Two closely coupled lasers, dynamics & applications

The dynamics of two mutually coupled identical single-mode semi-conductor lasers are theoretically investigated. For small separation and large coupling between the lasers, symmetry-broken one-colour states are shown to be stable. In this case the light output of the lasers have significantly different intensities whilst at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable two-colour states, where both single-mode lasers lase simultaneously at two optical frequencies which are separated by up to 150 GHz. For low coupling but possibly large separation, the frequency of the relaxation oscillations of the freerunning lasers defines the dynamics. Chaotic and quasi-periodic states are identified and shown to be stable. For weak coupling undamped relaxation oscillations dominate where each laser is locked to three or more odd number of colours spaced by the relaxation oscillation frequency. It is shown that the instabilities that lead to these states are directly connected to the two colour mechanism where the change in the number of optical colours due to a change in the plane of oscillation. At initial coupling, in-phase and anti-phase one colour states are shown to emerge from “on” uncoupled lasers using a perturbation method. Similarly symmetry-broken one-colour states come from considering one free-running laser initially “on” and the other laser initially “off”. The mechanism that leads to a bi-stability between in-phase and anti-phase one-colour states is understood. Due to an equivariant phase space symmetry of being able to exchange the identical lasers, a symmetric and symmetry-broken variant of all states mentioned above exists and is shown to be stable. Using a five dimensional model we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-colour, symmetric and symmetry-broken two-colour, symmetric and symmetry-broken undamped relaxation oscillations, symmetric and symmetry-broken quasi-periodic, and symmetric and symmetry-broken chaotic states. As symmetry-broken states always exist in pairs, they naturally give rise to bi-stability. Several of these states show multistabilities between symmetric and symmetry-broken variants and among states. Three memory elements on the basis of bi-stabilities in one and two colour states for two coupled single-mode lasers are proposed. The switching performance of selected designs of optical memory elements is studied numerically.

Room temperature ferroelectric and magnetic investigations and detailed phase analysis of Aurivillius phase Bi 5Ti 3Fe 0.7Co 0.3O 15 thin films

Aurivillius phase Bi 5Ti 3Fe 0.7Co 0.3O 15 (BTF7C3O) thin films on α-quartz substrates were fabricated by a chemical solution deposition method and the room temperature ferroelectric and magnetic properties of this candidate multiferroic were compared with those of thin films of Mn 3 substituted, Bi 5Ti 3Fe 0.7Mn 0.3O 15 (BTF7M3O). Vertical and lateral piezoresponse force microscopy (PFM) measurements of the films conclusively demonstrate that BTF7C3O and BTF7M3O thin films are piezoelectric and ferroelectric at room temperature, with the major polarization vector in the lateral plane of the films. No net magnetization was observed for the in-plane superconducting quantum interference device (SQUID) magnetometry measurements of BTF7M3O thin films. In contrast, SQUID measurements of the BTF7C3O films clearly demonstrated ferromagnetic behavior, with a remanent magnetization, B r, of 6.37 emu/cm 3 (or 804 memu/g), remanent moment 4.99 × 10 -5 emu. The BTF7C3O films were scrutinized by x-ray diffraction, high resolution transmission electron microscopy, scanning transmission electron microscopy, and energy dispersive x-ray analysis mapping to assess the prospect of the observed multiferroic properties being intrinsic to the main phase. The results of extensive micro-structural phase analysis demonstrated that the BTF7C3O films comprised of a 3.95 Fe/Co-rich spinel phase, likely CoFe 2 - xTi xO 4, which would account for the observed magnetic moment in the films. Additionally, x-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM) imaging confirmed that the majority of magnetic response arises from the Fe sites of Fe/Co-rich spinel phase inclusions. While the magnetic contribution from the main phase could not be determined by the XMCD-PEEM images, these data however imply that the Bi 5Ti 3Fe 0.7Co 0.3O 15 thin films are likely not single phase multiferroics at room temperature. The PFM results presented demonstrate that the naturally 2D nanostructured Bi 5Ti 3Fe 0.7Co 0.3O 15 phase is a novel ferroelectric and has potential commercial applications in high temperature piezoelectric and ferroelectric memory technologies. The implications for the conclusive demonstration of ferroelectric and ferromagnetic properties in single-phase materials of this type are discussed.

Magnetic field-induced ferroelectric switching in multiferroic aurivillius phase thin films at room temperature

Single-phase multiferroic materials are of considerable interest for future memory and sensing applications. Thin films of Aurivillius phase Bi 7Ti3Fe3O21 and Bi6Ti 2.8Fe1.52Mn0.68O18 (possessing six and five perovskite units per half-cell, respectively) have been prepared by chemical solution deposition on c-plane sapphire. Superconducting quantum interference device magnetometry reveal Bi7Ti3Fe 3O21 to be antiferromagnetic (TN = 190 K) and weakly ferromagnetic below 35 K, however, Bi6Ti2.8Fe 1.52Mn0.68O18 gives a distinct room-temperature in-plane ferromagnetic signature (Ms = 0.74 emu/g, μ0Hc =7 mT). Microstructural analysis, coupled with the use of a statistical analysis of the data, allows us to conclude that ferromagnetism does not originate from second phase inclusions, with a confidence level of 99.5%. Piezoresponse force microscopy (PFM) demonstrates room-temperature ferroelectricity in both films, whereas PFM observations on Bi6Ti2.8Fe1.52Mn0.68O18 show Aurivillius grains undergo ferroelectric domain polarization switching induced by an applied magnetic field. Here, we show for the first time that Bi6Ti2.8Fe1.52Mn0.68O18 thin films are both ferroelectric and ferromagnetic and, demonstrate magnetic field-induced switching of ferroelectric polarization in individual Aurivillius phase grains at room temperature.