Investigating the characteristics ofTM-pass/TE-stop polarizer designedusing plasmonic nanostructuresAMR M. MAHROS,1,2,* MARWA M. THARWAT,3 AND ISLAM ASHRY2,41Department of Physics, University of Jeddah, Jeddah 21432, Saudi Arabia2Department of Engineering Mathematics and Physics, Alexandria University, Alexandria 21526, Egypt3Department of Electrical Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21432, Saudi Arabia4e-mail: ashry@vt.edu*Corresponding author: amr.mahros@mena.vt.edu

Received 18 February 2015; revised 9 April 2015; accepted 17 April 2015; posted 20 April 2015 (Doc. ID 234795); published 7 May 2015

Plasmonics-based polarizers are important for many photonic devices and applications. In this paper, wedesign and investigate the characteristics of a new TM-pass/TE-stop polarizer using silver nanograting of expo-nentially tapered slit sidewalls. Performance of the designed polarizer is determined through monitoring themodification of its insertion loss, return loss, extinction ratio, and far-field transform due to changing its struc-tural parameters. We find that the structural parameters of the reported polarizer such as a slit sidewall taperingcoefficient and slit opening widths have a significant impact on tuning the polarizer characteristics. 2015Optical Society of America

OCIS codes: (050.1950) Diffraction gratings; (130.5440) Polarization-selective devices; (250.5403) Plasmonics.

http://dx.doi.org/10.1364/AO.54.004464

1. INTRODUCTION

Plasmonic structures incorporated with periodic nanogratingshave received a significant amount of attention since the dis-covery of their extraordinary optical transmission (EOT) [1].Surface plasmons (SPs) and EOT have been recently employedin a myriad of applications including biomedical sensing, spon-taneous emission engineering, efficient solar cells, and fabrica-tion of nanoantennas [25].

Polarization steering plays a fundamental rule in the fulfill-ment of integrated photonics devices and systems such asskylight-based navigation systems, fiber-optic gyroscopes,electro-optic switching arrays, and coherent optical communi-cation modules [68]. Formerly, external expensive bulk opti-cal components were used to realize polarization control.Recently, polarization control of a light source can be achievedthrough the use of metallic subwavelength gratings [911].

Efficiency of a designed polarizer is determined throughcalculating its extinction ratio (ER), insertion loss (IL), andreturn loss (RL). The ER is defined as the ratio of a transmittedpower through a polarizer in the desired polarization to thatin the undesired polarization. The polarizer IL mainly deter-mines the optical power lost due to inserting a polarizer inan optical network. It is determined by dividing the opticalpower after the polarizer to that before it. The optical power

lost due to reflection by a polarizer is identified by measuringthe RL.

In the literature, most of theoretical and experimental stud-ies about designing plasmonic gratings have focused on usingstraight metallic slits [12,13]. The reason might be that the slitwidth-to-period ratio is well defined and can be straightfor-wardly compared with the measured transmission. This makestheir theoretical analysis relatively easy. Furthermore, thestraight holes are experimentally easy to fabricate using afocused ion beam. However, in contrast, linearly tapered slitsprovide a larger transmission band, more light transmission en-hancement, and more light localization at the slit exits due togradual impedance variation. As a result, the EOT of such laterstructures have been recently thoroughly investigated in theexisting studies [1416].

Furthermore, the impact of changing the curvature of the slitsidewalls has not been thoroughly investigated in most of plas-monic polarizer designs based on straight and linearly taperedslits. Minor studies explored using plasmonic gratings ofnonlinearly slit sidewalls as optical polarizers. For example,Liang et al. [17] introduced designing aTM-pass/TE-stop polar-izer using plasmonic grating of ellipse sidewalls, which showedhigh ER. However, in their design, the curvature of the ellipsesidewalls and the top and bottom slit openings widths cannot be

4464 Vol. 54, No. 14 / May 10 2015 / Applied Optics Research Article

1559-128X/15/144464-07$15/0$15.00 2015 Optical Society of America

OptiFDTDHighlight

OptiFDTDHighlight

OptiFDTDHighlight

changed separately, which prevents obtaining maximum TMtransmission at a desired ER.

In this paper, we design a new TM-pass/TE-stop opticalpolarizer using plasmonic grating of nonlinearly exponentiallytapered slit sidewalls. Using the finite difference time domain(FDTD) method, we theoretically investigate the influence ofchanging the design key parameters of the reported structuresuch as sidewall curvature, slit opening widths, and gratingperiod on the polarizer performance efficiency. The perfor-mance efficiency of the designed polarizer is determinedthrough calculating its ER, insertion loss (IL), return loss(RL), and wide-angle far-field transform. The main advantageof the reported polarizer over those found in the literature is theability to change its structural parameters independently.Therefore, based on the application, we can tune the absorbedoptical power at a specific extinction ratio value. Additionally,we compare the zero- and first-order transmitted resonancepower enhancement of the designed structure with those foundin the literature. The results presented here should be relevantfor a large number of applications involving color filters andplanar lenses.

This paper is organized as follows: the reported structureand FDTD simulation parameters are described in Section 2.Section 3 represents the performance characteristics of theproposed TM-pass/TE-stop optical designed polarizer and dis-cussions for the effect of varying different key parameters.Finally, Section 4 provides conclusions of the obtained results.

2. STRUCTURE DESCRIPTION AND FDTDSIMULATION

In this work, optical transmission spectra of the reported plas-monic optical polarizer structure are obtained by solvingMaxwells equations of different materials using the FDTD al-gorithm. Figure 1(a) is a schematic of the designed polarizer,which consists of silver nanograting sandwiched betweenglass substrate and air cladding. Exponential shape for the gra-ting sidewalls was used to express its nonlinear shape, which ismathematically described as

wz wb wt wbe 1

ezh 1; (1)where wz represents the slit opening width at different posi-tions along the silver film of thickness h such that z 0 and

z h at the silver/substrate and air/silver interfaces, respec-tively. The slit opening widths at the silver/substrate andair/silver interfaces are, respectively, denoted by wb and wt .The sidewall exponential tapering coefficient is representedby . Figure 1(b) shows some examples for the shape of thenonlinear exponential tapered sidewalls at different values of when wt 400 nm and wb 100 nm.

The FDTD method was applied by using the OptiFDTDsimulation tool from Optiwave Inc. In Cartesian coordinates,periodic boundary conditions were used in the x and y direc-tions, while an anisotropic perfect matching layer was used inthe z direction to serve as an absorbing boundary condition.The relative permittivity r () of the dispersive silver filmwas determined using the LorentzDrude model:

r XMm0

f m2p

2m 2 im

; (2)

where is the permittivity at infinite frequency, f m denotesthe oscillator strengths, and m represents the dampingfrequency. The plasma, incident wave, and resonant frequen-cies are, respectively, represented by p, , and m. The usedplasma frequency for the silver substrate is 0.137 1017 rads,and the remaining parameters used in Eq. (2) are summarizedin Table 1 [18].

In order to realize a broadband simulation on the dispersivesilver film, a linearly polarized Gaussian modulated electromag-netic plane wave was used at 650 nm center wavelength. Thelight pulse in time domain has an offset time of 0.8 1014 sand half width of 0.1 1014 s. The simulation was performedat normal incidence, in the z direction, of the plane wavethrough the grating. An xy observation area at 400 nm awayfrom the air/film interface was used to calculate the transmis-sion spectrum through the designed polarizer.

We first investigate the behavior of the reported TM-pass/TE-stop polarizer in two different cases when the incident lightis TM or TE polarized. During this investigation, the gratingperiod, h, wb, and wt are kept constants at 500 nm, 400 nm,100 nm, and 400 nm, respectively. These values were chosenbecause this combination provides maximum transmissivity forTM-polarized light in the visible and near-infrared spectralbands; however, details of this analysis are not shown in thispaper because it is out of its scope. Figures 2(a) and 2(b),

Fig. 1. (a) Diagram of the designed optical polarizer. (b) Examples for the shape of the exponential tapered sidewalls at different values of .

Research Article Vol. 54, No. 14 / May 10 2015 / Applied Optics 4465

respectively, show the transmission spectrum through the de-signed polarizer for TM- and TE-polarized light at differentvalues of . The sidewalls exponential tapering coefficient waschanged from 9 to 9 passing through zero associated withlinearly tapered sidewalls.

Figure 2(a) shows that for TM-polarized light at differentvalues of , the transmission spectra are enhanced in two bands.The first band covers a portion of the visible spectral region andcentered at 650 nm wavelength, while the other is spread intothe near-infrared spectral region and centered at 1100 nmwavelength. When the incident p-mode photons interact withthe SPs on the metallic gratings, surface plasmon polaritons(SPPs) are excited to propagate along the grating surface.At a dielectric/metallic grating interface, the SPP excitationcondition is

2

sin l 2

2

r

r

s; (3)

where is the wavelength of the incident wave, represents theangle of incidence, l is an integer number, defines the gratingperiod, and denotes the relative permittivity of the dielectricabove and below the silver grating surfaces ( 1 for the topair medium and 1.5 for the bottom glass substrates). Thetransmission spectra have almost zero transmissivity at 530 nmand 755 nm wavelengths, which correspond to the SPPresonant wavelengths at the silver/air and silver/glass interfaces,respectively [Eq. (3)].

It is also worth noting that, in both of the visible and nearinfrared bands [shown in Fig. 2(a)], the polarizers of negativetapering coefficients show higher transmissivity than those ofpositive ones. This happens because negative values of pro-vide convex metallic sidewalls, which collect more optical en-ergy to funnel to the other side of the metal surface. On theother hand, positive values of define concave metallic side-walls, which are associated with higher reflection and lower

transmission. Furthermore, as decreases, the bandwidth inthe visible band increases until its peak at 3 and thensaturates.

The transmission spectra of the designed polarizertapered for normal TE-polarized incident wave are shown inFig. 2(b). In sharp contrast, the transmission is quenched withdecreasing the exponential tapering coefficient. The concavemetallic sidewalls show higher reflection to the TE-polarizedlight.

As demonstrated by Eq. (3), the SPP resonance wavelengthsare not tuned by the silver thickness. For more investigation, westudied the impact of changing the silver thickness on the res-onance wavelengths. In this simulation, the grating period, ,wb, and wt are kept constants at 500, 4 nm, 100 nm, and420 nm, respectively. As shown in Fig. 3, the resonance wave-lengths due to exciting the SPP, according to Eq. (3), at thesilver/air and silver/glass interfaces are kept constants atdifferent values of the silver thickness. However, the effectof changing the film thickness appears as changing in the trans-mitted power.

3. PERFORMANCE EFFICIENCY OF THEDESIGNED TM-PASS/TE-STOP POLARIZER

In this section, using the FDTD method, we start on the per-formance efficiency of the designed TM-pass/TE-stop polarizeras a function of different structural parameters such as, ,wt ,wb,h, and . The performance efficiency is determined throughmonitoring the values of the polarizer IL, and RL when usinga TM-polarized light, and measuring its ER. A good polarizeris characterized by low IL, high RL, and high ER.

Figures 4(a), 3(b), and 3(c), respectively, demonstrate themodification of IL, RL, and ER spectra due to the changeof when keeping , h, wb, and wt constants at the same val-ues mentioned in the previous section. In these figures, thehorizontal white dotted line represents the grating with linear

Table 1. Plasmonic Parameters Used for the Silver Substrate

m 0 m 1 m 2 m 3 m 4 m 5f m 0.8450 0.0650 0.1240 0.0110 0.8400 5.6460m (rad/s) 0.0000 0.12 1016 0.68 1016 0.12 1017 0.14 1017 0.31 1017

m (rad/s) 0.73 1014 0.59 1016 0.69 1015 0.99 1014 0.14 1016 0.37 1016

Fig. 2. Transmission spectra of the designed polarizer at different values of when the incident light is (a) TM and (b) TE polarized.

4466 Vol. 54, No. 14 / May 10 2015 / Applied Optics Research Article

tapering coefficient ( 0), and the vertical one correspondsto the SPP resonance wavelength at silver/glass interface. Onecan observe in Fig. 4 that at all wavelengths, except aroundthose of the SPP resonances at the silver/air and silver/glass in-terfaces, as increases, the IL and ER decrease, while the returnloss increases.

Table 2 summarizes the characteristics of the designed TM-pass/TE-stop polarizer in the visible and near-infrared spectral

bands for different exponential tapering coefficients. InTable 2, the bandwidth of the polarizer is defined as thedifference between the upper and lower wavelengths at whichthe IL is half its maximum (3 dB). Based on the application inwhich the designed polarizer will be used, we can select theproper value of .

For example, in the visible spectral region, grating with 3 is the best choice to get minimum IL and maximum band-width (Fig. 5). It shows a wide TM-transmission band of about200 nm in the visible range with high ER of 37.5 dB and lowreturn loss of 9 dB. In addition, its TM transmission in theinfrared range exhibits bandwidth of 550 nm with RL and IR of4 dB and 50 dB, respectively.

Other important structural parameters that may have sig-nificant influence on the optical transmission spectrumthrough the designed polarizer and its characteristics are theslit opening widths at the silver/substrate and air/silver interfa-ces. Here, we fix the values of , , h at 3 nm, 500 nm, and400 nm, respectively. Figure 6 demonstrates the modificationof the transmission spectrum through the designed polarizer forthe normally incident TM-polarized light due to the change ofboth wt and wb. These simulations were performed at thecenter wavelength of the visible and near-infrared spectral re-gions such that Figs. 6(a) and 6(b) are illustrated at 650 nm and1100 nm wavelengths, respectively.

Fig. 3. Impact of changing the silver thickness on the resonancewavelength.

Fig. 4. (a) IL, (b) RL, and (c) ER spectra as functions of the tapering coefficient.

Table 2. Characteristics of the Designed Polarizer at Different Values of

Return Loss (dB) Extinction Ratio (dB)

() Insertion Loss (dB) Bandwidth (nm) Min Max Min Max

9 0.78 183 nm (568751) 10.16 3.39 39.6 51.20.74 471 nm (10291500) 12.61 2.53 60.1 65.9

6 0.55 186 nm (565751) 8.96 3.71 34.5 47.51.14 510 nm (09901500) 8.31 2.32 54.4 61.1

3 0.41 196 nm (556751) 9.66 4.04 22.2 37.52.42 554 nm (09451500) 4.35 1.91 42.4 51.5

0 0.60 188 nm (563751) 8.17 3.91 6.50 21.43.60 533 nm (09671500) 2.78 1.29 27.6 38.6

3 1.81 119 nm (632751) 3.88 2.43 0.00 7.433.76 409 nm (10911500) 2.76 1.22 19.5 28.5

Research Article Vol. 54, No. 14 / May 10 2015 / Applied Optics 4467

In Fig. 6, the white diagonal dashed line represents the con-dition when wt wb. On this line, as the slit opening widthincreases, the transmission spectra show higher peaks. It isexpected that increasing the size of the slits magnifies the tun-neling of light via coupled plasmonic modes localized in thegrooves. The polarizer exhibits high transmission in the caseof wt > wb (below the white diagonal dashed line) comparedto the opposite case with the same values. This behavior hap-pens because the top silver surface at air is responsible for re-flecting the incident light wave before penetrating the polarizer,and, consequently, when wt is larger, it collects more incidencepower to funnel to the other side.

The two white circles, shown in Fig. 6, indicate the posi-tions of two selected points P1 and P2 corresponding totransmission maxima in the visible and near-infrared bands, re-spectively. At P1, a maximum transmissivity of 93% is obtainedat wt 325 nm and wb 225 nm. On the other hand, at P2,

maximum transmissivity of 95% is obtained at wt 370 nmand wb 310 nm.

For further investigation, we demonstrate the polarizer char-acteristics (IL, RL, and ER) when using wt and wb of P1 andP2. Figures 7(a) and 7(b) represent the polarizer characteristicsat P1, while Figs. 7(c) and 7(d) demonstrate those at P2. Asshown in Figs. 7(a) and 7(c), almost zero dB IL is achievedin the visible and near-infrared spectral transmission bands.Other characteristics of the polarizer, shown in Fig. 7, aresummarized in Table 3.

Finally, we extract the wide-angle far-field transform basedon the FresnelKirchhoff diffraction formula in order to calcu-late the diffraction angle and efficiency of the designed polar-izer. Fifty periodic grating cells were used to obtain a moreaccurate transform. Figure 8 shows the far-field pattern for gra-tings with uniform, linearly tapered, exponentially tapered con-cave, and exponentially tapered convex sidewalls. Here, wekeep , h, wb, and wt constants at 500 nm, 400 nm, 310 nmand 370 nm, respectively. One can notice that the grating withlinearly tapered or negative exponential tapered sidewalls sig-nificantly enhances both zero- and first-order slit resonance.The diffraction efficiencies for these different types of polarizersare calculated and summarized in Table 4. In Table 4, the dif-fraction efficiencies are calculated by the fraction of the incidentradiation, which is diffracted into a single specified order suchthat the positive and negative orders are treated separately. Inthis simulation, the FDTD method was used to obtain thenear-field pattern and transmission. Afterward, the diffractionangle and diffraction efficiency are extracted in the far-field re-gion at distance d from the origin using the FresnelKirchhoffdiffraction formula [19]:

Ex; y; z d

i

ZZEx; y; 0 e

ikR

R

1 cosR z

2

dx 0dy 0; (4)

where R is the vector connecting the point in the near field tothat in the far field and k is the wavenumber. Consequently, we

Fig. 6. Modification of transmission spectra through the designed polarizer for the TM-polarized incident light due to the change of wt and wb at(a) 650 nm and (b) 1100 nm.

Fig. 5. Bandwidth and IL of the designed polarizer at differentvalues of in the visible spectral region.

4468 Vol. 54, No. 14 / May 10 2015 / Applied Optics Research Article

can calculate the power ratio and diffraction angle for differentdiffraction beams, as shown in Fig. 8 and Table 4.

It is worth mentioning that several successful trials for de-signing non-SPP polarizers have been achieved in the literature.In general, the benchmark characteristics of a good polarizerare high ER and low RL, IL, and price and reliability. Manycompetitive non-SPP polarizers such as wire-grid [20], absorp-tive [21], beam-splitting [22], and birefringent polarizers [23]can relatively satisfy these conditions. For example, the wire-grid polarizer, which consists of parallel metallic wires placedperpendicularly to an incident beam, has nearly the same op-eration concept of our reported polarizer but for larger scale.Therefore, it is generally used for microwave communications[20]. Also, the crystal absorptive polarizers show dichroism,which can absorb light in particular directions. However, itsusage is limited by the wavelength dependence of the dichroiceffect [24]. The beam-splitting polarizers are commonly usedwith high intensity lasers, since they do not absorb light. Suchcommon types of these polarizers split the incident beam to onefully polarized beam and another one of mixture polarization,which yields to high IL [25]. In a birefringent polarizer, theincident beam is divided into two polarized beams by refractiondue to polarization dependence of its refractive index [26].Regarding the reported polarizer in this paper, it is competitivewith the non-SPP ones because of its nanoscale size, which fitspolarizing light from nanoantennas and can be incorporated indifferent modern nanostructures [27]. Furthermore, by select-ing the proper designing parameters, it provides relatively highER and low IR and RL.

Fig. 7. (a) RL, IL, and (b) ER of the designed polarizer at wt and wb of P1. (c) RL, IL, and (d) ER of the designed polarizer at wt and wb of P2.

Table 3. Summary of Characteristics of DesignedPolarizer at Structural Parameters of P1 and P2

StructuralParameters

Polarizer Characteristics Transmission Band P1 P2

Bandwidth (nm) Visible 190 120Infrared 450 600

Max. return loss (dB) Visible 10 8Infrared 9 12

Min. extinction ratio (dB) Visible 7 3Infrared 30 17

Fig. 8. Far-field pattern for different types of the designed polarizer.

Research Article Vol. 54, No. 14 / May 10 2015 / Applied Optics 4469

4. CONCLUSION

In conclusion, we reported a design for a TM-pass/TE-stopoptical polarizer using silver plasmonic grating deposited aboveglass substrate. In this design, the slit sidewalls have an expo-nential tapered shape, which can be convex, concave, or linear.It is found that convex-shaped sidewalls are preferred in ourdesign because they provide high ER and RL and low IL.Furthermore, in order to obtain high TM-polarized light trans-mission through the designed polarizer, it is observed that theslit opening width at the air/silver interface should be largerthan that at the silver/glass interface. Transmissivity of 93%and 95% for TM-polarized light are, respectively, obtained inthe visible and near-infrared spectral regions when wt > wb.Finally, our results indicate that the reported polarizer hashigher zero- and first-order transmitted resonance powercompared with those found in the literature.

The Deanship of Scientific Research (DSR), King AbdulazizUniversity, Jeddah (135-664-D1435).

The authors gratefully acknowledge the DSR technical and fi-nancial support.

REFERENCES1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff,

Extraordinary optical transmission through sub-wavelength holearrays, Nature 391, 667669 (1998).

2. P. K. Jain, X. Huang, I. H. El-Sayed, and M. A. El-Sayad, Review ofsome interesting surface plasmon resonance-enhanced properties ofnoble metal nanoparticles and their applications to biosystems,Plasmonics 2, 107118 (2007).

3. Y. Akimov and W. Koh, Design of plasmonic nanoparticles forefficient subwavelength light trapping in thin-film solar cells,Plasmonics 6, 155161 (2011).

4. I. Ashry, B. Zhang, S. V. Stoianov, C. Daengngam, J. R. Heflin, H. D.Robinson, and Y. Xu, Probing the photonic density of states usinglayer-by-layer self-assembly, Opt. Lett. 37, 18351837 (2012).

5. Q. Wang, X. Wang, X. Li, and S. Wu, Transmission control property ofa nano-optical system made by an antenna over a Bowtie aperture,Plasmonics 8, 11411146 (2013).

6. S. B. Karman, S. Z. M. Diah, and I. C. Gebeshuber, Bio-inspiredpolarized skylight-based navigation sensor: a review, Sensors 12,1423214261 (2012).

7. N. Song, P. Ma, and J. Jin, Reduced phase error of a fiber opticgyroscope using a polarization maintaining photonic crystal fiber,Opt. Fiber Technol. 18, 186189 (2012).

8. C. Chen, L. Pang, C. Tsai, U. Levy, and Y. Fainman, Compactand integrated TM-pass waveguide polarizer, Opt. Express 13,53475352 (2005).

9. D. Crouse and P. Keshavareddy, Polarization independent enhancedoptical transmission in one-dimensional gratings and device applica-tions, Opt. Express 15, 14151427 (2007).

10. Y. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, Polarization-independentextraordinary optical transmission in one dimensional metallic gra-tings with broad slits, Appl. Phys. Lett. 93, 061102 (2008).

11. A. Liu, F. Fu, Y. Wang, B. Jiang, and W. Zheng, Polarization-insensitive subwavelength grating reflector based on asemiconductor-insulator-metal structure, Opt. Express 20, 1499115000 (2012).

12. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Transmission res-onances on metallic gratings with very narrow slits, Phys. Rev. Lett.83, 28452848 (1999).

13. A. T. Rahman, P. Majewski, and K. Vasilev, Extraordinary opticaltransmission: coupling of the Wood Rayleigh anomaly and theFabryPerot resonance, Opt. Lett. 37, 17421744 (2012).

14. T. Sondergaard, S. Bozhevolnyi, J. Beermann, S. Novikov, E.Devaux, and T. Ebbesen, Extraordinary optical transmission withtapered slits: effect of higher diffraction and slit resonance orders,J. Opt. Soc. Am. B 29, 130137 (2012).

15. H. Shen and B. Maes, Enhanced optical transmission throughtapered metallic gratings, Appl. Phys. Lett. 100, 241104(2012).

16. T. Sondergaard, S. Bozhevolnyi, S. Novikov, J. Beermann, E.Devaux, and T. Ebbesen, Extraordinary optical transmissionenhanced by nano-focusing, Nano Lett. 10, 31233128(2010).

17. Y. Liang, W. Peng, R. Hu, and H. Zou, Extraordinary optical trans-mission based on subwavelength metallic grating with ellipse walls,Opt. Express 21, 61396152 (2013).

18. A. D. Raki, A. B. Djurii, J. M. Elazar, and M. L. Majewski, Opticalproperties of metallic films for vertical-cavity optoelectronic devices,Appl. Opt. 37, 52715283 (1998).

19. J. Peatross and M. Ware, Physics of Light and Optics (BrighamYoung University, 2011).

20. J. R. Middendorf, J. S. Cetnar, J. Owsley, and E. R. Brown, Highfill-factor substrate-based wire-grid polarizers with high extinctionratios, IEEE Trans. Terahertz Sci. Technol. 4, 376382 (2014).

21. S. Tavazzi, A. Borghesi, M. Laicini, and P. Spearman, Polarizedabsorption of quaterthiophene single crystals, J. Chem. Phys. 121,8542 (2004).

22. X. Hu and K. M. Ho, Brewster angle phenomenon in two-dimensionalmetallic photonic crystals and its application to polarization beam split-ting, Appl. Phys. Lett. 89, 201906 (2006).

23. I. Hodgkinson and Q. H. Wu, Birefringent thin-film polarizers for use atnormal incidence and with planar technologies, Appl. Phys. Lett. 74,1794 (1999).

24. D. K. Yang, Review of operating principle and performance ofpolarizer-free reflective liquid-crystal displays, J. Soc. Inf. Disp. 16,117124 (2012).

25. A. Rizea and I. M. Popescu, Design techniques for all-dielectric polar-izing beam splitter cubes, under constrained situations, RomanianReports Phys. 64, 482491 (2012).

26. S. A. Mousavi, E. Plum, J. Shi, and N. I. Zheludev, Coherent control ofbirefringence and optical activity, Appl. Phys. Lett. 105, 011906(2014).

27. C. P. Huang, Q. J. Wang, X. G. Yin, Y. Zhang, J. Q. Li, and Y. Y. Zhu,Break through the limitation of Malus law with plasmonic polarizers,Adv. Opt. Mater. 2, 723728 (2014).

Table 4. Diffraction Efficiencies for Different Types of Polarizers

( 4) ( 0) ( 4) No Tapering0 Diffraction order 1.71E 09 1.55E 09 6.17E 08 6.89E 08+1 Diffraction order 1.38E 08 1.28E 08 6.71E 07 5.39E 071 Diffraction order 1.41E 08 1.29E 08 6.29E 07 5.69E 07Diffraction efficiency 75% 68% 27% 27%

4470 Vol. 54, No. 14 / May 10 2015 / Applied Optics Research Article