1. Introduction

Optical microresonators hold great potential for many fields of research and technology [1]. The light inside such resonators is strongly confined, both spatially and temporally. Consequently, very high intracavity intensities are obtained with only moderate optical powers coupled into the resonator. This makes optical microresonators ideal tools for efficient coupling of light and matter. More quantitatively, these light-confining properties are characterized by the resonator’s mode volume V and its quality factor Q. For a given in-coupled power, the resulting intra-cavity intensity is then proportional to the ratio of Q/V. The highest values of Q/V to date have been reached with whispering-gallery-mode (WGM) microresonators [2]. WGM microresonators are monolithic dielectric structures in which the light is guided near the surface by continuous total internal reflection [3]. Due to their strong intensity enhancement WGM microresonators have been successfully employed for numerous applications, ranging from microlasers [4–6] to cavity quantum electrodynamics (CQED) [7,8] and nonlinear optics where they greatly enhance light-light interactions [9,10]. If the resonator material exhibits a third-order susceptibility χ ⁽³⁾, its refractive index depends on the intracavity intensity via the Kerr effect n=n ₁+n ₂×I, where n is the refractive index, n ₂ = Re(χ ⁽³⁾) is the nonlinear refractive index, and I is the intensity of the light field. A variation of the intra-cavity intensity then modifies the cavities optical path length and thus changes the transmission properties of the microresonator. This effect is used in the field of “all-optical switching”, i.e., the control or redirection of the flow of light using a second light field. Here, we present all optical switching via the Kerr effect at record-low powers using a novel WGM microresonator, the so-called “bottle microresonator” [11–14].

For a given input power, the nonlinear shift of the resonance frequency in units of the resonator linewidth is proportional to n ₂ Q ²/V. We recently demonstrated that bottle microresonators can exhibit ultra-high intrinsic quality factors of up to Q ₀ = 3.6×10⁸, as well as mode volumes as small as 6070 (λ/n)³ at a wavelength of λ =852 nm, where n=1.467 is the refractive index of silica [14]. This results in an intrinsic Q ² ₀/V value as high as 2.1×10¹³(λ/n)⁻³. This enables the observation of nonlinear effects at very low powers which might even range down to the single photon level when resorting to cavity quantum electrodynamics effects. In addition, using the evanescent field of sub-micron diameter tapered fiber couplers, the bottle microresonator allows one to couple light into and out of its modes with high efficiency by frustrated total internal reflection [15–17]. Finally, the mode geometry allows one to simultaneously access the resonator with two coupling fibers, see Fig. 1, without the spatial constraints inherent to equatorial WGMs typically employed in microspheres and microtoroidal resonators. This facilitates the use of the bottle microresonator as a four-port device in a so-called “add-drop configuration”.

2. Experiment

We fabricate bottle microresonators from standard optical glass fibers. First, a few millimeters long section with a homogeneous diameter is created by elongating the fiber while heating the section with a scanned CO₂-laser beam. Next, two microtapers are realized by locally heating the tapered fiber waist with the focused CO₂-laser beam while slightly stretching it. The resulting bulge between the two microtapers forms the bottle microresonator. The resonators used here have a maximum diameter of 35-42 µm.

 

Fig. 1. Schematic of a bottle microresonator operated in the so-called “add-drop configuration”. The ray path corresponding to the whispering-gallery-mode is indicated by the red line. In addition to the radial confinement by continuous total internal reflection at the resonator surface, the light is confined in the axial direction by an angular momentum barrier. At the two axial turning points (called “caustics” in the following) the resonator light field can be accessed with two tapered fiber couplers. As a function of its frequency, light propagating on the “bus fiber” is selectively coupled into the resonator mode and exits the resonator through a second ultrathin fiber, referred to as the“drop fiber”.

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2.1. High-efficiency narrow-band add-drop filter

We first examine the linear optical properties of the bottle microresonator coupled to two fibers as shown in Fig. 1. In this configuration, the bottle microresonator acts as a filter which frequency selectively transfers light from the bus fiber to the drop fiber. In communication technology such devices are called add-drop filters and are used for de-/multiplexing optical signals [18, 19]. In the past, microresonator-based add-drop filters have been extensively studied [20–22]. However, most of these devices featured low to moderately high Q factors resonators and their Q ²/V values were comparatively low. Consequently high optical powers are required for potential non-linear applications. Moreover, high transfer efficiencies in resonator-based add-drop filters can only be obtained if the resonator-waveguide coupling rate dominates the resonator loss rate. This implies a further reduction of the Q factor of the loaded resonator. To our knowledge, the only add-drop filters based on ultra-high quality factor microresonators so far have been realized with WGMs [23]. In conjunction with the sub-percent losses of the resonator-waveguide coupling junction [17], this resulted in transfer efficiencies of 93 % at a loaded quality factor of 3.3×10⁶. However, optical switching has not been studied with this system.

In order to realize the add-drop configuration shown in Fig. 1, we place the waists of two tapered fibers with a diameter of 500 nm at the axial position of the caustics of one particular resonator mode. The transmission of the bare tapered fibers after fabrication is as high as 97 %. Different axial modes can be accessed by scanning the position of both fibers along the resonator axis via servomotor-driven translators with 100 nm resolution. The gap between the fiber waists and the resonator is comparable to the decay lengths of the evanescent fields of both structures, i.e., a few hundred nanometers, and is controlled with a resolution of 10 nm using a piezoelectric actuator. We investigate the spectral properties of this system by means of a distributed feedback (DFB) diode laser operating around 850 nm with a short-term (< 5 µs) linewidth of 400 kHz. The frequency of this laser can be tuned over 1.1 THz by temperature modulation while fine tuning over a range of 20 GHz is achieved by modulating the input current (−3 dB modulation bandwidth of 10 kHz). The polarization of the laser light field at the bus fiber waist is matched to the respective “bottle mode” using a quarter- and a half-wave plate. A photodiode is used to monitor the transmission through the bus fiber. When light is coupled into a bottle mode, a Lorentzian-shaped dip in the detected power occurs, see Fig. 2. By carefully adjusting the coupling fiber—resonator gap, we realize so-called critical coupling [16] where the incident optical power is almost entirely transferred to the resonator and the transmission of the coupling fiber at resonance ideally drops to zero. By reducing the gap between the drop fiber and the resonator, light can be coupled into the second waveguide and is monitored via another photodiode (Fig. 2). The coupling strength of the waveguides to the bottle mode is characterized by the time constants τ _bus and τ _drop which quantify the exponential decay of the intracavity intensity caused by each waveguide. The resulting additional losses give rise to a loaded quality factor Q _load of the resonator which is given by

 

Fig. 2. Resonant power transfer between two tapered optical fibers coupled to the evanescent field of a bottle mode with ultra-high intrinsic quality factor. The plot shows the powers at the waists of the bus fiber P ^bus _out (purple dots) and the drop fiber P ^drop _out (blue dots) while the frequency of the probe laser is swept over the resonance. A loaded quality factor of Q _load = 7.2×10⁶ and a power transfer efficiency E = 0.93 was inferred by fitting a Lorentzian to both signals (red curve). The inset shows the power transfer efficiency between both fiber waists at the critical coupling point as a function of Q _load. The data shows excellent agreement with the theoretical linear prediction, however, for high loaded quality factors, we observe a slight modal splitting [47], leading to an underestimation of the quality factor. Excluding the three rightmost datapoints, a fit of Eq. (4) (blue line) yields an intrinsic quality factor of Q ₀ = 1.8×10⁸. The red arrow indicates the datapoint extracted from the measurement shown in the main plot.

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where Q ₀ and τ ₀ correspond to the intrinsic quality factor and the intrinsic photon lifetime of the resonator, respectively, and ω/2π is the frequency of the light field. In order to achieve efficient power transfer between the fibers, the light has to be coupled to the drop fiber much faster than it is dissipated inside the resonator. Quantitatively, this is described by the relation

where T and E are the transmitted and dropped powers normalized to the input intensity [23]. The highest transfer efficiency between both fiber waists is obtained for critical coupling, defined by

resulting in a vanishing value for T. Inserting Eq. (3)into Eq. (2), the transfer efficiency is then given by

Except when stated otherwise, we work under the condition of critical coupling in all measurements described in the following in order to obtain the highest possible power transfer on resonance. In order to verify the relation in Eq. (2), the frequency of the probe laser is scanned over a bottle mode with a 10−µm separation between the two caustics and an intrinsic quality factor of Q ₀ = 1.8×10⁸. The powers at both output ports are monitored. In order to characterize the performance of the resonator independently of the losses in the transitions of the tapered fibers we correct for these losses and obtain the powers at the waist of the bus fiber P ^bus _out and the drop fiber P ^drop _out behind the resonator-fiber coupling junction. We also correct the input power P _in to obtain the value at the fiber waist in front of the coupling junction. In the following we carry out this correction whenever only the resonator performance is to be characterized. In contrast, when demonstrating applications like all-optical switching or routing, we quote the power launched into the input of the bus fiber and the powers at the outputs of the bus and the drop fiber. In subsequent measurements, the gap between the drop fiber and the resonator is reduced while the bus fiber gap is simultaneously adjusted to maintain the condition of critical coupling. Fig. 2 shows one such measurement for a particular gap size. From a Lorentzian fit, we determine a line width of Δν _load = 49 MHz, corresponding to a loaded quality factor of Q _load = 7.2×10⁶, and a transfer efficiency of E = 93 % between the fiber waists. The overall transfer efficiency E _tot, including the losses at the taper transitions to the ultrathin fiber waists, remains as high as E _tot = 90 %. The inset shows the power transfer efficiency between the fiber waists versus Q _load. Fitting Eq. (4) to this data yields an intrinsic quality factor of Q ₀ = 1.8×10⁸. We note that the performance of our device in terms of combining high-efficiency filter functionality, high loaded quality factor, and single mode fiber operation lines up with the best to date [23].

2.2. Optical Kerr bistability at microwatt power levels

Next we investigate the nonlinear properties of the bottle resonator that arise from the third order susceptibility of silica χ ⁽³⁾. The nonlinear refractive index of silica is n ₂ = Re(χ ⁽³⁾) = 2.5×10⁻¹⁶ cm²/W for a wavelength of 804 nm [24]. It thus is two to three orders of magnitude lower than for common nonlinear materials like As₂Se₃ chalcogenide glass [25] or the common nonlinear polymer MEH-PPV [26]. At the same time, however, the absorption coefficient of As₂Se₃ chalcogenide glasses is on the order of α = 0.23 m⁻¹ and the losses in MEH-PPV are α = 1.6 m⁻¹. For comparison, silica exhibits a very low absorption coefficient of α = 4.5×10⁻⁴ m⁻¹ at 852 nm [27] which enables the ultrahigh quality factors observed in silica WGM resonators. Therefore, the n ₂ Q ²/V ratio of ultrahigh Q silica WGM microresonators ranks among the highest that can be realized, making them ideal candidates for all-optical switching applications.

 

Fig. 3. Optical bistability in a bottle resonator. In order to characterize the bistable behavior of bottle modes, the input power is pulsed and the laser frequency is initially detuned from resonance by δ =−1.2 Δν. (a) Response of the system to a pulse with a duration of τ _pulse = 1.25 µs (green). The plot shows P _in (green), P ^bus _out (blue) and P ^drop _out (purple). As soon as P _in exceeds a certain threshold, the light is resonantly switched to the drop fiber via the Kerr effect. (b) By plotting P ^bus _out and P ^drop _out versus P _in for the data shown in Fig. 3 (a) (identical color coding), bistable behavior is apparent for P _in ranging from 1.0 to 1.8 mW.

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Due to the nonlinearity of the bottle resonator material its transmission properties exhibit a bistable behavior. In order to observe this effect, we measure P ^bus _out and P ^drop _out as a function of P _in at a fixed “cold” laser—resonator detuning δ, i.e., the laser—resonator detuning for vanishing input powers. We control δ using a side-of-fringe power lock technique [28]: The output signal of the photodiode measuring the power transmitted through the bus fiber is fed back to the current modulation input of the laser via a PI control loop. The −3 dB bandwidth limit of the control loop is 10 kHz, limited by the bandwidth of the current modulation of the laser controller. The set-point of the lock corresponds to a negative detuning of δ = ν − ν ₀ = −1.2 Δν, where ν is the laser frequency, ν ₀ the frequency of the bottle mode under investigation, and Δν the FWHM value of the resonance. This corresponds to a 15 % reduction of the optical power transmitted through the bus fiber. In order to obtain a photodiode signal with a sufficient signal-to-noise ratio, input powers of 2–10 µW are used. For measuring the nonlinear response, the input power is then pulsed with a peak power of up to a few milliwatts, a bell-shaped envelope, and FWHM pulse durations ranging from τ _pulse = 30 ns − 10 ms using an acousto-optic modulator. A sample-and-hold circuit “freezes” the lock during this pulse.

Figure 3(a) shows the corresponding powers at the bus and drop fiber waists for the same mode as in Fig. 2 and for τ _pulse = 1.25 µs. The gap between the resonator and the drop fiber is chosen to yield a loaded quality factor of Q _load = 1.7×10⁷ for critical coupling. When P _in exceeds a threshold P ₁, the intracavity intensity reaches a critical value and the Kerr effect “pulls” the resonator mode into resonance with the laser frequency in a self-amplified process. Consequently, the intracavity intensity increases significantly and P _in has to be decreased to another threshold value P ₂, well below P ₁, before the resonator returns to the initial situation. Between the two switching events, the transmission through the bus fiber is strongly reduced due to critical coupling. At the same time, 84 % of P _in is transferred to the drop output. Fig. 3 (b) shows P ^bus _out and P ^drop _out as a function of P _in. The system shows a pronounced hysteretic behavior and, for a certain range of P _in, exhibits two stable states that are dependent on the previous history. This phenomenon is referred to as optical bistability and is well known in WGM resonators [29–31].

 

Fig. 4. (a) Dependence of the threshold power for optical bistability on the FWHM duration of the input pulses. This measurement was taken without the drop fiber. For pulse durations shorter than 100 µs the quasi-instantaneous Kerr effect dominates the thermo-optical effect due to the finite thermal relaxation time (~ 15 ms) of the resonator mode. “ON-OFF” switching of the transmission through the bus fiber via the Kerr effect is achieved at a threshold power of 50 µW. (b) Variation of the switching threshold as a function of the resonator bandwidth. The solid line is a square-law fit to the experimental data, confirming the quadratic dependency.

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We now show that the Kerr effect is indeed at the origin of the bistable behavior reported above. For this purpose, we measure the threshold P ₁ as a function of τ _pulse. For simplicity, we omit the drop fiber in this measurement and readjust the bus fiber-resonator gap such that critical coupling is restored. The measurement results are shown in Fig. 4 (a). For short pulse durations below 50 µs, the threshold power at the resonator fiber coupling junction has a constant value of about P ₁ = 50 µW. For longer pulses we observe a strong decrease of the threshold power. This is attributed to the onset of thermal effects which are known to dominate over the Kerr effect for pulse durations that are longer than the thermal relaxation time of the resonator mode [32]. The fact that P ₁ does not depend on the pulse duration for short pulses is a strong indication that the instantaneous Kerr effect is the prevailing non-linear mechanism and that thermal effects can be neglected for high switching speeds. In order to further confirm this conclusion, we independently measure the thermal relaxation time of the resonator mode under investigation by tracing its frequency shift over time after an abrupt change of the intracavity power. This measurement yields a relaxation time of τ _therm = 13−15 ms, consistent with results obtained for microspheres [33]. For pulse durations τ _pulse ≪ τ _therm switching is therefore exclusively due to the Kerr effect. We note that for pulse durations τ_pulse ≫ τ _therm one expects a second plateau of P _in. However, such pulse durations are inaccessible in our experiment because the drift of the laser—microresonator detuning in the absence of active stabilization is too large on these timescales. The values measured for P _in in this work are consistent with powers for which Kerr bistability is observed in microspheres with comparable quality factors at cryogenic temperatures via deformation of the line shape [31]. We note that our value of P ₁ = 50 µW is, to the best of our knowledge, the smallest value ever reported for bistable switching via the Kerr effect.

In principle, the Kerr effect allows one to realize almost arbitrary switching speeds due to its instantaneous response. In resonator-based switching schemes, however, the speed is limited by the −3 dB bandwidth of the resonator, given by B = Δν = ν/Q _load. This means that the switching speed can be raised at the expense of reducing Q _load which will in turn increase the switching threshold, P ₁ ~ Q ⁻² _load. Our set-up allows us to investigate this mechanism. By changing the gap between the resonator and the drop fiber while simultaneously adjusting the bus fiber gap to maintain critical coupling, Q _load can be varied over a wide range. Figure 4 (b) shows the dependency of P ₁ on B. As expected, the ratio of P ₁/B ² is constant at a value of 4.5 µW/MHz² All-optical signal processing is thus possible within the rage of bandwidths accessible with this method, albeit at higher threshold powers. For example, a switch with a bandwidth of 1 GHz will require a threshold power of 4.5 W.

We now compare the performance of our system in terms of switching threshold and speed with the state-of-the-art. We limit our discussion to schemes that rely, as for our case, on an optical bistability which allows power-controlled switching of a single-wavelength signal. We note that another class of all-optical switching schemes relies on the switching of the signal by means of a pump field which modifies the resonator properties. However, the one- and two-wavelength schemes are neither directly comparable nor do they provide the same functionality.

The lowest bistable switching thresholds were reported for photonic crystal cavities using the thermo-optic effect [34, 35]. The lowest measured value of P ₁ = 6.5 µW was observed in a photonic crystal microresonator made of GaAs [35]. The bandwidth for such thermo-optical switches is, however, only on the order of 1 MHz because the thermal relaxation times in photonic crystal cavities amount to at least 100 ns [34, 36]. These switches thus offer a slightly lower switching threshold but are fundamentally limited in their switching speed and yield a P ₁/B ² ratio comparable to our system. Moreover, to our knowledge, no add-drop functionality has been experimentally realized with photonic crystal cavities so far. Thermo-optical bistability has also been observed in silicon ring-resonators at a switching threshold of 1.3 mW [37]. Here, the bandwidth was found to be 500 kHz, thereby reaching a P ₁/B ² ratio three orders of magnitude worse than in our case.

Optical switching can also be achieved using free carrier nonlinearities induced by one- or two-photon absorption in semiconductors. Many of the corresponding experiments rely on the above-mentioned two-wavelength pump-probe optical switching schemes [38–40] and will not be further discussed here. At the same time, free carrier nonlinearities were employed to realize single-wavelength optical switching in bistable semiconductor etalons, see [41] and references therein. In these devices, typical switching threshold powers exceed 1 mW while the bandwidth ranges around 100 MHz, limited by the carrier recombination time and/or diffusion speed. For example, values of P ₁ = 8mW and B=160 MHz or P ₁ =2mW and B=80 MHz were reported in [41] and [42], respectively. In both cases, this yields the same P ₁/B ² ratio which exceeds our value by one order of magnitude. However, due to their relatively high intrinsic losses, the bistable etalons are not suited for operation in transmission. Operation in reflection mode therefore limits their use in all-optical signal processing to “ON-OFF” switching of the power in one channel while routing of signals between two channels is not possible. Moreover, the physical mechanism leading to the nonlinearity is strongly wavelength dependent. The devices therefore have to be optimized for operation at a particular wavelength. The Kerr effect used in our system, on the other hand, prevails over a much larger spectral range.

2.3. All-optical signal processing

Next, we demonstrate all-optical signal processing using a bottle mode in add-drop configuration. The loaded quality factor in this case is Q _load = 1.5×10⁷ at critical coupling. The laser frequency is initially locked to the mode with a detuning of δ =−1.2 Δν from resonance. Fig. 5 shows the realization of all-optical routing. The signal beam is repeatedly routed between the bus and the drop fiber with a rate of 1 MHz. The signal path is controlled by the input power P _in. As already mentioned above, in order to characterize the performance of the system as a whole, we now quote the powers launched into the input of the bus fiber and detected at the outputs of the bus and the drop fibers. For simplicity we keep the notation used above and denote these values as P _in, P ^bus _out and P ^drop _out. Consequently, P ₁ and P ₂ also refer to values at the input of the bus fiber. Using an acousto-optical modulator driven by an arbitrary waveform generator, we abruptly change P _in from a value below to a value above the bistable regime, delimited by P ₂ and P ₁. About 70%of the power launched into the bus fiber exits the drop fiber in the corresponding “HIGH” state. The modulation depth between the HIGH-state and the LOW-state power levels at both outputs is 9 dB. To the best of our knowledge, this is the first time that a continuous wave signal is routed between two output channels using a single-wavelength scheme. As pointed out above, all previous bistable single-wavelength schemes only demonstrated ON-OFF switching. Single-wavelength all-optical routing of a pulsed signal was demonstrated in an interferometric switch incorporating a microring resonator [43]. Intense laser pulses, corresponding to peak powers of 40 W, were necessary to operate this device.

 

Fig. 5. Demonstration of all-optical switching using the optical Kerr bistability in a bottle microresonator. P _in (green) is varied between two levels which are located below and above the bistable regime (schematically indicated by the dashed lines) as shown in the inset. At the same time the power at the outputs of the bus fiber (blue) and the drop fiber (purple) is monitored. As soon as the input power exceeds P ₁, i.e., the threshold power for optical bistability, 70 % of the incident light is transferred to the output of the drop fiber. Lowering the input power below P ₂ again reverses the situation at the outputs.

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Due to its bistability, our system can also be operated as a so-called “optical memory”. For this purpose, we choose an operating power P _in = P ₃ which lies within the bistable regime, see Fig. 6. At this power, the system exhibits two stable output states. Changing P _in to a power higher than P ₁ or lower than P ₂ switches between these two states. When returning to P ₃, the system then stays in the chosen state. Single wavelength optical memories have so far been realized with microring resonators using thermally induced bistability [37] and with etalons using free carrier nonlinearities [42]. In both cases, only ON-OFF functionality was demonstrated since no drop channel was implemented. Our optical memory, on the other hand, is a true add-drop device, meaning that it allows one to route a signal between its two output ports. Since the optical memory is operated in the bistable regime, it is quite sensitive to thermal fluctuations and drifts. Therefore, the residual absorption of the signal light currently limits the storage time of our optical memory to the sub-microsecond range, see Fig. 6. A similar limiting effect has also been reported in [42].

 

Fig. 6. Demonstration of optical memory functionality in a bottle resonator using the Kerr effect. For an input power level (green) in the bistable regime (P _in = P ₃, as indicated by the arrow) the power at the outputs of the bus fiber (blue) and of the drop fiber (purple) exhibits two stable states. The output state is chosen by temporarily lowering (raising) P _in below (above) the bistable regime, which is schematically indicated by the dashed lines.

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3. Conclusion

We have presented optical add-drop filters and switches based on bottle microresonators, evanescently coupled to two sub-micron diameter fibers. This coupling method introduces only very small losses and allowed us to adjust the fiber-resonator coupling at will by varying the fiber-resonator gap. This enabled us to systematically study the power transfer efficiency of the add-drop filter as a function of its linewidth or, equivalently, its quality factor. We found excellent agreement between our data and the theoretical prediction and realized a power transfer efficiency of up to 93 % for a filter linewidth of only 49 MHz, corresponding to a loaded quality factor as high as 7.2×10⁶. Due to the favorable ratio of absorption losses to nonlinear refractive index of silica, we were able to observe optical bistability due to the Kerr effect at a record low threshold of 50 µW. Single wavelength all-optical switching of light between two standard optical single mode fibers with an overall efficiency of 70 % was demonstrated at rates of 1 MHz. This bandwidth depends on the loaded quality factor of the resonator and increases when this quality factor decreases. However, the increased bandwidth comes at the expense of an increased switching threshold. We investigated the corresponding dependency and found very good agreement with the predicted square law. Finally, we showed that the bottle resonator coupled to two fibers can also be operated as an optical memory that allows switching between its two bistable states with a single-wavelength signal which was accordingly routed to one of the two output ports.

Besides the all-optical functionality demonstrated here, we see future applications of the bottle resonator in the field of quantum information processing. In [14] we showed that the bottle resonator is well suited for experiments in cavity quantum electrodynamics. In particular, for the values listed above, Q _load/V is high enough to realize light-matter interaction in the so-called strong coupling regime [44]. Single atoms, resonantly coupled to the light field of the bottle resonator, would then give rise to single photon nonlinearities. At the same time, photons can be coupled into and out of the resonator mode with a high efficiency. In conjunction with the switching and filter functionality shown in this paper, this opens the route towards the realization of next-generation communication and information processing devices such as single photon all-optical switches [45] and single photon transistors [46].