinsic diffraction efficiency vs. diffraction angle for c-PPD with different birefringent media at normal incidence.

Download Full Size | PPT Slide | PDF

From Eq. (3), we can see that for light to exit with high efficiency, the polarization state needs to be totally converted to its complementary polarization state. Based on this structure, we have shown that it is possible with an optimized dual-twist design to convert LCP to RCP and vice versa [25,26].

3. Experimental procedures

This type of Pancharatnam phase device is fabricated using a method proposed by Crawford et al. [5], as shown in Fig. 3. It involves using the azo dye Brilliant Yellow (BY), which defines the orientation of the local optic axis of a half-wave retarder fabricated subsequently using reactive mesogen (RM), a type of LC monomer.

 figure: Fig. 3

Fig. 3 Schematics of the procedure for fabricating a Pancharatnam phase deflector.

Download Full Size | PPT Slide | PDF

To prepare photo-alignment films, the BY material was dissolved in dimethylformamide (DMF) solution with fixed concentration of 1.5% by weight. The solution was spin-coated onto substrates at 800 rpm for 5 seconds and then 3000 rpm for 30 seconds. The films were dried in an oven at 120 °C for 30 minutes. This layer is a thin photo-sensitive film showing anisotropic response to the polarization axis of light. We then use a polarization holography alignment technique to expose the BY, and coat several layers of 10% RM257 dissolved in toluene until it achieves the thickness of a half-wave plate at a 633nm wavelength.

Figure 4(a) shows a schematic of the polarization holography setup to expose the photo-alignment layer. The blue laser beam is first expanded to 5 mm diameter by a beam expander, then split into two optical paths with opposite circular polarizations. The recording angle can be calculated from Θrec = 2sin−1(λrec/2Λ), where λrec is the wavelength used for recording. In our experiment, λrec = 457 nm, and Θrec = ~27°. To visualize the resulting interference pattern, a linear polarizer can be placed in front of a CCD camera with a 20 × objective lens that is focused on the plane where the BY sample is placed. The interference pattern can then be directly seen by the camera, as shown in Fig. 4(b). During the exposure, the substrate with the photo-alignment layer is placed at the position where two interfered beams both have the same 5 mm diameter and the same power. The substrate is then exposed for 8 minutes. Right after this process, we can see a chromatic reflection from the exposure area under white light, as shown in Fig. 4(c).

 figure: Fig. 4

Fig. 4 Experimental setup for holographic exposure. (a) The blue laser (457 nm) with 200 mW power is used to expose the photo-alignment layer, and two coherent laser beams with the same intensity interfere at the place of the sample. (b) Observation of the interference pattern using a camera. (c) The appearance of written BY immediately after the exposure.

Download Full Size | PPT Slide | PDF

Next in the process, an RM film is spin-coated on the BY layer, and the RM molecules self-align to the BY molecules. The optical retardation of the RM film must be equal to half of the wavelength of interest; however, it is not possible to deposit a single RM layer thick enough to provide the required retardation, because the monomers tend to orient themselves out of the plane of the film to reduce the high elastic energy. To overcome this, we need to coat multiple thin RM layers. Each layer self-aligns to the one beneath it and is then polymerized to lock in the desired orientation. (Note that it takes multiple thin RM layers to create one DTPPD, and our final device will consist of two DTPPDs.) In this work, we use RM257 (Δn~0.14 [8]) dissolved in toluene solution with a concentration of 10% by weight. A photo-initiator (Irgacure 651) was also added so that its concentration was 5% of the RM by weight. The RM–photo-initiator–toluene solution is spin-coated on the BY layer at 2000 rpm for 30 seconds immediately after the holographic exposure. During subsequent exposure to UV lamps (spectral peak at 365 nm and power density of 2 mW/cm2) for about 6 minutes in an N2-rich environment, the LC monomers form a cross-linked polymer. This process is sufficient to fabricate a c-PPD, but for a DTPPD with a half-pitch close to the exposure wavelength, we add a small amount of chiral dopant to the RM257 to produce the dual-twist structure shown in Fig. 1(b), specifically the Merck R-811/S-811 enantiomers.

This layer-by-layer process is continued until the desired half-wave retardation is reached for the c-PPD or DTPPD, as determined by the setup shown in Fig. 5. The efficiency test is done by using the Newport power-meter (Model 2832C). The beam power can be directly read out from the power-meter screen when the laser takes normal incidence into the detector head. The loss at interfaces is counted by the instrument itself to the final data, which can give out the accurate readout for any measurement. Light from a 633 nm, 500 µW continuous-wave laser passes through a circular polarizer and then through our sample. We measure the intensity of each diffracted order after every RM257 layer is coated, and we calculate the efficiency based on the total transmission from Eq. (4). At half-wave retardation, the zero-order (straight-through beam) intensity is minimized. For the final device, a second DTPPD is then fabricated using the same process (but with the opposite-handed chiral dopant).

 figure: Fig. 5

Fig. 5 Schematics of optical setup for diffraction efficiency test.

Download Full Size | PPT Slide | PDF

4. Results and discussions

To provide a comparison with previously reported devices, we fabricated 20° and 40° c-PPDs. The 20° one achieves an efficiency of 97% as shown in Fig. 6(a). As a comparison, we also show the results of the 40° c-PPD in Fig. 6(b). Its efficiency is lower than 50%, as predicted in the simulation.

 figure: Fig. 6

Fig. 6 Diffraction efficiency for a c-PPD. (a) A c-PPD with 20° deflection angle can achieve up to 97% efficiency upon the increased retardation, which is realized by coating RM257 layers and tested using a 633 nm wavelength of laser. (b) A c-PPD with 40° deflection angle can only achieve up to ~50% efficiency, experimentally tested using a 633 nm wavelength of laser.

Download Full Size | PPT Slide | PDF

Experimentally, we find that doping the RM257 material prior to spin coating with 0.65% of the chiral dopant ZLI-811 (S-811) from Merck provides the highest deflection efficiency of a single 40° DTPPD when the thickness of the device is optimized by controlling the number of layers of deposited RM257, as shown in Fig. 7(a). However, if the thickness is more than the optimal one, the efficiency will also go down, similar to the trend shown in Fig. 6(b). Figure 7(b) shows the effect of the optimized layer on incident light with left circular polarization (LCP) or right-circular polarization (RCP).

 figure: Fig. 7

Fig. 7 Diffraction efficiency for a single DTPPD. (a) The efficiency of the 1st DTPPD upon the increased retardation is measured with input of LCP. Insets show photograph of the light intensity of each diffraction order with input of LCP/RCP after the 10th layer of RM257 is coated (photograph taken in a darkened room). (b) The schematic of optical performance observed in experiments when LCP/RCP is input to the 1st DTPPD, as shown in Fig. 1(b).

Download Full Size | PPT Slide | PDF

The diffraction efficiency from a 40° DTPPD with 10 layers of RM257 doped with R-811 is shown in Fig. 8. It has a maximum efficiency of ~95% for its + 1st order, but produces an opposite twist effect to that shown in Fig. 7.

 figure: Fig. 8

Fig. 8 (a) The efficiency of a DTPPD as retardation increases with RCP input. (b) The schematic of optical performance observed in experiments when LCP/RCP is input to the 2nd DTPPD, as shown in Fig. 1(b).

Download Full Size | PPT Slide | PDF

Figure 9 shows the x component of the instantaneous E field of a single optimized 40° DTPPD with 105° twist angle in our FDTD simulation. The result matches with our experiment exactly as shown in Fig. 7(b).

 figure: Fig. 9

Fig. 9 The x component of the instantaneous E field in FDTD simulation for the 1st DTPPD with input of (a) LCP light and (b) RCP light. The black and white lines represent the wave front; red arrows represent the direction of light propagation.

Download Full Size | PPT Slide | PDF

Figure 10 shows the far-field intensity resulting from the simulation in Fig. 9, which is further normalized to show its efficiency based on its −1st, 0, and + 1st terms of diffraction orders. The efficiency of the −1st order is ~97% when LCP is input in Fig. 10(a), which is comparable to the experimental one of ~95%, as shown in Fig. 7(a).

 figure: Fig. 10

Fig. 10 The diffraction efficiency of the 1st DTPPD with input of (a) LCP light and (b) RCP light.

Download Full Size | PPT Slide | PDF

As proposed in Fig. 1(b), an optimized ± 40° beam-steering device with birefringence Δn ~0.14, twist angle θtwist = 105°, and retardation Γ = π has been simulated under conditions identical to our experiments. Figure 11 shows the y component of the instantaneous E field for this ± 40° beam-steering device. Only the intensity of the deflected eigenmode is shown. The dashed yellow lines indicate the boundaries of the DTPPDs. It can be seen clearly that the intensity of the deflected light is increased only in the 2nd DTPPD for the case of RCP input (for + 40° beam steering), but is increased in the 1st one for the case of LCP input (for −40° beam steering). Also, the resulting diffraction efficiency of this device at half-wave thickness is about 92%, as shown in the inset of Fig. 12.

 figure: Fig. 11

Fig. 11 The y component of the instantaneous E field in FDTD simulation for this ± 40° beam steering device as (a) a positive deflector and (b) a negative deflector. S/M/E correspond to the position as shown in Fig. 1(b). The black and white lines represent the wave front; red arrows represent the direction of light propagation.

Download Full Size | PPT Slide | PDF

 figure: Fig. 12

Fig. 12 Realization of a ± 40° beam steering from two combined DTPPDs. (a) By using the input of RCP, the red laser beam is diffracted to its + 1st-order with + 40° deflection angle (see Visualization 1). (b) By using the input of LCP, the red laser beam is diffracted to its −1st- order with −40° deflection angle (see Visualization 2). Insets show the simulation result of far field intensity in both cases with the same unit and coordinate as shown in Fig. 10.

Download Full Size | PPT Slide | PDF

When the first DTPPD is combined with a second constructed using a chiral dopant ZLI-3786 (R-811) with the opposite twist effect to S-811, the proposed structure of Fig. 1(b) is realized. It is worth mentioning that RM molecules rotating along the y axis in the first and second DTPPD have the same twist angle but different direction. Then the molecules can go back to their original placement when we look at the first layer of RM coating on both substrates. Once these two DTPPDs have been made, respectively, we then assemble them together (with the coating-side facing to each other) to measure the efficiency of ± 40° beam steering. Actually, we have not fabricated the second DTPPD directly on top of the first one, in order to also have the ability to test them separately. In general, we do expect some losses of light intensity and reduction of efficiency from imperfect alignment of the two DTPPDs. However, the approach taken does not affect the results presented in this work.

The resultant device can deflect light to + 40° or −40° by changing the input polarization state of light from RCP to LCP, as shown in Fig. 12. Accordingly, it can change the direction of light in 80° FOV, but it is not a continuously steerable device.

The measured data for ± 40° deflection angle from the efficiency tests shown in Fig. 12 is recorded in Table 1. Our device achieves 90% diffraction efficiency, based on the total transmission in both cases. Since there is no observable order beyond ± 1 and 0-order, we only consider these three terms (both transmission and reflection). The total intensity at the input of this device is measured to be 171.1 and 177.9 µW for + 40° and −40° beam steering, respectively. Also, the measured efficiency of this device is 90%, very close to the result of 92% in our FDTD simulation.

Tables Icon

Table 1. Transmission and reflection of ± 40° steered beam

5. Conclusion

Using simulations and experiments, we have demonstrated a ± 40° beam-steering device with high efficiency based on a Pancharatnam phase deflector with a dual-twist structure. While these devices have a strong wavelength dependence, this report demonstrates that a device with a structural periodicity near the wavelength of light can deflect light to large angles with efficiencies close to 100%. The demonstrated dual-twist design and fabrication procedure opens the possibility for making ultra-compact high-efficiency wide-angle beam-steering devices, lenses with f-number less than 1.0, and a wide range of other potential applications in the optical and display industries.

Funding

M.I.T. Lincoln Laboratory and the Army Research Laboratory (Agreement # W911NF-14-1-0650); Air Force Contract No. FA8721-05-C-0002 and/or FA8702-15-D-0001.

Acknowledgments

We express thanks for financial support from M.I.T. Lincoln Laboratory and the Army Research Laboratory (Agreement # W911NF-14-1-0650). This material is based upon work supported under Air Force Contract No. FA8721-05-C-0002 and/or FA8702-15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the U.S. Air Force.

References and links

1. M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990). [CrossRef]  

2. T. Todorov, L. Nikolova, and N. Tomova, “Polarization holography. 2: Polarization holographic gratings in photoanisotropic materials with and without intrinsic birefringence,” Appl. Opt. 23(24), 4588–4591 (1984). [CrossRef]   [PubMed]  

3. Y. Weng, D. Xu, Y. Zhang, X. Li, and S. T. Wu, “Polarization volume grating with high efficiency and large diffraction angle,” Opt. Express 24(16), 17746–17759 (2016). [CrossRef]   [PubMed]  

4. P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009). [CrossRef]  

5. G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005). [CrossRef]  

6. M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006). [CrossRef]  

7. J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015). [CrossRef]  

8. K. Gao, H. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Thin-film Pancharatnam lens with low f-number and high quality,” Opt. Express 23(20), 26086–26094 (2015). [CrossRef]   [PubMed]  

9. C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006). [CrossRef]  

10. U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013). [CrossRef]  

11. U. Ruiz, P. Pagliusi, C. Provenzano, K. Volke-Sepúlveda, and G. Cipparrone, “Polarization holograms allow highly efficient generation of complex light beams,” Opt. Express 21(6), 7505–7510 (2013). [CrossRef]   [PubMed]  

12. N. Tabirian, S. Nersisyan, B. Kimball, and D. Steeves, “Broadband optics for manipulating light beams and images,” U.S. Patent Application No. 12/697,083, August 4, 2011.

13. J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50(17), 2636–2639 (2011). [CrossRef]   [PubMed]  

14. H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,” SID Symp. Dig. Tech. Papers 45, 739–742 (2014). [CrossRef]  

15. H. Chen, Y. Weng, D. Xu, N. V. Tabiryan, and S. T. Wu, “Beam steering for virtual/augmented reality displays with a cycloidal diffractive waveplate,” Opt. Express 24(7), 7287–7298 (2016). [CrossRef]   [PubMed]  

16. T. Li, Liquid crystal polarization gratings and their applications (Ph. D. Thesis, Hong Kong University of Science and Technology, 2013).

17. C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006). [CrossRef]   [PubMed]  

18. C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008). [CrossRef]   [PubMed]  

19. C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007). [CrossRef]  

20. M. J. Escuti, C. Oh, and R. Komanduri, “Low-twist chiral liquid crystal polarization gratings and related fabrication methods,” U.S. Patent Application No. 12/596,189, September 9, 2010.

21. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]  

22. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).

23. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE, 2000).

24. C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007). [CrossRef]  

25. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Analysis of a dual-twist Pancharatnam phase device with ultrahigh-efficiency large-angle optical beam steering,” Appl. Opt. 54(34), 10035–10043 (2015). [CrossRef]   [PubMed]  

26. H. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Concept for a transmissive, large angle, light steering device with high efficiency,” Opt. Lett. 40(9), 2080–2083 (2015). [CrossRef]   [PubMed]  

References

  • View by:

  1. M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
    [Crossref]
  2. T. Todorov, L. Nikolova, and N. Tomova, “Polarization holography. 2: Polarization holographic gratings in photoanisotropic materials with and without intrinsic birefringence,” Appl. Opt. 23(24), 4588–4591 (1984).
    [Crossref] [PubMed]
  3. Y. Weng, D. Xu, Y. Zhang, X. Li, and S. T. Wu, “Polarization volume grating with high efficiency and large diffraction angle,” Opt. Express 24(16), 17746–17759 (2016).
    [Crossref] [PubMed]
  4. P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
    [Crossref]
  5. G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
    [Crossref]
  6. M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
    [Crossref]
  7. J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015).
    [Crossref]
  8. K. Gao, H. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Thin-film Pancharatnam lens with low f-number and high quality,” Opt. Express 23(20), 26086–26094 (2015).
    [Crossref] [PubMed]
  9. C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
    [Crossref]
  10. U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
    [Crossref]
  11. U. Ruiz, P. Pagliusi, C. Provenzano, K. Volke-Sepúlveda, and G. Cipparrone, “Polarization holograms allow highly efficient generation of complex light beams,” Opt. Express 21(6), 7505–7510 (2013).
    [Crossref] [PubMed]
  12. N. Tabirian, S. Nersisyan, B. Kimball, and D. Steeves, “Broadband optics for manipulating light beams and images,” U.S. Patent Application No. 12/697,083, August 4, 2011.
  13. J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50(17), 2636–2639 (2011).
    [Crossref] [PubMed]
  14. H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,” SID Symp. Dig. Tech. Papers 45, 739–742 (2014).
    [Crossref]
  15. H. Chen, Y. Weng, D. Xu, N. V. Tabiryan, and S. T. Wu, “Beam steering for virtual/augmented reality displays with a cycloidal diffractive waveplate,” Opt. Express 24(7), 7287–7298 (2016).
    [Crossref] [PubMed]
  16. T. Li, Liquid crystal polarization gratings and their applications (Ph. D. Thesis, Hong Kong University of Science and Technology, 2013).
  17. C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006).
    [Crossref] [PubMed]
  18. C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008).
    [Crossref] [PubMed]
  19. C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
    [Crossref]
  20. M. J. Escuti, C. Oh, and R. Komanduri, “Low-twist chiral liquid crystal polarization gratings and related fabrication methods,” U.S. Patent Application No. 12/596,189, September 9, 2010.
  21. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
    [Crossref]
  22. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).
  23. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE, 2000).
  24. C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
    [Crossref]
  25. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Analysis of a dual-twist Pancharatnam phase device with ultrahigh-efficiency large-angle optical beam steering,” Appl. Opt. 54(34), 10035–10043 (2015).
    [Crossref] [PubMed]
  26. H. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Concept for a transmissive, large angle, light steering device with high efficiency,” Opt. Lett. 40(9), 2080–2083 (2015).
    [Crossref] [PubMed]

2016 (2)

2015 (4)

2013 (2)

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
[Crossref]

U. Ruiz, P. Pagliusi, C. Provenzano, K. Volke-Sepúlveda, and G. Cipparrone, “Polarization holograms allow highly efficient generation of complex light beams,” Opt. Express 21(6), 7505–7510 (2013).
[Crossref] [PubMed]

2011 (1)

2009 (1)

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

2008 (1)

2007 (2)

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

2006 (3)

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006).
[Crossref] [PubMed]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
[Crossref]

2005 (1)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

1990 (1)

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

1984 (1)

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Bastiaansen, C. W. M.

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Bhowmik, A. K.

Bos, P. J.

Broer, D. J.

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Callan-Jones, A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Chen, H.

Cheng, H.

Cheng, H. H.

Cipparrone, G.

U. Ruiz, P. Pagliusi, C. Provenzano, K. Volke-Sepúlveda, and G. Cipparrone, “Polarization holograms allow highly efficient generation of complex light beams,” Opt. Express 21(6), 7505–7510 (2013).
[Crossref] [PubMed]

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
[Crossref]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
[Crossref]

Crawford, G. P.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Eakin, J. N.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Escuti, M. J.

J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015).
[Crossref]

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50(17), 2636–2639 (2011).
[Crossref] [PubMed]

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008).
[Crossref] [PubMed]

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006).
[Crossref] [PubMed]

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Gao, K.

Heikenfeld, J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Kim, J.

Kudenov, M. W.

Li, X.

Li, Y.

Martinelli, M.

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

McManamon, P. F.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Miskiewicz, M. N.

Nikolova, L.

Oh, C.

Pagliusi, P.

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
[Crossref]

U. Ruiz, P. Pagliusi, C. Provenzano, K. Volke-Sepúlveda, and G. Cipparrone, “Polarization holograms allow highly efficient generation of complex light beams,” Opt. Express 21(6), 7505–7510 (2013).
[Crossref] [PubMed]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
[Crossref]

Pelcovits, R. A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Provenzano, C.

U. Ruiz, P. Pagliusi, C. Provenzano, K. Volke-Sepúlveda, and G. Cipparrone, “Polarization holograms allow highly efficient generation of complex light beams,” Opt. Express 21(6), 7505–7510 (2013).
[Crossref] [PubMed]

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
[Crossref]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
[Crossref]

Radcliffe, M. D.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Ruiz, U.

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
[Crossref]

U. Ruiz, P. Pagliusi, C. Provenzano, K. Volke-Sepúlveda, and G. Cipparrone, “Polarization holograms allow highly efficient generation of complex light beams,” Opt. Express 21(6), 7505–7510 (2013).
[Crossref] [PubMed]

Sánchez, C.

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Serati, S.

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50(17), 2636–2639 (2011).
[Crossref] [PubMed]

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Tabiryan, N. V.

Todorov, T.

Tomova, N.

Vavassori, P.

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

Volke-Sepúlveda, K.

Watson, E. A.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Weng, Y.

Wu, S. T.

Xie, H.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Xu, D.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Zhang, Y.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
[Crossref]

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

J. Appl. Phys. (1)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Opt. Commun. (1)

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Optica (1)

Phys. Rev. A (1)

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

Proc. IEEE (1)

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Proc. SPIE (2)

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

Other (6)

M. J. Escuti, C. Oh, and R. Komanduri, “Low-twist chiral liquid crystal polarization gratings and related fabrication methods,” U.S. Patent Application No. 12/596,189, September 9, 2010.

H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,” SID Symp. Dig. Tech. Papers 45, 739–742 (2014).
[Crossref]

N. Tabirian, S. Nersisyan, B. Kimball, and D. Steeves, “Broadband optics for manipulating light beams and images,” U.S. Patent Application No. 12/697,083, August 4, 2011.

T. Li, Liquid crystal polarization gratings and their applications (Ph. D. Thesis, Hong Kong University of Science and Technology, 2013).

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE, 2000).

Supplementary Material (2)

NameDescription
Visualization 1: MP4 (1088 KB)      +40 beam steering
Visualization 2: MP4 (1117 KB)      -40 beam steering

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1 Concept of Pancharatnam phase deflector. (a) A c-PPD in its side-view and top-view. The inset shows a molecular alignment of reactive mesogen (RM). (b) A revolutionary dual-twist design in its side view with two combined DTPPDs, in which the twist angle is mirror symmetric. S/M/E correspond to the position of simulation in Fig. 11.
Fig. 2
Fig. 2 Simulation of the 1st-order intrinsic diffraction efficiency vs. diffraction angle for c-PPD with different birefringent media at normal incidence.
Fig. 3
Fig. 3 Schematics of the procedure for fabricating a Pancharatnam phase deflector.
Fig. 4
Fig. 4 Experimental setup for holographic exposure. (a) The blue laser (457 nm) with 200 mW power is used to expose the photo-alignment layer, and two coherent laser beams with the same intensity interfere at the place of the sample. (b) Observation of the interference pattern using a camera. (c) The appearance of written BY immediately after the exposure.
Fig. 5
Fig. 5 Schematics of optical setup for diffraction efficiency test.
Fig. 6
Fig. 6 Diffraction efficiency for a c-PPD. (a) A c-PPD with 20° deflection angle can achieve up to 97% efficiency upon the increased retardation, which is realized by coating RM257 layers and tested using a 633 nm wavelength of laser. (b) A c-PPD with 40° deflection angle can only achieve up to ~50% efficiency, experimentally tested using a 633 nm wavelength of laser.
Fig. 7
Fig. 7 Diffraction efficiency for a single DTPPD. (a) The efficiency of the 1st DTPPD upon the increased retardation is measured with input of LCP. Insets show photograph of the light intensity of each diffraction order with input of LCP/RCP after the 10th layer of RM257 is coated (photograph taken in a darkened room). (b) The schematic of optical performance observed in experiments when LCP/RCP is input to the 1st DTPPD, as shown in Fig. 1(b).
Fig. 8
Fig. 8 (a) The efficiency of a DTPPD as retardation increases with RCP input. (b) The schematic of optical performance observed in experiments when LCP/RCP is input to the 2nd DTPPD, as shown in Fig. 1(b).
Fig. 9
Fig. 9 The x component of the instantaneous E field in FDTD simulation for the 1st DTPPD with input of (a) LCP light and (b) RCP light. The black and white lines represent the wave front; red arrows represent the direction of light propagation.
Fig. 10
Fig. 10 The diffraction efficiency of the 1st DTPPD with input of (a) LCP light and (b) RCP light.
Fig. 11
Fig. 11 The y component of the instantaneous E field in FDTD simulation for this ± 40° beam steering device as (a) a positive deflector and (b) a negative deflector. S/M/E correspond to the position as shown in Fig. 1(b). The black and white lines represent the wave front; red arrows represent the direction of light propagation.
Fig. 12
Fig. 12 Realization of a ± 40° beam steering from two combined DTPPDs. (a) By using the input of RCP, the red laser beam is diffracted to its + 1st-order with + 40° deflection angle (see Visualization 1). (b) By using the input of LCP, the red laser beam is diffracted to its −1st- order with −40° deflection angle (see Visualization 2). Insets show the simulation result of far field intensity in both cases with the same unit and coordinate as shown in Fig. 10.

Tables (1)

Tables Icon

Table 1 Transmission and reflection of ± 40° steered beam

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

[ E out ]=[M(Γ,φ)][ E in ], with [M(Γ,φ)]=[R(φ)][ e iΓ/2 0 0 e iΓ/2 ][R(φ)].
[ E zout E xout ]=cos Γ 2 [ 1 ±i ]isin Γ 2 e i(2φ(x)) [ 1 i ],
[ E zout E xout ]=i e i(2φ(x)) [ 1 i ].
η mth i = I mth I Totaldiff , with I Totaldiff = m I mth .

Metrics