Optical magnetic field-induced

A brief review is given on electronic properties of carbon nanotubes, in particular those in magnetic fields, mainly from a theoretical point of view. The topics include a giant Aharonov-Bohm effect on the band gap and optical absorption spectra, a magnetic-field induced lattice distortion and a magnetisation and susceptibility of ensembles, calculated based on a k p scheme. 

In n-type GaAs Ming-Way Lee et al. (1988) used far-infrared optical absorption to show that, in the metallic state near the magnetic-field-induced transition, the ls-2p absorption by donors persists, giving evidence that the transition lies in an impurity band. 

Magnetic circular dichroism (MCD) is a technique for studying magnetic-field induced perturbations in the energy levels of a system. It provides additional information about the nature of the energy levels that cause a transition in optical spectroscopy. Recent reviews of iron porphyrin MCD have been written by Dawson and Dooley [10] and Cheesman et al. [29]. 

The poor sister of electric-field-induced non-linear optics is that of magnetic-field-induced non-linear optics, of which the Cotton-Mouton effect is the most important example attention is drawn to this in Section 4. Finally, some thoughts on the future of quantum chemistry in this subject are given in Section 5. It is an area which is a tough test of computational quantum chemistry but recent achievements show it to be one well worth pursuing. 

I believe that this account has shown the enormous interplay between quantum-chemical computation and experiment in the science of non-linear optics over the past few years. It is heartening to realize that calibrational-quality results have led to the un-masking of quite obscure technical problems in some of the electric-field-induced experiments. This has still to happen for the magnetic-field-induced experiments, but I am sure that it will. 

A. J. Karn, S. M. Arakelian, Y. R. Shen and H. L. Ong, "Observation of Magnetic-field-induced First-order Optical Freedericksz Transition in... 

MCD spectroscopy combines the CD experiment with a longitudinal magnetic field, where the application of the magnetic field induces optical activity in any material so that all substances exhibit MCD activity. MCD probes the Zeeman splittings in the ground and excited states and the field-induced mixing between states. 

A well-known nonlinear process taking place in the liquid state of anisotropic molecules is the optical-field induced birefringence (optical Kerr effect ). This nonlinearity results from the reorientation of the molecules in the electric field of a light beam. In the isotropic phase the optical field perturbs the orientational distribution of the molecules. In the perturbed state more molecules are aligned parallel to the electric field than perpendicularly to it and as a consequence the medium becomes birefringent. On the other hand in liquid crystals the orientational distribution of the molecules is inherently anisotropic. The optical field, just as a d.c. electric or magnetic field, induces a collective rotation of the molecules. This process can be described as a reorientation of the director. 

The dominant term in the surface spectroscopy is the one of the second order, and the theory commonly used for the interpretation of SHG and SFG surface spectra is based on the electric dipole approximation. Within this approximation, the effect of optical magnetic fields and multipoles are neglected. This assumption can be at stake in some scenarios, especially for the interpretation of non-resonant SHG phenomena. Quadrupolar contributions are much weaker than the dipolar ones, but they scale with the number density and can amount to noticeable levels which may interfere with the surface term. There is no general solution to this problem, and it is often not known a priori in SHG and SFG studies whether interfacial contribution is dominant over that of the bulk in an interface system.Furthermore, it is commonly assumed that the dipoles induced in the molecules are solely due to the external laser field and that contribution from neighbouring molecules can be neglected. The local fields are hard to capture at a molecular level and require further theoretical work. In this framework, the simplest description of SFG is given by... 

In Sec. 2 the effective mass equation is introduced and the band structure is discussed with a special emphasis on an Aharonov-Bohm effect. Optical absorption spectra are discussed in Sec. 3. A lattice instability, in particular induced by a magnetic field perpendicular to the tube axis, is discussed in Sec. 4 and magnetic properties of ensembles of CNTs are discussed in Sec. 5. 

Electronic properties of CNTs, in particular, electronic states, optical spectra, lattice instabilities, and magnetic properties, have been discussed theoretically based on a k p scheme. The motion of electrons in CNTs is described by Weyl s equation for a massless neutrino, which turns into the Dirac equation for a massive electron in the presence of lattice distortions. This leads to interesting properties of CNTs in the presence of a magnetic field including various kinds of Aharonov-Bohm effects and field-induced lattice distortions. 

This review deals with LC polymers containing mesogenic groups in the side chains of macromolecules. Having no pretence to cover the abundant literature related to thermotropic LC polymers, it seemed reasonable to deal with the most important topics associated with synthesis of nematic, smectic and cholesteric liquid crystals, the peculiarities of their structure and properties, and to discuss structural-optical transformations induced in these systems by electric and magnetic fields. Some aspects of this topic are also discussed in the reviews by Rehage and Finkelmann 27), and Hardy 28). Here we shall pay relatively more attention to the results of Soviet researchers working in the field. 

---