Angular tuning of defect modes spectra for one dimensionalphotonic crystal filters with a liquid crystal layer

HE Jie 1, SONG Li-tao 2**, WANG Hua-lei 2, HAN Yi-ang 2, and LI Tao 2

1. College of science, Henan University of Technology, Zhengzhou 450001, China2. Physical Engineering college, Zhengzhou University, Zhengzhou 450052, China

(Received 28 June 2011) Tianjin University of Technology and Springer-Verlag Berlin Heidelberg 2011C

A tunable photonic crystal filter with a twisted nematic liquid crystal layer is proposed. The defect modes spectra withvarying incident angles are discussed in detail by 4×4 matrix method. The results show that the defect modes are mainlydecided by the applied voltage when the incident angle is smaller than 8o. As the incident angle further increases, the bandgap and the defect modes shift toward the shorter wavelength side, and the changes of the two modes are different. In thelower voltage range, the defect modes can be tuned not only by the applied voltage but also by the incident angle. In thehigher voltage range, the defect modes can be further tuned by varying incident angle and the different modes can beseparated from each other by a big incident angle.Document code: A Article ID: 1673-1905(2011)06-0437-3DOI 10.1007/s11801-011-1077-9

OPTOELECTRONICS LETTERS Vol.7 No.6, 1 November 2011

Inserting a defect into photonic crystals (PCs) may createthe defect modes within band gaps. The property can be ex-ploited for tunable filters. Tunable photonic crystal (PC) fil-ters can be realized using various materials such as semicon-ductor[1], metal[2], liquid crystal (LC)[3]. Many studies on PCfilters with LC defect layer have been reported[6-9]. Lately,we have analyzed the eigenmodes, the polarization sensitiveperformance and the transmission spectra for the PC filterswith parallel and twisted nematic LC as defect layers in Refs.[10] and [11], respectively. In this letter, the angular depen-dences of defect modes are discussed in detail.

Schematic diagram of a one dimensional PC filter withthe (HL)6H-LC-(HL)6H structure is shown in Fig.1. Here Land H represent the dielectric layers with the low refractiveindex nL=1.465 (SiO2) and high refractive index nH=2.065(TiO2). The optical thicknesses of them are both 0/4.

0=1.55 m is the central wavelength of photonic band gaps(PBGs). A 90o twisted nematic E7 LC is used as the defectlayer. The thickness of the defect layer is d = 500 nm. Thematerial parameters of E7 are ne=1.71 and n0=1.50. The pro-cessing technique, structure, director alignment and electro-optical properties of the 90o twisted nematic LC cell are wellstudied in Refs.[12] and [14].

The modeling of a multilayer structure with anisotropic

Fig.1 Schematic diagram of a one dimensional PC filterwith a LC layer

component has been well developed in several refer-ences[15-18]. Here we only aim at giving an overview of the4×4 matrix method which we have used. Now we considerthat a monochromatic plane wave with wave number k in-jects to the surface of a thin homogeneous uniaxial mediumlayer. The coordinate system is illustrated in Fig.1. The x-yplane parallels to the surface of the medium, the reflectedplane and incident plane are in x-z plane, the medium layerextends from z1 to z2 , and the incident angle is . FromMaxwell’s equations we can derive the following equationsfor the tangential components of the electric and magneticfield vectors:

* This work has been supported by the National Natural Science Foundation of China (No.10805040), and the Talent Introduction Program of HenanUniversity of Technology (No.2007BS041).

** E-mail: songlt12@yahoo.com.cn

, (1)

where (z) = [Ex(z), Hy(z), Ey(z), Hx(z)]T is the generalized

Qkz

idd

Optoelectron. Lett. Vol.7 No.6

field vector, and Q is the Berreman’s 4 4 matrix. Supposethe dielectric tensor of the uniaxial medium is

then the explicit expression of Q is

, (2)

. (3)

Supposing z1=0 and z2=L, the solution of Eq.(1) can be writ-ten by a 4×4 transfer matrix P as follows:

(L) = P (0) . (4)

With the same method, the 4×4 transfer matrix of an isotro-pic medium can be derived. Then the total transfer matrix ofa structure composed of N layers is

(5)

As an anisotropic optical medium, the refractive index ofLC depends on the distribution of directors. So the directordistribution needs to be obtained before its optical perfor-mance is investigated. Using iterative finite-difference met-hod[14], the directors are calculated under strong anchoringcondition. The director profile is used as the initial profilewhen the applied voltage is zero[14]. Fig.2 shows the relationof 90o twisted nematic LC directors and voltage. We can seethat the bulk LC directors are reoriented perpendicular to thesubstrate by the electric field as the voltage increases, and asa result the twist effect decreases gradually. When the volt-age is greater than 8 V, the director profiles have becomesaturated, and the curve shape has been unchanged basically.Then the transmission spectra of the PC filters are calculatedby 4 4 matrix method. The incident plane is in x-z plane,

zzzyzx

yzyyyx

xzxyxx

0sinsin

1000

0sin

0sinsin1sin

2

2

zz

zyyzyy

zz

xz

zz

zxyzyx

zz

zyxzxy

zz

xz

zz

zxxzxx

zz

zy

zzzz

zx

Q

Fig.2 Relation of twisted nematic LC directors and voltage

and the air is assumed to be both the input and output medium.Fig.3 shows the simulated transmission spectra of differ-

ent incident angles. As we can see from the Fig.3, there is noobvious change on the transmission spectra, and the wave-length of defect modes is mainly decided by the applied volt-age when the incident angles are smaller than 8o. So in theregime, we can select the different defect modes by the po-larization sensitive performance of the filter, and then tune itby changing voltage[11].

Fig. 4 depicts the transmission spectra of different inci-dent angles. Obviously, the two defect modes and PBGs shifttoward the shorter wavelength side quickly with increasingincident angle in the regime greater than 8o. The defect modesbecome relate to the incident angle closely. So the filter canbe tuned by the external voltage and incident angle doubly.It expands the tunable range as well as the filter’s applica-tion flexibility. Furthermore, we can see that one defect modeoccurs in the other’s eigen transmission spectrum when theincident angle is bigger in the lower voltage range. And itsamplitude increases as the incident angle increases. As aresult, when the incident angle is bigger, we can no longeranalyze the transmission spectrum of an arbitrary polarizedlight by decomposing it along 45o and 135o directions, whichcan be used to analyze the transmission spectra as two basicdirections for the normal incident polarized light[11]. Thereare two main causes. One is the optical admittance of dielec-tric relevant to the incident angle, the other is the relativeposition of the polarized direction of the incident light andthe directors of LC relevant to the incident angle. For thesame reasons, the two modes which merge into one in thehigher voltage range separate with the increasing incidentangle gradually .

Fig.3 Transmission spectra of different incident angles

.1

N

iiPT

HE et al. Optoelectron. Lett. Vol.7 No.6

Fig.4 Transmission spectra of different incident angles

In order to facilitate comparison of the defect modeswavelength of different incident angles, we extract them fromthe transmission spectra of 0 V and 8 V and then comparethem in Fig.5. As shown in Fig.5, the incident angle has dif-ferent effects on the two modes in the range of bigger inci-dent angles, especially for the higher voltage. Although boththe two modes shift toward the shorter wavelength side asthe incident angle increases, the e mode lags behind the omode when the voltage is higher. So the different modes canbe separated from each other by a big incident angle whenthe voltage is higher.

Fig.5 Defect modes wavelength of different incidentangles

In conclusion, the defect modes are mainly decided bythe external voltage when the incident angles are smaller than80. In this range, we can select the different defect modes bythe polarization sensitive performance of the filter, and thentune it by changing voltage[11]. As the incident angle furtherincreases, the two modes and PBGs shift toward the shorter

wavelength side, but the changes of two modes are different.So the defect modes can be tuned not only by the externalvoltage[11] but also by the incident angle in the lower voltagerange. In the higher voltage range, the defect modes can befurther tuned by changing the incident angle, and the differ-ent defect modes can be separated from each other by a bigincident angle. Thus both the tunable range and the flexibil-ity of application are enlarged.

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