Weak material nonlinearity at optical frequencies poses a serious hurdle to realizing optical bistability at low optical powers, which is a critical component for digital optical computing. In this paper, we explore the cavity enhancement of the second-order optical nonlinearity in order to determine the feasibility of few photon optical bistability. Starting from a quantum optical formalism of a doubly resonant cavity (required to meet the condition of phase matching), we derive a dynamic classical model of a cavity that is bistable at the fundamental mode. We analyze the optical energy and the switching speed as a function of the cavity quality factors and mode volumes and identify the regime where only ten's of photons are required to perform the switching. An unusual trend in the switching speed is also observed, where the speed monotonically decreases as the cavity linewidth increases. This is ascribed to the increase in the switching gain with increasing cavity linewidth.
Weak material nonlinearity at optical frequencies poses a serious hurdle to realizing optical bistability at low optical powers, which is a critical component for digital optical computing. In this paper, we explore the cavity enhancement of the second-order optical nonlinearity in order to determine the feasibility of few photon optical bistability. Starting from a quantum optical formalism of a doubly resonant cavity (required to meet the condition of phase matching), we derive a dynamic classical model of a cavity that is bistable at the fundamental mode. We analyze the optical energy and the switching speed as a function of the cavity quality factors and mode volumes and identify the regime where only ten's of photons are required to perform the switching. An unusual trend in the switching speed is also observed, where the speed monotonically decreases as the cavity linewidth increases. This is ascribed to the increase in the switching gain with increasing cavity linewidth.
Two-dimensional, atomically thin materials offer unique physical properties, such as a large second-order optical nonlinearity. Integrating these materials into a scalable and silicon-compatible platform could provide a pathway toward realizing low-power nonlinear optics. We have presented a formalism to calculate the effective nonlinear optical coefficient for a cavity integrated 2D material system as well as the cavity enhanced absorptive loss, which can be used to guide future experiments. We have also shown that the few-photon regime of cavity QED is within reach with a cavity quality factor of ∼10 5 –10 6, provided the loss at the second harmonic mode is minimized. As test applications, we have simulated the performances of (a) an optically bistable device and (b) a nanostructured device exhibiting single-photon blockade.
Focus Serial: Frontiers of Nonlinear Optics Nonlinear photonic-crystal microresonators offer unique fundamental ways of enhancing a variety of nonlinear optical processes. This enhancement improves the performance of nonlinear optical devices to such an extent that their corresponding operation powers and switching times are suitable for their implementation in realistic ultrafast integrated optical devices. Here, we review three different nonlinear optical phenomena that can be strongly enhanced in photonic crystal microcavities. First, we discuss a system in which this enhancement has been successfully demonstrated both theoretically and experimentally, namely, a photonic crystal cavity showing optical bistability properties. In this part, we also present the physical basis for this dramatic improvement with respect to the case of traditional nonlinear devices based on nonlinear Fabry-Perot etalons. Secondly, we show how nonlinear photonic crystal cavities can be also used to obtain complete second-harmonic frequency conversion at very low input powers. Finally, we demonstrate that the nonlinear susceptibility of materials can be strongly modified via the so-called Purcell effect, present in the resonant cavities under study.
We report on the observation of a novel manifestation of saturation-induced optical bistability in a resonantly pumped optical ring cavity interacting strongly with a cloud of atoms via a narrow atomic transition. The bistability emerges, above a critical pump rate, as an additional peak in the cavity's normal mode spectrum close to atomic resonance. This third transmission peak is usually suppressed due to strong resonant absorption, but in our experiment it is visible because of the linewidth of the atomic transition being much smaller than that of the cavity, which sets the experiment into the bad-cavity regime. Relying on complete saturation of the transition, this bistability has a quantum origin and cannot be mimicked by a classical material presenting a nonlinear refraction index. The appearance of the central peak in addition to the normal modes is predicted by a semi-classical model derived from the Tavis-Cummings Hamiltonian from which we derive a bistability phase diagram that connects our observations with former work on optical bistability in the good cavity regime. The phase diagram reveals several so far unexplored bistable phases.
We demonstrate extremely low-power all-optical bistability by using photonic crystal linear resonators based on InGaAsP quantum-wells. Since the photonic crystal cavity has a high quality-factor and a small mode-volume, the photon density in the cavity is extremely high, which makes it possible to reduce the bistable power. The measured minimum bistable threshold power was 37 muW by using a fiber coupling technique, and the estimated nonlinear refractive index (n2) was -6.84times10-14m2/W at a wavelength of 1610.8 nm which is near the resonant wavelength of quantum-well. The low-power optical bistable operations in a single photonic crystal cavity open the possibility of integrated optical devices such as an all-optical memory and switch, based on photonic crystals
Over the last two decades, the emergence of quantum information science has uncovered many practical applications in areas such as communications, imaging, and sensing where harnessing quantum features of Nature provides tremendous benefits over existing methods exploiting classical physical phenomena. In this effort, one of the frontiers of research has been to identify and utilize quantum phenomena that are not susceptible to environmental and parasitic noise processes. Quantum photonics has been at the forefront of these studies because it allows room-temperature access to its inherently quantum-mechanical features, and allows leveraging the mature telecommunication industry. Accompanying the weak environmental influence, however, are also weak optical nonlinearities. Efficient nonlinear optical interactions are indispensible for many of the existing protocols for quantum optical computation and communication, e.g. high-fidelity entangling quantum logic gates rely on large nonlinear responses at the one- or few-photon-level. While this has been addressed to a great extent by interfacing photons with single quantum emitters and cold atomic gases, scalability has remained elusive. In this work, we identify the macroscopic second-order nonlinear polarization as a robust platform to address this challenge, and utilize the recent advances in the burgeoning field of optical microcavities to enhance this nonlinear response. In particular, we show theoretically that by using the quantum Zeno effect, low-noise, single-photon-level optical nonlinearities can be realized in lithium niobate whispering-gallery-mode microcavities, and present experimental progress toward this goal. Using the measured strength of the second-order nonlinear response in lithium niobate, we modeled the nonlinear system in the strong coupling regime using the Schrödinger picture framework and theoretically demonstrated that the single-photon-level operation can be observed for cavity lifetimes in excess of 500 ns for all the three waves in the interaction, provided a cavity of radius R < 10 μm is fabricated. Experimentally, we showed that the absorption-limited quality ( Q) factors for lithium niobate, Qintrinsic ≈ 108, can be achieved using diamond-turning methods for disk radii, R > 100 μm, whereas for the smaller disks, additional rigorous polishing may be required. We also fabricated resonators as small as R ∼ 40 μm via this method. In a millimeter-sized resonator, we experimentally demonstrated triply resonant sum-frequency generation, which allowed for an observation of the classical manifestation of the quantum Zeno effect, wherein line-splitting occurs due to the high efficiency intracavity frequency conversion. For the sub-100 μm resonators, we present phase-matching calculations and dispersion-management techniques using analytical approximations and rigorous finite-element-method simulations. Experimentally, Q -factor measurements are shown, and we identify the specific short-comings of the fabrication procedure that may have led to the lower, surface-roughness-limited Q-factors. Finally, we identify pathways toward achieving the single-photon-level nonlinear optics using off-resonant nonlinear optics, which requires the simultaneous realization of phase-matching, large cavity lifetimes, and small mode volumes. We believe this would be feasible in the near future as more advanced fabrication and processing methods are developed for crystalline materials and novel nonlinear crystals are synthesized.