COIN - ACOFT 200724 - 27 June 2007, Melbourne, Australia

Design of high-Q photonic crystal cavities designed by air-holesinfiltrat'ion

S. Tomljenovic-Hanic, C. Martijn de Sterke, and M. J. Steel*

ARC Centre of Excellence for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School ofPhysics, University of Sydney, NSW, 2006, Austarlia

* also with: RSoft Design Group, Inc., 65 O'Connor St, Chippendale, NSW 2008, Australia

Abstract - We design novel photonic crystal slabheterostructures, substituting the air in the holes with liquidcrystal, polymer or nano-porous silica. We demonstratenumerically that such cavities can have quality factors up toQ=106.

I. INTRODUCTION

Some of the most promising applications of photoniccrystal slabs (PCS) involve a cavity with high quality factorand small modal volume. Such cavities could be used in areasas diverse as optical telecommunications [1] and cavityquantum electrodynamics [2] The highest Q values that havebeen achieved to date involve double-heterostructures [3,4].For example Song et al constructed a double-heterostructure,combining two PCSs with slightly different lattice constants[3] These lattices are combined similarly to the designillustrated in Fig. 1(a): in the outer regions (PC 1) the lattice ishexagonal, whereas in the central region (PC2), the lattice isslightly elongated (by 10 nm) in the direction orthogonal tothe heterostructure (parallel to the waveguide) A waveguideintroduced across these PCSs has different dispersion curveswithin the different parts of the PCS. Therefore within thesame photonic band, gap (PBG) there is a "mode-gap"between these curves The mode "propagates" in thewaveguide of PC2 and decays exponentially elsewhere. Themode-gap effect can be also achieved, via lateral holedisplacement [4].

There are many other ways to form heterostructures Wehave proposed two designs that can be fabricated without anychange in the geometry of the regular structure [5, 6]. Herewe present a heterostructure design based on the refractiveindex change within the holes in the central part of thehomogenous structure; the air in the holes of PC can bereplaced with material of refractive index n > 1. We considermaterials having refractive index in the range n= 1 .11- 1.7, suchas liquid crystal, polymer or nano-porous silica [7-9]. It hasbeen experimentally demonstrated that a nematic liquidcrystal (LC) infiltrated, photonic crystal laser can beconstructed by encasing the PCS between two indium tinoxide glass plates [7]. The LC refractive index range fromn= 1.45 to n= 1.7 [7] whilst the refractive index of "photonic"polymers ranges from n=1.3 to n=1.75 [9]. It has been alsoexperimentally demonstrated the air-holes infiltration of InP-based two-dimensional photonic crystal by polymers [11 ]. Itis even feasible to control the microinfiltration of fluids byaddressing and infiltrating each pore separately [12]. In

contrast, here we use novel heterostructure design bychanging the refractive index within the holes only of the PCScentral part PC2 The aim of this design is to increase theaverage refractive index of the PCS which, to lowest order,has the effect of lowering the optical frequency of features inthe photonic band structure of PC2 with respect to that of PC,.Since the waveguide mode in PC2 has a lower opticalfrequency than in PCI1 there is a mode-gap, a narrowfrequency range for which PC2 supports such a mode, but notPC1. Thus, the structure can confine light to the defect regionOf PC2-

10 4

0

-10

10 0 10

Fig. 1 Refractive index distribution in the plane of thestructure darker circles indicate n light gray circles indicaten> 1 and the. backgroundl gray indicate silicon slab.

,I MODEL AND METHOD

We consider a silicon-based, n=3.4, PCS consisting of ahexagonal array of cylindrical air holks with lattice constanta, hole radius R=0.29a and slab thickness h=0.6a. Across thePCS there is a line defect, a WIl waveguide, in the FKdirection. We start with a homogeneous PCS and design theheterostructures by changing the holes' refractive index in thecentral region of the PCS (indicated by the light gray circlesin Fig. 1). The PC2 length is d, d=mna-2R, where mn is an

integer.The concept of the cavity design in heterostructures relies

on the mode gap effect [3] Therefore we first examine ifthere is a sufficient mode-gap between structures havingmaterials other than air within the holes. For these purposes,PBG calculations and associated eigenstates of the photonic

ISBN 978-0-9775657-3-3

crystal waveguide, we use the plane wave expansion (PWE)method.Then we use the finite difference time domain (FDTD)

method, combined with techniques of fast harmonic analysisL5, 6] for the quality factor calculations. Details on numericalparameters for the calculations can be found in Ref [5] withthe satisfactory convergence obtained by using 32 points perperiod.

III. RESULTS

A. Mode-gap

First we examine if there is a sufficient mode gap betweenstructures having materials other than air within the holes.The dispersion curves of this mode for both the unperturbedstructure, PC1, and PC2 where air holes are filled withmaterial having refractive index n=1 6, are plotted in Fig. 2In the same figure the lower band edge is indicated by solidhorizontal lines both for the regular and modified structure.Obviously, filling the holes with material of higher refractiveindex than air increases the refractive index of the structure inwhole and consequently lowers the dispersion curve The gapbetween these dispersion curves, measured at the edge of theBrillouin zone, is Aa =3.25 X10 -, where ox/ 2rc a/The size of the mode-gap is comparable with the mode-gap ofthe heterostructures formed of different lattices [3].

.-Ili.11ukl.

cliRs1-1

v

cu

0.28 A

02 PC> A.PC,0.27- X

_ e , mode gap

0.26- PC,PBG edge shift

PPC2

0.3 0.4

waxevector (2,g/a)

Fig. 2 Dispersion curves for WI I within the region of thelowest gap of the regular structure PC, (empty triangles) andWI of the structure PC (full circles) nl =1 6 the dashedline represents the light line, the horizontal solid linesrepresent the lower band gap edge for PC, and PC2

There is a large difference between the PBG edge shiftand the size of the mode gap in Fig. 2. The largest shift isobtained for the upper PBG edge, the "air band", whereas thesmallest shift is obtained for the lower PBG edge, "dielectricband", plotted in Fig. 2. These bands are defined by wherethe power of their mode lies. As the power of air band modeslies in the low refractive index region (air holes) changing therefractive index within these regions will mostly affect the airband. This finding is also consistent with experimental resultsreported in Refs. [ 10, 1 1].

B. Cavity

Now we vary the holes' refractive index for two differentcavity lengths, a small cavity m=1I and larger cavity m=4The results are shown in Fig. 3. For the mX=1 cavity themaximum of Q=2.5x105 appears at n=1.4. This coincideswith the refractive indices of polymer materials and liquidcrystals [7 9]

The maximum value for the 7X=4 cavity of Q=9.7x 105 iSobtained at n =1.25. In practice this structure can be attainedby filling the holes with nano-porous silica [7]. If polymer isused, the quality factor decreases but still remains high. Forexample, filling the holes with polyhexafluoropropyleneoxide with the refractive index of n=1.3 provides a cavityQ=7 6x 10 [9]. The maximum occurs at different refractiveindex values, for l=l at n=1.4 and form=4 at n=1.25. Inspite of this, the resonant frequencies are very close, for iX= 1,M 0.2628 and for in=4, M 0.2625. Therefore for differentmaterials the maximum quality factor is achieved usingdifferent number of PC2 layers. For smaller refractive indexmaterials it is necessary to use longer cavity.

It is worth pointing out that there is a large range ofrefractive indices, n=1.25-1.6, where the quality factors areof order of 105 for both, m= 1L andim=4, cavities. Thiscoincides with the refractive indices of polymer materials andliquid crystals [7- 1].

In

0

x0-

10 9

8 6 ~ ~~~~~ \

m=44 0

2 - ml

a~~~~

0O1. 112 14

n(holes)1.6 1,8

Fig. 3 Quality factor Q for in=4 (rectangles) and for mn=1(crosses) as a function of the refractive index of the centralholes.

Our results suggest that the relative position of theresonant frequency within the mode-gap is an importantparameter in the design of high-Q heterostructures as well asthe mode-gap position within the PBG.

First we discus the mode-gap position within the PBG form=1 cavity, Fig. 3. As the holes' refractive index is increased,the average refractive index of the structures increases. Thisresults in better out-of-plane confinement and thereforesmaller out-of-plane losses, increasing the Q. However atn=1.4 the Q starts to decrease. We believe this happensbecause the dispersion curves for higher refractive indicesshift lower whilst the lower band edge for PC,, denoted by theupper horizontal solid line in Fig. 2, is fixed. Consequentlywith increasing index, the dispersion curve of PC2 approachesthe lower band gap edge of PC,.

Next we investigate the relative position of the resonantfrequency within the mode-gap. We calculate the quality

2

factor and resonant frequencies for the cavities d=ma 2R,where m =1,2,... ,5. The results for the fixed refractive indexn=1 4 are shown in Fig 4 The mode-gap edges are indicatedby the horizontal dotted lines. As the refractive index is fixed,the mode-gap that ranges from a -002636 to 0 2607,does not change as m changes.

7 C

homogenous PCS with nano-porous silica. The maximumvalues of this design achievable by using polymer materials orLC exceed Q=7x 105. This approach represents a noveltechnique for creating ultrahigh-Q cavities that furthernnoreopens the possibility of post-processing in PCS-basedmicrocavities.

10.265 ACKNOWLEDGEMENT6

I--e<

0.26 '-U0

rn

_X

0

0 2 4

m

Fig. 4 Quality factor Q (rectangles) (a) and resonantfrequencies (crosses) as a function of the number of periodswithin the cavity m, for fixed nh,,=* 1 .4.

Up to m=4, increasing the cavity length increases thequality factor with the maximum exceeding Q=6x 105 Theresonant frequency for m=l occurs just below the uppermode-gap edge. As m increases the frequency crosses over

the mode-gap almost linearly passing the mid mode-gapclosest to m=3. The resonant frequency that corresponds tothe maximum Q=6x 105, =0.2617, is in the lower half ofthe mode-gap. Further one as the resonant frequency isapproaching the lower mode-gap edge the quality factordecreases. Therefore both, the relative mode-gap position

within the PBG and the relative position of the resonantfrequency within the mode-gap can be used as importantindicators in the high-Q cavity design

IV. Discussion and ConclusionWe note that the use of polymers and liquid crystals for a

point cavity design decreases the quality factor because of the

weaker vertical confinement that increases the out of-plainlosses [7]. On the other hand we show here that filling theholes with these materials enables ultrahigh-Qheterostructures because it allows for the mode-gap operationthat relies on the refractive index perturbation

The processing of air-hole infiltration can be done at any

time after fabrication opening possibility for post-processingand rewriting of photonics circuits [7, 10-12]. If the structureis filled with LC, electro-optic or nonlinear polymer there isalso the possibility of tuning these structures when voltage isapplied.

In conclusion we have shown that ultrahigh-Q cavitiescan be designed in PCS heterostructures without change ofthe structure geometry. Quality factors of order Q 10o6 can beobtained by filling the holes in the central region of the

This work was produced with the assistance of theAustralian Research Council (ARC) under the ARC Centresof Excellence Program. CUDOS (the Centre for Ultrahigh-bandwidth Devices fur Optical Systems) is an ARC Centre ofExcellence.

REFERENCES

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[9] G. P. Harmon, "Polymers for optical fibers and waveguides: AnOverview" in Optical polymers fibers and waveguides J PHarmon, and G. K. Noren, eds. (American Chemical Society,2001) pp. 1-23.

[tO] J. Martz, R. Ferrini, F. Nnesch, L. Zuppiroli, B. Wild, L. A.Dunbar, R. Houdre, M. Mulot and S. Anand, "Liquid crystalinfiltration of InP-based planar photonic crystals," J Appl.Phys vol 99 103105 (2006).

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[12] F. Intonti, S. Vignolini., V. Turk, M. Colocci, P. Bettoti, L.Pavesi, S. L. Schweizer, R. Wehrspohn, and D. Wiersma,"Rewritable photonic circuits." Appl. Phys. Lett., vol. 89,21L1117, 006.

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