Spectroscopy of photonic molecular states in

Spectroscopy of photonic molecular states in supermonodispersive bispheres Seungmoo Yang* and Vasily N. Astratov† Department of Physics and Optical Science, Center for Optoelectronics and Optical Communications, University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, North Carolina 28223-0001, USA ABSTRACT Strong coupling between whispering gallery modes (WGMs) is studied in polystyrene bispheres by using spatially resolved spectroscopy. The supermonodispersive pairs of spheres (size deviation >104) of individual resonances integrated on the same chip. This includes patterned semiconductor microcavities15, photonic crystal cavities16-18, and microrings19-21. Due to controllable dispersion relations for photons these structures can be used for developing delay lines, spectral filters and sensor devices. Although theoretically coupled cavity structures can provide almost lossless optical transport4 in the pass bands under condition κ>>1/Q, where κ – is a coupling constant, this is only true under assumption that the cavities and their coupling conditions are identical. In real physical structures the disorder22-24 becomes to be a major factor of optical losses. This remains true even for structures obtained by the best semiconductor technology21 such as CMOS where the random variations of the individual cavity frequencies are typically limited at δ~0.1% over the millimeter scale distances. For such structures the losses ~ 0.3 dB per microring have been reported21 for a chain of 100 coupled microrings. From the time of initial proposal4 of CROW devices it has been well recognized that there is an alternative way of building such structures based on using spherical building blocks. Conventional technologies of fabrication of * †

[email protected]; phone 1 704 687-8297; fax 1 704 687-8197; http://physics.uncc.edu/people/graduates/ [email protected]; phone 1 704 687-8131; fax 1 704 687-8197; http://maxwell.uncc.edu/astratov/astratov.htm Laser Resonators and Beam Control XI, edited by Alexis V. Kudryashov, Alan H. Paxton, Vladimir S. Ilchenko, Lutz Aschke, Proc. of SPIE Vol. 7194, 719411 · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.821753

Proc. of SPIE Vol. 7194 719411-1

microdisks, rings and toroids are not easily compatible with 3D integration of cavities whereas the microspheres can be assembled in arbitrary 3D structures. In addition the microspheres are characterized with extremely high Q factors of whispering gallery modes (WGM)25-28 (>104 for 4 µm spheres and up to 1010 for submillimeter spheres). The inexpensive microspheres can be obtained from different materials with different indices of refraction such as silica (index 1.45), PMMS (1.48), polystyrene (1.59), melamine resin (1.68), titania (~2.0), and even silicon29 (~3.5). The versatility of structures formed by microspheres stimulated studies of optical coupling phenomena in bispheres30-36, linear chains37-40, 2D clusters41,42 and 3D crystal structures43,44. Particularly interesting results have been obtained in the area of basic studies of optical transport properties of microsphere resonator circuits where two novel concepts were proposed. The first concept concerns the mechanism of transport of WGMs in 2D and 3D coupled cavity systems with the size disorder. It was argued44 that in such systems the optical transport can be considered based on an analogy with the mathematical percolation theory45,46 where the WGM coupling efficiencies play the part of the optical bonds connecting the microspheres. Another concept is connected with the focusing properties of such chains of spheres which can be considered as periodically coupled thick lenses. It has been shown47-49 that a single sphere can focus plane waves into tiny spots termed “photonic nanojets”. In chains of spheres such photonic nanojets can be periodically reproduced along the chain50 giving rise to so-called “nanojetinduced modes”51-54 with progressively smaller nanojet sizes and extremely small propagation losses. As a result of these studies microsphere resonator circuits (MRCs) emerged as an interesting alternative way of developing CROW structures suitable for 3D integration of resonators. The technology of MRCs, however, has been challenged by several problems. First, a supermonodispersive selection of spheres with δ1/Q requires a detailed knowledge of the coupling constant for WGMs in spheres with different sizes, indices, etc. Although some measurements of κ have been performed30,32,33 this parameter has not been systematically studied in a broad range of spheres’ sizes. Finally, MRCs are assembled on a substrate which represents an asymmentric boundary condition for WGMs. The substrate plays a very important role in the WGM transport phenomena causing a significant leakage in the substrate for some of the modes. In this work we study a bispherical system on a substrate as the simplest building block of MRCs. We selected bispheres with the size uniformity ~0.03% on the basis of spectroscopy using their uncoupled WGM peaks’ positions. By using novel geometries of capturing light by the imaging spectrometer we observed clear spectral signatures of strong coupling between WGMs for bispheres with the mean sizes from 2.9 to 10 μm. In a specific geometry we observed unusual and characteristic kites in the spectral images of such spheres which allow an unambiguous relating of coupled split components to their uncoupled WGM eigenstates. In many cases such kites simplify the interpretation of the dense spectral images of bispheres. We quantified κ for WGMs located in the equatorial plane of spheres parallel to the substrate which play the most important role in the optical transport properties of MRCs. The results show the feasibility of achieving a coherent WGM-based optical transport with small losses in more complicated MRCs.

2. RESULTS AND DISCUSSION 2.1. Single sphere on a substrate We begin with a brief summary of the case of a single sphere on a substrate56. Generally, WGMs in spherical cavities are characterized27,28 by radial n, angular l, and azimuthal m quantum numbers and the polarizations (TE - transverse electric and TM - transverse magnetic field modes). The radial number indicates the number of peaks in the radial direction of the sphere. The two angular momentum numbers l and m are the number of modal wavelengths that fits into the circumference of the equatorial plane and the number of field maxima within π azimuthal angle, respectively. A single sphere on the substrate is rotationally invariant around normal to the surface Z playing the part of the polar axis. In this case the fundamental WGMs with m=l are defined56 in the equatorial plane of spheres parallel to the substrate, as illustrated in Fig. 1 (a). Such fundamental modes have the highest quality (Q) factors due to the fact they are separated from the surface of substrate by the radius of the sphere. In contrast, the modes with m0.3 μm) cavities. In a strong coupling regime (d=0) the WGM hybridization effects in the presence of the substrate require additional theoretical studies. In this work we will assume that the same WGM eigenstates determined by the substrate contribute to the formation of such molecular states.


(a) m=- l

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Fig. 2. (a) A schematic of two spheres on a glass substrate separated by a distance d. It illustrates the WGM eigenstates with m=±l determined by the substrate. (b) Emission spectrum of a green fluorescent 5.0 μm sphere at the ~0.5 μm wide central section in the sphere equatorial plane with TEnl and TEnl WGM peaks indentified. (c) Emission spectral image obtained from two selected nominally 5 µm spheres separated by 3.5 µm gap on a substrate. The inset illustrates the geometry of collection of light. The spectrum in Fig. 2 (b) corresponds to the top sphere. (d) Same spheres are in the contact position. The substrate is rotated by 900 to provide optical access in the equatorial plane of bispheres, as schematically shown in the inset. A large number of additional bright spots at the edges and center of the spectral image of bisphere are due to bonding and antibonding photonic molecular states. Note that in many cases these peaks are superimposed or overlapped that complicates their interpretation.

In order to experimentally study optical coupling phenomena we selected resonant pairs of cavities using spectroscopy and micromanipulation, as illustrated in Fig. 2 (c) for two nominally 5 µm spheres separated by 3.5 µm gap on the substrate. The hydraulic micromanipulators connected with a tapered fiber provided accurate control of the positions of spheres. The fluorescence (FL) excitation was provided at 460–500 nm by a mercury lamp with intensity below the threshold for lasing WGMs. The spatially resolved spectroscopy was performed in an inverted IX-71 Olympus microscope coupled to an imaging spectrometer. As schematically shown in the inset of Fig. 2 (c) the collection of light was provided through the substrate similar to that in Fig. 1 (b). The spectral images in Fig. 2 (c) show that the WGM peaks are aligned very well in such uncoupled cavities. The FL spectrum of one of these photonic “atoms” measured at ~0.5 µm wide top section in the top sphere’s equatorial plane with TEnl and TMnl WGM peaks is presented in Fig. 2 (b). The shifts of the WGM peaks positions for two selected spheres in Fig. 2 (c) are smaller than the linewidths of the corresponding resonances. Such level of size uniformity of cavities (δ~0.03%) exceeds that achievable by conventional techniques of fabrication of microrings or microdisks integrated on the same chip. In our work this was achieved due to an individual inspection of tenths of commercially available microspheres (Duke Scientific, Inc.) with the initial ~1-3% size dispersion.


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Fig. 3. (a) SEM image of a supermonodispersive bisphere assembled near the cleaved edge of the substrate. (b) Geometry of the experiment with the collection of light along the axis of bisphere with the slit oriented perpendicular to the substrate. (c) Spectral image illustrating unusual and characteristic kites occurring near each WGM resonance. For clarity the kites occurring near the second order TM peaks are shown by using dashed boxed.

In order to open an optical access to such bispheres along their equatorial plane they were assembled in a touching position near the cleaved edge of the structure. The substrate was then rotated in the inverted microscope by 90°. The axis of the image of bisphere was aligned with the slit of the spectrometer, as shown in the inset of Fig. 2 (d). This geometry provides excellent conditions for capturing scattered light originated from the coupled WGMs located in the equatorial plane of spheres parallel to its substrate. The spectral image in Fig. 2 (d) shows that each uncoupled WGM peak gives rise to two split components, antibonding and bonding states, located on both sides30-34 of the uncoupled resonance. The antiboding states are better seen at the edges of the spectral image of bisphere (on the shorter wavelength side), whereas the bonding states are seen at the center of the bisphere (on the longer wavelength side). We used this experimental geometry for measuring normal mode splitting (NMS) for WGMs which are well separated from for the neighboring peaks such as the second order (n=2) TM peaks in Fig. 2 (b). It should be noted however that for most of the WGM resonances such measurements are not feasible since the coupled components from different WGMs are superimposed or overlapped. This becomes to be an increasingly difficult problem for larger spheres (≥5 µm) where the separation between the WGM peaks is reduced. We found that geometry of experiment illustrated in Fig. 3 (b) is very helpful for interpreting complicated coupling phenomena in bispheres. In this case the axis of the assembled bisphere was perpendicular to the edge of the substrate, as shown in Fig. 3 (a), with the slit of the spectrometer oriented perpendicular to the substrate. As a result not only equatorial but all modes presenting in the bispheres on substrate are captured by the spectrometer. As can be seen in Fig. 3 (c) in this geometry the uncoupled resonances are weakened whereas the coupled components display an unusual and characteristic kites near each uncoupled resonance, as illustrated for the second order TM peaks. We attribute this effect to the manifestation of coupling between multiple pairs of azimuthal modes with different coherent coupling strength. The maximal splitting is provided for the fundamental WGMs (m=l) located in the equatorial plane of spheres corresponding to the horizontal diagonal of the kites. On the other hand the azimuthal modes with m