Mode beating in spot-size converter lasers

An anomalous modulation in the wavelength spectrum has been observed in lasers with spot-size converters. This intensity modulation is shown to be caused by beating between the fundamental lasing mode and radiation modes in the taper. This results in a periodic modulation in the net gain spectrum, which causes wavelength jumps between adjacent net gain maxima, and a drive current dependent spectral width that is expected to affect system performance. The amplitude of this spectral modulation is reduced significantly by either using an angled rear-facet which reflects the beating radiation modes away from the laser axis, or by using a nonlinear, adiabatic taper.     

Green's functions for Maxwell's equations: application to spontaneous emission

We present a new formalism for calculating the Green's function for Maxwell's equations. As our aim is to apply our formalism to light scattering at surfaces of arbitrary materials, we derive the Green's function in a surface representation. The only requirement on the material is that it should have periodicity parallel to the surface. We calculate this Green's function for light of a specific frequency and a specific incident direction and distance with respect to the surface. The material properties entering the Green's function are the reflection coefficients for plane waves at the surface. Using the close relationship between the Green's function and the density of states (DOS), we apply our method to calculate the spontaneous emission rate as a function of the distance to a material surface. The spontaneous emission rate can be calculated using Fermi's Golden Rule, which can be expressed in terms of the DOS of the optical modes available to the emitted photon. We present calculations for a finite slab of cylindrical rods, embedded in air on a square lattice. It is shown that the enhancement or suppression of spontaneous emission strongly depends on the frequency of the light. This revised version was published online in November 2006 with corrections to the Cover Date.     

Two different copper sites in hexakis(1-methyltetrazole)copper(II) bis(tetrafluoroborate)

An electron spin resonance study at temperatures between 300 and 4 K demonstrates that the two crystallographically inequivalent Cu(II) sites in the title compound are subject to different Jahn-Teller behaviour. It is shown that this is not induced by cooperative interactions between the Jahn-Teller sites but arises from the different lattice symmetries of the two sites.     

From Multi-Site to On-Site Transfer Matrix Models for Self-Similar Chains

We show how transfer matrix models on chains that are self-similar (renormalizable) with respect to a substitution rule can be transformed from multi-site models in which transfer matrices depend on the nature of a finite number of neighboring sites, to on-site models in which transfer matrices depend on the nature of one site only. We present sufficient conditions and show that these conditions are satisfied in the case of quasiperiodic chains of two symbols that are renormalizable with respect to an invertible substitution rule. We illustrate the application of our results to tight-binding Schrödinger equations modeling the electronic behavior of self-similar chains of atoms and to models describing the transmission of light through self-similarly stacked multilayers.     

Efficient interface conditions for the semi-vectorial finite-difference beam propagation method

Efficient interface conditions (EICs) are derived for the propagation equation using the slowly varying envelope approximation for the dominant electric field component. At the interface between two different media, the two lateral second derivatives in the discretized propagation equation are adapted such that the discretized modal field equation is correct up to second order in the lateral grid spacing. Since the error term is then of the order of the lateral grid spacing, our EICs are first-order EICs. These interface conditions are compared with well-known zero-order EICs derived by Stern and Kim and Ramaswamy. It is shown that the first-order EICs yield faster convergence to the exact effective index value as the lateral grid spacing is decreased than do the zero-order EICs. It turns out that our EICs are very much like those derived by Vassallo. Using essentially the same method, he derived EICs of second and first order for the field component respectively parallel and perpendicular, to the interface. Hence the accuracy of his EICs is one order higher for the field component parallel to the interface, although it introduces an extra asymmetry in the propagation matrix.     

Disordered CuN(6) Jahn-Teller Centers in Hexakis(1-methyltetrazole)copper(II) Tetrafluoroborate: A Temperature-Dependent X-ray Diffraction and EPR Study

The influence of the molecular crystalline arrangement upon the state of a Jahn-Teller-active center has been investigated in crystals of the complex Cu(mtz)(6)(BF(4))(2), where mtz = 1-methyltetrazole. Crystal structures at 293, 123, and 93 K were determined by X-ray diffraction for the copper complex and at 293 and 100 K also for the analogous zinc complex, Zn(mtz)(6)(BF(4))(2). The respective lattice parameters for the copper complex at 293, 123, and 93 K are as follows: a = 18.137(4), 17.597(4), 17.575(4) ?; b = 10.247(4), 10.131(4), 10.133(4); c = 18.446(5), 18.531(4), 18.535(4) ?; beta = 112.62(2), 113.55(2), 113.61(2) degrees. Those for the zinc complexes at 293 and 100 K, respectively, are as follows: a = 18.153(2), 17.663(2) ?; b = 10.289(1), 10.159(2) ?; c = 18.506(3), 18.578(3) ?; beta = 113.21(1), 114.15(2) degrees. The crystal system is monoclinic, space group P2(1)/n (Z = 4), for all crystals with two crystallographically inequivalent pairs of centrosymmetric molecules, M(mtz)(6)(BF(4))(2), in the unit cell. The two inequivalent Cu(mtz)(6)(2+) complexes, Cu(A) and Cu(B), both exhibit Jahn-Teller distortions, but in different ways, the Cu-N distances for the unit on site A being 2.015(4), 2.031(5), and 2.384(5) ? at 93 K, while those for the unit on site B are 2.053(5), 2.126(5), and 2.204(5) ?. However, the Jahn-Teller radii of the two complexes, as calculated from the metal-ligand distances and the U tensors of the two CuN(6) units, were both found to be 0.41(3) ?. EPR experiments at room temperature on polycrystalline samples of the pure copper compound and of the copper-doped zinc compound confirm the presence of two different Jahn-Teller centers; both complexes are rapidly pulsating, but the CuN(6) units on site A are confined predominantly to one potential well of the warped Mexican hat potential, whereas the CuN(6) units on site B have density in all three wells. At 78 K, however, the spectrum of the polycrystalline material is consistent with a single site having an axial g tensor with maximum anisotropy (g( parallel) = 2.300(5), g( perpendicular) = 2.068(5)). While the low-temperature X-ray results also indicate a structure in which the Cu(A) center is exclusively populated in one potential well, the U tensor and potential well population data for the Cu(B) centers indicate that at 93 K a nonpulsating averaged structure based on tetragonally elongated CuN(6) units is being observed. The more pronounced preference for the CuN(6) octahedron on site A to show elongation in one specific direction, in contrast to that on the B site, appears to be due to the differing impacts of the local-site strains at the two distinct centers of symmetry, and a simple model for evaluating a crystal "packing" strain from the bond length data for the isomorphous zinc complex is described.