Identification of Dielectric, Plasmonic, and Hybrid Modes in Metal

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Identification of Dielectric, Plasmonic, and Hybrid Modes in Metal Coated Whispering-Gallery-Mode Resonators Carolin Klusmann, Jens Oppermann, Patrick Forster, Carsten Rockstuhl, and Heinz Kalt ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00160 • Publication Date (Web): 07 Apr 2018 Downloaded from http://pubs.acs.org on April 7, 2018

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Identification of Dielectric, Plasmonic, and Hybrid Modes in Metal Coated Whispering-Gallery-Mode Resonators Carolin Klusmann,∗,† Jens Oppermann,∗,‡ Patrick Forster,† Carsten Rockstuhl,‡,¶ and Heinz Kalt† †Institute of Applied Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany ‡Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany ¶Institute of Nanotechology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany E-mail: [email protected]; [email protected]

Abstract Making available and accessing in a controlled manner optical modes with largely disparate properties in a given system constitutes a prime challenge for different applications. Here, we propose, realize, and optically characterize a high-Q polymeric wedge-like whispering-gallery-mode resonator coated with a thin silver layer that supports pure surface plasmon polariton modes, pure dielectric modes, as well as hybrid photonic-plasmonic modes with Q-factors larger than one thousand and modal volumes as small as only a few cubic microns. We demonstrate both, theoretically and experimentally, that all three distinct kinds of cavity eigenmodes can be efficiently excited in the infrared via evanescent coupling to a tapered fiber. Performing finite-element simulations and coupled-mode theory, we develop an experimental procedure based on mode

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filtering to unambiguously identify the resonances observed in fiber transmission spectra. By controlling both the position of the tapered fiber with respect to the resonator and the input laser polarization, we successfully demonstrate that dielectric, plasmonic, and hybrid modes can be selectively excited, allowing for an explicit classification of the distinct cavity eigenmodes. Experimental results are in excellent agreement with the simulations.

Keywords whispering-gallery-modes, optical microresonator, surface plasmon polaritons, hybrid photonicplasmonic modes, fiber-resonator-coupling, plasmonics Dielectric whispering-gallery-mode (WGM) resonators have attracted a lot of attention during the last decade. Their high quality factors (Q-factors) in combination with relatively small modal volumes make them an ideal platform for plenty of photonic applications, ranging from low-threshold microlasers (1 ),(2 ),(3 ),(4 ) to ultra-sensitive biosensors (5 ),(6 ), as well as for fundamental research, e.g. strong light-matter interaction (7 ), nonlinear optics (8 ),(9 ),(10 ), or cavity quantum electrodynamics (11 ),(12 ),(13 ),(14 ),(15 ). Whereas modal volumes in high-Q dielectric WGM microcavities are limited by diffraction to values of typically a few hundred cubic wavelengths (16 ), their metallic counterparts, surface plasmon polariton (SPP) cavities, can break the diffraction limit. SPP cavities rely on the collective excitation of the electron gas in a metallic structure, which is coherently interacting with the electromagnetic field and sustained at the metal-dielectric interface (17 ). Exploiting the highly localized electromagnetic fields connected with SPPs, a controlled confinement of electromagnetic energy to nanometric volumes can be achieved (18 ),(19 ),(20 ). However, owing to large ohmic losses in the metal, their Q-factors are restricted to values less than one hundred for wavelengths in the visible and near-infrared (21 ),(22 ),(23 ),(24 ). Inspired by the complementary characteristics of dielectric WGM and plasmonic cavities, several approaches have been pursued recently to combine the advantages of both worlds in a 2


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single hybrid photonic-plasmonic microcavity (25 ),(26 ),(27 ),(28 ),(29 ),(30 ),(31 ),(32 ),(33 ),(34 ). Among those, coating a high-Q silica microdisk with a thin silver layer was shown to result in a hybrid resonator supporting SPP eigenmodes with reduced modal volumes compared to dielectric (DE) eigenmodes and Q-factors in the order of a thousand, which is close to the theoretical loss-limited Q-factor (26 ). To further improve the Q-factors while maintaining the small modal volumes related to SPPs, combined photonic-plasmonic resonators supporting hybrid photonic-plasmonic (HY) modes have been proposed, e.g. toroidal silica WGM resonators coated with a thin silver layer (27 ) or a silver-nanoring (28 ), metal-nanocapped microtubular cavities (29 ), and metal-coated microspheres (30 ). Benefitting from both the low-loss characteristics of WGMs and the strong field localization of SPP modes, these HY modes exhibit Q-factors in the order of a few thousand and small modal volumes, which paves the way for numerous applications requiring strong light-matter interactions. In this contribution, we introduce a novel type of microresonator, a polymeric wedge-like resonator made from poly(methylmethacrylate) (PMMA) with low surface roughness and Q-factors in the order of 105 in the infrared, which serves as a template for the realization of hybrid photonic-plasmonic cavities. Coating the template resonator with a thin silver layer from the top is shown to result in a hybrid resonator supporting DE, SPP, as well as HY modes with Q-factors larger than one thousand and modal volumes as small as a few cubic microns. A scanning electron micrograph of the investigated silver-coated polymeric wedge-like resonator is depicted in Fig. 1(a). The different kinds of modes are accessed evanescently using a tapered optical fiber and operation wavelengths in the infrared. To unambiguously classify the resonances obtained from the fiber transmission spectra, we develop an experimental procedure based on mode filtering. Applying finite-element simulations and coupled-mode theory, we extract coupling efficiencies between the tapered fiber and the distinct kinds of modes for varying fiber positions and show that the modes can be selectively excited. In combination with a polarization-dependent excitation scheme, we demonstrate the successful categorization of the three distinct kinds of modes supported by the hybrid 3


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a

b

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Rotational axis Simulation domain

5 µm

Figure 1: Scanning electron micrograph of the investigated silver-coated wedge-like polymeric WGM resonator (a). Exploiting its cylindrical symmetry together with the confinement of WGMs to the resonator rim allows for a significant reduction of the simulation domain (b). resonator.

Results and discussion Theory Mode Modeling. To verify that the hybrid resonator depicted in Fig. 1(a) supports DE, SPP, and HY modes and to determine its modal properties, finite-element method (FEM) simulations were performed using the commercially available software JCMsuite (35 ). In order to keep the numerical costs of the simulations feasible, we exploit two characteristics of WGM resonators. First, we exploit the cylindrical symmetry of these resonators in order to reduce the problem to two dimensions. Second, we exploit the fact that WGMs are confined to the rim of the resonator, allowing for a further significant local confinement of the simulation domain. Utilizing these peculiarities, the resonator rim can be modeled as a bent waveguide forming a concentric ring around the rotational axis of the resonator, as illustrated in Fig. 1(b). The eigenmodes of the WGM resonator, hence, can be described by a set of leaky modes of a bent waveguide (36 ),(37 ),(38 ),(39 ) described by their cross-sectional field distribution and characterized by a complex effective refractive index neff , which is the outcome of the FEM simulations. Please note that the FEM simulations don’t take into account that the propagating modes interfere with themselves after one round trip through the bent waveguide.

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SPP1 Q~870 V~1.2 µm³

l75~1532.95 nm

SPP2 Q~890 V~1.6 µm³

l70~1546.48 nm

DE1

Q~6360 V~51.4 µm³

l63~1554.97 nm

DE2

Q~4760 V~39.0 µm³

l60~1548.33 nm

HY1

Q~1880 V~3.2 µm³

l55~1540.19 nm

Figure 2: Intensity distribution (left) and vector plot (right) of the electric field of the SPP1, SPP2, DE1, DE2, and HY1 modes supported by the investigated hybrid resonator together with the corresponding simulated resonance positions λm . Distinct field distributions and polarization characteristics together with differing Q-factors and modal volumes V , as calculated from the electromagnetic energy density (see Supporting Information A), indicate the distinct nature of the cavity eigenmodes. Accounting for the self-consistent resonant condition for the loop resonator, which requires that both the phase and the amplitude of the modal field distribution are reproduced after each round trip, allows to calculate the WGM resonance wavelengths λm and quality factors Qm (36 ): 2πR Re {neff } , m Re {neff } Qm = , 2Im {neff } λm =

(1) (2)

where 2πR is the geometrical path of the guided mode with respect to its center of gravity and m ∈ Z the azimuthal mode number. Please note that the effective refractive index is a function of the wavelength and, therefore, Eq. (1) has to be solved in a self-consistent manner. This was achieved by iterating over the wavelength λm until convergence. To simulate the modal spectrum of the experimentally realized silver-coated wedge-like resonator, we measure its size from the scanning electron micrograph depicted in Fig. 1(a)

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and plug the measured geometry into the FEM simulations, considering the silver (40 ) and PMMA (41 ) material dispersion. The cavity radius is determined to be redge =14.63 µm, the wedge-angle is 21.6◦ . The silver thickness was measured with a piezoelectric crystal during silver evaporation to be 103 nm. To demonstrate that the resonator supports SPP, DE, and HY modes and to work out differences between the three distinct types of modes, we show in Fig. 2 the intensity distributions and the vector plots of the cross-sectional electric field exemplarily for a first and second order SPP mode (SPP1 and SPP2), a first and second order DE mode (DE1), and a first order HY mode (HY1). The simulated resonance positions λm of these modes are listed in Fig. 2. We would like to emphasize at this point that higher order HY modes cannot be observed experimentally due to their small effective refractive indices preventing their excitation via evanescent coupling to a tapered fiber due to lack of phase-matching. In the following, we restrict our theoretical discussion to experimentally relevant modes. While the DE1 and DE2 modes are localized inside the PMMA layer, the SPP1 and SPP2 modes propagate along the silver-polymer interface. The HY1 mode is clearly seen to contain dielectric as well as plasmonic contributions. From the vectorial distribution it is visible that the DE1 and DE2 modes are polarized mainly parallel to the silver layer (TE polarization), whereas the SPP1, SPP2 and HY1 modes are polarized mainly orthogonal to the silver-polymer interface (TM polarization). This is in accordance with SPPs on planar metal-dielectric interfaces, which are also polarized mainly orthogonal to the interface (42 ). Besides their different polarization characteristics, also their distinct Q-factors and modal volumes can be utilized to distinguish between the cavity eigenmodes of different nature. Whereas the lossy SPP1 and SPP2 modes exhibit low Q-factors of only ∼900 together with very small, subwavelength-dimensional modal volumes of 1.2 µm3 and 1.6 µm3 , respectively, due to the light-focusing characteristics of SPPs, the Q-factors of the low-loss DE1 and DE2 modes (Q∼6400 and Q∼4800, respectively) exceed the Q-factors of the SPP modes by an order of magnitude. However, the modal volumes of the DE1 and DE2 modes are with 6


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1.8

Effective refractive index neff

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1.7 1.6 SPP1

1.5 1.4

DE1

1.3 1.2

HY1

1.1 1.0

0

10

20

30

90

100

Silver layer thickness (nm)

Figure 3: Dispersive behaviour of a fundamental SPP1, DE1, and HY1 modes of the silvercoated wedge-like resonator under variation of the silver layer thickness. 51.4 µm3 and 39.0 µm3 significantly larger than those of the SPP modes. The slightly smaller modal volume of the DE2 mode compared to the DE1 mode can be traced back to the fact that a larger fraction of the DE2 mode penetrates into the silver layer, which is reflected according to our definition of the modal volume (see Eq. (3) in the Methods) in a reduced modal volume. The HY1 mode with a Q-factor of 1900 and a small modal volume of only 3.2 µm3 is clearly seen to combine the advantages of the high-Q DE modes with the ability of the SPP modes to confine light to very small modal volumes. In order to further study, whether the HY1 mode unites dielectric and SPP properties and hence can be identified as such, we study in Fig. 3 the effective index of the three types of cavity eigenmodes as a function of the silver layer thickness. As obvious from Fig. 3, the SPP1 mode (black) is strongly dispersive until it reaches saturation beyond a silver layer thickness of 20 nm, while the DE1 mode (red) is almost dispersionless. The HY1 mode (blue) shows an intermediate dispersive behaviour and saturates at the same thickness as the purely SPP mode, which further suggests that it indeed has a plasmonic component. This, together with the intermediate values of the mode volume calculated above suggests, that the HY1 mode found above can be clearly identified as such. Please note, that we also included into Fig. 3 the dispersive behaviour around the experimentally fabricated layer

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thickness of 103 nm. As suspected, this far above the saturation threshold all modes show no dispersion under small changes in silver layer thickness. Numerical Modeling of Fiber-Resonator Coupling. Although the distinct ranges of Q-factors of SPP, DE, and HY modes can be exploited, to distinguish between the distinct cavity eigenmodes, a clear categorization of modes only by means of a Q-factor analysis is challenging in experiments. Therefore, we develop as a last step of our theoretical analysis, an experimental procedure based on mode filtering to unambiguously classify the resonances observed in fiber transmission spectra. To be as close as possible to the experimental system, where we excite the cavity eigenmodes evanescently from underneath the silver-free bottom-surface of the hybrid resonator with a tapered fiber, we explicitly include the coupling of the fiber to the cavity eigenmodes in our FEM simulations. Details regarding the simulation approach can be found in the Supporting Information B. In order to excite the different cavity eigenmodes with the evanescent field of the tapered fiber, two conditions need to be satisfied. First, the effective refractive indices of fiber and resonator modes have to match (phase-matching), so that energy can be coherently exchanged between both systems. Second, the modal overlap between fiber and resonator modes has to be sufficiently large. As a consequence, both the radius as well as the position of the fiber relative to the cavity eigenmodes have to be chosen appropriately to excite the cavity eigenmodes evanescently. Applying coupled-mode theory, we derive in the Supporting Information B a method to calculate the power P transferred from the tapered fiber into a specific cavity eigenmode, which serves as a measure for the fiber-resonator coupling efficiency, for varying fiber positions. To demonstrate the phase-matched excitation of the different cavity eigenmodes, we plot in Fig. 4 exemplarily the so obtained results for the transferred power from a tapered fiber with 700 nm radius into the different cavity eigenmodes depicted in Fig. 2 for varying horizontal fiber positions. The vertical distance between fiber axis and bottom-surface of the

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Transferred power P (arb.u.)

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DE1

HY1 SPP2 SPP1 DE2 10

11

12

13

14

15

Horizontal fiber position r (µm)

Figure 4: Theoretical results for the power P transferred from a tapered fiber of radius 700 nm into different resonator modes for varying fiber positions. Selective excitation of SPP1 and SPP2, DE1 and DE2, and HY1 modes is achieved when moving the fiber horizontally from the resonator edge (redge =14.63 µm) towards its rotational axis (r=0 µm). resonator is kept fixed at 900 nm. Moving the tapered fiber horizontally from the resonator edge redge =14.63 µm towards its rotational axis r=0 µm is seen to result in a successive excitation of the SPP1 and SPP2 modes, the DE1 and DE2 modes, and the HY1 mode, respectively. Sufficient phase-matching and modal overlap is shown for all cavity eigenmodes for the selected fiber radius. We note here that increasing the fiber radius changes the relative coupling efficiencies in favour of SPP modes, while decreasing it favours DE and HY1 modes. Additionally, the point of maximal coupling for each mode shifts towards slightly smaller horizontal fiber positions r with increasing fiber radius. However, the order of appearance of the different modes when moving the fiber underneath the resonator remains unaltered. The experimental procedure developed here, shows that using the horizontal fiber position as a tuning parameter allows to selectively address the different kinds of cavity eigenmodes paving the way for an unambiguous modal classification of the resonances observed experimentally.

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a

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b PMMA

1460-1570 nm

tunable laser

Silicon

Lithography

cameras

Development z

y x

Thermal reflow

Etching

FPC

PD tapered fiber

Osci

Figure 5: (a) Schematic illustration of the fabrication process of high-Q polymeric wedge-like resonators serving as a template for the creation of hybrid photonic-plasmonic resonators. The fabrication is based on ebeam lithography in combination with a thermal reflow process to obtain the desired wedge-like resonator geometry. (b) The silver-coated template resonators are optically characterized with the aid of a tapered fiber, which is positioned underneath the silver-free bottom surface of the resonator to evanescently address the cavity eigenmodes. The transmission through the fiber is monitored with a photodiode and an oscilloscope while sweeping the wavelength of a tunable laser.

Experiment Hybrid Resonator Fabrication. The creation of a hybrid resonator supporting modes of plasmonic nature with high Q-factors requires a well-engineered high-Q template resonator with a smooth surface, and hence, low scattering losses. In the experiments demonstrating nearly ideal values for the Q-factors of SPPs in silver-coated silica microdisks, such a lowloss template resonator was realized utilizing a very slow etching process, which results in a wedge-like geometry with ultra-smooth side walls. Both the geometry, as well as the fabrication process are responsible for the high Q-factors in the order of 107 for those resonators (26 ),(43 ). The low-loss template resonator we present is made from PMMA and fabricated in a four-step-process using electron beam lithography, as schematically depicted in Fig. 5(a). A thermal reflow process to smoothen the resonator surface and obtain the wedge-like structure is at the heart of the fabrication process. Polymeric microdisks lithographically structured onto the silicon substrate serve as a starting point for the template. To transform the cylindrical geometry of the microdisks into 10


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the desired wedge geometry, we perform a thermal reflow process. Heating the resist cylinders to temperatures well above the glass-transition temperature of PMMA (105 ◦ C) results in the formation of pronounced wedges at the rim of the former microdisks due to surface tension (44 ),(45 ). The resulting wedge-angle is thereby determined by the reflow temperature. The thermal reflow process also leads to a smoothening of the resonator surface, which is critical for the realization of a template resonator with low scattering losses and essential for a uniform silver coating. Subsequent etching of the silicon with XeF2 leads to free-standing polymeric wedge-like micoresonators on a silicon pedestal exhibiting Q-factors in the order of 105 . Finally, the resonator template is coated with a 103 nm thick silver layer using physical vapor deposition and a slow silver evaporation rate to minimize collision-induced deposition of silver atoms at the bottom-surface of the resonator. Further fabrication details can be found in the Methods. Optical characterization of the hybrid resonator. To experimentally extract the modal structure of the hybrid resonator, a narrow-linewidth tunable laser is coupled into a tapered fiber and swept over the 1460-1570 nm wavelength range. To ensure a large overlap of the evanescent fields of the tapered fiber and resonator modes, the tapered fiber is positioned underneath the silver-free bottom-surface of the resonator, as depicted in Fig. 5(b). The transmission through the fiber is collected with a photodiode and monitored onto a digital oscilloscope. A fiber polarization controller (FPC) allows to control the input laser polarization. Polarization-sensitive excitation of eigenmodes. To get a first experimental insight into the modal characteristics of the silver-coated resonator, we exploit the different polarization characteristics of the individual cavity eigenmodes. As specified in the theoretical discussion above, the DE1 and DE2 modes exhibit a polarization parallel to the silver-polymer interface, whereas both the SPP1 and SPP2 modes, as well as the HY1 modes are polarized perpendicular to the silver layer - due to the TM11


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characteristics of SPPs. Optimal coupling into a specific eigenmode occurs if the polarization vector of the exciting fiber field coincides with the polarization vector of the electric field of the resonator mode. This manifests itself as a minimum in the fiber transmission spectrum at the resonance frequency of the eigenmode. In other words, for maximum fiber-resonator coupling efficiency, the Lorentzian-shaped dip in the transmission spectrum corresponding to this specific eigenmode is most strongly pronounced. Polarization angles differing from the optimal angle lead to reduced coupling efficiencies and, hence, higher transmitted intensities and less pronounced dips in the transmission spectrum. To identify experimentally the optimal polarization state of the exciting fiber field, we rotate the polarization of the incoming light continuously with the FPC until the corresponding Lorentzian-shaped dip in the transmission spectrum shows a global minimum. Please note, that the polarization state inside an optical fiber is highly sensitive to slight bending and twisting of the fiber which lead to a rotation of the polarization inside the fiber. Since such stress-induced rotations may also occur in the transition from the tapered area of the fiber to the fiber end where the transmitted intensity is recorded, quantitative statements about the polarization angle in the tapered fiber region cannot be made. However, once the fiber is fixed in experiment, relative changes in the polarization angle of the excitation light can be deduced from the different paddle configurations of the FPC which correspond to different polarization states inside the optical fiber. To verify that the orthogonality of the polarizations can be utilized experimentally to distinguish between DE modes on the one hand and SPP and HY1 modes on the other hand, we plot in Fig. 6 normalized transmission spectra for three different input laser polarizations (indicated with black, red and blue arrows). Since the coupling efficiency between the input fiber and a specific cavity eigenmode is affected not only by the polarization state of the exciting fiber field, but also by the horizontal fiber position r (see Fig. 4), we record the transmission spectra for two different horizontal fiber positions r to ensure observation of a variety of different modes. 12


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The upper three spectra highlighted in grey in Fig. 6 are recorded at a horizontal fiber position r∼13.75 µm. For the input polarization state denoted with two crossed black arrows, two types of modes with differing spectral linewidths are present in the transmission spectrum (black curve) which repeat spectrally according to their free spectral ranges. By rotating the input polarization with the fiber polarization controller, the relative intensities of both types of modes can be varied. When optimizing the input polarization for the different cavity eigenmodes with respect to maximum coupling as described above, we observe that the optimal polarization angle to excite the spectrally sharp resonances is rotated by ∼90◦ with respect to that of the spectrally broad ones. From the vector plots of the electric field of the different cavity eigenmodes (see Fig. 2) together with the measured polarization contrast of ∼90◦ for optimal excitation of the two distinct types of modes and their different Q-factor ranges, we conclude that the input polarization state denoted with a red arrow corresponds to a polarization perpendicular to the silver-polymer interface leading to optimal coupling into modes with SPP character, whereas the input polarization state denoted with a blue arrow corresponds to a polarization parallel to this interface leading to optimal coupling into DE modes. We will indicate these two polarization states in the following graphs with the same red and blue arrows, which must be interpreted from a fiber-cross-sectional point of view and point in a direction normal to the fiber axis. Similar polarization characteristics are observed in the three transmission spectra highlighted in orange in Fig. 6 which are recorded with the same three input polarizations, but with the fiber positioned more towards the rotational axis of the resonator at r∼11.5 µm. In contrast to the spectra recorded close to the resonator edge, the spectrally broad resonances cannot be accessed anymore, instead, a new type of mode with moderate linewidth is excited (magenta curve) in addition to the spectrally sharp DE modes excited already before. This mode with intermediate Q-factor is optimally excited for an input fiber polarization perpendicular to the silver-polymer interface which indicates the SPP character of this mode. In accordance with our expectation and the previous observations, for input polarizations 13


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parallel to the silver-polymer interface, only the spectrally sharp DE modes are excited (blue curve), for input polarizations in-between the two polarization angles corresponding to optimal coupling into the DE modes and modes with SPP character (black curve), both types of modes are excited, however, with reduced efficiencies. To make a first attempt to identify the experimentally observed resonances, we compare the simulated resonance positions of the modes presented in Fig. 2 with the measured resonances. The simulated resonance positions for the SPP2, DE1, DE2, and HY1 modes show a remarkably good agreement with the observed resonances around 1550 nm and are marked by vertical dashed lines in Fig. 6. This allows us to identify the sharp resonances resonances in the blue spectra in Fig. 6 with the DE1 and DE2 modes, the spectrally broad resonances in the red spectrum with the SPP2 modes, and the resonances with intermediate linewidth in the magenta spectrum with the HY1 modes. The different polarization characteristics observed for the DE modes and the modes with SPP character together with the differing measured Q-factors ranging from ∼600 in the case of the SPP modes, 900 in the case of the HY1 modes, and up to 3000 for the DE modes underpin this assignment of the experimentally observed resonances. Selective excitation of eigenmodes. Although the different polarization characteristics together with the good agreement between simulated and experimentally observed spectral features, e.g. resonance positions and Q-factors, allows already for a convincing assignment of the observed resonances, an unambiguous identification of the modes can be obtained by following the experimental procedure developed above with the aid of finite-element simulations. The advantage of this classification scheme is that it does not rely on a quantitative comparison between simulated and experimentally observed spectral features, but instead utilizes qualitative differences in the modal propagation and the localization characteristics of the different modes which makes it robust against slight deviations in resonator geometry and material properties. Uncertainties in the resonator geometry, which are extracted from

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Normalized transmission

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SPP2 DE2 DE1

HY1 DE1 1480

1500

1520

1540

1560

Wavelength (nm)

Figure 6: Normalized transmission spectra of the silver-coated wedge-like resonator for three distinct input laser polarizations (black, red and blue arrows) recorded at two different horizontal fiber positions r∼13.75 µm (grey) and r∼11.5 µm (orange). For input polarizations parallel to the silver-polymer interface, only the DE modes are excited (blue), whereas for polarizations perpendicular to this interface, either the SPP modes (red) or the HY1 modes (magenta) are excited - depending on the fiber position. For polarization states in-between, both DE and modes of plasmonic nature are excited (black). Simulated resonance positions for the individual modes at the long-wavelength side of the recorded spectrum are marked by vertical dashed lines. A comparison with the measured resonance position shows a remarkably good agreement, when considering the high sensitivity of the resonance wavelengths to tiny variations in the resonator geometry and silver permittivity. SEM-images, or uncertainties in the silver permittivity (46 ),(47 ),(48 ),(49 ) can easily lead to significant deviations in both the resonance wavelengths and the Q-factors, which makes an assignment of the simulated resonances to the experimentally observed ones challenging. To identify all the different modes present in the hybrid resonator, we plot in Fig. 7(a) selected normalized fiber transmission spectra with an input fiber positioned close to the resonator edge at r∼14 µm (top) and more towards the rotational axis of the resonator at r∼12 µm (middle) and r∼10 µm (bottom). At each fiber position, the input laser polarization is rotated until the Lorentzian-shaped dips in the transmission spectrum corresponding to SPP modes (top), DE modes (middle), and HY1 modes (bottom) exhibit a global minimum. In addition to the four resonances already observed in the transmission spectra in Fig. 6, we can identify a fifth mode for the fiber positioned at r∼14 µm, which is only weakly excited and probably a SPP1 mode. One set of modes spectrally located around 1550 nm, 15


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(a)

SPP1 SPP2

r~14µm

1.0

Coupling efficiency c

Normalized transmission

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DE2 DE1

r~12µm

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HY1

(b)

DE1

11.5µm

0.8

SPP2 0.6 HY1 0.4 0.2

DE2 SPP1

r~10µm

1480

13.75µm

1500

1520

1540

0.0 10

1560

11

12

13

14

15

Horizontal fiber position r (µm)

Wavelength (nm)

Figure 7: (a) Normalized fiber transmission spectra of the investigated silver-coated wedgelike resonator recorded at different horizontal fiber positions r (top: close to the resonator edge r∼14 µm, middle: r∼12 µm, bottom: r∼10 µm). For each fiber position the input laser polarization (indicated by arrows) is rotated until the Lorentzian-shaped dips in the transmission spectra corresponding to DE modes (middle) and modes with SPP character (top and bottom) exhibit a global minimum. In that case, the polarization vector of the electric field of the input fiber coincides with that of the eigenmode and the fiber-resonator coupling efficiency c for a given fiber position r is maximal. (b) Experimentally obtained coupling efficiencies c between the tapered fiber with radius ∼700 nm and the cavity eigenmodes highlighted in color in (a) plotted as a function of r and fitted with Lorentzian functions (solid lines). Moving the fiber from the resonator edge (redge =14.63 µm) towards its rotational axis (r=0 µm) results in a successive excitation of the individual cavity modes. containing all the five different modes supported by the hybrid resonator, is highlighted in color in Fig. 7(a). The corresponding simulated resonance positions for the different modes are marked by vertical dashed lines and agree with those listed in Fig. 2. To unambiguously assign the distinct resonances to the simulated cavity eigenmodes and to build the connection to Fig. 4, we track the five resonances highlighted in color when moving the fiber from the resonator edge towards its rotational axis. For each horizontal fiber position, we optimize the input laser polarization and extract the coupling efficiencies of these modes from the absolute depth of the corresponding Lorentzian-shaped dips in the normalized transmission spectra (see Supporting Information C for details). Since the radius of the tapered fiber used in the experiment is estimated from top-view micrographs to lie in-between 600−800 nm, and hence, is comparable to the fiber radius used to produce Fig. 4, a qualitative comparison between the experimentally measured coupling efficiencies and the 16


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ACS Photonics

simulated transmitted power is possible, since both quantities are proportional to leading order in the coupling strength. Small deviations can be explained by the disregard of power coupled back from the resonator to the fiber in the theoretical calculations. To demonstrate the phase-matched, selective excitation of the cavity eigenmodes, we plot in Fig. 7(b) the experimentally obtained coupling efficiencies (colored dots) between the tapered fiber and the selected cavity eigenmodes as a function of the horizontal fiber position r and fit the data points with Lorentzian functions (solid lines). An excellent qualitative agreement with the simulated results is manifested. As predicted by the simulations, five distinct Lorentzians with spatially separated maxima are observed. In line with the simulation, and according to their order of appearance when moving the fiber from the resonator edge redge towards the rotational axis, these Lorentzians can now be unambiguously associated with the SPP1 and SPP2, DE1 and DE2, and HY1 modes, respectively. For fiber positions r close to the resonator rim (14 µm

Identification of Dielectric, Plasmonic, and Hybrid Modes in Metal

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