Glasses for Raman nonlinear optics

The Raman effect, by which light is frequency shifted by a vibrational mode, enters into a number of phenomena in nonlinear optics. Here, we summarize our progress in identifying glass materials with potentially useful Raman properties, methods for measuring the strength of the Raman effect and its spectral dependence, and the properties of a number of different families of glasses. Glasses with both larger peak Raman susceptibilities and larger bandwidths relative to fused silica are reported.     

Nonlinear optical excitation and dispersion relation of surface exciton polaritons in ZnO

The dispersion relation and the theory of nonlinear excitation of surface exciton polaritons are presented for a geometry consisting of a prism, and airgap and a spatially dispersive medium. We compare DeMartini et al.'s experimental results for the Cl-surface exciton polaritons in ZnO with the predictions of two models for the ABC (additional boundary conditions), i.e. P_ex = 0 and $\text{?}\text{P}{}_{\mathrm{ex}}\text{?}\text{z}\text{= 0}$ and found reasonable agreement for the second case only.     

The Carroll and Chang conjecture of equal Indscal components when Candecomp/Parafac gives perfect fit

The Candecomp/Parafac algorithm approximates a set of matrices ${\mathbf{X}}_1\text{,}\dots \text{,}{\mathbf{X}}_I$ by products of the form ${\mathbf{AC}}_i{\mathbf{B}}^{\prime }$, with ${\mathbf{C}}_i$ diagonal, $i=1\text{,}\dots \text{,}I$. Carroll and Chang have conjectured that, when the matrices are symmetric, the resulting $\mathbf{A}$ and $\mathbf{B}$ will be column wise proportional. For cases of perfect fit, Ten Berge et al. have shown that the conjecture holds true in a variety of cases, but may fail when there is no unique solution. In such cases, obtaining proportionality by changing (part of) the solution seems possible. The present paper extends and further clarifies their results. In particular, where Ten Berge et al. solved all $I\times 2\times 2$ cases, now all $I\times 3\times 3$ cases, and also the $I\times 4\times 4$ cases for $I=2\text{,}8$, and 9 are clarified. In a number of cases, $\mathbf{A}$ and $\mathbf{B}$ necessarily have column wise proportionality when Candecomp/Parafac is run to convergence. In other cases, proportionality can be obtained by using specific methods. No cases were found that seem to resist proportionality.     

All-optical waveguide switching

We present a tutorial review of all-optical switching in fibre and integrated optics waveguides. These switching devices require non-linear refractive index changes in single or coupled waveguides, and involve either the low-power guided modes of the structure or soliton-type waves guided, emitted or captured by waveguides. We discuss the physical principles involved in these all-optical switching schemes, material requirements, recent experiments and limitations. A representative rather than comprehensive list of references is provided.An invited paper     

Discrete Talbot effect in waveguide arrays

We report the first observation of discrete Talbot revivals in one-dimensional waveguide arrays. Unlike continuous systems where the Talbot self-imaging effect always occurs irrespective of the pattern period, in discrete configurations this process is only possible for a specific set of periodicities. Recurrence of different input periodic patterns is observed in good agreement with theory.     

Discrete surface solitons

It is theoretically shown that discrete nonlinear surface waves are possible in waveguide lattices. These self-trapped states are located at the edge of the array and can exist only above a certain power threshold. The excitation characteristics and stability properties of these surface waves are systematically investigated.     

Properties of type II quadratic solitons excited by imbalanced fundamental waves

It was shown experimentally for type II second-harmonic generation in KTP that the family of quadratic spatial solitons exists over a wide range of imbalances for the two fundamental wave inputs. The threshold for soliton formation was measured as a function of both phase mismatch and relative input fraction of the energy in the two fundamental polarizations. Launching unequal fundamental inputs led to an imbalanced three-coupled-field output composition.     

Interactions between one-dimensionalquadratic soliton-like beams

The interaction between two quadratic soliton-like beams was investigated for beams launched parallel to one another, and at small crossing angles. The experiments were performed in titanium in-diffused lithium niobate slab waveguides near a Type I phase-matching condition for second harmonic generation (SHG). Only beams at the fundamental frequency were launched and the second harmonic required for quadratic soliton formation was generated upon propagation into the waveguide. The results of the interaction were found to depend on the relative phase between the input fundamental beams, the net phase mismatch for SHG and on the beam crossing angle. Good agreement with numerical simulations of the different interactions was found. In general, the results of the interactions were similar to those found in saturable Kerr-like media.     

Symmetry transformations for square sliced three-way arrays, with applications to their typical rank

The typical 3-tensorial rank has been much studied over algebraically closed fields, but very little has been achieved in the way of results pertaining to the real field. The present paper examines the typical 3-tensorial rank over the real field, when the slices of the array involved are square matrices. The typical rank of 3 × 3 × 3 arrays is shown to be five. The typical rank of p × q × q arrays is shown to be larger than q + 1 unless there are only two slices (p = 2), or there are three slices of order 2 × 2 (p = 3 and q = 2). The key result is that when the rank is q + 1, there usually exists a rank-preserving transformation of the array to one with symmetric slices.