tunable photonic crystal filter with dispersive and non-dispersive 2013

8/9/2019 Tunable Photonic Crystal Filter With Dispersive and Non-dispersive 2013

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Tunable photonic crystal lter with dispersive and non-dispersive

chiral rods

Amir Mehr a,n, Farzin Emami a, Farzad Mohajeri b

a Optoelectronic Research Center of Electronic Department, Shiraz University of Technology, Airport Boulevard, Shiraz, Iranb Electronic and Computer Department, School of Engineering, Shiraz University, Zand Boulevard, Shiraz, Iran

a r t i c l e i n f o

Article history:

Received 13 November 2012Received in revised form

13 March 2013

Accepted 24 March 2013Available online 16 April 2013

Keywords:

Finite element method

Photonic band gap material

Chiral photonic crystal

Dispersive chirality

Opticallter

Filter tunability

a b s t r a c t

Applying the nite element method, microcavity photonic crystal lter with chiral rods is studied and

tuning of its bandwidth and transmission peak under system's stability condition is discussed. In order tostudy the tunability of this structure, the effects of variation in its rods electromagnetic parameters on its

ltering operation are analyzed. It is shown that the increase in the rods' relative permittivity cause the

increase of bandwidth and transmission peak, and also decrease the photonic band gap width. On the

other hand, the increase in the rods' relative permeability cause the decrease of bandwidth and

transmission peak, and also increase the photonic band gap width. In both cases, peak wavelength red

shift occurs. The effects of rods chirality on ltering characteristics are studied. The real and imaginary

terms of chirality is introduced respectively as a cause for worsening and bettering ltering nature of

chiral photonic crystal, while they do not have effect on peak wavelength and photonic band gap. The

effect of dispersive chirality model parameters on structure ltering is discussed and a design of chiral

photonic crystal lters with appropriate high peak amplitude and small bandwidth in optical integrated

circuits is proposed.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Photonic crystals (PCs) have recently had great applications

in different elds of optical communication, radio frequency,

and terahertz integrated circuits. PCs are a new class of optical

devices made by a periodic modulation of refractive index. PC is

highly dispersive, so the rate of its transmission and reection are

strongly dependent on wavelength. The most important effect

resulting from periodicity is the presence of continuous and

bounded ranges in the frequency domain where there is no

possibility of wave propagation in the structure. These ranges are

called photonic band gap (PBG). There is an allowed frequency band

between each two successive PBGs (and vice versa) where wave

propagation would be possible under certain circumstances [1,2].

Due to their ability in controlling the electromagnetic wave propa-gation, and also integration, these structures have many applica-

tions. The most important applications of this type of structures are

lasers with very small threshold current [3], PC bers (PCFs) [4],

waveguides[5], couplers [6], multiplexers [7], resonators [8], and

other optical devices such as tunable lenses [9], polarization

converters[10]and PC MachZehnder interferometer[11].

Inserting a defect in PCs periodic structure, the propagation ofsome special frequencies in PBG region are possible. This idea is

applied in the various structures of optical lters [12,13]. More-

over, the applications of add/drop channels [14] and PC optical

switching[15]are studied. Also, a new all optical switching device,

which is constructed by connecting an erbium doped ber with

two symmetrical long period ber gratings (EDF LPFGs), is demon-

strated[1619].

The incidence of meta-materials in PCs is recently considered.

A group of meta-materials is a major subgroup of bi-anisotropic

medium which is called chiral. Chiral elements do not match their

image under mirror effect. This can also be known as handedness

structures [20]. Two important features of these media are

electromagnetic coupling[21], and optical rotation[22]. The rst

arises from the simultaneous production of electric and magneticpolarization which is the cause of optical activity. Under the

second feature, the linearly polarized incident wave is rotated by

chiral medium. Chiral medium has so many applications in

microwave eld. Also, in the recent decade, various applications

of these media are reported in optical eld, such as polarization

convertor [23,24], chiral ber networks [25], tunable lasers [26],

negative refraction[27], and magneto optics[28].

Chiral Photonic Crystals (CPCs) are recently taken up due to

their dispersive behaviors, losses and polarization characteristics.

Wave scattering from these media are studied [29], and the

reectivity from these structures are investigated [30]. Also,

characteristics of incident wave polarization control, by these

Contents lists available atSciVerse ScienceDirect

journal homepage: www.elsevier.com/locate/optcom

Optics Communications

0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.optcom.2013.03.046

n Corresponding author. Tel.:+98 711 7266262; fax: +98 711 7353502.

E-mail addresses:[email protected] (A. Mehr), [email protected]

(F. Emami), [email protected] (F. Mohajeri).

Optics Communications 301302 (2013) 8895
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structures are simulated [31,32]. Properties of defect modes and

CPC reection spectrum are investigated, and the characteristics of

photonic states density are studied, and it is shown that the

system can operate similar to a tunable narrow band lter [33].

Negative refraction, and chiral/achiral periodic structure ltering

are perused [34], and switching property of this structure is

improved [35]. Tunability of PC lters is a major challenge of

designing optical devices of integrated circuits [3638].

In this paper CPC structure is designed based on embeddingchiral rods in achiral material, and its ltering operation is studied.

The purpose of the relevant researches is to design lters with

high transmission and small band width. Here, also, after obser-

ving the operation of ltering variation with changes in permit-

tivity and permeability, the effect of chirality of PC rods on CPC

ltering is analyzed. Dispersive and nondispersive chiral models

are discussed for tunability of this structure.

2. Theory

2.1. Structure description

As shown inFig. 1 the proposed structure is designed so that

chiral rods with the radiusrand the separationPare embedded in

achiral waveguide. The cavity length, formed by defect, is denoted

by D.

The dielectric silicon waveguide with a predened index ofn2, a

constant length L and width of Walong x and y, respectively, is

surrounded by air with a width ofH. The air layers decrease the

radiation losses [39]. Assume that, the structure in innite along

thezdirection so that the variations for each eld components are

considered to be zero along this direction. It is desirable to have

no any reected waves from the structure edges in an innite PC

which could be interfere with the incident eld. Therefore,

absorbing boundary conditions are considered for this simulation

around the main structure. The outer layer is covered by perfect

magnetic conductor (PMC). To reduce the interferences between

incident wave and reected wave from rods, the rods are embedded

far from the exciting source. In this structure and with an innite

dimension, in such a way that there is no any reected electro-

magnetic wave from the structure edges, perfectly matched layers

(PMLs), with a thickness of , are used. The refractive indices of

these layers are matched with the neighboring layers; at the end of

the dielectric waveguide with n n2and air with n 1.Dene as the distance from the PML edge. To diminish the

electromagnetic waves inside these layers, the electrical conduc-

tivity must be chosen as[40]

s sm

21

where smis the maximum value of sat with the optimum of

soptK

2

where is the characteristic impedance and Kis a constant related

to the PML order.

2.2. Formulation of chiral medium

Assuming eld's time dependency in the form of expjt,constitutive relations in chiral medium are as follows based on

BassiriEnghetaPapas formulation[41]:

D BPEEjB 3a

H BBPE

jE 3b

where is designated as chiral admittance. This form is resulted by

analyzing the characteristics of media made from small helices

regardless of helices variance elds' effect on each other. Another

formulation known as the Condon model is presented for electric

and magnetic displacement of chiral media as follows [41]:

D CEj

c0 H 4a

B CHj

c0E 4b

In these equations is chirality factor, and c0 1= ffiffiffiffiffiffiffiffiffiffi00p is thespeed of light in vacuum. The relation between permittivity,

permeability, and chirality of these two models are as follows[41]:

BPE C; BPE C2=c02C; =c0C 5

In general, chirality factor is a complex variable, so that optical

rotatory dispersion (ORD) property is related to its real part, and

circular dichroism (CD), which denotes the difference of absorp-

tion coefcients of the two circularly polarized eigen-waves, is

related to the imaginary part. The restriction of chirality factor is

dened as follows[41]:

oc0ffiffiffiffiffiffiffiffiffiffiCC

p 6In this paper, rc,rchave been considered for relative perme-

ability and relative permittivity, respectively, and the rods chirality

factor is .

2.3. Source description

To prevent the wave scattering in the simulation region and

considering the practical conditions, a source is used at the input

port of the waveguide. Dene the input magnetic eld pulse as

[42]

H;y

H

Hy

7

Its wavelength dependency has Gaussian shape with the

following denition:

H exp 02

! 8

where 0 is the central frequency and is a constant to cover a

wide frequency range. In a case of single mode guide this source

must be considered in the form of[43]:

Hy cosy 9where is chosen based on the source width (equal to the

waveguide width). Wave propagation is in the x direction and

TM mode is considered in this simulation. Therefore, the desired

output is the zcomponent of the magnetic intensity, Hz, with theFig. 1. Schematic diagram of CPC.

A. Mehr et al. / Optics Communications 301302 (2013) 8895 89


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power in the core () based on its relation as

2n0

B 12

wheren0 is the variation in refractive index.

The slope of increase in PC lter band width is steep as the rods

permittivity is increased, so that as of the PC rods doubles, the

band width of its ltering would be nearly doubled too.

3.2. The effect of rods permeability

In this section, assuming relative permittivity of PC rods as

constant equal to r1, and putting chirality factor as zero,variation in the ltering of the proposed PC with a change in its

rods permeability with the radius of 116.5 nm is analyzed and

plotted based on theFig. 5.

As it is distinguished from the gure, the increase in relative

permeability of PC rods causes the increase in PBG width. Indeed,

this increase is due to the raise of high cutoff frequency of PC,

while the low cutoff frequency has no signicant change.

The increase in permeability of rods causes a decrease in

transmission peak value. This is more manifest in Fig. 6 which

shows transmission peak versus peak wavelength for different

values of rods relative permeability. Physically, wave scattering is

increased due to increment of characteristic impedance of rods

and increase of its difference with waveguide's characteristic

impedance. The gure also shows that the increase of rods

permeability leads to the shift of peak wavelength to the higher

wavelengths. This phenomenon is explainable similar to shift of

the reection peak wavelength for FBG due to increase of effective

refractive index based on Eq. (11).

On the other hand, the increase in permeability of PC rods

decreases the ltering band width. This is specied inFig. 7which

shows the FWHM versus peak wavelength and according to the

previous values of relative permeability of PC rods. Similarly, based

on Eq.(12)the bandwidth size is reduced for FBG as the fraction of

power in the core reduced.

It is worth mentioning that the simulations show that inserting

the imaginary term to,parameter of PC rods disturb its ltering

nature.

3.3. The effect of rods chirality

Typically, in infrared range, the relative permittivity of chiral

medium is within the range of about rc2. As it was mentioned,in order to compensate for the increase in bandwidth of CPC, we

consider relative permeability greater than 1. In other words, we

consider chiral medium with paramagnetic material. In this paper

rc1.15 is selected so that, based on Fig. 8, transmission peak ofabout 0.9 and bandwidth less than 10 nm is achievable.

Furthermore, in this case, the PBG is also increased a little,

so that its low cutoff frequency would collate with PC low cutoff

frequency with the parameters ofrc2,

rc1 for its rods whereasits high cutoff frequency would collate with PC high cutoff

frequency with the parameters of rc1, rc1.15 for its rods.Moreover, in this case, larger peak wavelength shift toward higher

wavelengths occurs.

Now, we analyze the effect of chirality factor of PC rods

on ltering operation of CPC. The simulations are done in two

categories based on dispersive and nondispersive nature of

chirality factor. In all these cases, chirality has no effect on the

PBG, and transmission nature, out of PBG is remained with no

signicant change.

3.3.1. Nondispersive chirality

In this part, for proposed PC's rods with radius ofr116.5 nm fromchiral elements with relative permittivity and relative permeability

Fig. 5. Filtering operation of PC with deferent permeability of rods.

Fig. 6. Transmission peak of PC versus peak wavelength for different permeability

of rods.

Fig. 7. FWHM of PC versus peak wavelength for different permeability of rods.

Fig. 8. Transmission pulse of PC for some different permittivity and permeability

of rods.



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equal to rc2 , rc1.15 respectively, we study ltering operation ofthe PC structure for different values of chirality factor () independent

from frequency.

First, we consider chirality factor as a real variable, and then,

we simulate the structure with its usual chirality factors in

infrared range. The results show that with the change in chirality

value, the peak wavelength remains unchanged whereas the peak

value and the bandwidth are changed.Fig. 9shows the amplitude

of transmission peak versus the chirality factor for transmission

bandwidth less than 10 nm.

This gure shows that the value of transmission peak is

decreased with the increase in the real part of CPC rods chirality

factor, while the peak wavelength is xed; here it is equal to

1604.3 nm.

The change in CPC lter bandwidth with the change in real part

of the chirality parameter of CPC rods is shown in Fig. 10. The

gure shows that the increase of the real part of CPC rods chirality

factor results the slight increase in the lter bandwidth.

So, generally, the increase of the real part of the chiralityparameter of CPC rods makes its ltering nature more unsuitable.

Moreover, the sign of the real part of chirality factor would have no

effect on CPC ltering operation. In other words, right or left

handedness of the chiral helices does not make any difference. In

continuation of this part, we investigate the effect of imaginary

part of the chirality of PC rods on its ltering operation. It is to be

mentioned that typically in this range Im0. So, givenRe 0:04, our simulation is done for different values of ima-ginary part of rods chirality factor. The results of this part show

that although shift in the peak wavelength occurs, it is very small.

In Fig. 11 the value of transmission peak of the proposed CPC

structure is plotted versus the peak wavelength, for different

values of rods chirality factor in stable condition. It is shown that

as the imaginary part of rods chirality factor gets more negative,

generally, transmission peak value is increased, and the very slight

shift of peak wavelength toward lower wavelengths occurs.

This phenomenon can be regarded as similar to reduce of

reectivity of FabryPerot mirrors due to their antireection

coating, so that the rate of wave transmission is increased. Also,

the increase of imaginary part of the rods chirality, which is an

expression of the increase of their absorbency and decrease of

their reectivity, cause the increase in the transmission peak of PC

lter[45].

The changes in bandwidth of CPC lter are not uniform with

the increase of imaginary part of its rods chirality. This simulation

is plotted inFig. 12, which shows FWHM of CPC lter versus peak

wavelength and for changes in the imaginary part of the rods

chirality factor. In general, in the concerning range, the changes

along bandwidth is small, and it is specially decreased for the

values of chirality with ImRe.Therefore, generally, as the imaginary part of CPC rods chirality

factor gets more negative, its ltering operation is improved, so

that the access to larger transmission peaks and smaller band-width with no signicant changes in the peak wavelength is

possible. This result provides the possibility of designing special

tunable PC lters.

3.3.2. Dispersive CPCs

Generally, chirality has a dispersive nature, and this feature

causes its optical activity in chiral medium. To express chirality

dispersive nature, Condon considered a frequency dependent

model for chirality factor. This model used for simulation of

dispersive chirality medium[46,47], is as follows:

k2k

2

k

2

j2kk 13

Fig. 9. Transmission peak of CPC versus real part of chirality factor, peak wavelength

is constant and equal to 1604.3 nm.

Fig. 10. FWHM of CPC versus real part of chirality factor, peak wavelength is

constant and equal to 1604.3 nm.

Fig. 11. Transmission of CPC versus peak wavelength for different imaginary parts

of chirality factor.

Fig. 12. FWHM of CPC versus peak wavelength for different imaginary parts of

chirality factor.

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Fig. 17 shows transmission peak and bandwidth of CPC lter

versus some different values of magneto electric coupling factor.

Values of k is selected So that the system remains stable and

acceptable variations in the ltering nature is observed.

As it is shown in the gure, increase of coupling factor, causes

the increase in transmission peak of about 20%. Especially, the

amplitude of transmission peak of CPC lter reaches over 0.99 for

k0.045 fs. On the other hand, increasing the coupling factordecreases the lter bandwidth desirably. Especially, the size of

bandwidth reaches 7.4 nm for k0.045 fs. Therefore tuning theCPClter is possible both for its peak amplitude and its bandwidth

by changing the magneto electric coupling factor of chiral rods.

It should be mentioned that changes in chirality parameters do

not make a signicant change in the transmission peak wave-

length of CPC lter, and the peak wavelength remains about thesame 1550 nm.

Fabrication of CPC is available and is demonstrated based on

various methods such as holographic lithography [48], standard

direct laser writing in the commercially available photoresist SU-8

[49], hot embossing combining with a UV curing process[50], and

combined nano-imprint and reversal lithography in SU-8 [51].

4. Conclusion

This paper uses FEM to study PC microcavity lter with chiral

rods and also to discuss the tunability of its transmission peak and

bandwidth under system stability condition.

The effect of electromagnetic parameters of PC rods on

lteringoperation is studied. It is shown that increased permittivity of rods

results in increased peak amplitude and bandwidth of PC lter. It

shifts the peak toward larger wavelengths and decreases the PBG.

The PC rods with larger permeability show a smaller transmission

peak and bandwidth in PC lter operation. In this state, the

transmission peak shifts toward larger wavelengths, and the PBG

increases.

The chirality factor effect of chiral rods on ltering operation is

studied for both dispersive and nondispersive CPC structure. It is

concluded that the increase in real part of chirality factor

decreases the transmission peak of CPC and increases its band-

width. On the other hand, the increase of the imaginary part of

chirality factor increases the transmission peak and decreases the

bandwidth. As a result of changes in chirality factor of CPC rods,

the changes in peak wavelength and the size of PBG are negligible.

The Condon model is used to study the chirality dispersion

effect and as it is shown the parameters of this model cause a

change in ltering operation of CPC. As claried, it is possible to

adjust the transmission peak up to 10% through a change in the

resonance wavelength in this model. As found in this research, the

reduction in the damping factor results in increased transmission

peak and decreased bandwidth. Moreover, an increased magneto

electric coupling factor increases transmission peak and decreases

the bandwidth considerably.

Designing of monolithic and tunable lters in optical commu-

nication, with large peak amplitude and small bandwidth, using

CPC structure, has been discussed here.

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