cpl New Configuration of Ring Resonator in Photonic Crystal Based on self collimations beams

CHIN.PHYS.LETT.Vol.25,No.12(2008)4288 New Configuration of Ring Resonator in Photonic Crystal Based on

Self-Collimation*

SHEN Xiao-Peng(沈晓鹏)1**,HAN Kui(韩奎)1,YUAN Fang(袁芳)2,LI Hai-Peng(李海鹏)1,

WANG Zi-Yu(王子煜)1,ZHONG Qi(钟琪)1

1Department of Physics,China University of Mining and Technology,Xuzhou221116 2College of Applied Science and Technology,China University of Mining and Technology,Xuzhou221116

(Received12September2008)

We propose a novel ring resonator configuration in a channelless photonic crystal.The proposed ring resonator utilizes the self-collimation effect and the bending and splitting mechanisms of line defects to route the propagation of light,instead of conventional indexed-guided waveguides or photonic crystal band gap waveguides.The finite-difference time-domain method(FDTD)is used to investigate the characteristics of the ring resonator.The new design exhibits an ON–OFF contrast with an extinction ratio of more than12dB,and has an ultra-compact footprint of3.3×3.3μm2when it operates at the optical communication wavelengthλ=1.55μm.The design presented may find applications in the areas including ultra-compact optical switch and wavelength filer in integrated optical circuits.

PACS:42.60.Da,42.70.Qs

Photonic crystals(PCs)have attracted growing at-tention mainly due to their potential application to control the?ow of light at optical wavelength scale, which in turn results in a signi?cant reduction in the size and power consumption of the PC based opto-electronic devices.[1]During the past decade,PC?-bres,PC lasers,PC nanocavities and various other devices have been proposed and demonstrated theo-retically and experimentally.[2?5]Initially,most com-mon implementation of PC devices is usually created by introducing line defect within a photonic band gap (PBG)structure,where the PBG defect waveguide is used to route the propagation of light.More recently, another con?nement mechanism of light guiding has been increasingly investigated,i.e.,the so-called self-collimation e?ect.[6]It exploits the spatial dispersion properties of Bloch waves in PCs to achieve di?rac-tionless light propagation,retaining spatial width con-?nement without line-defect waveguide or nonlinear-ities.Self-collimation has been achieved experimen-tally both in two-and three-dimensional(2-D,3-D) PCs.[7,8]Various photonic devices,such as polariza-tion beam splitters,Mach–Zehnder interferometers, logic gates for self-collimated beams,have also been demonstrated by several groups.[9?12]Theories and experiments demonstrate that these dispersion-based nonchannel virtual waveguide and optical components have potentials to function as various signal process-ing and logic functions in integrated photonic circuits.

Ring resonators are important optical compo-nents which can act as multiplexers,optical switches, add/drop?lters and sensors.[13?16]Their wide uses and functions have led to the fabrication of ring res-onator devices in?bres,rib and slot waveguides.[17,18]Recently,ring resonators based on photonic band gap (PBG)waveguide,hybrid photonic crystal and con-ventional waveguide structures have been proposed in2D PCs.[19?23]Kim et al.designed an ultra-compact ring resonator using hybrid PCs and conven-tional waveguide structures.It uses the PC struc-ture as mirrors to achieve sharp bend and reduce the size of the resonator.[19]Ogusu and Kumar et al.proposed a line defect waveguide coupled ring res-onators in PCs,and discussed their performance re-garding various con?gurations,respectively.[20,21]Re-cently,Qiang et al.proposed an optical add-drop?lter design based on ultra-compact photonic crystal sin-gle and dual ring resonators.[23]An important key is-sue for the PCs-based resonator mentioned above is that the line defect waveguide or conventional waveg-uide is necessary to control the propagation of light. In this Letter,we demonstrate a new con?guration of ring resonator in a bulk of photonic crystal.It uses self-collimation e?ect as a virtual waveguide to route the?ow of light.The ring resonator is anal-ysed and simulated by equi-frequency contour(EFC) analysis and rigorous two-dimensional?nite-di?erence time-domain(FDTD)method.The simulation results show that the ultra compact non-channel PCs ring res-onator exhibits highly unconventional properties that could provide novel response characteristics for future ring resonator devices.

The self-collimating structure we investigate is shown in the inset of Fig.1,which consists of a square lattice of air holes introduced in dielectric with refrac-tive index n=3.5(e.g.,Si at1.55μm).The radius is taken as R=0.33a,where a is the lattice constant. The transverse electric(TE)polarization(magnetic

*Supported by the Science Foundation of China University of Mining and Technology under Grant No2007A031. **Email:xiaopeng.shen@https://www.360docs.net/doc/8112266558.html,

c○2008Chinese Physical Society and IOP Publishing Ltd

No.12SHEN Xiao-Peng et al.4289?eld parallel to the hole axis)is investigated for this

structure.To determine the propagation direction of

TE polarization in the PC structure,an EFC analy-

sis is adopted.Figure1shows the EFCs of the self-

collimation structure which are obtained by using the

plane wave method.In PCs,the direction of energy

?ow of light propagation is de?ned by the group ve-

locity V g=?k w(k),which implies that it is perpen-

dicular to the EFCs and coincides with the steepest

ascent of the dispersion surface.[24]As shown in Fig.1,

a variety of wave vectors of the same normalized fre-

quency f=0.18(c/a)on relatively?at EFCs near

the M point have group velocities collimated near the

ΓM direction,which implies that this structure can

provide with a wide-angle self-collimated propagation

along theΓM direction.Therefore,the PC structure

can act as a non-channel virtual waveguide to route

the light without introducing a line defect or a tradi-

tional waveguide.

g

Fig.1.First band equi-frequency contours(EFCs)of the

PCs dispersion surface in the first Brillouin zone.Solid line

arrows show the group velocity directions for a variety of

wave vectors(dashed arrows).The thick solid lines indi-

cate the contours of normalized frequency f=0.18(c/a).

The flat contour of the PCs means that a finite-width

beam made of those wave vectors will collimating prop-

agate along theΓM direction.The inset shows the PCs

structure,which consists of a square lattice of air holes

introduced in the dielectric(n=3.5).

Source

Through

Drop M1

M2

BS2

BS1

Fig.2.Schematic structure of the ring resonator with two beam splitters(BS1,BS2)and two mirrors(M1,M2) embedded in a self-collimating PC structure.The arrows indicate the propagation direction of the self-collimated beams in the ring resonator.

The self-collimation based ring resonator is shown schematically in Fig.2.Two line defects are intro-duced to act as the1:1beam splitter(BS1,BS2),and two small rectangular air blocks are introduced to be-have as45°mirrors to achieve90°light bending[M1, M2].

1.0 1.1 1.2 1.3 1.4 1.5

0.0

0.5

1.0

N

o

r

m

a

l

i

z

e

d

i

n

t

e

n

s

i

t

y

Radius (a)

Transmission

Bend

Sum

(a)

(b)

Ref

Inc

M

G

Air

Fig.3.Magnetic field distribution of a self-collimated beam propagates through(a)the beam splitter and(b) mirror.

The beam splitters in the lower left and right cor-ners with a hole radius R s=1.43R designed to equally split the optical signal,as shown in Fig.3(a).By vary-ing one row of air holes along theΓX direction,the incident self-collimated beam will be separated into two parts:one part is along the original direction, and the other is perpendicular to the original propa-gation direction.The process of the self-collimated beam confronted by the line defect is analysed by FDTD method.The inset in Fig.3(a)shows the ra-tio of transmission and re?ection vs the defect radius from R to1.5R at frequency f=0.18(c/a),where R is the radius of the self-collimation structure.It is worth noting that the fraction of the incident optical power directed into each output is47%at R s=1.43R.In the ring resonator design,the defect radius of1.43R is chosen to divide one beam into two beams of equal intensity.

4290SHEN Xiao-Peng et al.Vol.25

As demonstrated previously by Fan et al.,[25]mir-rors can be realized by introducing a rectangular air block into the PCs.When the light impinges upon the interface between PC and air at an incident an-gle of 45°,it will be re?ected at an angle of 90°by total internal re?ection.This can be seen from the construction in the inset of Fig.3(b).Two mirrors in the upper right and left corners direct the beam to circulate in the rectangular ring.

(a)

(b)

Fig.4.Magnetic-field distribution as a self-collimated beam propagating inside the ring resonator:(a)on-resonance at frequency f =0.1814(c/a );(b)off-resonance at frequency f =0.1868(c/a ),where c is the vacuum light velocity and a is the lattice constant.

In order to investigate the performance of the ring resonator,the FDTD method is used to simulate the propagation of light and quantify the e?ciency.In the simulation,a 4√2a wide continuous Gaussian beam normally incidents into the PC structure and self-guided through the self-collimation region.The beam is divided at the 50%re?ecting/50%transmitting BS 1into two beams of equal intensity.When light of the appropriate frequency is coupled to the rect-angular loop by BS 1,it builds up in intensity over multiple round-trips due to constructive interference.It can then be picked up by BS 2and directed to the drop port.At o?-resonance,input signal will by-pass the ring and redirect to the through port.We plot the special distribution of magnetic-?eld at dif-

ferent frequency f =0.1814(c/a )which is the reso-nant frequency of the ring resonator,and at frequency f =0.1868(c/a )which is o?-resonance,as shown in Figs.4(a)and 4(b),respectively.As prospected,at resonant frequency f =0.1814(c/a ),the ?eld fully couples to the drop port,whereas at o?-resonance it does not couple and continues to propagate to the through

port.

Fig.5.Frequency response of a ring resonator of 11a ×11a for the through port (solid)and the drop port (dashed).

The transmission spectrum of the ring resonator is shown in Fig.5.Solid and dashed lines show the through and drop transmission spectra of the ring resonator over the 0.179–0.189(c/a )frequency range.As can be seen,the free spectral range (FSR)is from 0.1814(c/a )to 0.1868(c/a ).The full width at half maximum (FWHM f )of the resonance peak at f =0.1814(c/a )is 0.0005(c/a )and a quality fac-tor (f drop /FWHM f )Q =363,?nesse (FSR/FWHM)F =18.The extinction ratio calculated (i.e.,ratio of the through port power to the drop port power for the drop wavelength)is more than 12dB.To render working frequency of the design in the range of optical communication,the lattice constant and the radius of the air holes should be a =285nm,R =95nm and R s =135nm,respectively.The FSR =45nm (1526–1571nm)which is wide enough to cover almost the entire C band.The ring resonator occupies an area as small as 10μm 2,which is feasible for manufacture of current technology.A subsequent increase of the quality factor is expected if we optimize the ring res-onator structure and increase the computation.Fur-ther improvement in devices performance is expected by optimizing the design of the ring resonator.We expect that the ring resonator has wide applications in optical communication and signal processing.

In summary,we have proposed a self-collimating ring resonator con?guration by exploiting PC’s dis-persion characteristic.The ring resonator can be used either as optical switch,add/drop ?lter in optical cir-cuits.It can also be made active by tuning some

No.12SHEN Xiao-Peng et al.4291

of the parameters and consequently its wavelength response by thermo-optic e?ect,optic-optical e?ect, electro-optic e?ect,etc.Due to the scaling property of PC,all the results presented here apply equally across infrared and visible wavelengths.With all pho-tonic crystal designed,the ring resonator does not need waveguide or line defect to route the propaga-tion of light.It has a high e?ciency,and can be made ultra compact.These features of the proposed device make self-collimation based ring resonator a promising candidate for integrated elements in photonic crystal circuits and optical communication applications. References

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