## Research: Modeling in Micro- and Nano-photonicsThis research is concerned in part with nonlinear dynamics in
light confining – closed and open – systems, a set of
themes that we loosely classify as ## Cavity-based photonics: the fundamentals## To understand the ray-wave dynamics of closed and open planar electromagnetic resonators.From the point of view of dynamics, in the
short wavelength limit (geometrical or classical), we refer to
closed systems as Our fundamental interests
lie in the characterisation of ## Cavity-based photonics: microlasers without mirrors, sensors without labels## To enhance, confine, and channel light in optical structures for lasing and sensing applications.Confinement and manipulation of light in optical microcavities has been a subject of intense fundamental and applied research for more than a decade [Vahala04]. Recent advances in micro- and nano-technology and in the field of optoelectronics have indeed allowed the realization of small micron size cavities capable, among other things, of low-threshold coherent light emission [Spillane02]. In fact, dielectric optical microcavities (for recent reviews, see [Vahala04, Astratov07]) are already used in various applications such as filters [Bergeron08], single-molecule sensors [Armani07, Vollmer08], tunable optical frequency combs [Savchenkov08], and optomechanical oscillators [Kippenberg07] to name a few. The operating principle of
these small resonators is based on the concept of planar dielectric
cavities, owing their interest to the high-quality factor
The resonance spectrum, the free spectral range (FSR), the
potentially high quality factor x,y,z)
are the principal characteristics of these resonators. In turn,
these properties are highly sensitive to the medium composing the
cavity, to its geometry and to its immediate surroundings. It is
precisely this sensitivity that makes these resonators such
versatile candidates for a number of applications as noted
aboveDepending on the symmetry of the cavity, two classes of WG resonators exist. The first class, having rotational or axial symmetry, is characterized by low radiation loss, therefore high quality factor, and isotropic emission patterns. To this category belong for instance the geometry of the sphere [Chiasera10], the cylinder [Kippenberg03] and the torus [Armani03]. It is the very long circulation time of the light inside the cavity that allows for superlative performances for applications ranging from sensors, to cavity quantum electrodynamics and multifunction optical circuit devices [Malekin06]. However, despite these impressive results,
the highly symmetrical cavities present a serious disadvantage in
terms of emission properties. The rotational symmetry imposes an
isotropic field distribution, a major drawback for their use as
Ever since the demonstration of a directional
emission of coherent light from microcavities, the Grail of this
line of research has been the production and control of the laser
directionality through various combinations of geometry and medium
optimization. Our recent efforts (theory and experiment, see below)
have been directed towards Among the vast possibilities of geometry/medium for
microresonators, our choice has fallen on a special class of
cavities called
In this system we break the rotational symmetry by introducing
an off-center defect (a circular inclusion, a noble metal
nanoparticle or a quantum dot) inside the circular cavity. This
kind of cavity supports non-directional long lived modes (high
For optimal delivery of
the laser light, the evanescent coupling with a waveguide addresses
the NF intensity. Concentrating this field in the vicinity of the
waveguide for maximal output efficiency, while keeping a large
enough One of the advantages of these studies is that the same system
can be the basis of two independent applications: whereas shaping
the FF turns the microcavity into a directional
microlaser,exploiting the NF can make it a highly sensitive ## Modeling in photonics: optimization of photonics structuresThe design of on-chip optical elements is paramount to many
applications such as micro-manipulation, sensing and optical
communications. Moreover, engineering such planar micro-structures
with great precision is now possible due to advances in
photo-lithographic techniques. Prior to the experimental step, it
is often necessary to model the interplay of light with in-plane
scattering elements in order to harness the full potential of
integrated optical devices. Our group has been interested lately in
the design of integrated devices based on cylindrical scatterers,
as shown on Fig. 4. Since our goal is to enable new device
functionalities such as beam shaping and lensing, a large number of
adjustable geometric parameters have to be considered, for instance
the position of scatterers on a given cylinder lattice. This means
a large number of lattice configurations must be tested before
converging to acceptable design. Therefore, the speed of the
algorithms used to solve Maxwell's equations is critical. Keeping
this speed requirement in mind, we advocate the use of algorithms
exploiting the circular symmetry of scatterers, loosely called
2D-GLMT (
Using our implementation of 2D-GLMT, we have proposed integrated
optical elements tailored for the conversion of a Gaussian beam
into Hermite-Gauss profiles (see Fig. 5). These devices are
designed without making any
## Numerical instrumentsOur group has developed (and is continuing development of) versatile numerical algorithms for computing resonances of closed and open dielectric resonators/cavities. The emphasis is on the generality of the system's configuration, i.e. the geometry of the (main) cavity (and possible inclusions) and the internal and external dielectric media (homogeneous and inhomogeneous). Two complementary techniques have now reached maturity for 2D resonators, and are currently being extended to photonic molecules (combination of a few cavities), and more generally, to photonic complexes (periodic or aperiodic arrangements of cavities). The first method is applicable to cavities of
arbitrary shape and arbitrary inhomogeneities of the medium
(continuous or discontinuous) and is based on a The second method is a generalization to
multiply connected regions of the boundary integral equation (BIE),
implemented as a Full finite-element algorithms are also available to model 3D resonators. At present, tests are underway to validate the methods for geometries of interest: torus, ring, (thick) disk, and sphere. We are also working on semi-analytic and perturbative methods to complete our 3D arsenal. ## Theoretical & Experimental CollaborationsThe ## A new class of optical microcavities – inhomogeneous dielectric resonators –
## Label free high sensitivity detection of bacteria by phages using functionalized optical microcavities
In addition, a further in situ collaboration is developing with the Chair of Excellence for Innovations in Photonics of Prof. Y. Messaddeq. Funding for this research is provided in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Fonds de Recherche du Québec - Nature et Technologies (FRQ-NT). |