Oskar Painter

Nonlinear optical phenomena in silicon waveguides: Modeling and applications

Focus Serial: Frontiers of Nonlinear Optics Several kinds of nonlinear optical effects have been observed in recent years using silicon waveguides, and their device applications are attracting considerable attention. In this review, we provide a unified theoretical platform that not only can be used for understanding the underlying physics but should also provide guidance toward new and useful applications. We begin with a description of the third-order nonlinearity of silicon and consider the tensorial nature of both the electronic and Raman contributions. The generation of free carriers through two-photon absorption and their impact on various nonlinear phenomena is included fully within the theory presented here. We derive a general propagation equation in the frequency domain and show how it leads to a generalized nonlinear Schrodinger equation when it is converted to the time domain. We use this equation to study propagation of ultrashort optical pulses in the presence of self-phase modulation and show the possibility of soliton formation and supercontinuum generation. The nonlinear phenomena of cross-phase modulation and stimulated Raman scattering are discussed next with emphasis on the impact of free carriers on Raman amplification and lasing. We also consider the four-wave mixing process for both continuous-wave and pulsed pumping and discuss the conditions under which parametric amplification and wavelength conversion can be realized with net gain in the telecommunication band.

A picogram- and nanometre-scale photonic-crystal optomechanical cavity

The dynamic back-action caused by electromagnetic forces (radiation pressure) in optical and microwave cavities is of growing interest. Back-action cooling, for example, is being pursued as a means of achieving the quantum ground state of macroscopic mechanical oscillators. Work in the optical domain has revolved around millimetre- or micrometre-scale structures using the radiation pressure force. By comparison, in microwave devices, low-loss superconducting structures have been used for gradient-force-mediated coupling to a nanomechanical oscillator of picogram mass. Here we describe measurements of an optical system consisting of a pair of specially patterned nanoscale beams in which optical and mechanical energies are simultaneously localized to a cubic-micron-scale volume, and for which large per-photon optical gradient forces are realized. The resulting scale of the per-photon force and the mass of the structure enable the exploration of cavity optomechanical regimes in which, for example, the mechanical rigidity of the structure is dominantly provided by the internal light field itself. In addition to precision measurement and sensitive force detection, nano-optomechanics may find application in reconfigurable and tunable photonic systems, light-based radio-frequency communication and the generation of giant optical nonlinearities for wavelength conversion and optical buffering.

Electromagnetically induced transparency and slow light with optomechanics

Controlling the interaction between localized optical and mechanical excitations has recently become possible following advances in micro- and nanofabrication techniques. So far, most experimental studies of optomechanics have focused on measurement and control of the mechanical subsystem through its interaction with optics, and have led to the experimental demonstration of dynamical back-action cooling and optical rigidity of the mechanical system. Conversely, the optical response of these systems is also modified in the presence of mechanical interactions, leading to effects such as electromagnetically induced transparency (EIT) and parametric normal-mode splitting. In atomic systems, studies of slow and stopped light (applicable to modern optical networks and future quantum networks) have thrust EIT to the forefront of experimental study during the past two decades. Here we demonstrate EIT and tunable optical delays in a nanoscale optomechanical crystal, using the optomechanical nonlinearity to control the velocity of light by way of engineered photon–phonon interactions. Our device is fabricated by simply etching holes into a thin film of silicon. At low temperature (8.7 kelvin), we report an optically tunable delay of 50 nanoseconds with near-unity optical transparency, and superluminal light with a 1.4 microsecond signal advance. These results, while indicating significant progress towards an integrated quantum optomechanical memory, are also relevant to classical signal processing applications. Measurements at room temperature in the analogous regime of electromagnetically induced absorption show the utility of these chip-scale optomechanical systems for optical buffering, amplification, and filtering of microwave-over-optical signals.

Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab

We present a three-dimensional finite-difference time-domain analysis of localized defect modes in an optically thin dielectric slab that is patterned with a two-dimensional array of air holes. The symmetry, quality factor, and radiation pattern of the defect modes and their dependence on the slab thickness are investigated.

Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment

Using a combination of resist reflow to form a highly circular etch mask pattern and a low-damage plasma dry etch, high-quality-factor silicon optical microdisk resonators are fabricated out of silicon-on-insulator (SOI) wafers. Quality factors as high as Q = 5x10(6) are measured in these microresonators, corresponding to a propagation loss coefficient as small as alpha ~ 0.1 dB/cm. The different optical loss mechanisms are identified through a study of the total optical loss, mode coupling, and thermally-induced optical bistability as a function of microdisk radius (5-30 microm). These measurements indicate that optical loss in these high-Q microresonators is limited not by surface roughness, but rather by surface state absorption and bulk free-carrier absorption.

Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper

A technique is demonstrated which efficiently transfers light between a tapered standard single-mode optical fiber and a high-Q, ultra-small mode volume, silicon photonic crystal resonant cavity. Cavity mode quality factors of 4.7x10(4) are measured, and a total fiber-to-cavity coupling efficiency of 44% is demonstrated. Using this efficient cavity input and output channel, the steady-state nonlinear absorption and dispersion of the photonic crystal cavity is studied. Optical bistability is observed for fiber input powers as low as 250 microW, corresponding to a dropped power of 100 microW and 3 fJ of stored cavity energy. A high-density effective free-carrier lifetime for these silicon photonic crystal resonators of ~ 0.5 ns is also estimated from power dependent loss and dispersion measurements.

Momentum space design of high-Q photonic crystal optical cavities

The design of high quality factor (Q) optical cavities in two dimensional photonic crystal (PC) slab waveguides based upon a momentum space picture is presented. The results of a symmetry analysis of defect modes in hexagonal and square host photonic lattices are used to determine cavity geometries that produce modes which by their very symmetry reduce the vertical radiation loss from the PC slab. Further improvements in the Q are achieved through tailoring of the defect geometry in Fourier space to limit coupling between the dominant momentum components of a given defect mode and those momentum components which are either not reflected by the PC mirror or which lie within the radiation cone of the cladding surrounding the PC slab. Numerical investigations using the finite-difference time-domain (FDTD) method predict that radiation losses can be significantly suppressed through these methods, culminating with a graded square lattice design whose total Q approaches 10;5 with a mode volume of approximately 0.25 cubic half-wavelengths in vacuum.

Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system.

Cavity quantum electrodynamics, the study of coherent quantum interactions between the electromagnetic field and matter inside a resonator, has received attention as both a test bed for ideas in quantum mechanics and a building block for applications in the field of quantum information processing. The canonical experimental system studied in the optical domain is a single alkali atom coupled to a high-finesse Fabry–Perot cavity. Progress made in this system has recently been complemented by research involving trapped ions, chip-based microtoroid cavities, integrated microcavity-atom-chips, nanocrystalline quantum dots coupled to microsphere cavities, and semiconductor quantum dots embedded in micropillars, photonic crystals and microdisks. The last system has been of particular interest owing to its relative simplicity and scalability. Here we use a fibre taper waveguide to perform direct optical spectroscopy of a system consisting of a quantum dot embedded in a microdisk. In contrast to earlier work with semiconductor systems, which has focused on photoluminescence measurements, we excite the system through the photonic (light) channel rather than the excitonic (matter) channel. Strong coupling, the regime of coherent quantum interactions, is demonstrated through observation of vacuum Rabi splitting in the transmitted and reflected signals from the cavity. The fibre coupling method also allows us to examine the system’s steady-state nonlinear properties, where we see a saturation of the cavity–quantum dot response for less than one intracavity photon. The excitation of the cavity–quantum dot system through a fibre optic waveguide is central to applications such as high-efficiency single photon sources, and to more fundamental studies of the quantum character of the system.

A high-resolution microchip optomechanical accelerometer

The monitoring of acceleration is essential for a variety of applications ranging from inertial navigation to consumer electronics. Typical accelerometer operation involves the sensitive displacement measurement of a flexibly mounted test mass, which can be realized using capacitive, piezo-electric, tunnel-current or optical methods. Although optical detection provides superior displacement resolution, resilience to electromagnetic interference and long-range readout, current optical accelerometers either do not allow for chip-scale integration or utilize relatively bulky test mass sensors of low bandwidth. Here, we demonstrate an optomechanical accelerometer that makes use of ultrasensitive displacement readout using a photonic-crystal nanocavity monolithically integrated with a nanotethered test mass of high mechanical Q-factor This device achieves an acceleration resolution of 10 µg Hz^(−1/2) with submilliwatt optical power, bandwidth greater than 20 kHz and a dynamic range of greater than 40 dB. Moreover, the nanogram test masses used here allow for strong optomechanical backaction, setting the stage for a new class of motional sensors.

Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces

Optical forces can produce significant mechanical effects in micro- and nanophotonic systems. Here we demonstrate a novel optomechanical system using a movable, micrometre-scale waveguide evanescently coupled to a high-Q optical microresonator. Micrometre-scale displacements of the waveguide are observed for milliwatt-level optical input powers. Measurement of the spatial variation of the force on the waveguide indicates that it arises from a cavity-enhanced optical dipole force resulting from the stored optical field of the resonator. This force is used to realize an all-optical tunable filter operating with submilliwatt control power. A theoretical model of the system shows that the maximum achievable force is independent of the intrinsic Q of the optical resonator and scales inversely with the cavity mode volume, suggesting that such forces may become even more effective as devices approach the nanoscale.