1. Introduction

A pivotal figure of merit of integrated optical components for future chip-to-chip or on-chip optical interconnects is the size of their footprints. Shrinking well-established device concepts known from telecom applications down to dimensions of only a few optical wavelengths suffers from the fact that the (electro-)optical material properties do not scale accordingly. Resonant structures compensate this deficiency by creating an effectively longer propagation path for the light inside the active material. Prominent examples are electro-optical modulators [1], all-optical switches [2] and microring lasers [3]. Also passive devices such as spectral filters [4], delay lines [5] and add/drop multiplexers [6] benefit from ultra-small low-loss optical resonators. However, for the smallest resonator mode volumes on the order of a few cubic wavelengths, ring or disc resonators are ultimately limited by bending losses. Alternative structures, that do not rely on whispering-gallery modes, such as photonic crystal-defect cavities [7] and circular grating resonators [8, 9, 10] (CGRs) enable ultra-small cavities and maintain very high quality factors Q. Compared to linear structures they offer enhanced photonic confinement due to the photonic band gap in the two lateral dimensions. In photonic crystal defect cavities the photonic band gap is induced by a lattice with high refractive index contrast which is achieved in suspended semiconductor membranes. CGRs consist of a central defect surrounded by concentric circular Bragg mirrors. CGRs do not require high-index-contrast materials to achieve a complete band gap for radial wavevectors. They open up the feasibility of highly integrated novel devices with unprecedented small footprint [11, 12, 13, 14], and promise a leap in performance because of their large free spectral range and small optically active volume. Furthermore, beyond classical optics, they pave the way to integrated devices harnessing cavity quantum electrodynamics effects [15]. Other fields such as sensing [16] and spectroscopy [17] also benefit from advances in microcavity design. Another key requirement for photonic circuits is an efficient coupling of the microcavities to waveguides, something that so far has only been demonstrated for photonic crystal defect resonators [18].

In this work, we design and fabricate waveguide-coupled CGRs and explore their optical properties. We optimize the dimensions of the concentric Bragg rings such that the band gap of the Bragg mirror is maximized to achieve a large reflectivity. By varying the radius of the central defect, we select resonance frequencies of the resonator near the telecom wavelength of 1550nm. The CGR devices are fabricated with silicon-on-insulator (SOI) by electron-beam lithography and subsequent reactive ion etching. We perform linear transmission measurements to analyze the CGR structures. We identify the measured resonances by comparison to 3D finite-difference time-domain (FDTD) simulations of the isolated CGRs. Scanning near-field optical microscopy (SNOM) allows us to measure the field distributions of the resonance selected. Finally, we demonstrate the operation of CGRs as fast all-optical switches by performing pump and probe measurements.

The paper is structured as follows: In Sec. 2 we describe the design, and in Sec. 3 the fabrication process of the device. In Sec. 4 we report on the experimental characterization of the device using complementary techniques, namely, transmission measurements, SNOM and pump and probe experiments. Finally, we discuss our results and conclude in Sec. 5.

2. Design

A CGR is schematically illustrated in Fig. 1(a). A circular Bragg mirror is formed by a number Z_in of concentric silicon rings around the central defect. The Bragg mirror imposes a photonic band gap, i.e., a stop band for a range of radial wavevectors, which prevents lateral leakage of light from the cavity. The radius of the central defect r _c determines the resonance wavelength λ of the resonator. For a given periodicity and duty cycle, the reflectivity of the Bragg mirror can be increased by adding more rings. For small central defect sizes, only few nodes of the resonant optical field are located in the center, and the field exponentially decays radially in the Bragg rings. Hence, the effective modal volume can be strongly reduced to a few cubic wavelengths. In- and out-coupling of light is achieved by waveguides partially penetrating the circular grating. Scattered light is additionally confined by a number Z_out of surrounding silicon rings, which are interrupted by the in- and out-coupling waveguides.

 

Fig. 1. (a) Circular grating resonator consisting of a central defect surrounded by concentric rings and in- and out-going waveguides. Z_in is the number of rings defining the Bragg mirror and Z_out is the number of additional surrounding rings confining scattered light. (b) Cross section of the circular grating. The duty cycle D is the ratio between the width of the trench q and the grating period a, i.e., D = q/a, and the total height is h.

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To minimize the spatial extension of the cavity mode and at the same time maximize the quality factor of the resonator, we optimize the geometry of the circular Bragg rings. We approximate the circular Bragg rings by their corresponding linear grating [12, 19], of which the cross section is illustrated in Fig. 1(b). The relevant geometric parameters are the height h and the duty cycle D = q/a, where q is the width of the grooves and a the grating period. These parameters are varied to obtain the largest possible band gap of the Bragg mirror centered around the target wavelength of λ = 1550nm. Therefore, we compute the eigenstates and eigenvalues of Maxwell’s equation in a plane-wave basis using the MIT Photonic Bands (MPB) tool [20]. Without restricting the general applicability for other polarizations, we focus in this paper on TM polarization, where the magnetic field is in the r, y-plane and the electric field is in the z-direction (E_z,H_r,H_y).

The total height h of the structure is about 430nm. It consists of 340nm Si and a 90nm layer of hydrogen silsesquioxane (HSQ) on top of the Si ridges, which is a residual transparent resist layer from the process flow, see Fig. 1(b). Instead of removing this residual HSQ layer, which would expose the structures to the risk of damage, we chose to leave the HSQ on the silicon structure and account for it in our simulations. Hence, the free parameters of the simulation are reduced to the duty cycle D and the grating period a. At a wavelength of λ = 1550nm, the refractive indices of Si, SiO₂ and HSQ are n _Si = 3.48, n _SiO2 = 1.46 and n _HSQ = 1.46, respectively. We find a configuration with a band gap of Δλ/λ = 7% which has a duty cycle of D = 0.3 and a grating period of a = 400 nm. We fabricated devices for r _c = 850 – 900 nm in order to find resonances with high quality factors and different azimuthal symmetries in the wavelength range of interest.

 

Fig. 2. SEM images of the CGR structure. The grating grooves appear as dark lines. (a) Overview with in- and out-coupling waveguides. (b),(c) Close-ups of the circular grating.

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To couple light into and from the CGR, waveguides penetrate the outer circular grating ridges at opposing positions. The waveguides have a width of 300 nm, and an air gap of 250 nm separates them from the outer grating. This coupling reduces the total Q-factor of the isolated resonator: Q _total = Q ^-1 _isolated + Q ^-1 _waveguide)^-1. From coupled-mode theory it is known that the resonator transmission T ∝ (1 - Q _total/Q _isolated)² is highest when Q _waveguide is significantly lower than Q _isolated [21] and when the coupling strength of the in- and out-coupling waveguides is equal. In the simulations we find that resonances of low azimuthal order (m < 10) exhibit Q _isolated < 500, and hence, such resonances are not suitable for high-transmission resonators due to their large vertical losses. As a trade-off between resonator quality factor and device area, we chose Z_in = 7 and Z_out =10. This yields a theoretical Q _total of the waveguide-loaded CGR on the order of a few thousands, which enables ultra-fast optical response and ring-down times on the order of a few picoseconds. Higher Q-factors would increase the photon lifetime inside the resonator which prevents fast optical switching and limits the optical bandwidth.

3. Fabrication

The CGR devices are fabricated on SOI substrates consisting of a 2 μm-thick buried oxide layer and a 340nm Si device layer. The structures are defined by electron-beam lithography using HSQ as negative tone resist. The pattern transfer is achieved in a two-step HBr-chemistry-based inductively coupled reactive-ion etch process [22]. First, in the main etch step, pure HBr is used. The etching time for this step is set to stop at a residual top-Si thickness of 20nm. Then the etch conditions are changed to the second or over-etch step by using a mixture of HBr and O₂. The over-etch step exhibits an excellent selectivity between the top-Si and the buried oxide. The entire process flow, including lithography and etching, is optimized to minimize the side-wall roughness of the CGRs while maintaining the dimensional accuracy of the circular grating structures.

Scanning electron microscopy (SEM) images of the CGR device are shown in Fig. 2. Figure 2(a) shows the entire structure with in- and out-coupling waveguides. Figures 2(b) and (c) are close-ups of the rings. In Fig. 2(c), the measured width of the Si ring is 282nm matching the target width of 280nm within the resolution of the SEM. This highlights the precision of device fabrication. The overall diameter of the CGR is between 10 to 20μm, depending on the central defect size and the number of Bragg rings.

4. Measurements

First we characterize the CGRs as passive devices by measuring their transmission spectra. Polarized light from a tunable single-mode continuous-wave laser source is coupled into the device using tapered lensed fibers near the cleaved waveguide facets. To reduce coupling losses, an inverse taper adiabatically reduces the width from 5μm at the cleaved facet to 300nm over a distance of 100μm. Light from the output waveguide is collected with a tapered lensed fiber and then detected with a power meter. We use the transmission through straight waveguides in the vicinity of the CGRs to normalize the transmission through the device.

Figure 3 shows the measured transmission spectra of the CGRs with different central defect radii. The highest transmission through each CGR is in the range of 10 to 20%. The spectra exhibit several sharp resonances with Q-factors of up to a few thousands. A number of spectrally broader or asymmetric features is also observed. The CGR with r _c = 870nm has a resonance with Q-factor of approximately 1820 at a wavelength of 1562nm, which we investigate further by SNOM and pump-probe spectroscopy. The on/off contrast ratio reaches 10 – 20dB, which is determined by the height of the corresponding peaks compared with the transmission background. For resonances in the range 1520nm < λ < 1590nm, increasing the defect radius shifts certain resonances to longer wavelengths, as can be seen in Fig. 3. Outside this wavelength range towards the band edges of the circular Bragg mirror, no clear dependence on the size of the central defect is observed because these resonances are located in the outermost rings, which are not part of the Bragg mirror around the central defect.

In Fig. 4 the resonance wavelength is plotted as a function of the defect radius for five measured resonances presented in Fig. 3. Increasing the defect radius results in a linear increase of the wavelength which shows the very accurate fabrication. To identify the measured resonances, we calculate the dependence of the resonance wavelengths on the defect radius using 3D FDTD calculations on the isolated CGRs for various azimuthal orders m exploiting the cylindrical symmetry. The Q-factors of the calculated modes shown in Fig. 4 are between 400 and 12000. Increasing m leads to a decrease of the linear slope when the resonance wavelength is plotted as a function of the defect radius. Comparing the experimental data points with the simulations we find that the resonances with m = 15, m = 16 and 1550nm and 1580nm, m = 12 and m = 22 are the nearest simulated resonances, respectively. However, the agreement is not perfect, most probably because the influence of the waveguides is not taken into account in the simulations of the isolated CGR. Notably the resonance with m = 22 extends spatially into the outer Bragg rings where the waveguides penetrate the CGR. m = 19 match best. The optical field is mainly localized in the third and fourth ring around the defect, as illustrated at the top of Fig. 4, corresponding to the high azimuthal order of the resonances. For the resonances near 1550nm and 1580nm, m = 12 and m = 22 are the nearest simulated resonances, respectively. However, the agreement is not perfect, most probably because the influence of the waveguides is not taken into account in the simulations of the isolated CGR. Notably the resonance with m = 22 extends spatially into the outer Bragg rings where the waveguides penetrate the CGR.

 

Fig. 3. Measured transmission spectra of CGRs with the central defect radii r _c = 830, 850 and 870nm. The arrow indicates the resonance at λ = 1562 nm which is further investigated by near-field optical microscopy and pump-and-probe.

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For the waveguide-coupled CGRs it is not possible to take advantage of the cylindrical symmetry in the simulations as for the isolated CGRs. Hence, the required full 3D FDTD calculations with 5nm grid resolution in order to match quantitatively the measured and simulated transmission spectrum is not tractable even with a 2048-CPU supercomputer. Furthermore, effective-index approaches with mapping to a 2D device are not able model the essential device properties correctly because out-of-plane scattering is not taken into account. Yet for the resonances which are located within the inner Bragg rings the comparison to the isolated CGR seems reasonable because the waveguides do not alter the resonance mode significantly. An important point that can be derived from the simulations is that a fabrication inaccuracy of a few nanometers (see Sec. 3) would shift the resonances only slightly, which strengthens the confidence in the correct identification of the modes.

As can be seen from the transmission spectra of the CGRs, a large number of resonances exist. For applications such as ultrafast modulators it is necessary to work with a certain subclass of resonances in which the mode is almost exclusively located in the central defect. In what follows we focus on the device with a defect radius of 870nm showing a resonance at the wavelength of 1562nm. Simulations of the isolated CGR of this configuration yield a Q-factor of 3000. Adding the in- and out-coupling waveguides reduce the Q-factor, which is in agreement with the measured Q-factor of about 1820. We find additional modes in the simulation with m = 5 – 8 near this wavelength with Q < 400 which are not shown in Fig. 4. They are localized in the central defect but due to large vertical and radial losses they are not expected to be observed as a sharp resonance in the transmission experiment. Hence, such modes constitute the “background” around the transmission peak in Fig. 3 and are responsible for the broader features in the spectrum.

 

Fig. 4. The resonance wavelength as a function of the defect radius for the experimentally determined resonances as well as for isolated CGR calculated for different azimuthal orders m. Experimental data is indicated by black circles and lines, the calculations are shown as colored lines. Resonances with lower m feature a larger slope, e.g. the two very steep lines belong to resonances with m = 4 and m = 6. In order to avoid confusion only the resonances from the simulation which are near the experimental ones are labeled by their respective m. The calculated electric field distributions at the resonance wavelength of the modes m = 15, 16 and 19 with r _c = 870nm are displayed above the graph.

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To study the modal intensity distribution in more detail, we perform SNOM measurements. This allows us to probe the details in the optical intensity distribution inside the CGR at a resolution that cannot be obtained by conventional far-field microscopy. In addition to a resolution of about 100nm (λ/15), SNOM provides direct access to evanescent fields [23] and allows a quantitative measurement of propagation losses [24].

 

Fig. 5. Intensity distribution of the resonance at λ = 1562nm indicated in Fig. 3 measured with the SNOM. The layout of the CGR is schematically illustrated.

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The SNOM tip is produced from a single-mode optical fiber with a commercial pipette puller and is glued along the side of one prong of a quartz-crystal tuning fork. The other end is connected to an infrared single-photon-counting avalanche photodiode. To image the surface topography, the tip is scanned over the surface of the device, while the distance is actively controlled to about 10nm using a shear-force mechanism [25]. At the same time, the laser frequency is tuned across the resonance at each scan position, and thus the topography and a high resolution optical image are recorded simultaneously. The observed intensity distribution is in general a combined measure of the evanescent field as well as the scattering losses. Details about the application of SNOM in imaging light propagation and confinement in photonic structures can be found in [26].

We investigate the resonance at λ = 1562nm of the CGR with r _c = 870nm [see arrow in Fig. 3(a)]. Continuous-wave laser light at the resonance wavelength is coupled into the device from a waveguide. In order to compensate for possible resonance shifts due to the vicinity of the SNOM probe we continuously sweep the wavelength between λ-0.5nm and λ +0.5nm during the measurement. Figure 5 shows a SNOM image, onto which a schematic design of the CGR has been overlaid. The light enters from the bottom. We observe a scattering at the junction between the waveguides and the CGR as well as a confinement in the central region that is consistent with a mode of small azimuthal order. However, the observed intensity distribution extends beyond the central defect into the innermost Bragg rings which might be an indication that both the high-Q mode with m = 15 and low-Q modes with lower azimuthal order are excited at the same time. This would be consistent with the measured transmission spectrum with a sharp peak and a broad “background”. While the high-Q mode with m = 15 is detected by its evanescent field, the modes with lower azimuthal order are detected by the fiber probe in an amplified way due to the large vertical losses from the central defect which causes the low Q. The light at the outer circular edge originates from radial leakage from the resonator.

From the SNOM measurement we find that scattering at the waveguides’ ends due to mode-mismatch is a major source of transmission loss. However, the nature of SNOM does not allow us to derive further quantitative conclusions on the losses. Furthermore, the mode is not fully confined within the central defect. When the CGR device is used as a light modulator the shift of the resonant wavelength will be reduced when the refractive index of the central defect is modulated. These results help to locate the issues that could be addressed in improved future CGR designs.

In the following, we evaluate the applicability of this new type of resonant device as fast optical modulator. Optical or electrical injection of charge carriers into the resonator induces shifts of the resonance wavelengths due to the plasma dispersion effect. This can be exploited for intensity modulations of signal light [1,2, 27]. For an analysis of the spectral and temporal switching characteristics of CGRs, the resonance of a device with a defect radius of 870 nm, showing a resonance at λ = 1562nm, is investigated in a femtosecond pump probe setup [28, 29].

Pump pulses of 120fs duration at a repetition rate of 82MHz are derived from a Ti:sapphire laser at 800 nm wavelength and focused onto the CGR for photoexcitation of electron-hole pairs. The spectral response of the CGR resonator is probed by 220 fs pulses from a synchronously pumped optical parametric oscillator tuned to the central wavelength and full width at half maximum of 1565nm and 15nm, respectively. These pulses are coupled to and from the CGR device as described above for linear characterizations. In this case, however, the transmitted light is detected by an optical spectrum analyzer with the resolution set to 0.1nm. An adjustable time delay between the pump and probe pulses is provided by a motorized translation stage, thus enabling a time-resolved investigation of the transmission spectrum after optical excitation.

The temporal evolution of the transmission spectrum of the CGR investigated is shown in Fig. 6(a). The energy per incident laser pulse is 0.21 nJ, and the spot diameter on the sample is 28 μm. Photo excitation of charge carriers in the silicon CGR structures results in a clear blue shift of the resonance from its initial value of λ ₀ = 1563.6nm due to the plasma dispersion effect [30]. Here we have defined Δt = 0 as the point of maximum wavelength shift, and the time delay is varied in steps of 6ps. At positive time delays, the resonance shifts back towards its equilibrium on a time scale that is determined by the free carrier lifetime inside the silicon structures and is obviously longer than the measured time window.

For quantitative analysis, Fig. 6(b) depicts the time-dependent center wavelength of the CGR resonance extracted from the data in part (a). The maximum wavelength shift at zero time delay is Δλ = -0.41nm, corresponding to a relative wavelength shift Δλ/λ ₀ = -2.6 × 10^-4. The time evolution of the wavelength shift is a direct measure of the transient charge carrier density in the CGR device. Applying an exponential fit to the wavelength shift recovery after optical excitation results in an exponential decay constant, i.e., a free carrier lifetime, of 500ps. This value is comparable to typical lifetimes of charge carriers in SOI microring resonators and represents a fundamental limit for data rates in all-optical switching applications [2]. For high-speed applications, however, this lifetime can be further reduced by, e.g., ion implanting [28, 29, 31, 32] or electrically biasing the central defect of the CGR [1, 27].

As the excitation spot covers the entire device including the circular Bragg mirrors, the observed resonance shift must be a result of refractive index modulations in both the central defect and the ring structure. Hence, in a first approximation, we can assume that the wavelength shift of the CGR resonance is given by Δλ/λ ₀ = Δn/n ₀, with n ₀ = n _Si = 3.48 the unperturbed silicon refractive index. By calculating the excited electron-hole density N _eh in the CGR device, taking into account the laser spot size and the silicon absorption coefficient at 800 nm wavelength, α _Si = 1500 cm^-1, it is possible to estimate the maximum refractive index change Δn at zero time delay. We obtain an excitation density N _eh = 2.1 × 10¹⁷cm^-3, which corresponds to Δn = -8.0 × 10^-4 or Δn/n ₀ = -2.3 Δ 10^-4 according to the well-known Soref equation [30]. This value is in good agreement with the measured resonance shift Δλ/λ ₀ = -2.6 × 10^-4. However, we have not taken into account confinement effects of the optical mode in the silicon structures, and thus this agreement can only been understood as a rough comparison. Furthermore, one has to consider that slight variations in the laser spot size result in strong modifications of the excitation density.

 

Fig. 6. (a) Time-resolved transmission spectrum of the CGR (r _c = 870nm) after optical excitation with 0.21 - nJ femtosecond pulses. The normalized intensity scale is colored in linear units. (b) Extracted shift Δλ of the center wavelength as function of time delay.

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We further evaluate the dependence of excitation intensity on the CGR resonance wavelength shift. Figure 7(a) shows the time-dependent wavelength shift of the CGR investigated for different switching pulse energies between 0.11 and 0.53 nJ. In each measurement, the resonance wavelength is blue-shifted upon optical excitation and a rise time down to 10 ps. The resonance wavelength shift Δλ(Δt = 0) depicted in Fig. 7(b) increases with increasing pulse energies from -0.20 to -0.88nm. Applying a linear fit to these data results in a slope δ(Δλ)/δE = -1.71 nm/nJ that describes a linear relation between the wavelength shift and the laser pulse energy E at 800 nm wavelength. Thus about 500 pJ are required to switch the resonance wavelength by one full width at half maximum of the resonance peak. This dependence can easily be optimized by choosing a shorter wavelength with higher absorption coefficient in silicon and tighter focusing of the laser spot – preferably down to the dimension of the central defect. Furthermore, this device also allows lateral on-chip coupling of switching pulses in the IR wavelength range below the silicon band gap by adding a second straight silicon waveguide, e.g., perpendicular to the intensity modulated waveguide [33].

 

Fig. 7. (a) Time-resolved wavelength shift of the CGR (r _c = 870 nm) after optical excitation with pulse energies between 0.11 and 0.53nJ. (b) Extracted maximum wavelength shift Δλ(Δt = 0) as function of pulse energy. The dashed line is a linear fit to the data.

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5. Conclusion

We have demonstrated the basic viability of waveguide-coupled CGRs as integrated optical resonators with small modal volume. The structures are fabricated with SOI technology, which allows the mode volume to be shrunk down to a few cubic wavelengths. Transmission measurements show that the CGRs investigated have a quality factor of a few thousands with a peak-to-background contrast ratio of 10 to 20dB and a transmission of about 10 to 20%. Increasing the central defect size of the CGR shifts the resonances to longer wavelengths, as expected. From 3D FDTD simulations of the isolated CGR, we were able to identify the measured resonances. With SNOM we were able to obtain a high-resolution optical image of the evanescent field distribution as well as the vertical losses of the resonances. Furthermore, we performed pump and probe measurements to demonstrate the all-optical switching behavior. We observe a shift of the resonant wavelength within about 10ps after optical pumping, whereas the relaxation time back towards its equilibrium is a few hundreds of picoseconds because of the large carrier lifetime in silicon.

These results represent the first steps towards a novel kind of waveguide-coupled ultra-small footprint microcavity as a candidate for switching devices. Further improvements in the CGR design will address the coupling to the waveguides in order to reduce coupling loss and increase the total device transmission. Azimuthal trenches in the Bragg mirrors will help to suppress unwanted resonances in the Bragg mirror rings.