High-Q conical polymeric microcavities

APPLIED PHYSICS LETTERS 96, 013303 共2010兲

High-Q conical polymeric microcavities Tobias Grossmann,1,a兲,b兲 Mario Hauser,1 Torsten Beck,1 Cristian Gohn-Kreuz,1 Matthias Karl,1 Heinz Kalt,1 Christoph Vannahme,2,c兲 and Timo Mappes2,b兲 1

Institut für Angewandte Physik, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Str.1, 76131 Karlsruhe, Germany 2 Institut für Mikrostrukturtechnik, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

共Received 14 October 2009; accepted 6 December 2009; published online 4 January 2010兲 We report on the fabrication of high-Q microresonators made of low-loss, thermoplastic polymer poly共methyl methacrylate兲 共PMMA兲 directly processed on a silicon substrate. Using this polymer-on-silicon material in combination with a thermal reflow step enables cavities of conical geometry with an ultrasmooth surface. The cavity Q factor of these PMMA resonators is above 2 ⫻ 106 in the 1300 nm wavelength range. Finite element simulations show the existence of a variety of “whispering gallery” modes in these resonators explaining the complexity of the measured transmission spectra. © 2010 American Institute of Physics. 关doi:10.1063/1.3280044兴 Polymer microresonators are essential components for the realization of low-cost and large-scale fabricated photonic devices, such as lasers,1–3 filters,4,5 and sensors.6–9 High quality factors 共Q factors兲 in the order of 106 can be achieved by replica-molding silica microtoroids. Such resonators have the major disadvantage of needing a master array of ultrahigh-Q microtoroids in order to attain a high surface quality.10,11 Here we present the fabrication process of high-Q microresonators made of low-loss, thermoplastic polymer poly共methyl methacrylate兲 共PMMA兲, which are directly processed on a silicon substrate. Using this polymer-on-silicon material in combination with a thermal reflow step enables cavities of conical geometry with an ultrasmooth surface. Finite element simulations show that a variety of “whispering gallery” modes 共WGMs兲 exist in these conical microresonators and explain the complexity of the measured transmission spectra. The cavity Q factor of these PMMA resonators is above 2 ⫻ 106 in the 1300 nm wavelength range and can theoretically reach values greater than 107 in the visible.11 The PMMA microcavities are fabricated in a four step process that is applicable for mass production 共Fig. 1兲. In a first step, a 1 ␮m thick PMMA layer 共MicroChem PMMA 950k A7, high molecular weight PMMA dissolved in anisole兲 is spin coated on top of a silicon substrate. The sample is baked at 110 ° C in order to reduce the solvent content. While cooling down the sample, stress is introduced between the PMMA and the silicon substrate due to the difference in the thermal expansion coefficient of both materials. PMMA circles are then directly patterned by UV lithography using deep UV light 共␭ = 240– 250 nm兲 and a quartz-chromium mask or by electron beam lithography 关Fig. 1共a兲兴. For geometrical parameter studies, first samples were fabricated using electron beam lithography. After development 关Fig. 1共b兲兴, the exposed silicon substrate is isotropically etched using

XeF2,12 resulting in freestanding PMMA microdisks on silicon pedestals 关Fig. 1共c兲兴. The measured Q values 共the exact measurement method is described below兲 of these microdisks are above 5 ⫻ 104, which is more than a factor of 4 above the Q factors of polymer microdisks published up to now.13 The dominating loss mechanism is surface scattering caused by the lithographic roughness at the disk periphery, where the WGMs are located. In order to take advantage of the stress in the PMMA layer, a specific thermal reflow step was developed, which allows the reduction of surface roughness and formation of the conical geometry. When the PMMA islands are melted during the reflow process, the liquid photoresist surfaces are pulled into a shape, which minimizes the energy of the system.14 During reflow, one may assume a domination of the surface effects over the influence of gravity for polymer disks with diameters below 100 ␮m standing on a heat conducting inorganic pillar; as for the production of polymer microlenses of diameters below 1000 ␮m, the gravitation effect during standard reflow is negligible.15 By heating the sample for 30 s on a hotplate at a temperature of 125 ° C slightly above the glass transition tem(a) Exposure

(b) Development

PMMA

Silicon

(c) XeF2 etch

(d) Reflow

a兲

Electronic mail: [email protected]. Also at Institut für Mikrostrukturtechnik, Karlsruhe Institute of Technology 共KIT兲, 76128 Karlsruhe, Germany. c兲 Also at Lichttechnisches Institut, Karlsruhe Institute of Technology 共KIT兲, 76128 Karlsruhe, Germany. b兲

0003-6951/2010/96共1兲/013303/3/$30.00

FIG. 1. 共Color online兲 Process steps for fabricating high-Q conical microcavities. After exposure 共a兲 and development 共b兲 of PMMA, the silicon substrate is etched using XeF2 共c兲. A thermal reflow 共d兲 then forms the conical geometry of the cavities.

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© 2010 American Institute of Physics

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5 µm

Transmitted Intensity (arb. u.)

(a)

0.8

0.6

0.4

0.2

ΔλFSR=9.36 nm 6

Q=2x10

1321.83 1321.85

(c)

(b)

10 µm

0.0 1305

10 µm

FIG. 2. Scanning electron micrographs of polymer microcavities. The images show a conical resonator with a maximum diameter of 40 ␮m 关共a兲 and 共c兲兴 and a microdisk 共b兲 of 47 ␮m diameter fabricated with electron beam lithography. The Q factor of the conical microresonator is 2 ⫻ 106.

perature of PMMA, heat is transported well defined through the silicon pedestal to the center of the cavity. The temperature of the PMMA, being above the glass transition, allows the surface tension in the PMMA layer to smoothen the cavity surface.14 In addition, the glass transition state enables the formation of a conical resonator by allowing the PMMA surface tension to relax on the upper side of the disk, while the central part of the lower side is fixed by the pedestal. This process is self-quenching, as a further treatment on the hotplate has no effect. Figure 2 shows micrographs of the PMMA microdisk 关Fig. 2共b兲兴 and a microcone 关Figs. 2共a兲 and 2共c兲兴 before and after reflow, respectively. One can clearly see the smooth surface and the conical geometry formed by the surface tension during the reflow. Measurement of the modal structure and quality factor of the conical resonators was performed in the 1300 nm wavelength region. WGMs of the cavity were efficiently excited by coupling a single-mode, tunable, external-cavity laser 共linewidth 200 kHz兲 to a tapered optical fiber waveguide. These fibers are fabricated by heating and stretching a standard optical fiber 共SMF-28兲.16 Typical taper diameters are about 1 ␮m. In order to achieve precise alignment of tapered fiber and microresonator, the tapered fiber was positioned on a five axis positioning stage with a resolution of 20 nm and monitored by two cameras from the top and the side. While bringing the tapered section of the fiber close to the resonator, the tunable laser was continuously swept between 1300 and 1350 nm. The transmitted intensity was monitored using a photodiode. The resonator-waveguide gap was adjusted until the cavity resonances appeared as sharp dips in the transmission spectrum and could be measured. Figure 3 shows a typical transmission spectrum. The laser power was kept below several microwatts, avoiding thermal distortion of the resonances, due to field buildup in the cavity and the one order of magnitude larger thermo-optic coefficient of PMMA compared to SiO2.17 A further influence on the measurements was found to be the relative humidity of the air. It is known that with increasing humidity, water vapor is distinctly absorbed by PMMA.18 The strong optical

1310

1315

1320 1325 1330 Wavelength (nm)

1335

1340

FIG. 3. 共Color online兲 Transmission spectrum of a tapered fiber optically coupled to a conical resonator. Simulations show that the deep peaks are fundamental TE and TM modes of the resonator. They are mainly accompanied by higher order radial modes of both polarizations. The measured free spectral range is 9.36 nm.

absorption of water in the 1300 nm wavelength region then leads to reduced quality factors. The Q factor is determined by measuring the linewidth 共full width at half maximum兲 of the Lorentzian-shaped dips in the undercoupled regime.19 Measurements yield quality factors above 2 ⫻ 106. The Q factors are as high as in replicamolded polymer microtoroids,10 while the conical microresonators take advantage of an inexpensive, large-scalecompatible fabrication technique not needing a master array of ultrahigh-Q silica microtoroids for replica molding. Due to the introduced effective reflow step, the Q values are two orders of magnitude higher than in the PMMA microdisks and are one order of magnitude higher than in other polymer microcavities fabricated by direct lithography,4 further benefiting from a considerably smaller mode volume, which is a figure of merit, e.g., in biosensing devices.20 Due to an ultrasmooth cavity surface and efficient coupling by a tapered fiber, the dominating loss mechanism in the conical microcavities is material absorption rather than surface scattering.11 The absorption in the infrared wavelength region is mainly caused by vibrational absorption bands of PMMA.21 For a better understanding of the measured modes and for visualization of the spatial distribution of the excited WGMs in the conical microcavities, finite element simulations were performed with the eigensolver JCMResonance 共part of the simulation software package JCMSUITE兲. Computational costs are reduced by taking advantage of the rotational symmetry of the resonator. The eigenvalues 共frequencies兲 are thus computed using cylindrical coordinates in a two-dimensional system by solving Maxwell’s equations on a finite number of elements, into which the computational domain is divided 共triangulation兲 before the computation starts. Further information about the algorithm and the adaptive refinement technique of the mesh has been presented by Pomplun et al.22 The mode structure of the conical microcavity is highly complex and each mode is characterized by the polarization of its electromagnetic field, the azimuthal mode number m 共describing the integer number of wavelengths in the plane of the cavity in direction of the unit vector e
兲, ␾ the axial mode number l 共number of field maxima minus 1 in e
z direction兲 and the radial mode number n 共number of field

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êz êΦ

êr TE0,0 λ= 1526.11 nm

TE1,0 λ= 1442.31 nm

TE2,0 λ= 1364.25 nm

TE3,0 λ= 1337.47 nm

TE4,0 λ= 1295.71 nm

TE2,1 λ= 1325.22 nm

FIG. 4. 共Color online兲 Simulated mode structure of a conical microcavity. The intensity distribution and resonance wavelength of the WGMs are calculated. The azimuthal mode number m of the presented WGMs is 105.

maxima minus 1 in e
r direction兲. The used nomenclature of m m or TMn,l depending on whether the field the modes is TEn,l strength in radial or axial direction, respectively, dominates. Figure 4 exemplarily shows the calculated intensity distribu105 modes in the conical microresonators. The tions of the TEn,l spectral positions of the resonances are between 1290 and 105 mode is located at the rim 1530 nm. The fundamental TE0,0 of the cavity and has the highest resonance wavelength. As the radial order of the modes increases, the maximum of intensity moves toward the center of the cone. In the analyzed wavelength region, only one higher order axial mode 105 兲 for each polarization was found. This is ac共TE/ TM2,1 counted for the dimension and the refractive index of the cavity. As the thickness of the resonator is in the order of the wavelength and the refractive index contrast between PMMA and air is only approximately 0.5, further higher axial modes are not confined in the cavity. The free spectral range 共describing the spectral distance between two adjacent azimuthal modes兲 was found to be 9.4 nm and perfectly fits to the measured free spectral range denoted in Fig. 3. Comparison of the simulation results with the measurements clearly indicates that the modal structure in the conical microcavities is dominated by the fundamental mode and higher order radial modes of both polarizations. We have fabricated conical microcavities made of PMMA, directly processed on a silicon substrate by combining direct lithographic patterning with an effective thermal reflow step. Finite element simulations are in good agreement with measured transmission spectra and show that a variety of WGMs can efficiently be excited in the coneshaped microresonators. In a future step, additional gain media such as dyes or quantum dots can easily be integrated in the microcavities with the presented fabrication method. The robustness of PMMA to laser radiation23 and the high Q’s of the resonators will enhance the progression of low-threshold

polymeric microlasers. Thus, the inexpensive fabrication method combined with potential Q factors above 107 make these resonators promising candidates for the development of versatile, low-cost, and ultracompact photonic devices for research and technology. This work has been supported by the DFG Research Center for Functional Nanostructures 共CFN兲 Karlsruhe 共Project No. A5.4兲 and by a grant from the Ministry of Science, Research and the Arts of Baden-Württemberg 共Grant No. Az:7713.14-300兲. T.M.’s Young Investigator Group 共YIG 08兲 received financial support from the Concept for the Future of the Karlsruhe Institute of Technology 共KIT兲 within the framework of the German Excellence Initiative. M.H., T.B., and C.V. acknowledge financial support from the Karlsruhe School of Optics and Photonics 共KSOP兲. Furthermore, we acknowledge JCMwave GmbH for academic use of their JCMSUITE. 1

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