Two-dimensional photonic crystal Mach–Zehnder interferometersM. H. Shih, W. J. Kim, Wan Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K.Marshall Citation: Applied Physics Letters 84, 460 (2004); doi: 10.1063/1.1642758 View online: http://dx.doi.org/10.1063/1.1642758 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/84/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Ultrafast all-optical switching in AlGaAs photonic crystal waveguide interferometers Appl. Phys. Lett. 95, 141108 (2009); 10.1063/1.3236542 Photonic crystal Mach-Zehnder interferometer based on self-collimation Appl. Phys. Lett. 90, 231114 (2007); 10.1063/1.2746942 A temperature modulation photonic crystal Mach-Zehnder interferometer composed of copper oxide high-temperature superconductor J. Appl. Phys. 101, 084502 (2007); 10.1063/1.2714649 Losses and transmission in two-dimensional slab photonic crystals J. Appl. Phys. 96, 4033 (2004); 10.1063/1.1790068 Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals Appl. Phys. Lett. 82, 1009 (2003); 10.1063/1.1545167

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Two-dimensional photonic crystal Mach–Zehnder interferometersM. H. Shih,a) W. J. Kim, Wan Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien,and P. D. DapkusDepartment of Electrical Engineering–Electrophysics, University of Southern California, Powell Hallof Engineering, 3737 Watt Way, Los Angeles, California 90089-0271

W. K. MarshallEpilimnion Technology Consulting, P.O. Box 3322, South Pasadena, California 91031-6322

~Received 9 September 2003; accepted 24 November 2003!

Mach–Zehnder interferometers were fabricated from suspended membrane photonic crystalwaveguides. Transmission spectra were measured and device operation was shown to be inagreement with theoretical predictions. ©2004 American Institute of Physics.@DOI: 10.1063/1.1642758#

Planar photonic crystal waveguide~PCWG! technologyhas the potential to be a fundamental building block for fu-ture optical integrated circuits. Some of this potential arisesfrom the ability to form small turning radius waveguidebends and wide angleY branches1 leading to the possibilityof dense device integration. There have been many experi-mental demonstrations of two-dimensional photonic crystalwaveguides recently including quantitative optical lossmeasurements.2–4 However, there have been few demonstra-tions published to date of photonic crystal waveguide bendsand branches.5–7 In this letter, we report on a demonstrationof Mach–Zehnder interferometers formed in two-dimensional photonic crystals.

In this work we have fabricated Mach–Zehnder interfer-ometers in two-dimensional photonic crystals with a range ofpath length differences between the arms of the interferom-eter. We expect therefore that the intensity transmittedthrough the interferometers will exhibit oscillations in thetransmitted intensity as a function of the optical frequencywith a period that depends on the path length difference andthe propagation coefficient. The finite element method wasused to calculate the band structure of the even guided modefor the PCWGs. Figure 1~a! shows the calculated dispersionrelations of guided modes of waveguides with ratios of thehole radius to lattice constant,r /a, of 0.27, 0.30, and 0.33.Only the lowest order guided mode is included in this figure.In this work, we intend to operate the fabricated Mach–Zehnder interferometers in the spectral region in which thereis very little chromatic dispersion. This simplifies the dataanalysis because we expect a fixed propagation coefficientand therefore a fixed oscillation period in the transmittedintensity over the wavelength range of operation. From thedata in Fig. 1~a!, for anr /a value of 0.3 and a lattice constantvalue of 420 nm, this low chromatic dispersion region cor-responds to the wavelength range of 1500–1550 nm andpropagation coefficient in the range of 0.30–0.35. The ex-perimental data in each case was taken in this low chromaticdispersion region. The group index can be obtained by dif-ferentiating the dispersion relation in Fig. 1~a! and is plottedas a function of normalized wavelength in Fig. 1~b!. Included

in this figure are traces for different values ofr /a. The r /aratio is one of the least tightly controlled lattice parametersin our fabrication process. We have collected data from anumber of devices. Each of these devices has a constantr /a

a!Electronic mail: minhsius@usc.edu

FIG. 1. ~a! Finite element method~FEM! band structure calculation ofPCWG. The waveguide modes are indicated by solid lines, while the pho-tonic crystal cladding band edge states do not have lines through them.~b!Group index from FEM band structure calculation of PCWG with differentr /a, 0.27, 0.30, and 0.33.

APPLIED PHYSICS LETTERS VOLUME 84, NUMBER 4 26 JANUARY 2004

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value. The range ofr /a values of these devices is between0.28 and 0.32. Based on the data in Fig. 1~b!, we thereforeexpect that we should experimentally observe values of thegroup index between about 5 and 7.

The Mach–Zehnder interferometers were formed by lin-ear defects in a two-dimensional triangular lattice photoniccrystal that was patterned into a suspendedIn0.74Ga0.26As0.56P0.44 membrane. This layer was depositedon an InP substrate by metalorganic chemical vapor deposi-tion. The photonic crystal was then defined by electron-beamlithography in 2% polymethylmethacrylate~PMMA!. Afterdeveloping the resist, the PMMA was used as a mask totransfer the pattern into a Au/Cr layer using an Ar1 beammilling step. This metal layer was then used as a mask in anelectron cyclotron resonance~ECR! etch to transfer the pat-tern into the semiconductor. The ECR etch was done using aCH4 /H2 /Ar gas chemistry with flow rates of 38.3/24.2/12.0sccm respectively. The suspended membrane was formed us-ing a 4/1 HCl/H2O wet chemical etch at 0 °C for 8–12 min.8

Open areas were defined outside of the photonic crystalwaveguide cladding in these devices in order to facilitate theformation of suspended membranes. Devices having pathlength differences between the two arms of 0, 75, and 121mm were fabricated for this work. The devices reported herehave a lattice constant,a, of 420 nm and hole radius to latticeconstant ratio,r /a, of 0.28–0.32. The interferometers had 15periods of photonic crystal cladding on each side of thewaveguide core. Figure 2 shows a scanning electron micro-scope~SEM! image of a fabricated PCWG Mach–Zehnderstructure near one of the Y branches. The fabricated PCWGMach–Zehnder structures were cleaved at both ends. Figure3 shows SEM micrographs of three such devices beforecleaving.

A lensed fiber was used to launch transverse electric po-larized light from a tunable laser into the PCWG Mach–Zehnder interferometers, and a cleaved single mode fiberwas used to collect the output signal. We observed the ex-pected oscillations in the transmitted intensity as the wave-length of the tunable laser was varied. Figure 4 shows theFourier transform of the experimental transmission data as afunction of the inverse optical wavelength, 1/l, for deviceswith path length differences of: 0mm ~a!, 75 mm ~b!, and121mm ~c!. The unit associated with the transformed data ismicrons and the abscissas are scaled so that the values rep-

resent the product of the group index and the path lengthdifference,DL, of the Mach–Zehnder interferometer. Peaksin the Fourier transforms corresponding to oscillations intransmitted intensity due to Mach–Zehnder interferencesshow up clearly at the expected locations. Figures 4~b! and4~c! show the strong contributions at 502 and 637mm, whichcorrespond to the group indices ofng56.7 and 5.3, for pathlength differences of 75 and 121mm, respectively. The groupindices obtained from the measured transmission spectra fallwithin the range of values predicted by the finite-element-method results in Fig. 1~b!. There is also a second peak in theFourier spectrum shown in Fig. 4~c!. This peak at 2230mmis attributed to the Fabry–Pe´rot mode that exists in the sub-strate between the cleaved facets of the Mach–Zehnder in-terferometer. We have verified that this peak originates from

FIG. 2. SEM micrograph showing the part of the Mach–Zehnder structurenear one of the Y branches.

FIG. 3. SEM images of the Mach–Zehnder PCWG with path-length differ-ences of:~a! 0 mm, ~b! 75 mm, and~c! 121 mm.

461Appl. Phys. Lett., Vol. 84, No. 4, 26 January 2004 Shih et al.

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propagation through the substrate by lowering the fiber usedto collect the transmitted intensity below the suspendedmembrane. Under these conditions, the peak at 2230mmremains while the peak at 637mm disappears. The symmet-

ric Mach–Zehnder was also fabricated and the transmittedintensity as a function of optical frequency was measured.The Fourier transform of the observed transmission spectrumis shown in Fig. 4~a!. In these data we observed no oscilla-tions as evidenced by the fact that there are no significantpeaks in the Fourier transform. Resonances formed by reflec-tions from the photonic crystal waveguide junctions and thecleaved facets were not observed in any data. We expect,based on finite-element method transmission calculations,that the transmission through a photonic crystal Y branch isabout 25% over the spectral region considered here and thatthe transmission through a photonic crystal waveguide bendis about 99% in this spectral range.9 We did not observeresonances between the Y branches and the facets due to thelow quality of the cleaved facets of the devices used in thisstudy.

In summary, we have demonstrated transmission throughMach–Zehnder interferometers formed from single-line de-fects in suspended membrane two-dimensional photoniccrystal waveguides. This has been done in a series of deviceswith varying path length differences. We have shown that theoscillations in the transmitted intensity as a function of opti-cal frequency are due to the interference between two arms.

This study is based on research supported by the De-fense Advanced Research Projects Agency~DARPA! underContract Nos. F49620-02-1-0403 and 96428CDVOS and bythe National Science Foundation under Grant No. ECS0094020. Computation for the work described in this letterwas, in part, supported by the University of Southern Cali-fornia Center for High Performance Computing and Commu-nications.

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FIG. 4. Fast Fourier transform spectra of the transmitted intensity throughMach–Zehnder PCWGs with branch-path differences:~a! 0 mm, ~b! 75 mm,and ~c! 121 mm.

462 Appl. Phys. Lett., Vol. 84, No. 4, 26 January 2004 Shih et al.

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