Pump-Induced Dynamical Tunneling in a Deformed Microcavity Laser

Abstract

Pump-induced dynamical tunneling has been observed in free-space resonant optical pumping of a deformed microcavity by employing excitation spectroscopy. A focused-pump beam was injected into the cavity by refraction and then coupled to a high-Q cavity mode via dynamical tunneling. Pump-coupling efficiency as high as 50% and an effective coupling constant responsible for the tunneling were obtained from the observed pumping efficiency with a mode-mode coupling model. DOI: 10.1103/PhysRevLett.104.243601 PACS numbers: 42.55.Sa, 03.65.Xp, 05.45.Mt, 42.50.Àp Efficient optical pumping of high-Q cavity modes is of primary concern in microcavity applications such as microlasers and optoelectronic components and devices [1]. Prism and tapered-fiber couplings are commonly used for ultrahigh-Q whispering gallery modes [2,3]. However, simple free-space coupling without near-field couplers is often needed for practical reasons such as experimental limitations or implementation cost. Microcavities deformed from rotational symmetry can provide directional emission of high-Q modes, and, moreover, allow one to excite them by a free-space pump beam. Recently, cryogenic cooling of an optomechanical resonator assisted by free-space evanescent coupling has been reported in a slightly deformed microsphere [4]. Efficient nonresonant optical pumping based on ray chaos has also been demonstrated in deformed microcavities [5,6], suggesting further enhancements by resonant optical pumping.In a significantly deformed microcavity, the ray dynamics typically exhibits both regular and chaotic trajectories [7], resulting in a mixed phase space: high-Q modes are usually localized on regular regions such as invariant tori and regular islands surrounded by a chaotic sea. It is known that light in high-Q modes localized on those regular regions can be transferred to the nearest chaotic sea by a dynamical process and then transported by ray chaos resulting in a directional refractive output. The dynamical process is called dynamical tunneling [8] since the transport from a regular region to the chaotic sea is strictly forbidden classically.The dynamical tunneling is thus an essential link between high-Q modes and directional output, important assets for the aforementioned photonic applications. In fact, dynamical tunneling is of great current interest and has been studied theoretically in various physical systems [9][10][11][12][13][14]. Experimental signatures of dynamical tunneling were reported in a microwave billiard in energy splitting [15,16], in an acoustical resonator through spectral statistics [17], and in a cold atomic sample in atomic momentum distribution [18,19]. In microcavities, although it has been studied theoretically [20][21][22][23], there is no direct experimental evidence for dynamical tunneling.How can then the dynamical tunneling be used to improve the optical pumping? The answer lies in the reverse of the aforementioned output process. If we inject a pump beam in a time reversed way, the pump light might be transferre...

Dynamical tunneling-assisted coupling of high-Qdeformed microcavities using a free-space beam

“…(11), |a ω | 2 describes the excitation probability by the free-space beam, from which we can deduce that the FWHM (full width at half maximum) of the regular mode is expressed as κ + γ ≡ γ t . It should be noted that γ t remains unchanged when the free-space coupling efficiency changes [27], while in fiber taper coupling the total decay rate will vary.…”

“…It has been demonstrated that WGMs in a specially designed deformed cavity can be directly excited by a freespace optical beam [26,27]. This direct free-space coupling is of importance because it is robust and requires less rigorous experimental condition than the evanescent couplers mentioned above.…”

“…This direct free-space coupling is of importance because it is robust and requires less rigorous experimental condition than the evanescent couplers mentioned above. This efficient free-space coupling originates from breaking of rotational symmetry in deformed microcavities, which produces a highly directional emission assisted by the dynamical tunneling, different from the isotropic nature of a circular WGM cavity [26][27][28][29]. According to the time re-version, i.e., the reversibility of light path, free-space beams at certain positions are expected to couple into the high-Q modes via chaotic modes when they are on resonance.…”

End-fire injection of guided light into optical microcavity

“…As the time reversal process, the WGMs of microcavity can also be excited by the focused light in free space, which is known as free space coupling [12,13]. The free space coupling does not require precise position control and the coupling efficiency can be higher than 30% [14][15][16][17]. This method has been successfully applied in biosensors and laser pumping [9,17].…”

Chaos-assisted broadband momentum transformation in optical microresonators

“…Ray dynamically, these three different structures are disjoint in SOS. However, in wave optics, dynamic tunneling between the regular orbits and neighboring chaotic orbits can take place (25,(29)(30)(31)(43)(44)(45)(46), where the latter eventually refract out from the cavity following an unstable manifolds channel (green curves) (44) when crossing the total internal reflection critical line (red dashed line). It is worth noting that the chaotic motion along the unstable manifolds channel is a momentum transformation process.…”