Theoretical and experimental study of stimulated and cascaded Raman scattering in ultra-high-Q optical microcavities

Stimulated Raman scattering (SRS) in ultra-high-Q surface-tension-induced spherical and chip-based toroid microcavities is considered both theoretically and experimentally. These microcavities are fabricated from silica, exhibit small mode volume (typically 1000 $\mu m^{3}$) and possess whispering-gallery type modes with long photon storage times (in the range of 100 ns), significantly reducing the threshold for stimulated nonlinear optical phenomena. Oscillation threshold levels of less than 100 $\mu$% -Watts of launched fiber pump power, in microcavities with quality factors of 100 million are observed. Using a steady state analysis of the coupled-mode equations for the pump and Raman whispering-gallery modes, the threshold, efficiencies and cascading properties of SRS in UHQ devices are derived. The results are experimentally confirmed in the telecommunication band (1550nm) using tapered optical fibers as highly efficient waveguide coupling elements for both pumping and signal extraction. The device performance dependence on coupling, quality factor and modal volume are measured and found to be in good agreement with theory. This includes analysis of the threshold and efficiency for cascaded Raman scattering. The side-by-side study of nonlinear oscillation in both spherical microcavities and toroid microcavities on-a-chip also allows for comparison of their properties. In addition to the benefits of a wafer-scale geometry, including integration with optical, electrical or mechanical functionality, microtoroids on-a-chip exhibit single mode Raman oscillation over a wide range of pump powers.Comment: 12 pages, 15 figure

Optical Nanofibers: a new platform for quantum optics

The development of optical nanofibers (ONF) and the study and control of their optical properties when coupling atoms to their electromagnetic modes has opened new possibilities for their use in quantum optics and quantum information science. These ONFs offer tight optical mode confinement (less than the wavelength of light) and diffraction-free propagation. The small cross section of the transverse field allows probing of linear and non-linear spectroscopic features of atoms with exquisitely low power. The cooperativity -- the figure of merit in many quantum optics and quantum information systems -- tends to be large even for a single atom in the mode of an ONF, as it is proportional to the ratio of the atomic cross section to the electromagnetic mode cross section. ONFs offer a natural bus for information and for inter-atomic coupling through the tightly-confined modes, which opens the possibility of one-dimensional many-body physics and interesting quantum interconnection applications. The presence of the ONF modifies the vacuum field, affecting the spontaneous emission rates of atoms in its vicinity. The high gradients in the radial intensity naturally provide the potential for trapping atoms around the ONF, allowing the creation of one-dimensional arrays of atoms. The same radial gradient in the transverse direction of the field is responsible for the existence of a large longitudinal component that introduces the possibility of spin-orbit coupling of the light and the atom, enabling the exploration of chiral quantum optics.Comment: 65 pages, to appear in Advances in Atomic, Molecular and Optical Physic

Stabilized large mode area in tapered photonic crystal fiber for stable coupling

A rigorous modal solution approach based on the numerically efficient finite element method (FEM) has been used to design a tapered photonic crystal fiber with a large mode area that could be efficiently coupled to an optical fiber. Here, for the first time, we report that the expanded mode area can be stabilized against possible fabrication tolerances by introducing a secondary surrounding waveguide with larger air holes in the outer ring. A full-vectorial -field approach is employed to obtain mode field areas along the tapered section, and the Least Squares Boundary Residual (LSBR) method is used to obtain the coupling coefficients to a butt-coupled fiber

Mode Transforming Properties of Tapered Single-Mode Fiber Microlenses

The Gaussian approximation that is typically used to estimate single-mode fiber microlens performance is investigated. It is applied to hemispheric lenses on two types of tapered single-mode fiber. Theoretical and experimental results are compared. The first type of taper, which is fabricated by pulling a fiber while it is melted, has a tapered core and a tapered cladding. The second type of taper, which is fabricated by etching the cladding, has a tapered cladding only. For a tapered-core fiber, coupling to the cladding-guided modes and the finite radius of curvature of the wave front before the lens must be considered to predict the lens spot size accurately, whereas the spot size of a tapered-cladding lens can be predicted from the lens diameter alone. Thus the spot size of a lens on a tapered-cladding fiber is easier to predict and control than that of a lens on a tapered-core fiber. It is also shown that the usual theory used to predict the spot size gives accepted values for tapered-cladding lenses but not for tapered-core lenses

Ultrafast, low-power, all-optical switching via birefringent phase-matched transverse mode conversion in integrated waveguides

We demonstrate the potential of birefringence-based, all-optical, ultrafast conversion between the transverse modes in integrated optical waveguides by modelling the conversion process by numerically solving the multi-mode coupled nonlinear Schroedinger equations. The observed conversion is induced by a control beam and due to the Kerr effect, resulting in a transient index grating which coherently scatters probe light from one transverse waveguide mode into another. We introduce birefringent phase matching to enable efficient all-optically induced mode conversion at different wavelengths of the control and probe beam. It is shown that tailoring the waveguide geometry can be exploited to explicitly minimize intermodal group delay as well as to maximize the nonlinear coefficient, under the constraint of a phase matching condition. The waveguide geometries investigated here, allow for mode conversion with over two orders of magnitude reduced control pulse energy compared to previous schemes and thereby promise nonlinear mode switching exceeding efficiencies of 90% at switching energies below 1 nJ

Fabrication and coupling to planar high-Q silica disk microcavities

Using standard lithographic techniques, we demonstrate fabrication of silica disk microcavities, which exhibit whispering-gallery-type modes having quality factors (Q) in excess of 1 million. Efficient coupling (high extinction at critical coupling and low, nonresonant insertion loss) to and from the disk structure is achieved by the use of tapered optical fibers. The observed high Q is attributed to the wedged-shaped edge of the disk microcavity, which is believed to isolate modes from the disk perimeter and thereby reduce scattering loss. The mode spectrum is measured and the influence of planar confinement on the mode structure is investigated. We analyze the use of these resonators for very low loss devices, such as add/drop filters

Perturbative analytic theory of an ultrahigh-Q toroidal microcavity

A perturbation theoretic approach is proposed as an efficient characterization tool for a tapered fiber coupled ultrahigh-quality factor (Q) toroidal microcavity with a small inverse aspect ratio. The Helmholtz equation with an assumption of quasi-TE/TM modes in local toroidal coordinates is solved via a power series expansion in terms of the inverse aspect ratio and the expanded eigenmode solutions are further manipulated iteratively to generate various characteristic metrics of the ultrahigh-Q toroidal microcavity coupled to a tapered fiber waveguide. Resonance wavelengths, free spectral ranges, cavity mode volumes, phase-matching conditions, and radiative Q factors are derived along with a mode characterization given by a characteristic equation. Calculated results are in excellent agreement with full vectorial finite-element simulations. The results are useful as a shortcut to avoid full numerical simulation, and also render intuitive insight into the modal properties of toroidal microcavities

Efficient Photon Coupling from a Diamond Nitrogen Vacancy Centre by Integration with Silica Fibre

A central goal in quantum information science is to efficiently interface photons with single optical modes for quantum networking and distributed quantum computing. Here, we introduce and experimentally demonstrate a compact and efficient method for the low-loss coupling of a solid-state qubit, the nitrogen vacancy (NV) centre in diamond, with a single-mode optical fibre. In this approach, single-mode tapered diamond waveguides containing exactly one high quality NV memory are selected and integrated on tapered silica fibres. Numerical optimization of an adiabatic coupler indicates that near-unity-efficiency photon transfer is possible between the two modes. Experimentally, we find an overall collection efficiency between 18-40 % and observe a raw single photon count rate above 700 kHz. This integrated system enables robust, alignment-free, and efficient interfacing of single-mode optical fibres with single photon emitters and quantum memories in solids