3D printing of optical materials: an investigation of the microscopic properties

3D printing technologies are currently enabling the fabrication of objects with complex architectures and tailored properties. In such framework, the production of 3D optical structures, which are typically based on optical transparent matrices, optionally doped with active molecular compounds and nanoparticles, is still limited by the poor uniformity of the printed structures. Both bulk inhomogeneities and surface roughness of the printed structures can negatively affect the propagation of light in 3D printed optical components. Here we investigate photopolymerization-based printing processes by laser confocal microscopy. The experimental method we developed allows the printing process to be investigated in-situ, with microscale spatial resolution, and in real-time. The modelling of the photo-polymerization kinetics allows the different polymerization regimes to be investigated and the influence of process variables to be rationalized. In addition, the origin of the factors limiting light propagation in printed materials are rationalized, with the aim of envisaging effective experimental strategies to improve optical properties of printed materials.Comment: 8 pages, 3 figure

Quantum Solitons in Affine Toda Field Theories

The spectra of $A_r$ affine Toda field theories with imaginary coupling constant, are investigated. Soliton solutions are found, which, despite the non-unitary form of the Lagrangian, have real classical masses and are stable to small perturbations. The quantum corrections to the soliton masses are determined, to lowest order in $\hbar$. The solitons have the same spectrum as the fundamental Toda particles; a feature that is preserved in the quantum theory.Comment: 21 page

Reflection Amplitudes of Boundary Toda Theories and Thermodynamic Bethe Ansatz

We study the ultraviolet asymptotics in $A_n$ affine Toda theories with integrable boundary actions. The reflection amplitudes of non-affine Toda theories in the presence of conformal boundary actions have been obtained from the quantum mechanical reflections of the wave functional in the Weyl chamber and used for the quantization conditions and ground-state energies. We compare these results with the thermodynamic Bethe ansatz derived from both the bulk and (conjectured) boundary scattering amplitudes. The two independent approaches match very well and provide the non-perturbative checks of the boundary scattering amplitudes for Neumann and $(+)$ boundary conditions. Our results also confirm the conjectured boundary vacuum energies and the duality conjecture between the two boundary conditions.Comment: 20 pages, 3 figures, LaTeX2

Reflection Amplitudes of ADE Toda Theories and Thermodynamic Bethe Ansatz

We study the ultraviolet asymptotics in affine Toda theories. These models are considered as perturbed non-affine Toda theories. We calculate the reflection amplitudes, which relate different exponential fields with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with thermodynamic Bethe ansatz results.Comment: 20 pages, 2 ps figures, LaTeX 2e. We added the last section, "Concluding Remarks", in which the new result for the one point function < \exp a\cdot\phi > in ADE affine Toda theories is given explicitly. Version to appear in Nucl. Phys.

The Analytic Structure of Trigonometric S Matrices

$S$-matrices associated to the vector representations of the quantum groups for the classical Lie algebras are constructed. For the $a_{m-1}$ and $c_m$ algebras the complete $S$-matrix is found by an application of the bootstrap equations. It is shown that the simplest form for the $S$-matrix which generalizes that of the Gross-Neveu model is not consistent for the non-simply-laced algebras due to the existence of unexplained singularities on the physical strip. However, a form which generalizes the $S$-matrix of the principal chiral model is shown to be consistent via an argument which uses a novel application of the Coleman-Thun mechanism. The analysis also gives a correct description of the analytic structure of the $S$-matrix of the principle chiral model for $c_m$.Comment: 25 pages (macro included, 6 figures included as uuencoded compressed tar file), CERN-TH.6888/93, (An important argument is corrected leading to a novel application of the Coleman-Thun mechanism. Also decided to risk some figures.

Anapole moment of an exotic nucleus

We demonstrate that there is no appreciable enhancement of the anapole moment of $^{11}$Be. The effect of small energy intervals is compensated for by a small overlap of the halo neutron wave function with core.Comment: 5 pages, LaTe

Realization of Haldane's Exclusion Statistics in a Model of Electron-Phonon Interactions

We discuss an integrable model describing one-dimensional electrons interacting with two-dimensional anharmonic phonons. In the low temperature limit it is possible to decouple phonons and consider one-dimensional excitations separately. They have a trivial two-body scattering matrix and obey fractional statistics. As far as we know the original model presents the first example of a model with local bare interactions generating purely statistical interactions between renormalized particles. As a by-product we obtain non-trivial thermodynamic equations for the interacting system of two-dimensional phonons.Comment: 4 page

Non linear integral equation and excited--states scaling functions in the sine-Gordon model

The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length $L$ using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large $L$ (perturbative) and small $L$ (conformal) regimes as well as numerically.Comment: LaTeX file, 40 pages, 4 figures in a tar.Z file (3 figures added and few misprints corrected w.r.t. previous version

Dynkin Diagrams and Integrable Models Based on Lie Superalgebras

An analysis is given of the structure of a general two-dimensional Toda field theory involving bosons and fermions which is defined in terms of a set of simple roots for a Lie superalgebra. It is shown that a simple root system for a superalgebra has two natural bosonic root systems associated with it which can be found very simply using Dynkin diagrams; the construction is closely related to the question of how to recover the signs of the entries of a Cartan matrix for a superalgebra from its Dynkin diagram. The significance for Toda theories is that the bosonic root systems correspond to the purely bosonic sector of the integrable model, knowledge of which can determine the bosonic part of the extended conformal symmetry in the theory, or its classical mass spectrum, as appropriate. These results are applied to some special kinds of models and their implications are investigated for features such as supersymmetry, positive kinetic energy and generalized reality conditions for the Toda fields. As a result, some new families of integrable theories with positive kinetic energy are constructed, some containing a mixture of massless and massive degrees of freedom, others being purely massive and supersymmetric, involving a number of coupled sine/sinh-Gordon theories.Comment: 31 pages; plain TeX, macros included; 5 main Figs., more in tables; v2: minor but confusing inaccuracy corrected in statement of one proposition (already corrected in published version

Scattering Theory and Correlation Functions in Statistical Models with a Line of Defect

The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of inhomegeneity to the scattering amplitudes in the bulk. The factorization condition for the new amplitudes gives rise to a set of Reflection-Transmission equations. The solutions of these equations in the case of diagonal $S$-matrix in the bulk are only those with $S =\pm 1$. The choice $S=-1$ corresponds to the Ising model. We compute the exact expressions of the transmission and reflection amplitudes relative to the interaction of the Majorana fermion of the Ising model with the defect. These amplitudes present a weak-strong duality in the coupling constant, the self-dual points being the special values where the defect line acts as a reflecting surface. We also discuss the bosonic case $S=1$ which presents instability properties and resonance states. Multi-defect systems which may give rise to a band structure are also considered. The exact expressions of correlation functions is obtained in terms of Form Factors of the bulk theory and matrix elements of the defect operator.Comment: 50 pages, LATEX file, ISAS/EP/94-12