Abstract
Optical microresonators with low quality factor (
1 Introduction
Optical microresonators are one of the main building blocks of photonic integrated circuits [1, 2], lasers [3], and flat optical elements [4], [5], [6]. Waveguide-coupled on-chip microresonators such as microtoroid [7], microring, microdisk, and 1D and 2D photonic crystal resonators are used as filters [8, 9], sensors [10, 11], laser cavities [12], and for the enhancement of light–matter interaction [13], but they require coupling light to optical waveguides, which is an intricate and typically inefficient process. Free-space-coupled (FSC) optical resonators such as guided-mode resonators, vertical Fabry–Pérot resonators [14], [15], [16], and Mie resonators [17] can be readily excited and probed using free space excitations; however, they have larger footprints or lower quality factors (
Large and dense arrays of FSC resonators such as Mie or vertical Fabry–Pérot resonators with subwavelength footprints and low and moderate
Here we present the theory, design, and experimental demonstration of high-
2 Results
Figure 1a schematically shows an arbitrary open resonator and the radiation pattern of its resonant mode. The mode has a resonant angular frequency
where
A microdisk resonator supports high-
The polarization current density of the mode
The perturbations shown in Figure 1c form an azimuthal grating. Azimuthal gratings could be realized by adding periodic structures close to the microdisk, but to reduce the device footprint, we chose to modulate its radius instead. The azimuthal gratings considered here are created by modifying the disk radius as
Figure 1d shows the resonant mode and the radiation pattern of the microdisk shown in Figure 1b after adding
To confirm the excitation of the microdisk mode by normally incident plane waves and to quantify the effect of varying grating strengths, we found the energy stored in the microdisk when illuminated by a plane wave. Figure 2a shows a schematic of the simulated microdisk. The microdisk is the one shown in Figure 1d and is illuminated by a plane wave normally incident from the substrate. The energy stored inside the microdisk is normalized to the energy of the incident plane wave in a
To demonstrate the feasibility and performance of the FSC microdisk resonators, an array of microdisks were designed, fabricated, and characterized. Amorphous silicon microdisks with a thickness of 0.25 µm and diameters between 1.4 and 2.3 µm, corresponding to
The microdisks were characterized by measuring their transmission spectrum using the setup shown in Figure 3b. The resonators were illuminated by focused polarized light from a tunable laser, and the transmitted light was collected using an objective lens and measured (Methods). Figure 3c shows an example of the measured spectrum for a microdisk with
A microdisk supports two degenerate resonant modes at each resonant wavelength, both with
The quality factors of the microdisks were determined by fitting Fano line shapes to the measured transmission spectra (see Methods). Figure 3e shows the quality factor of microdisks with
The microdisks can also be probed by measuring their reflection spectra using the confocal setup shown in Figure 3f. Measuring the reflection spectrum is the preferred method for resonators fabricated on silicon-on-insulator (SOI) wafers. Figure 3g shows the reflection spectrum of the resonator, whose transmission spectrum is presented in Figure 3c. A reflection dip is observed at the resonant wavelength of the microdisk, which is consistent with the peak observed in the transmission spectrum. Many resonators may be probed in series in reflection mode using the setup shown in Fig. 3f, or in parallel by imaging the light reflected from the resonators while tuning the incident light’s wavelength.
To further verify the strong excitation of the resonant mode by free-space excitation, we measured the transmission spectrum of the microdisks at different incident optical powers. Thermally-induced optical nonlinearity, which is due to absorption losses in a-Si and its temperature-dependent refractive index, can be used as an indicator of the resonant mode’s excitation strength. Figure 3h shows the transmission spectra of a microdisk with
3 Discussion
The universal model we presented for the excitation of resonators by freely propagating waves describes the dynamic response of the resonator, provides simple relations for the accurate determination of stored energy and absorbed power, and enables the intuitive design of FSC resonators. FSC microdisk resonators with moderate and high
4 Methods
4.1 Design
An array of FSC microdisk resonators for six different azimuthal mode orders from
4.2 Fabrication
To fabricate the FSC microdisks, a 250-nm-thick layer of hydrogenated a-Si was deposited on a fused silica substrate by plasma-enhanced chemical vapor deposition using silane at 190 °C. A ∼250-nm-thick layer of a negative electron beam resist (AR-N 7520.11 new, Allresist GmbH) was coated on the a-Si layer and baked at 90 °C and then a layer of conductive polymer (AR-PC 5091, Allresist GmbH) was spin-coated on the resist and baked at 50 °C to serve as a charge dissipation layer. The resonators’ pattern was written on the resist using a 125-keV electron beam lithography system (ELS-F125, Elionix). Subsequently, the charge dissipation layer was removed using deionized water, and the resist was developed for 1 min in a developer (AR 300-47, Allresist GmbH). The resist’s pattern was then transferred to the a-Si layer by inductively coupled reactive ion etching in a mixture of SF6 and C4F8 gases, and the resist was removed using a solvent (Remover PG, Kayaku Advanced Materials Inc.).
4.3 Characterization
The transmission spectra of the FSC microdisk resonators were measured using the setup shown in Figure S4. Polarized light from a tunable laser (AQ4312A, Ando) covering the 1480–1580 nm range was amplified using an optical amplifier (FIBERAMP-BT 20, Photonetics), passed through a manual polarization controller (FPC560, Thorlabs), and was free-space coupled using a fiber collimation package (F240FC-C, Thorlabs). A fiber-coupled visible laser was also coupled to the same collimation package using an optical switch (EK703-FC, Thorlabs). The output beam was sampled using a beam splitter (BP108, Thorlabs) and the reflected power was monitored using a photodetector (PDA10CF, Thorlabs) and was used for the normalization of incident power. The beam transmitted through the beam splitter was focused through the substrate on a resonator using an objective lens (×20, 0.5NA, PE IR PlanAPO, Seiwa Optical). Light transmitted through and scattered by the resonator was collected by another objective lens (×100, 0.85NA, IR Plan, Nikon Hamamatsu) and was measured using a free-space-coupled photodiode (FGA01, Thorlabs) and imaged using an infrared camera (MicronViewer 7290A, Electrophysics). The resonator sample was mounted on a three-axis translation stage equipped with piezo actuators with submicron resolution (Picomotor Actuator, Newport Corporation) for accurate alignment of the resonators to the focused incident beam. The visible laser light reflected from the sample was imaged using the illumination objective lens and a tube lens (AC254-200-A, Thorlabs) on a visible camera (EO-5012M, Edmund Optics), assisting the alignment.
The reflection spectra of the resonators were also measured using the setup shown in Figure S4 by exciting the resonator with a tunable laser through the ×100 objective lens. The same objective lens also collected the reflected light, and the reflected light was sent to a fiber-coupled photodetector (ETX 75, JDS Uniphase) using an optical fiber circulator (6015-3-FC, Thorlabs).
The quality factor values reported in Figure 3e and S5b were obtained by fitting the measured resonant line shapes of the transmission spectra to
Funding source: Harvard University
Award Identifier / Grant number: Unassigned
Funding source: National Science Foundation
Award Identifier / Grant number: Unassigned
Funding source: University of Massachusetts
Award Identifier / Grant number: Unassigned
Acknowledgments
This work was performed in part at the Center for Nanoscale Systems (CNS) at Harvard University, a member of the National Nanotechnology Coordinated Infrastructure Network (NNCI), which is supported by the National Science Foundation under NSF award no. 1541959. Additional device fabrication was performed in the Conte Nanotechnology Cleanroom at the University of Massachusetts Amherst.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
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Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/nanoph-2022-0106).
© 2022 Babak Mirzapourbeinekalaye et al., published by De Gruyter, Berlin/Boston
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