MechanicallytunablePhotonicCrystals

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www.osa-opn.org40 | OPN January 2009

Mechanically Tunable

Photonic Crystals

Won Park and J.-B. Lee

The next frontier in photonic crystal research may be to achieve dynamic tunability that

allows real-time, on-demand control of the photonic band structure. Recently, researchers

have been working on a new strategy for achieving this goalby applying mechanical

force. This approach can produce much greater tunability than is possible with electro-optic

materials and may greatly expand the usefulness of photonic crystals.


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OPN January 2009 | 411047-6938/09/01/0040/6-$15.00 OSA

he term photonic crystal reers to a material thathas a periodic reractive index. Tis periodic indexprole aects the propagation o light in much thesame way that the periodic potential inuences

electronic motion in natural crystals, leading to novel opticalphenomena such as photonic band gaps, sel-collimation andnegative reraction. Tanks to recent progress in nanoabrica-tion technologies, researchers can now build these structureswith extreme precision.

Tese crystals oer great engineering reedom because theiroptical properties are derived rom their structural design. Inthis respect, photonic crystals (PCs) may also be considereda orm o optical metamaterial (although metamaterials aretypically dened more narrowly, as a composite structure withstructural units much smaller than the operating wavelength).In any case, PCs open a wealth o exciting research and engi-

neering possibilities that may lead to new applications in thin-lm optics, optical waveguiding and optical computing.

Te next rontier in the photonic crystal research may be toachieve dynamic tunability that allows real-time, on-demandcontrol o the photonic band structure. Tis would be a crucialimprovement that could greatly expand the useulness o PCs.Many researchers have tried using liquid crystals to achievedynamic tunability; these crystals are relatively easy to incor-porate into PC structures and allow electro-optic and thermaltuning. Busch and John predicted the tunability o the photo-nic band structure by inltrating liquid crystal into an opal. Inaddition, much theoretical and experimental research has been

done on temperature and electro-optic tuning o liquid-crystal-inltrated PC structures.

So ar, most o that work has involved shiting the photo-nic bandgap or deect modes using nematic liquid crystals.However, the index anisotropyDn is about 0.2 in most liquidcrystals, which is rather small. Furthermore, the inltratedliquid crystals oten occupy only a small raction o the totalvolume inside the photonic crystal. A 3D modeling study thattook into account the nite thickness o the slab PC structurepredicted only limited tunability due to the small attainablechanges in the reractive index o the liquid crystal and theirsmall volume raction.

Moreover, in most experimental realizations, the eectiveliquid crystal volume is urther diminished by the strong suracepinning eect. While there are other possible ways to enhancethe tunability (e.g., using a superlattice structure), it remainsdifcult to achieve wide tunability with liquid-crystal-inltratedPCs. Other electro-optic materials, such as lead lanthanumzirconium titanate (PbLaZriO3) and lithium niobate, ace asimilar problem and are much more difcult to process.

Recently, researchers have proposed a radically dierentapproach to achieving tunabilityby using mechanical orce.Te mechanically tunable PC (MPC) structure is comprised

o a periodic array o high-index dielectric materials embed-ded in a low-index polymer lm, such as polyimide and SU8(a standard polymer photoresist). Te structure is subject toan external mechanical orce by a silicon or metallic nano-/microelectromechanical system (NEMS/MEMS) actuator thatstretches and releases the exible polymer membrane. Teapplication o mechanical orce causes physical changes in thephotonic crystal structure to which the photonic bands areextremely sensitive. Tis approach can thereore produce muchgreater tunability than what is possible with electro-opticmaterials. Possible applications include modulators, lters andon-chip sensors.

T

[ Mechanically tunable photonic crystal structure ]

VV

Mechanically tunable photonic crystal consisting o a periodic

array o silicon nanorods embedded in a exible polymer

membrane. We applied mechanical orce using mechanical

actuators abricated with MEMS technology.


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Tuning light propagation in photonic crystals

o demonstrate the tunability achievable in MPCs, we rstpresent numerical modeling results on the eect o mechani-cal orce on optical beam propagation. Photonic crystals areknown to exhibit anomalous reraction behavior due to the

strong modication o the dispersive surace by the periodicity.Tis phenomenon is best illustrated by the equi-requency con-tour (EFC), which reers to the locus o allowed wave vectorsor a given requency. Te gure on the right shows the EFCor a triangular array o silicon pillars embedded in a exiblepolymer. Tis structure was ound to exhibit anomalous rerac-tion behavior at a normalized requency (wa/2pc) o 0.39.

Te EFC or the unstressed triangular PC had a star-likeshape. It exhibited sharp inection points along the high sym-metry directions, G-M and G-K. Tese points represented theregions where we expected anomalous reraction. When thesystem was under mechanical stress, the crystal symmetry waslowered and consequently the dispersive surace was stronglymodied. I the PC was uniormly stretched along the G-Kdirection, the dispersion curve became distorted.

Te dispersion curves along the G-M direction attenedsignicantly as the PC was stretched along the G-K direction.Tis resulted in a very large change in the reraction behavioror optical beams propagating near the G-M direction. Sincethe group velocity was dened as the gradient o dispersionsurace in k-space, we could estimate the reraction anglesrom the curvature o the EFC. Te perect triangular latticeexhibited giant negative reraction, in which the reractionangle reached roughly 708 or an incident angle as small as 58.

As the PC was mechanically stretched, however, due to

the attening o the dispersion contour, the reraction angledecreased dramatically and varied only slightly as the incidentangle was changed. Furthermore, or the case o 10 percentstretching, it no longer exhibited negative reraction andswitched to the normal positive reraction behavior. Te dier-ences in reraction angles between the perect triangular latticeand the 10 percent stretched crystal reached more than 758 asthe incident angle was varied between 58 and 158. Tis is anorder o magnitude greater than what is achievable with liquidcrystals, which typically exhibit at most a 15 percent change inreractive index.

We conducted two nite-dierence time-domain (FDD)

simulations or a perect triangular lattice and 10 percentstretched crystal with a Gaussian beam incident with an angleo 128. Te incident Gaussian beam was launched rom thebottom o the computational domain and the MPC structurewas placed in the upper region. Te large dierence in rerac-tion angles between the two cases was clearly shown.

We achieved this large change in reraction angle with arelatively small mechanical deormation. When the systemis designed or the communication wavelength o 1.54 mm,the pillar-to-pillar distance, a, is 0.6 mm and a 10 percentchange was a mere 60 nm per unit cell. A larger stretchingcould, o course, induce an even greater change in reraction

behaviorbut one must also consider atigue and the elasticitylimit o the polymer.

We perormed nite element modeling and conrmedthat, with up to 10 percent stretching, the polymer would bestretched uniormly with its displacement linearly propor-tional to the applied mechanical orce. Another importantconsideration was the Poisson ratio o the exible polymer.Polydimethylsiloxane (PDMS), or example, has a very largevalue o Poisson ratio, approaching nearly 0.5. Tis means thata 10 percent stretching along the G-K direction will result ina simultaneous reduction in lm thickness by 5 percent, or

15 nm, in our test structure. Fortunately, the photonic bandstructure was not very sensitive to the slab thickness. Tus,such small changes in slab thickness will not signicantlyaect the light propagation characteristics.

MPC can a lso be applied to negative index imaging. PCsare known to exhibit negative reraction through two dierentranges o operationnear the top o the rst photonic bandwhere the EFC has negative curvature or in the second photo-nic band, which has a negative gradient. Recently, researchershave demonstrated negative index imaging or both cases atthe telecommunication wavelength o 1.5 mm in silicon-basedPC structures. Negative reraction generally exhibits acute

(a) EFCs or perectly triangular (outer curve), 5% stretched

(middle curve) and 10% stretched (inner curve). PC struc-

tures calculated or a normalized requency o wa/2pc = 0.39.

Mechanical orce is applied along the G-K direction. The

hexagon represents the frst Brillouin zone or the unstressed

lattice. (b) FDTD simulations show the reraction o a gaussian

beam incident on the perectly triangular (b) and 10 percent

stretched (c) PC structures. The incident beam was launched

rom the bottom and the PCs were placed in the upper region

o the computational domain. The incident angle was 128 or

both cases.

(a)

(b) (c)

M

K

G

Equi-frequency contours for atriangular array of silicon pillars[ ]


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OPN January 2009 | 43

requency dependence, placing a severe limitation on the oper-

ating requency range.Obviously, achieving broadband operation would greatly

expand the utility o negative index materials. Recently,researchers have proposed that broadband negative index imag-

ing with minimal chromatic aberrations can be achieved by agraded negative index PC structure. Alternatively, the MPCconcept can be used to tune the negative index and realize

broadband negative index imaging.o demonstrate tunable negative index imaging, we inves-

tigated the eect o mechanical stress on a 2D honeycomblattice o silicon rods in polyimide. In this structure, the EFCs

were ound to be circular near the top o the second band and

gradually deormed to a hexagonal shape as the requency wasdecreased.

Te EFCs became smaller with increasing requency, whichis typical o the negative reraction regime. Since the eective

index was measured by the radius o the EFC, it decreased inmagnitude with increasing requency. We thereore expected

that the image should orm arther away rom the PC lens ata higher requency. In order to directly visualize the ocusing

properties o the PC lens, we perormed point source imaging

[ EFCs for honeycomb lattice of silicon nanorods ]

(a) EFCs or a honeycomb lattice o silicon nanorods in polymer matrix calculated or various requencies. (b) Electric feld distribution

o point sources and their images across a 2D honeycomb photonic crystal slab at various normalized requencies (=wa/2pc). Red

and blue represent positive and negative feld values. The locations o the point sources are at a distance o 1.0a rom the let edge

o the slab, where a is the lattice constant o the honeycomb lattice. (c) Electric feld distribution o point sources and their images

across a 2D honeycomb photonic crystal slab under various degrees o strain. The positions o the sources are also at a distance o

1.0a rom the let edge o the slabs, where a is the lattice constant o the unstressed honeycomb lattice.

(a) (b) (c)

=0.330 =0.370

Source Image=0.380

=0.390

=0.340

=0.340

=0.350

=0.360

M

KG

=0.295

=0.300 =0.315

=0.320=0.305

=0.309

Source Image

5% compressed

2% compressed

Honeycomb

2% stretched

5% stretched

Recently, researchers have proposed a radically different approach toachieving tunabilityby using mechanical force.

simulations using the FDD method. Consistent with our

analysis based on EFCs, the image did indeed move away romthe lens with increasing requency.

When we applied mechanical stress, the EFC was stronglydeormed, and, consequently, the ocusing characteristics

were modied. In the ollowing simulations, we assumed thatmechanical stress was applied along the G-K direction and thedimension along G-M direction remained unchanged. In real

space, G-K is the direction perpendicular to the optic axis othe PC lens and G-M corresponds to the direction along the

thickness o the PC lens. We modeled three cases o stretchingand compression by 2, 5 and 10 percent. Here, the 2 percent

stretched lattice means that the distance between the two

neighboring silicon pillars is 2 percent longer than that in theunstressed honeycomb lattice.

Te general trend was that the image moved arther awayrom the PC lens as the PC structure was stretched. On the

other hand, as the PC lattice was compressed, the imageappeared closer to the PC slabs. Te observed behavior was

also consistent with the EFCs. Te stretched lattices hadsmaller EFCs than the unstressed honeycomb PC. Conversely,

the EFCs o compressed lattices were larger. A smaller EFC


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corresponded to a smaller eective index. Consequently, theimage should be arther away rom the PC, which was exactlywhat we ound rom the FDD simulations.

By combining the requency dependence and the mechani-cal stress eect, we can develop a tunable negative index PClens, which ocuses only the desired requency component on

the detector at xed position. Te detected requency compo-nent can be tuned by the mechanical orce, enabling requen-cy-selective detection. We estimate that a 10 percent strain willprovide a requency bandwidth o 12.9 percent o the centerrequency. Tis corresponds to a tunable bandwidth o 200 nmat the communication wavelength o 1.54 m.

Demonstration o a mechanically tunable PC

In order or the MPC to be realized, the high-index dielectricrod array embedded in a low-index polymer membrane shouldbe exible enough to create the structural displacement, but

sufciently sti to ensure that the membrane does not sag andremains suspended in air. Our initial investigation began witha PDMS-based MPC. We ound this model to be ineasible:Because PDMS has an extremely low Youngs modulus (below1 MPa), the polymer membrane embedded with silicon nano-rods was not sti enough to remain suspended.

When we replaced PDMS with polyimide, which has amuch higher Youngs modulus (several GPa), the polymermembrane became sti enough to remain stably suspended.Te test structure consisted o a 10 3 100 triangular array osilicon nanorods embedded in a polyimide membrane. oobserve negative reraction in the near-inrared region, around1.5 m, we had to make the silicon nanorods with a diametero 400 nm and spacing o 613 nm; the total device size was5.2 3 61.4 m.

We abricated the device on a 0.35-m-thick undopedpolysilicon layer on top o a 3.0-m-thick silicon dioxide layer.A poly(methyl methacrylate) (PMMA) bi-layer copolymer pho-toresist stack was then exposed via electron-beam lithographyto orm the pattern or the silicon nanorods used to make thephotonic crystal device. Ten, we ormed a 15-nm-thick chro-mium mask by the lit-o process and subsequently etched thesilicon nanorods anistropically by using the CF4/8.75 percentO2 reactive ion etch plasma (RIE).

We then deposited polyimide over the silicon nanorod array

by spin coating and ormed a 400-nm-thick polyimide lm tototally encase the silicon nanorods. Te second-level polyimidemask was ormed using the same PMMA copolymer processand chromium lit-o process and etched anisotropically using100 percent O2 RIE.

Finally, we released the device using a buered oxide etchmethanol release process. Te completed device shows thesilicon-polyimide membrane ater the underlying SiO2 layer hasbeen etched away, leaving the PC matrix intact and suspendedover 3 m o air.

For optical characterizations, we co-abricated a 15-m-wideinput waveguide with the MPC structure. It was wide enough

to provide a plane-wave-like incident eld and make an inci-dent angle between 28 and 108. Light is rst end-re-coupled

into the silicon ridge waveguide rom a ber pigtailed tunablediode laser operating at 1,546 nm. Te scattered light is col-lected by an imaging system that projects the scattered image

onto an inrared vidicon camera.Te plane-wave-like incident eld allows us to measure the

reraction angle and estimate the eective index rom Snells

[ Etched silicon nanorods ]

[ Mechanically tunable photonic crystal ]

(a) SEM o ully abricated MTPC structure along with inputwaveguide or light coupling. (b) Inrared image o light propaga-tion through air (let) and mechanically tunable photonic crystalstructure (right). The reerence sample in the top panel shows

the incident light pattern and the bottom shows negative rerac-tion in the PC structure.

Scanning electron micrographs (SEMs) o (a) a silicon nanorodarray, (b) polyimide membrane containing silicon nanorod arrayand (c) air-suspended silicon-polyimide MTPC structure.

1.0 mm

5.0 mm

10.0 mm

Si pillar array embedded

in polyimide

Si pillar array

embedded in

polyimide

Scatter

block

Scatter block

Si pad

Si padSi pad

Waveguide

Input

waveguideInput

waveguide

Mechanically

tunable PC

Oxide2.0 mm

(a)

(a)

(b)

(b)

(c)


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OPN January 2009 | 45

law. As shown in part (b) o the bottom gure on p. 44, lightlet the ridge waveguide with the PC region absent to givethe prole o the incident eld. Te shape o the exiting waveresembled the lowest-order transverse mode, indicating thatthere had been only small mode coupling that was directedparallel to the input guide.

Te light path inside the PC that bent toward the upperright at an angle greater than the 68 incident wave clearlyexhibited negative reraction. Te optical eld stayed trans-versely conned inside the PC and then diracted ater leaving

the structure. Te angle o the negative reraction showed goodagreement with both the photonic band structure and theFDD simulations.

We used a micromechnical electro-thermal actuator to applythe external mechanical orce needed to mechanically tune thephotonic crystal. Te chevron electro-thermal actuator is anarray o pre-angled narrow beams through which current ows.Te nite resistance o the beams resulted in Joule heating,which in turn led to structural elongation o the beams. Sincethe beam arrays are joined at the center, such a structural elon-gation by individual beams will result in coordinated displace-ment at the center o the beams.

Member

[ References and Resources ]

>> K. Busch and S. John. Phys. Rev. Lett. 83, 967 (1999).

>> M. Notomi. Phys. Rev. B 62, 10696 (2000).

>> C. Luo et al. Phys. Rev. B 65, 201104 (2002).

>> W. Park and C.J. Summers. Opt. Lett. 27, 1397 (2002).

>> S. Xiong and H. Fukshima. J. Appl. Phys. 94, 1286 (2003).

>> W. Park and J.-B. Lee. Appl. Phys. Lett. 85, 4845 (2004).

>> W. Park and C.J. Summers. Appl. Phys. Lett. 84, 2013 (2004).>> C.J. Summers et al. J. Nonlinear Opt. Phys. Mater. 12, 587 (2003).

>> E. Schonbrun et al. IEEE Photon. Techol. Lett. 17, 1196 (2005).

>> M. Tinker et al. J. Vac. Sci. Tech. B 24, 705 (2006).

>> E. Schonbrun et al. Phys. Rev. B 73, 195117 (2006).

>> Q. Wu et al. J. Opt. Soc. Am. B 23, 479 (2006).

>> E. Schonbrun et al. Appl. Phys. Lett. 90, 041113 (2007).

>> M. Roussey et al. J. Opt. Soc. Am. B 24, 1416 (2007).

>> H.-S. Kitzerow et al. Phys. Stat. Sol. (a) 204, 3754 (2007).

>> K. Colinjivadi et al. Microsystem Technologies 14, 1627 (2008).

>> Q. Wu et al. Opt. Express 16, 16941 (2008).

The ully integrated system showing the mechanically tunable

photonic crystal structure in the center and a pair o chevron

electro-thermal actuators or mechanical tuning. Top-let

inset shows the SEM o the photonic crystal structure with a

tapered input waveguide. Bottom-right-corner inset shows the

fnite element modeling o mechanical actuators.

[ The fully integrated system ]

Recently, researchers have proposed that broadband negative indeximaging with minimal chromatic aberrations can be achieved by a gradednegative index PC structure.

Researchers are currently working toward complete integra-tion o a chevron electro-thermal actuator with the air-suspend-ed polymer matrix that encases the hexagonal single crystalsilicon rod array. In order to demonstrate tunable negativeindex imaging, the input waveguide tip was tapered and thusproduced a point-source-like incident eld. Finite elementanalysis showed that the system was mechanically stable andcould be expected to produce controlled mechanical strain.

Te ully integrated system will enable spectroscopic detec-tion in a compact geometry. Te process is based on silicontechnology and compatible with a variety o other devices ormore complex system integration. Te MPC is thereore ahighly promising route or on-chip integrated sensing or detec-tion. Te ability to perorm spectroscopy will greatly enhancesensitivity and specicity. Tis makes MPC a highly desirableplatorm or sensing applications that require portable deviceswith high sensitivity.

Te authors gratefully acknowledge financial support by theNational Science Foundation through grant BES-0608934 andone of us (W.P.) acknowledges the U.S. Army Research Offi ceunder MURI Contract 50432-PH-MUR.

Won Park ([email protected]) is with the department of

electrical and computer engineering, University of Colorado,Boulder, Colo., U.S.A. J.-B. Lee is with the department of electricalengineering, University of Texas, Dallas, Texas, U.S.A.

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