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Optics Communications ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Optics Communications

0030-40http://d

n CorrE-m

(F. Emam

Pleas

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

Tunable photonic crystal filter 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 form13 March 2013Accepted 24 March 2013

Keywords:Finite element methodPhotonic band gap materialChiral photonic crystalDispersive chiralityOptical filterFilter tunability

67

18/$ - see front matter & 2013 Published by Ex.doi.org/10.1016/j.optcom.2013.03.046

esponding author. Tel.: +98 711 7266262; faxail addresses: a.mehr@sutech.ac.ir (A. Mehr), ei), mohajeri@shirazu.ac.ir (F. Mohajeri).

e cite this article as: A. Mehr, et al.,

a b s t r a c t

Applying the finite element method, microcavity photonic crystal filter with chiral rods is studied andtuning 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 itsfiltering operation are analyzed. It is shown that the increase in the rods' relative permittivity cause theincrease of bandwidth and transmission peak, and also decrease the photonic band gap width. On theother hand, the increase in the rods' relative permeability cause the decrease of bandwidth andtransmission peak, and also increase the photonic band gap width. In both cases, peak wavelength redshift occurs. The effects of rods chirality on filtering characteristics are studied. The real and imaginaryterms of chirality is introduced respectively as a cause for worsening and bettering filtering nature ofchiral photonic crystal, while they do not have effect on peak wavelength and photonic band gap. Theeffect of dispersive chirality model parameters on structure filtering is discussed and a design of chiralphotonic crystal filters with appropriate high peak amplitude and small bandwidth in optical integratedcircuits is proposed.

& 2013 Published by Elsevier B.V.

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1. Introduction

Photonic crystals (PCs) have recently had great applicationsin different fields of optical communication, radio frequency,and terahertz integrated circuits. PCs are a new class of opticaldevices made by a periodic modulation of refractive index. PC ishighly dispersive, so the rate of its transmission and reflection arestrongly dependent on wavelength. The most important effectresulting from periodicity is the presence of continuous andbounded ranges in the frequency domain where there is nopossibility of wave propagation in the structure. These ranges arecalled photonic band gap (PBG). There is an allowed frequency bandbetween each two successive PBGs (and vice versa) where wavepropagation 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 arelasers with very small threshold current [3], PC fibers (PCFs) [4],waveguides [5], couplers [6], multiplexers [7], resonators [8], andother optical devices such as tunable lenses [9], polarizationconverters [10] and PC Mach–Zehnder interferometer [11].

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Optics Communications (20

Inserting a defect in PCs periodic structure, the propagation ofsome special frequencies in PBG region are possible. This idea isapplied in the various structures of optical filters [12,13]. More-over, the applications of add/drop channels [14] and PC opticalswitching [15] are studied. Also, a new all optical switching device,which is constructed by connecting an erbium doped fiber withtwo symmetrical long period fiber gratings (EDF LPFGs), is demon-strated [16–19].

The incidence of meta-materials in PCs is recently considered.A group of meta-materials is a major subgroup of bi-anisotropicmedium which is called chiral. Chiral elements do not match theirimage under mirror effect. This can also be known as handednessstructures [20]. Two important features of these media areelectromagnetic coupling [21], and optical rotation [22]. The firstarises from the simultaneous production of electric and magneticpolarization which is the cause of optical activity. Under thesecond feature, the linearly polarized incident wave is rotated bychiral medium. Chiral medium has so many applications inmicrowave field. Also, in the recent decade, various applicationsof these media are reported in optical field, such as polarizationconvertor [23,24], chiral fiber networks [25], tunable lasers [26],negative refraction [27], and magneto optics [28].

Chiral Photonic Crystals (CPCs) are recently taken up due totheir dispersive behaviors, losses and polarization characteristics.Wave scattering from these media are studied [29], and thereflectivity from these structures are investigated [30]. Also,characteristics of incident wave polarization control, by these

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structures are simulated [31,32]. Properties of defect modes andCPC reflection spectrum are investigated, and the characteristics ofphotonic states density are studied, and it is shown that thesystem can operate similar to a tunable narrow band filter [33].Negative refraction, and chiral/achiral periodic structure filteringare perused [34], and switching property of this structure isimproved [35]. Tunability of PC filters is a major challenge ofdesigning optical devices of integrated circuits [36–38].

In this paper CPC structure is designed based on embeddingchiral rods in achiral material, and its filtering operation is studied.The purpose of the relevant researches is to design filters withhigh transmission and small band width. Here, also, after obser-ving the operation of filtering variation with changes in permit-tivity and permeability, the effect of chirality of PC rods on CPCfiltering is analyzed. Dispersive and nondispersive chiral modelsare discussed for tunability of this structure.

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2. Theory

2.1. Structure description

As shown in Fig. 1 the proposed structure is designed so thatchiral rods with the radius r and the separation P are embedded inachiral waveguide. The cavity length, formed by defect, is denotedby D.

The dielectric siliconwaveguide with a predefined index of n2, aconstant length L and width of W along x and y, respectively, issurrounded by air with a width of H. The air layers decrease theradiation losses [39]. Assume that, the structure in infinite alongthe z direction so that the variations for each field components areconsidered to be zero along this direction. It is desirable to haveno any reflected waves from the structure edges in an infinite PCwhich could be interfere with the incident field. Therefore,absorbing boundary conditions are considered for this simulationaround the main structure. The outer layer is covered by perfectmagnetic conductor (PMC). To reduce the interferences betweenincident wave and reflected wave from rods, the rods are embeddedfar from the exciting source. In this structure and with an infinitedimension, in such a way that there is no any reflected electro-magnetic wave from the structure edges, perfectly matched layers(PMLs), with a thickness of δ, are used. The refractive indices ofthese layers are matched with the neighboring layers; at the end ofthe dielectric waveguide with n¼n2 and air with n¼1.

Define ρ as the distance from the PML edge. To diminish theelectromagnetic waves inside these layers, the electrical conduc-tivity must be chosen as [40]

sðρÞ ¼ smρ

δ

� �2ð1Þ

118119120121122123124125126127128129130131132Fig. 1. Schematic diagram of CPC.

Please cite this article as: A. Mehr, et al., Optics Communications (20

where sm is the maximum value of s at ρ¼δ with the optimum of

sopt≅Kη

ð2Þ

where η is the characteristic impedance and K is a constant relatedto the PML order.

2.2. Formulation of chiral medium

Assuming field's time dependency in the form of expðjωtÞ,constitutive relations in chiral medium are as follows based onBassiri–Engheta–Papas formulation [41]:

D¼ εBPEE−jξB ð3aÞ

H¼ BμBPE

−jξE ð3bÞ

where ξ is designated as chiral admittance. This form is resulted byanalyzing the characteristics of media made from small helicesregardless of helices variance fields' effect on each other. Anotherformulation known as the Condon model is presented for electricand magnetic displacement of chiral media as follows [41]:

D¼ εCE−jχ

c0H ð4aÞ

B¼ μCH þ jχ

c0E ð4bÞ

In these equations χ is chirality factor, and c0 ¼ 1= ffiffiffiffiffiffiffiffiffiffiμ0ε0

p is thespeed of light in vacuum. The relation between permittivity,permeability, and chirality of these two models are as follows [41]:

μBPE ¼ μC ; εBPE ¼ εC−ξ2=c02μC ; ξ¼ χ=c0μC ð5Þ

In general, chirality factor is a complex variable, so that opticalrotatory dispersion (ORD) property is related to its real part, andcircular dichroism (CD), which denotes the difference of absorp-tion coefficients of the two circularly polarized eigen-waves, isrelated to the imaginary part. The restriction of chirality factor isdefined as follows [41]:

χoc0ffiffiffiffiffiffiffiffiffiffiεCμC

p ð6ÞIn this paper, μrc,εrc have been considered for relative perme-

ability and relative permittivity, respectively, and the rods chiralityfactor is χ.

2.3. Source description

To prevent the wave scattering in the simulation region andconsidering the practical conditions, a source is used at the inputport of the waveguide. Define the input magnetic field pulse as[42]

Hðλ; yÞ ¼HðλÞ � HðyÞ ð7ÞIts wavelength dependency has Gaussian shape with the

following definition:

HðλÞ ¼ exp −ðλ−λ0Þ2

γ

!ð8Þ

where λ0 is the central frequency and γ is a constant to cover awide frequency range. In a case of single mode guide this sourcemust be considered in the form of [43]:

HðyÞ ¼ cosðκyÞ ð9Þwhere κ is chosen based on the source width (equal to thewaveguide width). Wave propagation is in the x direction andTM mode is considered in this simulation. Therefore, the desiredoutput is the z component of the magnetic intensity, Hz, with the

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Table1Simulation parameters.

Parameter Value Description

n1 1 Refraction index of air layersn2 3.4 Refraction index of waveguideL 6200 nm Waveguide lengthW 434 nm Waveguide widthP 364.25 nm Rods periodsD 503.75 nm Cavity lengthH 558 nm Air layers widthδ 77.5 nm PML layers widthK 310�106 Constantλ0 1550 nm Source central wavelengthγ 0.4 pm2 Source bandwidth factorκ 7:23 1

μmSource length factor

Fig. 2. Filtering operation of PC with deferent permittivity of rods.

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following equation:

∇� εr−jsωε0

� �−1

∇� Hz

!−μrk

20Hz ¼ 0 ð10Þ

Where μr¼1 for achiral region, ω is the angular frequency andffiffiffiffiεr

p ¼ n is the refractive index of region.

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Fig. 3. Transmission peak of PC versus peak wavelength for different permittivityof rods.

Fig. 4. FWHM of PC versus peak wavelength for different permittivity of rods.

3. Simulation results

To simulate the structure and based on the mesh generationaround the corners, field analysis is done by using FEM method.Applying the z component of magnetic field at the waveguideinput, Hzin, and computing the output field at the end rod gives thepulse transmission behavior. Simulation parameters are shown inTable1. To have lower interaction between the incident and thereflected waves from the rods, the source excites far from the rods;a distance of 3332.5 nm from the center of the first rod to thesource. The output point is in 5950 nm from the input edge of thewaveguide coincided with the rods center line.

As mentioned in [42], it is necessary to consider a proper timefor stability to remove the resonance peaks. This time must bechosen so that there is no any improper behavior in the filteringoperation. It is transferred in the frequency domain by using asmall phase change at the output. Utilizing the extremely finemeshes and to disappear the resonance peaks, a good value forthis change is selected as 0.3725 degree (note that the source formhas strong effects on the undesirable resonance peaks).

By changing the electromagnetic parameters of PC rods it ispossible to study the variation of its filtering operation. Then, theeffects of changing the permittivity, permeability and chirality ofPC rods are investigated.

3.1. The effect of rods permittivity

In this part, assuming rods permeability as constant equal toμrc¼1, and putting chirality factor as zero, changes in the trans-mission curve for some different values of relative permittivity ofPC rods with the radius of 116.5 nm is simulated. Results areplotted in Fig. 2. As seen, the increase in the rods relativepermittivity causes decrease of PBG width. Indeed, low cutofffrequency of PC is increased with the rods permittivity, while highcutoff frequency has no significant change.

The increase in the permittivity rate of PC filter rods increasestransmission peak value. This is more manifested in Fig. 3 whichshows the value of transmission peak versus peak wavelength fordifferent values of rods relative permittivity. Physically, wavescattering is reduced due to decrease of characteristic impedance

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ðZ ¼ffiffiffiffiffiffiffiffiffiffiffiffiμC=εC

pÞ of rods and reduce of its difference with waveguide's

characteristic impedance. So, the transmission peak is increasedwith the increase of relative permittivity of rods.

This figure also shows that the increase in relative permittivityof PC rods not only increases the peak value, but also it causes theshift of peak wavelength to the higher wavelengths. This shift isacceptable similar to shift of the reflection peak wavelength ofFiber Bragg Grating (FBG) with the increase of effective refractiveindex (neff) based on its relation as [44]

λB ¼ 2nef fΛ ð11Þ

where Λ is the grating period.The value of PC filter band width is raised with the increase in

rods permittivity. This phenomenon is indicated in Fig. 4 whichshows the value of FWHM versus the peak wavelength forprevious values of rods relative permittivity. Similarly, for FBGthe bandwidth size is increased with the increase of the fraction of

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

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

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power in the core (η) based on its relation as

Δλ¼ 2δn0η

π

� �λB ð12Þ

where δn0 is the variation in refractive index.The slope of increase in PC filter band width is steep as the rods

permittivity is increased, so that as ε of the PC rods doubles, theband width of its filtering would be nearly doubled too.

3.2. The effect of rods permeability

In this section, assuming relative permittivity of PC rods asconstant equal to εr¼1, and putting chirality factor as zero,variation in the filtering of the proposed PC with a change in itsrods permeability with the radius of 116.5 nm is analyzed andplotted based on the Fig. 5.

As it is distinguished from the figure, the increase in relativepermeability 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 significant change.

The increase in permeability of rods causes a decrease intransmission peak value. This is more manifest in Fig. 6 whichshows transmission peak versus peak wavelength for differentvalues of rods relative permeability. Physically, wave scattering isincreased due to increment of characteristic impedance of rodsand increase of its difference with waveguide's characteristicimpedance. The figure also shows that the increase of rodspermeability leads to the shift of peak wavelength to the higherwavelengths. This phenomenon is explainable similar to shift ofthe reflection peak wavelength for FBG due to increase of effectiverefractive index based on Eq. (11).

On the other hand, the increase in permeability of PC rodsdecreases the filtering band width. This is specified in Fig. 7 whichshows the FWHM versus peak wavelength and according to the

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

Fig. 6. Transmission peak of PC versus peak wavelength for different permeabilityof rods.

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previous values of relative permeability of PC rods. Similarly, basedon Eq. (12) the bandwidth size is reduced for FBG as the fraction ofpower in the core reduced.

It is worth mentioning that the simulations show that insertingthe imaginary term to ε,μ parameter of PC rods disturb its filteringnature.

3.3. The effect of rods chirality

Typically, in infrared range, the relative permittivity of chiralmedium is within the range of about εrc¼2. As it was mentioned,in order to compensate for the increase in bandwidth of CPC, weconsider relative permeability greater than 1. In other words, weconsider chiral medium with paramagnetic material. In this paperμrc¼1.15 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 cutofffrequency with the parameters of εrc¼2,μrc¼1 for its rods whereasits high cutoff frequency would collate with PC high cutofffrequency with the parameters of εrc¼1, μrc¼1.15 for its rods.Moreover, in this case, larger peak wavelength shift toward higherwavelengths occurs.

Now, we analyze the effect of chirality factor of PC rodson filtering operation of CPC. The simulations are done in twocategories based on dispersive and nondispersive nature ofchirality factor. In all these cases, chirality has no effect on thePBG, and transmission nature, out of PBG is remained with nosignificant change.

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3.3.1. Nondispersive chiralityIn this part, for proposed PC's rods with radius of r¼116.5 nm from

chiral elements with relative permittivity and relative permeability

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Fig. 9. Transmission peak of CPC versus real part of chirality factor, peak wavelengthis constant and equal to 1604.3 nm.

Fig. 10. FWHM of CPC versus real part of chirality factor, peak wavelength isconstant and equal to 1604.3 nm.

Fig. 11. Transmission of CPC versus peak wavelength for different imaginary partsof chirality factor.

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

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equal to εrc¼2 , μrc¼1.15 respectively, we study filtering operation ofthe PC structure for different values of chirality factor (χ) independentfrom frequency.

First, we consider chirality factor as a real variable, and then,we simulate the structure with its usual chirality factors ininfrared range. The results show that with the change in chiralityvalue, the peak wavelength remains unchanged whereas the peakvalue and the bandwidth are changed. Fig. 9 shows the amplitudeof transmission peak versus the chirality factor for transmissionbandwidth less than 10 nm.

This figure shows that the value of transmission peak isdecreased with the increase in the real part of CPC rods chiralityfactor, while the peak wavelength is fixed; here it is equal to1604.3 nm.

The change in CPC filter bandwidth with the change in real partof the chirality parameter of CPC rods is shown in Fig. 10. Thefigure shows that the increase of the real part of CPC rods chiralityfactor results the slight increase in the filter bandwidth.

So, generally, the increase of the real part of the chiralityparameter of CPC rods makes its filtering nature more unsuitable.Moreover, the sign of the real part of chirality factor would have noeffect on CPC filtering operation. In other words, right or lefthandedness of the chiral helices does not make any difference. Incontinuation of this part, we investigate the effect of imaginarypart of the chirality of PC rods on its filtering operation. It is to bementioned that typically in this range ImðχÞ≤0. So, givenReðχÞ ¼ 0:04, our simulation is done for different values of ima-ginary part of rods chirality factor. The results of this part showthat although shift in the peak wavelength occurs, it is very small.In Fig. 11 the value of transmission peak of the proposed CPCstructure is plotted versus the peak wavelength, for differentvalues of rods chirality factor in stable condition. It is shown thatas the imaginary part of rods chirality factor gets more negative,

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generally, transmission peak value is increased, and the very slightshift of peak wavelength toward lower wavelengths occurs.

This phenomenon can be regarded as similar to reduce ofreflectivity of Fabry–Perot mirrors due to their antireflectioncoating, so that the rate of wave transmission is increased. Also,the increase of imaginary part of the rods chirality, which is anexpression of the increase of their absorbency and decrease oftheir reflectivity, cause the increase in the transmission peak of PCfilter [45].

The changes in bandwidth of CPC filter are not uniform withthe increase of imaginary part of its rods chirality. This simulationis plotted in Fig. 12, which shows FWHM of CPC filter versus peakwavelength and for changes in the imaginary part of the rodschirality factor. In general, in the concerning range, the changesalong bandwidth is small, and it is specially decreased for thevalues of chirality with ImðχÞ≥ReðχÞ.

Therefore, generally, as the imaginary part of CPC rods chiralityfactor gets more negative, its filtering operation is improved, sothat the access to larger transmission peaks and smaller band-width with no significant changes in the peak wavelength ispossible. This result provides the possibility of designing specialtunable PC filters.

3.3.2. Dispersive CPCsGenerally, chirality has a dispersive nature, and this feature

causes its optical activity in chiral medium. To express chiralitydispersive nature, Condon considered a frequency dependentmodel for chirality factor. This model used for simulation ofdispersive chirality medium [46,47], is as follows:

χðωÞ ¼ τkω2kω

ω2k−ω

2 þ j2ωkξkωð13Þ

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Fig. 13. Real and imaginary part of dispersive chirality factor versus wavelength,parameters of Condon model are τk¼0.025 fs , ξk¼0.5, λk¼1.55 μm.

Fig. 14. Transmission pulse of CPC versus wavelength for parameters of Condonmodel as τk¼0.025 fs , ξk¼0.5, λk¼1.55 μm; Wave propagation is shown atλ2≅1550 nm, λ1¼1650 nm.

Fig. 15. (a) Transmission peak, (b) FWHM of CPC versus resonant wavelength;other parameters of the Condon model are ξk¼0.5 , τk¼0.025 fs.

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where ωk¼2πc0/λk is the resonance frequency, ξk is damping factor,andτk is the magneto electric coupling coefficient.

Assuming τk¼0.025 fs , ξk¼0.5, λk¼1.55 μm chirality factor isplotted versus wavelength on Fig. 13.

Here, Condon model is chosen to consider chirality dispersivenature of CPC rods. On the other hand, since the increase in thesize of PC rods cause the shift of transmission peak toward thelower wavelengths, for the purpose of tuning transmission peakwavelength on 1550 nm, which is a proper wavelength for opticalcommunication, the radius of chiral rods of the proposed CPCstructure is chosen as r¼127.25 nm. So that, for the mentionedparameters in Condon model, transmission pulse is plotted asshown on the Fig. 14. In this figure, propagation of z component ofthe magnetic field (Hz) is illustrated in two wavelengths. Atλ1¼1650 nm, due to being in the range of PBG, incident wave isnot transferred and is reflected completely. At λ2≅1550 nm,because of trapping the related modes in the cavity made of thedefect, the incident wave is transferred, and cause a transmissiongreater than 0.87. Bandwidth of CPC filter would be about 7.9 nmin this case.

Following, in this part, the effects of Condon model parametersfor chirality of CPC rods on its filtering operation is studiedseparately. In these simulations, we consider the radius of chiralrods equal to r¼127.25 nm. So, the peak wavelength is fixed on1550 nm without any considerable change. Also, the relativepermittivity and the relative permeability are considered equalto εrc¼2 , μrc¼1.15 respectively.

3.3.2.1. Resonance wavelength(λk) effect. In this part, assuming thatthe damping factor and the coupling coefficient are constant, equalto ξk¼0.5, τk¼0.025 fs respectively, the effect of resonancewavelength of chiral rods on CPC filtering operation is studied.In Fig. 15 transmission peak and bandwidth of CPC filter areplotted versus the resonance wavelength.

As seen from this figure, by changing λk in the source supportedwavelength range, change of about 10% in transmission peak ispossible. Especially the transmission peak would get over 0.88 atλ≅1400 nm. Bandwidth change with change in resonance wave-length is small and the figure shows the possibility of access tobandwidth smaller than 8 nm at λ≅1400 nm. Therefore, tuning theresonance wavelength of chiral rods is introduced as a factor oftuning of transmission of CPC filter.

3.3.2.2. Damping factor(ξk) effect. In this part, considering that theresonance wavelength and the coupling coefficient are constant,equal to λk¼1.55 μm , τk¼0.025 fs respectively, the CPC filteringoperation is studied by changing the damping factor of chiral rods.Fig. 16 shows the value of transmission peak and bandwidth of CPCfilter versus some different values of damping factors. The values

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of ξk are selected in such a way that: first, the changes intransmission peak and CPC bandwidth are being adequate, andsecond, system remains stable.

The figure shows that the decrease of damping factor increasesthe transmission peak more than 14%. Especially, the transmissionpeak reaches 0.97 when ξk¼0.3. Also decreasing the dampingfactor causes the very slight decrease in the amount of bandwidth.Especially, this amount reaches 7.6 nm for ξk¼0.3. Therefore, thechange of damping factor of chiral rods in CPC provides thepossibility of tuning the PC optical filters especially for amplitudeof transmission peak.

3.3.2.3. The effect of magneto electric coupling factor (τk). Finally,considering that the resonance wavelength and the dampingfactor are constant equal to ξk¼0.5 , λk¼1.55 μm respectively,changes in CPC filtering operation with changes in its chiral rodscoupling factor is studied.

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Fig. 16. (a) Transmission peak, (b) FWHM of CPC versus damping factor; otherparameters of the Condon model are λk¼1.55 μm , τk¼0.025 fs.

Fig. 17. Transmission peak, (b) FWHM of CPC versus magneto electric couplingfactor; other parameters of the Condon model are ξk¼0.5 , λk¼1.55 μm.

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Fig. 17 shows transmission peak and bandwidth of CPC filterversus some different values of magneto electric coupling factor.

Values of τk is selected So that the system remains stable andacceptable variations in the filtering nature is observed.

As it is shown in the figure, increase of coupling factor, causesthe increase in transmission peak of about 20%. Especially, the

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amplitude of transmission peak of CPC filter reaches over 0.99 forτk¼0.045 fs. On the other hand, increasing the coupling factordecreases the filter bandwidth desirably. Especially, the size ofbandwidth reaches 7.4 nm for τk¼0.045 fs. Therefore tuning theCPC filter is possible both for its peak amplitude and its bandwidthby changing the magneto electric coupling factor of chiral rods.

It should be mentioned that changes in chirality parameters donot make a significant change in the transmission peak wave-length of CPC filter, and the peak wavelength remains about thesame 1550 nm.

Fabrication of CPC is available and is demonstrated based onvarious methods such as holographic lithography [48], standarddirect laser writing in the commercially available photoresist SU-8[49], hot embossing combining with a UV curing process [50], andcombined nano-imprint and reversal lithography in SU-8 [51].

4. Conclusion

This paper uses FEM to study PC microcavity filter with chiralrods and also to discuss the tunability of its transmission peak andbandwidth under system stability condition.

The effect of electromagnetic parameters of PC rods on filteringoperation is studied. It is shown that increased permittivity of rodsresults in increased peak amplitude and bandwidth of PC filter. Itshifts the peak toward larger wavelengths and decreases the PBG.The PC rods with larger permeability show a smaller transmissionpeak and bandwidth in PC filter operation. In this state, thetransmission peak shifts toward larger wavelengths, and the PBGincreases.

The chirality factor effect of chiral rods on filtering operation isstudied for both dispersive and nondispersive CPC structure. It isconcluded that the increase in real part of chirality factordecreases the transmission peak of CPC and increases its band-width. On the other hand, the increase of the imaginary part ofchirality factor increases the transmission peak and decreases thebandwidth. 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 dispersioneffect and as it is shown the parameters of this model cause achange in filtering operation of CPC. As clarified, it is possible toadjust the transmission peak up to 10% through a change in theresonance wavelength in this model. As found in this research, thereduction in the damping factor results in increased transmissionpeak and decreased bandwidth. Moreover, an increased magnetoelectric coupling factor increases transmission peak and decreasesthe bandwidth considerably.

Designing of monolithic and tunable filters in optical commu-nication, with large peak amplitude and small bandwidth, usingCPC structure, has been discussed here.

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