Polarization-resolved far-field measurement of single-cell photonic crystallasing modes

Ju-Hyung Kang,1 Sun-Kyung Kim,1 Kwang-Yong Jeong,2 Yong-Hee Lee,2

Min-Kyo Seo,2,3,a� and Hong-Gyu Park1,a�

1Department of Physics, Korea University, Seoul 136-701, Republic of Korea2Department of Physics, KAIST, Daejeon 305-701, Republic of Korea3KAIST Institute for the NanoCentury, KAIST, Daejeon 305-701, Republic of Korea

�Received 14 March 2011; accepted 7 May 2011; published online 26 May 2011�

This paper reports the unambiguous identification of lasing modes observed in a single-cell photoniccrystal cavity using a solid angle scanning system. The polarization-resolved far-field measurementsshowed distinctive features of each mode and distinguished it from the other modes in contrastto conventional optical characterization methods. Monopole, quadrupole, and hexapole lasingmodes were observed and identified, showing good agreement with numerical simulations. Ourunderstanding of the lasing modes will be useful for determining practical applications as promisinglight sources in ultracompact photonic integrated circuits. © 2011 American Institute of Physics.�doi:10.1063/1.3595313�

Photonic crystals enable strong photon confinement inan ultrasmall region.1,2 It is particularly important for high-performance optical applications, such as low-thresholdlasers3–5 and high-efficiency single photon sources,6 to ob-tain the desired field distribution in a photonic crystal cavity.For example, a triangular-lattice single-cell photonic crystalcavity can support four resonant modes; monopole, quadru-pole, hexapole, and dipole modes.7 Each mode has its ownfield profile. The monopole and hexapole modes with a cen-tral intensity node are useful for current injection by placinga central post underneath the photonic crystal slab becausethe post at the node site does not cause an appreciable in-crease in optical loss.3,8 On the other hand, the dipole modewith a central intensity antinode is useful for demonstrating asingle photon source by positioning a single quantum dot atthe center of the cavity.9 Therefore, the excitation and iden-tification of a desired cavity mode should be achieved clearlyand efficiently.

The resonant spectra, mode profiles and net polarizationstates were measured using an objective lens-based system,and compared with numerical simulations to identify andcharacterize the lasing mode.7 These conventional methodsare useful but they often provide indirect and limited infor-mation for mode identification. A simple comparison of theresonant spectra with numerical simulations is efficient onlyin an ultrasmall cavity supporting spectrally well-separatedresonant modes. Furthermore, slight modification of the cav-ity structure or small fabrication imperfections tend to distortthe optical features of the modes, such as the resonant fre-quencies and net polarization states.10 Therefore, the above-mentioned optical measurements should be performed to-gether to minimize ambiguity. Although near-field scanningoptical microscopy �NSOM� can obtain the direct electro-magnetic field distribution of the resonant mode, perturba-tion of the mode by the NSOM tips cannot be avoided.11 Inthis study, to identify the cavity mode manifestly and effi-ciently, we measured polarization-resolved far-field emission

patterns using a solid angle scanning system. This powerful,stand-alone method, which was also used for characterizingthe far-field emission and polarization of photonic crystallasing modes,10 provides reliable and natural information indistinguishing the monopole, quadrupole and hexapolemodes in a single-cell photonic crystal cavity.

Figure 1�a� shows a fabricated single-cell photonic crys-tal cavity. Periodic air holes were defined in a freestandingInGaAsP slab with a thickness �t� of 280 nm, in which threepairs of InGaAsP quantum wells �QWs� with a photolumi-nescence �PL� peak at 1.55 �m were embedded. The sixnearest neighbor holes around the cavity were reduced andmoved outward to excite the monopole, quadrupole, andhexapole modes efficiently.7 Three-dimensional �3D� finite-difference time-domain �FDTD� simulation shows the elec-tric energy distributions of these high-quality �Q� resonantmodes �Fig. 1�b��. The optical properties of each mode canbe modified by changing the lattice constant and radii of thenearest neighbor holes slightly.3–5 In particular, the resonantwavelength of a mode can be controlled and overlapped wellwith the PL of the QWs to achieve rich gain. Indeed, photo-

a�Authors to whom correspondence should be addressed. Electronic ad-dresses: minkyo_seo@kaist.ac.kr and hgpark@korea.ac.kr.

FIG. 1. �Color online� �a� SEM image of a fabricated photonic crystal cav-ity. The scale bar is 1 �m. �b� Calculated electric energy distributions���E�2� of the monopole �left�, quadrupole �middle�, and hexapole modes�right� in the photonic crystal cavity with r=0.35a, rm=0.25a and t=0.5a,where a is the lattice constant.

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nic crystal cavities with optimized structural parameters toexcite each mode were fabricated, and optically pumpedsingle-mode lasing actions from them were demonstrated�Fig. 2�b��.

To examine the lasing properties, we used the far-fieldmeasurement setup as shown in Fig. 2�a�. A pulsed 980 nmpumping laser diode �1 MHz repetition rate and 10 ns pulseduration� was placed below the sample to optically excite thephotonic crystal lasing modes through the transparent bottomInP substrate.10 The PL spectra were measured on the top ofthe sample using an optical fiber. The far-field emission pat-terns of the lasing modes were measured over the entire up-per hemisphere by rotating both the photonic crystal sampleand photodetector. The photodetector was scanned from�90° to 90° in the polar ��−� direction, and the sample wasrotated from 0° to 180° in the azimuthal ��−� direction. Alinear polarizer was placed in front of the photodetector toexamine polarization-resolved emission patterns. The �- and�-polarization components were obtained with rotating thepolarizer in the directions parallel and normal to the plane inwhich the photodetector was moved, respectively. The dis-tance between the sample and photodetector was 30 cm. Toclearly understand the raw data obtained in the curved sur-face, the measured intensities over the hemisphere were pro-jected into a two-dimensional flat surface using the followingmapping equations: x=� cos � and y=� sin �.10 The pro-jected images were then plotted using a polynomial interpo-lation.

Several lasing modes were measured from the fabricatedphotonic crystal cavities. Figure 2�b� shows the above-threshold lasing spectra of the monopole �black�, quadrupole

�red�, and hexapole modes �blue�, respectively. The properstructural parameters, lattice constant �a�, radius of the regu-lar holes �r� and radius of the nearest neighbor holes aroundthe cavity �rm�, were used to spectrally match the resonantwavelength of the mode with the PL peak of the QWs. As aresult, the desired single-mode lasing was achieved in eachphotonic crystal cavity with a lasing wavelength of 1500–1550 nm, which is the maximum gain region of the QWs.

The measured far-field emission patterns of the mono-pole, quadrupole and hexapole lasing modes were shown inFigs. 3�a�–3�c�, respectively. The emission patterns were ob-served from the three photonic crystal cavities yielding thelasing spectra of Fig. 2�b�. The left panel shows the totalintensity distribution of each mode, and the middle and rightpanels show the �- and �-polarization components of theintensity distribution, respectively. We note that total inten-sity distributions are quite similar for all three modes, show-ing central intensity nodes and nearly zero net polarizationstates to the vertical direction.7 Slight perturbation in thetotal intensity distributions due to fabrication imperfection,washed out the rotational symmetric shapes of the quadru-pole and hexapole modes. Only the monopole mode couldpreserve the symmetric shape completely due to relativelylow electric field intensity in the nearest neighbor holesaround the cavity as shown in Fig. 1�b�. In addition, thesefar-field intensity distributions were similar to the mode im-ages captured by the infrared camera using a conventionalobjective lens.11 Indeed, it is not straightforward to distin-guish one lasing mode from the others only by the totalintensity distributions, particularly if the modes have highrotational symmetry.

On the other hand, the �- and �-polarization-resolvedfar-field emission patterns offer distinctive features of themodes and rich spatial information for mode identification.For example, the monopole mode shows negligible field in-tensity in the �-polarization component but fully stores the

FIG. 2. �Color online� �a� Schematic diagram of the far-field measure-ment setup. �b� Measured lasing spectra from the photonic crystalcavities. The fabricated structural parameters are as follows:�a ,r ,rm�= �515 nm,0.31a ,0.19a�, �490 nm,0.38a ,0.26a�, and �500 nm,0.35a ,0.25a� for the monopole �1509 nm�, quadrupole �1519 nm�, andhexapole modes �1547 nm�, respectively.

FIG. 3. �Color online� Measured far-field emission patterns of �a� monopole,�b� quadrupole, and �c� hexapole modes. The emission patterns were mea-sured from the photonic crystal structures fabricated in Fig. 2�b�. The leftpanel is the total intensity distribution. The middle and right panels are the�- and �-polarization components of the intensity distribution, respectively.

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total energy in the �-polarization component �Fig. 3�a��. Themonopole mode with such a �-polarized doughnut shapecan be used for optical manipulation of low index particles.12

In quadrupole mode, �- and �-polarization componentsshow recognizable four intensity lobes, and the lobes in the�-component are rotated by 45° relative to those of the�-component �Fig. 3�b��. In addition, the hexapole mode isclearly distinguishable from the other modes. As shown inFig. 3�c�, the hexapole mode has six intensity lobes in the �-and �-polarization-resolved far-field patterns owing to itssixfold symmetry. These measurements demonstrate thateach mode has unique �- and �-polarized far-field intensityprofiles as a result of either constructive or destructive inter-ference of the near-field profiles.13 Accordingly, even if asimilar total intensity distribution and polarization state aremeasured from the modes, each lasing mode can be identi-fied unambiguously by the polarization-resolved far-fieldemission patterns.

To better understand the experimental results, the far-field emission patterns were calculated in the single-cell pho-tonic crystal cavities using a 3D FDTD simulation �Fig. 4�.The near-field distributions were first calculated, and the far-field patterns were then transformed from the near-field onesusing a fast Fourier transform algorithm.13,14 The calculatedpolarization-resolved far-field patterns of the monopole,

quadrupole, and hexapole modes were shown in Figs.4�a�–4�c�, respectively. The structural parameters of the fab-ricated samples shown in Fig. 3 were used for this simula-tion. The �- and �-polarization components were normalizedto the maximum intensity of the total intensity distribution.Note that these simulation results show agreement with themeasured ones. In particular, for the quadrupole and hexa-pole modes, the angular positions of the intensity lobes aswell as the number of lobes in the simulations agree wellwith those of the measurements. Therefore, the FDTD simu-lations strongly support that inherent optical properties of alasing mode can be fully investigated in the polarization-resolved far-field measurements.

In summary, unambiguous identification of the lasingmodes in a single-cell photonic crystal cavity was demon-strated from polarization-resolved far-field measurements.The distinguishable, characteristic features of the monopole,quadrupole, and hexapole modes were observed, whichshowed good agreement with the numerical simulations. Thispolarization-resolved far-field measurement is expected to beused for the precise and immediate analysis of an ultrasmalloptical system, such as a plasmonic nanoantenna.15

H.-G.P. acknowledged the support of this work by Cre-ative Research Initiatives �Grant No. 2011-0000419� ofNRF/MEST. Y.-H.L. acknowledged the support of this workby NRF/MEST �Grant No. 2007-0093863�.

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FIG. 4. �Color online� Calculated far-field emission patterns of �a� mono-pole, �b� quadrupole, and �c� hexapole modes. The structural parameters ofFig. 2�b� were used in the FDTD simulation. The refractive index and thick-ness of the InGaAsP slab were 3.2 and 280 nm, respectively.

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