Gregory Kozyreff

Delay differential equations for mode-locked semiconductor lasers

We propose a new model for passive mode locking that is a set of ordinary delay differential equations. We assume a ring-cavity geometry and Lorentzian spectral filtering of the pulses but do not use small gain and loss and weak saturation approximations. By means of a continuation method, we study mode-locking solutions and their stability. We find that stable mode locking can exist even when the nonlasing state between pulses becomes unstable.

Whispering gallery microresonators for second harmonic light generation from a low number of small molecules

Unmarked sensitive detection of molecules is needed in environmental pollution monitoring, disease diagnosis, security screening systems and in many other situations in which a substance must be identified. When molecules are attached or adsorbed onto an interface, detecting their presence is possible using second harmonic light generation, because at interfaces the inversion symmetry is broken. However, such light generation usually requires either dense matter or a large number of molecules combined with high-power laser sources. Here we show that using high-Q spherical microresonators and low average power, between 50 and 100 small non-fluorescent molecules deposited on the outer surface of the microresonator can generate a detectable change in the second harmonic light. This generation requires phase matching in the whispering gallery modes, which we achieved using a new procedure to periodically pattern, with nanometric precision, a molecular surface monolayer.

Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities

Taking up to fourth-order dispersion effects into account, we show that fiber resonators become stable for a large intensity regime. The range of pump intensities leading to modulational instability becomes finite and controllable. Moreover, by computing analytically the thresholds and frequencies of these instabilities, we demonstrate the existence of a new unstable frequency at the primary threshold. This frequency exists for an arbitrary small but nonzero fourth-order dispersion coefficient. Numerical simulations for a low and flattened dispersion photonic crystal fiber resonator confirm analytical predictions and open the way to experimental implementation.

Backscattering position detection for photonic force microscopy

An optically trapped particle is an extremely sensitive probe for the measurement of pico- and femto-Newton forces between the particle and its environment in microscopic systems (photonic force microscopy). A typical setup comprises an optical trap, which holds the probe, and a position sensing system, which uses the scattering of a beam illuminating the probe. Usually the position is accurately determined by measuring the deflection of the forward-scattered light transmitted through the probe. However, geometrical constraints may prevent access to this side of the trap, forcing one to make use of the backscattered light instead. A theory is presented together with numerical results that describes the use of the backscattered light for position detection. With a Mie–Debye approach, we compute the total (incident plus scattered) field and follow its evolution as it is collected by the condenser lenses and projected onto the position detectors and the responses of position sensitive detectors and quadrant ...

Bragg localized structures in a passive cavity with transverse modulation of the refractive index and the pump

We consider a passive optical cavity containing a photonic crystal and a purely absorptive two-level medium. The cavity is driven by a superposition of two coherent beams forming a periodically modulated pump. Using a coupled mode reduction and direct numerical modeling of the full system we demonstrate the existence of bistability between uniformly periodic states, modulational instabilities and localized structures of light. All are found to exist within the conduction band of the photonic material. Moreover, contrary to similar previously found intra-band structures, we show that these localized structures can be truly stationary states.

Nonvariational real Swift-Hohenberg equation for biological, chemical, and optical systems

We derive asymptotically an order parameter equation in the limit where nascent bistability and long-wavelength modulation instabilities coalesce. This equation is a variant of the Swift-Hohenberg equation that generally contains nonvariational terms of the form psinabla(2)psi and /nablapsi/(2). We briefly review some of the properties already derived for this equation and derive it on three examples taken from chemical, biological, and optical contexts. Finally, we derive the equation on a general class of partial differential systems.

Light coupling into the Whispering Gallery Modes of a fiber array thin film solar cell for fixed partial Sun tracking

We propose the use of whispering gallery mode coupling in a novel configuration based on implementing a thin film cell on the backside of an array of parallel fibers. We performed numerical calculations using the parameters of a thin film organic cell which demonstrate that light coupling becomes more effective as the angle for the incident light relative to the fiber array normal increases up to an optimal angle close to 55 deg. At this angle the power conversion efficiency of the fiber array solar cell we propose becomes 30% times larger than the one from an equivalent planar cell configuration. We demonstrate that the micro fiber array solar cell we propose may perform an effective partial tracking of the sun movement for over 100 degrees without any mechanical help. In addition, in the event that such fiber array cell would be installed with the adequate orientation on a vertical façade, an optimal photon-to-charge conversion would be reached for sunlight incident at 55 deg with respect to the horizon line, very close to the yearly average position for the sun at Latitude of 40 deg.

Cavity-controlled radiative recombination of excitons in thin-film solar cells

We study the performance of photovoltaic devices when controlling the exciton radiative recombination time. We demonstrate that when high-quantum-yield fluorescent photovoltaic materials are placed within an optical cavity, the spontaneous emission of the radiative exciton is partially inhibited. The corresponding increase of the exciton lifetime results in an increase of the effective diffusion length and diffusion current. This performance maximizes when the thickness of the cell is comparable to the absorption length. We show that when typical parameter values of thin solar-cell devices are used, the efficiency may improve by as much as three times.

Singular Hopf bifurcation in a differential equation with large state-dependent delay.

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol’s equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays.

Analytical results for front pinning between an hexagonal pattern and a uniform state in pattern-formation systems.

In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an homogeneous background. In two dimensions, the ordered pattern is most often hexagonal and the conditions for fronts to stabilize are still unknown. In this Letter, we show how the locking of these fronts depends on their orientation relative to the pattern. The theory rests on general asymptotic arguments valid when the spatial scale of the front is slow compared to that of the hexagonal pattern. Our analytical results are confirmed by numerical simulations with the Swift-Hohenberg equation, relevant to hydrodynamical and buckling instabilities, and a nonlinear optical cavity model.