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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 17 — Aug. 16, 2010
  • pp: 17764–17775
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All-optical signal processing at ultra-low powers in bottle microresonators using the Kerr effect

Michael Pöllinger and Arno Rauschenbeutel  »View Author Affiliations


Optics Express, Vol. 18, Issue 17, pp. 17764-17775 (2010)
http://dx.doi.org/10.1364/OE.18.017764


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Abstract

We present experimental results on nonlinear, ultra-low power photonics applications based on a silica whispering-gallery-mode microresonator. Our bottle microresonator combines an ultrahigh quality factor of Q > 108 with a small mode volume V. The resulting Q2/V-ratio is among the highest realized for optical microresonators and allows us to observe bistable behavior at very low powers. We report single-wavelength all-optical switching via the Kerr effect at a record-low threshold of 50 µW. Moreover, an advantageous mode geometry enables the coupling of two tapered fiber waveguides to a bottle mode in an add-drop configuration. This allows us to route a CW optical signal between both fiber outputs with high efficiency by varying its power level. Finally, we demonstrate that the same set-up can also be operated as an optical memory.

© 2010 Optical Society of America

1. Introduction

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

14. M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q Tunable Whispering-Gallery-Mode Microresonator,” Phys. Rev. Lett. 103, 053901 (2009). [CrossRef] [PubMed]

]. 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

15. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]

]. 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”.

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

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

16. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere Whispering-Gallery Mode System,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]

] 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.
Qload1=Q01+Qbus1+Qdrop1=1ωτ0+1ωτbus+1ωτdrop,
(1)

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

(1+QdropQ0)E=1T,
(2)

where T and E are the transmitted and dropped powers normalized to the input intensity [23

23. H. Rokhsari and K. J. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004). [CrossRef] [PubMed]

]. The highest transfer efficiency between both fiber waists is obtained for critical coupling, defined by

1τbus=1τ0+1τdrop,
(3)

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

E=12QloadQ0.
(4)

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

23. H. Rokhsari and K. J. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004). [CrossRef] [PubMed]

].

2.2. Optical Kerr bistability at microwatt power levels

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.

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

28. T. Carmon, T. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. Vahala, “Feedback control of ultra-high-Q microcavities: application to micro-Raman lasers and microparametric oscillators,” Opt. Express 13, 3558–3566 (2005). [CrossRef] [PubMed]

]: 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 = νν 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.

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.

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

32. H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett. 30, 427–429 (2005). [CrossRef] [PubMed]

]. 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

33. H. C. Tapalian, J.-P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photonics Technol. Lett. 14, 1118–1120 (2002). [CrossRef]

]. For pulse durations τ pulseτ therm switching is therefore exclusively due to the Kerr effect. We note that for pulse durations τpulseτ 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

31. F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998). [CrossRef]

]. 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

34. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005). [CrossRef] [PubMed]

, 35

35. E. Weidner, S. Combrié, A. de Rossi, N. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118 (2007). [CrossRef]

]. The lowest measured value of P 1 = 6.5 µW was observed in a photonic crystal microresonator made of GaAs [35

35. E. Weidner, S. Combrié, A. de Rossi, N. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118 (2007). [CrossRef]

]. 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

34. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005). [CrossRef] [PubMed]

, 36

36. L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009). [CrossRef] [PubMed]

]. 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

37. V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004). [CrossRef] [PubMed]

]. 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

38. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]

] 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

41. N. Peychambarian and H. M. Gibbs, “Optical nonlinearity, bistability, and signal processing in semiconductors,” J. Opt. Soc. Am. B 2, 1215–1227 (1985). [CrossRef]

] 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

41. N. Peychambarian and H. M. Gibbs, “Optical nonlinearity, bistability, and signal processing in semiconductors,” J. Opt. Soc. Am. B 2, 1215–1227 (1985). [CrossRef]

] and [42

42. J. He, M. Cada, M.-A. Dupertuis, D. Martin, F. Morier-Genoud, C. Rolland, and A. J. SpringThorpe, “All-optical bistable switching and signal regeneration in a semiconductor layered distributed-feedback/Fabry-Perot structure,” Appl. Phys. Lett. 63, 866–868 (1993). [CrossRef]

], 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

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.

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

37. V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004). [CrossRef] [PubMed]

] and with etalons using free carrier nonlinearities [42

42. J. He, M. Cada, M.-A. Dupertuis, D. Martin, F. Morier-Genoud, C. Rolland, and A. J. SpringThorpe, “All-optical bistable switching and signal regeneration in a semiconductor layered distributed-feedback/Fabry-Perot structure,” Appl. Phys. Lett. 63, 866–868 (1993). [CrossRef]

]. 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

42. J. He, M. Cada, M.-A. Dupertuis, D. Martin, F. Morier-Genoud, C. Rolland, and A. J. SpringThorpe, “All-optical bistable switching and signal regeneration in a semiconductor layered distributed-feedback/Fabry-Perot structure,” Appl. Phys. Lett. 63, 866–868 (1993). [CrossRef]

].

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.

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

14. M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q Tunable Whispering-Gallery-Mode Microresonator,” Phys. Rev. Lett. 103, 053901 (2009). [CrossRef] [PubMed]

] 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

44. P. R. Berman, Cavity quantum electrodynamics (Academic Press, 1994).

]. 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

45. P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2008). [CrossRef]

] and single photon transistors [46

46. D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nature Physics 3, 807–812 (2007). [CrossRef]

].

Acknowledgements

Financial support by the DFG (Research Unit 557), the Volkswagen Foundation (Lichtenberg Professorship), and the ESF (EURYI Award) is gratefully acknowledged.

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G. S. Murugan, J. S. Wilkinson, and M. N. Zervas, “Selective excitation of whispering gallery modes in a novel bottle microresonator,” Opt. Express 17, 11916–11925 (2009). [CrossRef]

14.

M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q Tunable Whispering-Gallery-Mode Microresonator,” Phys. Rev. Lett. 103, 053901 (2009). [CrossRef] [PubMed]

15.

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]

16.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere Whispering-Gallery Mode System,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]

17.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003). [CrossRef] [PubMed]

18.

T. A. Ibrahim, V. Van, and P.-T. Ho, “All-optical time-division demultiplexing and spatial pulserouting with a GaAs/AlGaAs microring resonator,” Opt. Lett. 27, 803–805 (2002). [CrossRef]

19.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid,” IEEE Phot. Technol. Lett. 11, 691–693 (1999). [CrossRef]

20.

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery-modes - part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2006). [CrossRef]

21.

K. Vahala, Optical microcavities (World Scientific, 2004). [CrossRef]

22.

J. Heebner, R. Grover, and T. A. Ibrahim, Optical microresonators (Springer, 2008).

23.

H. Rokhsari and K. J. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004). [CrossRef] [PubMed]

24.

A. J. Taylor, G. Rodriguez, and T. S. Clement, “Determination of n2 by direct measurement of the optical phase,” Opt. Lett. 21, 1812–1814 (1996). [CrossRef] [PubMed]

25.

G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spälter, R. E. Slusher, S.-W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25, 254–256 (2000). [CrossRef]

26.

K. Koynov, N. Goutev, F. Fitrilawati, A. Bahtiar, A. Best, C. Bubeck, and H.-H. Hörhold, “Nonlinear prism coupling of waveguides of the conjugated polymer MEH-PPV and their figures of merit for all-optical switching,” Opt. Soc. Am. B 19, 895–901 (2002). [CrossRef]

27.

J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A 67, 033806 (2003). [CrossRef]

28.

T. Carmon, T. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. Vahala, “Feedback control of ultra-high-Q microcavities: application to micro-Raman lasers and microparametric oscillators,” Opt. Express 13, 3558–3566 (2005). [CrossRef] [PubMed]

29.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989). [CrossRef]

30.

V. S. Il’chenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

31.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998). [CrossRef]

32.

H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett. 30, 427–429 (2005). [CrossRef] [PubMed]

33.

H. C. Tapalian, J.-P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photonics Technol. Lett. 14, 1118–1120 (2002). [CrossRef]

34.

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005). [CrossRef] [PubMed]

35.

E. Weidner, S. Combrié, A. de Rossi, N. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118 (2007). [CrossRef]

36.

L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009). [CrossRef] [PubMed]

37.

V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004). [CrossRef] [PubMed]

38.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]

39.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photonics Technol. Lett. 14, 74–76 (2002). [CrossRef]

40.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and C. H. Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photonics Technol. Lett. 15, 36–38 (2003). [CrossRef]

41.

N. Peychambarian and H. M. Gibbs, “Optical nonlinearity, bistability, and signal processing in semiconductors,” J. Opt. Soc. Am. B 2, 1215–1227 (1985). [CrossRef]

42.

J. He, M. Cada, M.-A. Dupertuis, D. Martin, F. Morier-Genoud, C. Rolland, and A. J. SpringThorpe, “All-optical bistable switching and signal regeneration in a semiconductor layered distributed-feedback/Fabry-Perot structure,” Appl. Phys. Lett. 63, 866–868 (1993). [CrossRef]

43.

J. E. Heebner, N. N. Lepeshkin, A. Schweinsberg, G.W. Wicks, R.W. Boyd, R. Grover, and P.-T. Ho, “Enhanced linear and nonlinear optical phase response of AlGaAs microring resonators,” Opt. Lett. 29, 769–771 (2004). [CrossRef] [PubMed]

44.

P. R. Berman, Cavity quantum electrodynamics (Academic Press, 1994).

45.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2008). [CrossRef]

46.

D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nature Physics 3, 807–812 (2007). [CrossRef]

47.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669–1671 (2002). [CrossRef]

OCIS Codes
(190.1450) Nonlinear optics : Bistability
(190.3270) Nonlinear optics : Kerr effect
(210.4680) Optical data storage : Optical memories
(230.1150) Optical devices : All-optical devices

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 20, 2010
Revised Manuscript: July 26, 2010
Manuscript Accepted: July 28, 2010
Published: August 3, 2010

Citation
Michael Pöllinger and Arno Rauschenbeutel, "All-optical signal processing at ultra-low powers in bottle microresonators using the Kerr effect," Opt. Express 18, 17764-17775 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-17764


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References

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  2. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004). [CrossRef]
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  9. T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nature Phys. 3, 430–435 (2007). [CrossRef]
  10. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007). [CrossRef] [PubMed]
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  13. G. S. Murugan, J. S. Wilkinson, and M. N. Zervas, “Selective excitation of whispering gallery modes in a novel bottle microresonator,” Opt. Express 17, 11916–11925 (2009). [CrossRef]
  14. M. Pollinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q Tunable Whispering-Gallery-Mode Microresonator,” Phys. Rev. Lett. 103, 053901 (2009). [CrossRef] [PubMed]
  15. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]
  16. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere Whispering-Gallery Mode System,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]
  17. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003). [CrossRef] [PubMed]
  18. T. A. Ibrahim, V. Van, and P.-T. Ho, “All-optical time-division demultiplexing and spatial pulserouting with a GaAs/AlGaAs microring resonator,” Opt. Lett. 27, 803–805 (2002). [CrossRef]
  19. S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid,” IEEE Photon. Technol. Lett. 11, 691–693 (1999). [CrossRef]
  20. V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery-modes - part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2006). [CrossRef]
  21. K. Vahala, Optical microcavities (World Scientific, 2004). [CrossRef]
  22. J. Heebner, R. Grover, and T. A. Ibrahim, Optical microresonators (Springer, 2008).
  23. H. Rokhsari and K. J. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004). [CrossRef] [PubMed]
  24. A. J. Taylor, G. Rodriguez, and T. S. Clement, “Determination of n2 by direct measurement of the optical phase,” Opt. Lett. 21, 1812–1814 (1996). [CrossRef] [PubMed]
  25. G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Sp¨alter, R. E. Slusher, S.-W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25, 254–256 (2000). [CrossRef]
  26. K. Koynov, N. Goutev, F. Fitrilawati, A. Bahtiar, A. Best, C. Bubeck, and H.-H. H¨orhold, “Nonlinear prism coupling of waveguides of the conjugated polymerMEH-PPV and their figures of merit for all-optical switching,” Opt. Soc. Am. B 19, 895–901 (2002). [CrossRef]
  27. J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A 67, 033806 (2003). [CrossRef]
  28. T. Carmon, T. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. Vahala, “Feedback control of ultra-high-Q microcavities: application to micro-Raman lasers and microparametric oscillators,” Opt. Express 13, 3558-3566 (2005). [CrossRef] [PubMed]
  29. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989). [CrossRef]
  30. V. S. Il’chenko, M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).
  31. F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, and V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998). [CrossRef]
  32. H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett. 30, 427–429 (2005). [CrossRef] [PubMed]
  33. H. C. Tapalian, J.-P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14, 1118–1120 (2002). [CrossRef]
  34. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, and E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678-2687 (2005). [CrossRef] [PubMed]
  35. E. Weidner, S. Combrie, A. de Rossi, N. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118 (2007). [CrossRef]
  36. L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009). [CrossRef] [PubMed]
  37. V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004). [CrossRef] [PubMed]
  38. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]
  39. V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002). [CrossRef]
  40. T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and C. H. Lee, “All-optical switching in a laterally coupled microring resonator by carrier injection,” IEEE Photon Technol. Lett. 15, 36–38 (2003). [CrossRef]
  41. N. Peychambarian and H. M. Gibbs, “Optical nonlinearity, bistability, and signal processing in semiconductors,” J. Opt. Soc. Am. B 2, 1215–1227 (1985). [CrossRef]
  42. J. He, M. Cada, M.-A. Dupertuis, D. Martin, F. Morier-Genoud, C. Rolland, and A. J. SpringThorpe, “Alloptical bistable switching and signal regeneration in a semiconductor layered distributed-feedback/Fabry-Perot structure,” Appl. Phys. Lett. 63, 866–868 (1993). [CrossRef]
  43. J. E. Heebner, N. N. Lepeshkin, A. Schweinsberg, G. W. Wicks, R. W. Boyd, R. Grover, and P.-T. Ho, “Enhanced linear and nonlinear optical phase response of AlGaAs microring resonators,” Opt. Lett. 29, 769–771 (2004). [CrossRef] [PubMed]
  44. P. R. Berman, Cavity quantum electrodynamics (Academic Press, 1994).
  45. P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2008). [CrossRef]
  46. D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nature Physics 3, 807–812 (2007). [CrossRef]
  47. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669–1671 (2002). [CrossRef]

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