“Smart” Nanophotonic Elements and All-Optical Feedback Control Through Optical Forces and Potentials

Miloš A. Popović* and Peter T. Rakich

Research Laboratory of Electronics, Massachusetts Institute of Technology,

77 Massachusetts Avenue, Cambridge, Massachusetts, USA * e-mail: mpopovic@alum.mit.edu

Abstract

We describe recently proposed light-powered nanomachines and all-optical self-adaptive optomechanical circuits that rely on the interplay of resonantly-enhanced optical forces and the manipulation of optical resonances by mechanical degrees of freedom in nanophotonic structures [1]. This new class of devices facilitates resonantly tailored optomechanical potentials, enabling positional control of cantilevers with picometer precision and all-optically self-aligning microcavities that track the wavelength of an incident laser. These device concepts are examples of all-optical (optomechanical) feedback control that may be used to provide robustness and scalability in strong-confinement nanophotonic circuits that traditionally have extreme sensitivities.

1. Introduction Optical forces resulting from interacting modes and cavities can scale to large values as optical modes shrink to nanometer-scale dimensions [1-4]. Such forces can be harnessed in fundamentally new ways when optical elements are free to move and adapt to them through exchange of optical and mechanical energy. In recent work [1], we proposed the use of opto-mechanically coupled resonators as a general means of tailoring opto-mechanical potentials through the action of optical forces. We show that attractive and repulsive forces arising from opto-mechanically coupled cavity resonances can give rise to strong and highly localized opto-mechanical potential wells whose widths approach picometer scales. These potentials enable all-optical, self-adaptive behaviors such as the trapping and corralling (or dynamic-capture) of microcavity resonances with light [1]. As one example, we apply these concepts to the design of a novel resonator which dynamically self-aligns (or spectrally bonds) its resonance to an incident laser line all-optically (“passively”). Such “smart” resonators can adaptively track the wavelength of a laser-line through minimization of optomechanical energy [1]. Though these concepts are illustrated through dual-

Fig 1. Optomechanical potential synthesis in a dual-cavity system: (a) Proposed dual-ring cavity (b) ring cross-section (w = 500 nm, t = 200 nm, q = 250nm) (c) symmetric and (d) antisymmetric guided modes. (e) computed resonance map and (f) optomechanical potential. (g) potential with three different laser excitations in black. (h) computed potential (eV) for 1mW power. (i) computed potential (1mW) as detuning from resonance crossing tends to zero.

microring-cavity designs, broad extension to other photonic topologies is straightforward.

2. Dual-Microcavity Unit Cell for Optomechanical Potential Synthesis We explore these novel physical behaviors through coupled cavity systems such as the dual-microring resonator shown in Fig. 1(a). In this design, the lower ring and bus waveguide are assumed to be fixed while the upper ring moves unimpeded in the vertical direction in response to optically induced forces generated by the guided light. Close approximations of this arrangement can be realized using membrane or cantilever structures to suspend the upper ring, and could be achieved using available fabrication techniques [5]. This geometry enables strong coupling between nominally degenerate ring modes creating symmetric and antisymmetric supermodes [see Fig. 1(b)-(d)] whose frequencies are remarkably sensitive to device geometry. Fig. 1(e) shows that as the waveguide coupling strength, κ(q), is increased (or distance q decreased) a resonance frequency splitting that is linear in κ(q) (or exponential in q) results between the symmetric (blue) and antisymmetric (red) modes (4 µm microring radius assumed). Fig. 1(e) also reveals that strong coupling results in crossings between adjacent longitudinal resonance orders. These crossings give rise to fundamentally new means of manipulating optical resonances and mechanical structures when optomechanical forces and energy are considered, as illustrated in the following subsections.

2.1 Picometer-Scale Positional Control via Trapping Optomechanical Potentials Through open and closed system analyses of optomechanical energy [1], we show that the resonant excitation of the symmetric ring system supermode results in attractive forces between the rings, while excitation of the antisymmetric mode results in repulsive forces [1-3]. If the system is excited (via the bus waveguide) by a monochromatic laser-line both the symmetric and anti-symmetric microring supermodes can be excited as the separation between the rings (q) is varied (due to the large frequency splitting afforded by this geometry). If, for instance, the system is excited by a fixed laser-line at 200 THz, or 1500nm wavelength (represented by a vertical dotted line in Fig. 1(e)), resonant alignment of the cavity modes will be achieved at various coupling strengths, κ(q), corresponding to different positions, q. Since both attractive and repulsive forces are generated (respectively) by the symmetric and antisymmetric resonances excited along this trajectory of motion, nontrivial optomechanical potentials are created as well. For instance, the rigorously computed normalized effective potential (Un) is shown in Fig. 1(f) corresponding to the (laser) frequencies and coupling strengths seen in Fig. 1(e) [here Un(q) = Ueff(q)/ Φ, where Φ is the incident photon flux and is Planck’s constant]. The 200-THz laser frequency (shown as a vertical dotted line in Fig. 1(e)) can be seen as a solid projected line on the surface map of Fig. 1(f). Along this trajectory, two minima of optomechanical potential are seen, which result from resonant excitation of cavity modes of differing symmetries. These minima of potential indicate that the system can be trapped, effectively pinning the optomechanical system at positions, q, corresponding to the placement of symmetric and antisymmetric modes at positions q on either side of being resonant with the laser-line. Moreover, if a single laser-line is continuously swept toward the resonance crossing [over the trajectory shown by laser-lines indicated by the solid lines labeled (1)-(3) of Fig. 1(g)] one can adiabatically narrow the potential from a wide square-well to a δ-function, effectively allowing us to corral the system to one of several localized positions in space. The evolution of the potential for laser-lines (1)-(3) can be seen in Fig. 1(h) for a

Fig 2. Self-aligning, laser-line-following “smart” resonator: (a) Self-aligning cavity which combines (b) resonant and (c) non-resonant potentials; (d) computed optomechanical potential; (e) plot showing the alignment of the potential minimum (red) with the resonant field enhancement within the cavity mode (blue).

realistic guided power of 1 mW within the bus waveguide (or Φ ~ 1016 photons/sec). We note that for these modest powers the depth of the potential well (~30 eV) is far greater than kBT, and the optically induced forces corresponding to this potential are 1 to 10μN in magnitude, which are sufficient to dominate in experimentally realistic situations [1,4]. Furthermore, in the limit of small detuning from the resonance crossing, the spatial localization of the trapping potential scales to narrow values that go far below the linewidth of the resonances set by the external coupling to the waveguide. This interesting effect is due to the existence a narrow linewidth supermode [1], and will be explained further in the presentation.

2.2 Bound Optomechanical States and Self-Aligning “Smart” Microcavities

From the potential map seen in Fig. 1(f)-(g), it is clear that the microcavity system’s resonances – and its mechanical degree of freedom – can be manipulated in truly unique ways, all-optically. Of particular utility is the formation of a “resonantly-bound” optomechanical state, which can be used to stabilize a mechanical structure with remarkable spatial resolution, and tune the resonance over large frequency ranges through proper placement of one or more laser-lines [1]. In addition, these bound states can be made to adapt to the laser-line if resonant and non-resonant potentials are combined within a single device [Fig. 2(a)-(c)]. In this case, we showed that a localized optomechanical potential well can be formed which tends to pin the optomechanical system such that the cavity mode remains resonant with the laser line [e.g. see Fig. 2(d)-(e)]. Such self-adaptive (or “smart”) optomechanical systems would have the remarkable ability to self-align with an incident laser line, and follow it to any wavelength to which it is tuned.

3. Applications for Light-Powered Nanomachines and All-Optical Feedback These and similar self-adaptive optomechanical systems have the potential for far reaching impact in integrated photonic systems in part due to their ability to eliminate complex electronic feedback controls necessary to implement numerous optical functions. Strong-confinement nanophotonic circuits [6,7], due to their unique properties such as support for wavelength-scale, high-Q resonators, enable chip-scale solutions and unique functionalities for next-generation communication and computation technologies, including reconfigurable/tunable optical add-drop multiplexers for wavelength-routing optical networks, and scalable integrated photonic crossconnects for energy efficient manycore processor to memory communication for future supercomputers. Telecom-grade switchable and tunable filters [6], modulators [8] and other components have been demonstrated in this technology. However, strong-confinement (high-index-contrast) nanophotonic waveguides and resonators have been shown to have extreme intrinsic sensitivities – including subatomic dimensional tolerances [9,10], wall roughness optical losses, temperature sensitivity, etc. One of the principal challenges to unleashing the promise of strong-confinement photonics lies in taming these extreme sensitivities. One approach to solving this problem is to produce tuning capability and feedback control electronics for each photonic element. However, such solutions may lead to poor scaling of photonic circuits to higher complexities. All-optical (optomechanical) feedback control based on light-powered nanomachines, as described here, is one technology that may enable scalable, robust photonic circuits, through the engineering of self-adaptive devices, such as the proposed self-tuning cavity, capable of intrinsically circumventing sensitivities through their ability to “passively” lock onto an optical wavelength reference or respond in other ways directly to an optical input signal. Such optical-nanomechanical devices could have response times in the megahertz or faster.

4. Future Directions and Opportunities

The most immediate goal of our future work is the experimental demonstration of the concepts presented here. However, the basic concepts developed in this work also point the way to numerous interesting conceptual design problems to be explored in further work, including other new types of self-adaptive devices that are made possible by the strongly optically nonlinear behaviour of these systems and by harnessing this approach.

Furthermore, the optomechanical energy coupling involved, the highly nonlinear behaviour and the potential synthesis viewpoint make it desirable to develop a comprehensive design approach (a “circuit theory”) for the systematic design of all-optical optomechanical systems with prescribed desired properties.

5. Conclusions

We have proposed a new class of light-powered nanomachines and all-optical self-adaptive optomechanical circuits that rely on the interplay between optically-induced forces and mechanical-motion-induced change in optical properties of a system. By synthesizing optomechanical potentials through the action of optical forces, unique designs result enabling all-optical operations on light that would be difficult to achieve by any other means. As first examples of how this concept could be applied, we have shown how all-optical self-adaptive photonic devices can be made to effectively corral and trap microcavity resonances and achieve dynamic self-alignment of a microcavity resonance to a single laser line over very large wavelength ranges. Such devices have the potential to provide all-optical functionality. In the process, they may provide an approach to eliminate the extreme dimensional and other sensitivities of strong-confinement photonic devices. The potential of these concepts to lead to novel device concepts and applications has yet to be fully explored.

6. References 1. P.T. Rakich, M.A. Popović, M. Soljačić and E.P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nature Photonics 1, 658 - 665 (2007). 2. M.L. Povinelli, S.G. Johnson, M. Lončar, M. Ibanescu, E.J. Smythe, F. Capasso and J.D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators,” Optics Express 13, 8286-8295 (2005). 3. M.L. Povinelli, M. Lončar, M. Ibanescu, E.J. Smythe, S.G. Johnson, F. Capasso and J.D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Optics Letters 30, 3042-4 (2005). 4. M. Eichenfield, C.P. Michael, R. Perahia and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nature Photonics 1, 416–422 (2007). 5. A.J. Nichol, W.J. Arora and G. Barbastathis, “Thin membrane self-alignment using nanomagnets for three-dimensional nanomanufacturing,” J. Vac. Sci. Technol. B 24, 3128–3132 (2006). 6. M.A. Popović, T. Barwicz, M.R. Watts, P.T. Rakich, M.S. Dahlem, F. Gan, C.W. Holzwarth, L. Socci, H.I. Smith, F.X. Kärtner, E.P. Ippen and H.I. Smith, “Strong-confinement microring resonator photonic circuits (Invited),” presented at the 20th Annual Meeting of the IEEE Lasers and Electro-Optics Society (LEOS), Lake Buena Vista, Florida, Oct 2007, paper TuCC3. 7. P. Dumon, G. Priem, et al., “Linear and nonlinear nanophotonic devices based on silicon-on-insulator wire waveguides (Review paper),” Jpn. J. of Appl. Phys. 45, 6589 (2006). 8. Q. Xu, B. Schmidt, S. Pradhan and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325-327 (2005). 9. M.A. Popović, T. Barwicz, E.P. Ippen and F.X. Kärtner, “Global design rules for silicon microphotonic waveguides: sensitivity, polarization and resonance tunability,” in Conference on Lasers and Electro-Optics (CLEO), OSA Technical Digest (Optical Society of America, Washington DC, May 21-26, 2006), paper CTuCC1. 10. Supplementary information published with article: T. Barwicz, M.R. Watts, M.A. Popović, P.T. Rakich, L. Socci, F.X. Kärtner, E.P. Ippen and H.I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nature Photonics 1, 57-60 (2007).

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