Tuning and stability of a singly resonant continuous-wave optical parametric oscillator close to degeneracy

Wavelength tuning and stability characteristics of a singly resonant continuous-wave optical parametric oscillator (cw OPO) in the proximity of signal-idler degeneracy have been studied. The OPO is made singly resonant by using a Bragg grating as a spectral filter in the OPO cavity. The signal-idler frequency difference can be tuned from 0.5 to 7 THz, which makes the OPO suitable for cw THz generation by optical heterodyning. The operation of the OPO within this singly-resonant regime is characterized by a strong self-stabilization effect. A gradual transition to an unstable, doubly-resonant regime is observed for a signal-idler detuning smaller than ~ 0.5 THz.

Dynamics of free-running, pump-modulated and coupled semiconductor and solid-state lasers

The output of a laser is a high frequency propagating electromagnetic field with superior coherence and brightness compared to that emitted by thermal sources. A multitude of different types of lasers exist, which also translates into large differences in the properties of their output. Moreover, the characteristics of the electromagnetic field emitted by a laser can be influenced from the outside, e.g., by injecting an external optical field or by optical feedback. In the case of free-running solitary class-B lasers, such as semiconductor and Nd:YVO4 solid-state lasers, the phase space is two-dimensional, the dynamical variables being the population inversion and the amplitude of the electromagnetic field. The two-dimensional structure of the phase space means that no complex dynamics can be found. If a class-B laser is perturbed from its steady state, then the steady state is restored after a short transient. However, as discussed in part (i) of this Thesis, the static properties of class-B lasers, as well as their artificially or noise induced dynamics around the steady state, can be experimentally studied in order to gain insight on laser behaviour, and to determine model parameters that are not known ab initio. In this Thesis particular attention is given to the linewidth enhancement factor, which describes the coupling between the gain and the refractive index in the active material. A highly desirable attribute of an oscillator is stability, both in frequency and amplitude. Nowadays, however, instabilities in coupled lasers have become an active area of research motivated not only by the interesting complex nonlinear dynamics but also by potential applications. In part (ii) of this Thesis the complex dynamics of unidirectionally coupled, i.e., optically injected, class-B lasers is investigated. An injected optical field increases the dimensionality of the phase space to three by turning the phase of the electromagnetic field into an important variable. This has a radical effect on laser behaviour, since very complex dynamics, including chaos, can be found in a nonlinear system with three degrees of freedom. The output of the injected laser can be controlled in experiments by varying the injection rate and the frequency of the injected light. In this Thesis the dynamics of unidirectionally coupled semiconductor and Nd:YVO4 solid-state lasers is studied numerically and experimentally.

Embracing Integrability in Stellar and Planetary Dynamics

Hamiltonian systems in stellar and planetary dynamics are typically near integrable. For example, Solar System planets are almost in two-body orbits, and in simulations of the Galaxy, the orbits of stars seem regular. For such systems, sophisticated numerical methods can be developed through integrable approximations. Following this theme, we discuss three distinct problems. We start by considering numerical integration techniques for planetary systems. Perturbation methods (that utilize the integrability of the two-body motion) are preferred over conventional "blind" integration schemes. We introduce perturbation methods formulated with Cartesian variables. In our numerical comparisons, these are superior to their conventional counterparts, but, by definition, lack the energy-preserving properties of symplectic integrators. However, they are exceptionally well suited for relatively short-term integrations in which moderately high positional accuracy is required. The next exercise falls into the category of stability questions in solar systems. Traditionally, the interest has been on the orbital stability of planets, which have been quantified, e.g., by Liapunov exponents. We offer a complementary aspect by considering the protective effect that massive gas giants, like Jupiter, can offer to Earth-like planets inside the habitable zone of a planetary system. Our method produces a single quantity, called the escape rate, which characterizes the system of giant planets. We obtain some interesting results by computing escape rates for the Solar System. Galaxy modelling is our third and final topic. Because of the sheer number of stars (about 10^11 in Milky Way) galaxies are often modelled as smooth potentials hosting distributions of stars. Unfortunately, only a handful of suitable potentials are integrable (harmonic oscillator, isochrone and Stäckel potential). This severely limits the possibilities of finding an integrable approximation for an observed galaxy. A solution to this problem is torus construction; a method for numerically creating a foliation of invariant phase-space tori corresponding to a given target Hamiltonian. Canonically, the invariant tori are constructed by deforming the tori of some existing integrable toy Hamiltonian. Our contribution is to demonstrate how this can be accomplished by using a Stäckel toy Hamiltonian in ellipsoidal coordinates.

Frequency-comb-referenced molecular spectroscopy in the mid-infrared region

A simple method for absolute frequency measurements of molecular transitions in the mid-infrared region is reported. The method is based on a cw singly-resonant optical parametric oscillator (SRO), which is tunable from 3.2 to 3.45 µm. The mid- infrared frequency of the SRO is referenced to an optical frequency comb through its pump and signal beams. Sub-Doppler spectroscopy and absolute frequency measurement of the P(7) transition of the ν3 band of CH4 are demonstrated.