Vol. 52 No. 6 (2006): Revista Mexicana de Física.

Published: 2006-01-01

Articles

  • Óptica difractiva: una revisión al diseño y construcción de sistemas ópticos empleando lentes difractivas

    J. Castro-Ramos, S. Vázquez-Montiel, J. Hernández-de-la-Cruz, O. García-Lievanos, W. Calleja-Arriaga
    479-0

  • Torques on quadrupoles

    G.F. Torres del Castillo, A. Méndez Garrido
    501-0
    Abstract:
    Making use of the fact that a $2^{l}$-pole can be represented by means of $l$ vectors of the same magnitude, the torque on a quadrupole in an inhomogeneous external field is expressed in terms of the vectors that represent the quadrupole and the gradient of the external field. The conditions for rotational equilibrium are also expressed in terms of these vectors.
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  • Second virial coefficient of a series of polysiloxanes: the effect of side groups and molecular weight

    J.A. Villegas, J. Cervantes
    507-0
    Abstract:
    This study reports the results of analyzing the second virial coefficient (A$_{2})$ in a good solvent for a series of polysiloxane chains in which the pairs of substituents connected to the silicon are CH$_{3}$, CH$_{3; }$C$_{2}$H$_{5}$, C$_{2}$H$_{5}$; CH$_{3}$, C$_{6}$H$_{13; }$CH$_{3}$, C$_{16}$H$_{33; }$and CH$_{3}$, C$_{6}$H$_{5. }$The effect of the side group and molecular weight on A$_{2}$ was investigated using the Helical Wormlike (HW) chain model. A theoretical analysis of the interpenetration function ($\psi )$ was carried out using a Two-Parameter (TP) scheme. The theoretical-experimental behaviour of A$_{2 }$in a series of polysiloxanes was investigated considering the effects of the type of substituent on the main chain, molecular conformation, and molecular weight. The results obtained were strongly dependent on the flexibility of the side groups and the molecular weight of the polymer. Within the HW model and TP scheme, the A$_{2}$ value for poly(dimethylsiloxane) (PDMS1 and PDMS2), poly(diethylsiloxane) and poly(methylhexylsiloxane) agrees with the experimental results obtained through the coupled system (Gel Permeation Chromatography/Light Scattering: GPC/LS). However, the A$_{2}$ calculated for PDMS3, poly(methylhexadecylsiloxane) (PMHDS) and poly(methylphenylsiloxane) (PMPS) showed a significant difference from the experimental value. On the basis of the theory for the HW model, the deviation in PDMS3 may be due to the effect of the end chains. For PMHDS and PMPS, the model used is outside of the coil limit (validity of TP model). In PMHDS the determination of the (RMSradius)$^{2}$ value from the GPC/LS system is strongly influenced by the interaction between the bulky side group and the main chain, which affects the calculation of A$_{2}$.
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  • Some statistical mechanical properties of photon black holes

    X. Hern, ez., C.S. Lopez-Monsalvo, S. Mendoza, R.A. Sussman
    515-0
    Abstract:
    We show that if the total internal energy of a black hole is constructed as the sum of $N$ photons all having a fixed wavelength chosen to scale with the Schwarzschild radius as $\lambda=\alpha R_{s}$, then $N$ will scale with $R_{s}^{2}$. A statistical mechanical calculation of the configuration proposed yields \( \alpha = 4 \pi^2 / \ln(2) \) and a total entropy of the system $S=k_{B}N \ln(2)$, in agreement with the Bekenstein entropy of a black hole. It is shown that the critical temperature for Bose-Einstein condensation for relativistic particles of $\lambda=\alpha R_{s}$ is always well below the Hawking temperature of a black hole, in support of the proposed internal configuration. We then examine our results from the point of view of recent loop quantum gravity ideas and find that a natural consistency of both approaches appears. We show that the Jeans criterion for gravitational instability can be generalised to the special and general relativistic regimes and holds for any type of mass-energy distribution.
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  • Soliton instabilities in the easy plane ferromagnet Heisenberg chain with out-of-plane spin deviation

    J. Pozo, A. León
    522-0
    Abstract:
    In this paper we investigate the presence of out-of-plane spin deviation $% \rho (\xi )$ in the easy-plane ferromagnetic Heisenberg chain by using the coupled-boson operators together with the Schwinger transformation for the spin operator; this method allows us to conclude that the critical behaviour of the instability is due to the velocity of the nonlinear excitations (solitons) only for an appropriate range of the magnetic field. In this case, when the velocity becomes lower, the stable soliton corresponding to $\rho (\xi )$ is distorted by magnons and loses stability. If we increase the velocity of $\rho (\xi )$, it then decays into high frequency-oscillations. Nevertheless, we find an opposite competence effect produced by the velocity and the magnetic field on $\rho (\xi )$.
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  • Cubic optical nonlinearities with octupolar molecules at telecommunication wavelengths

    G. Ramos-Ortiz, S. Romero, J.L. Maldonado, O. Barbosa-García, M.A. Meneses-Nava, M. Romero, N. Farfán
    527-0
    Abstract:
    Here we report on the cubic nonlinear optical properties of octupolar organic molecules. A series of three compounds that were of triphenylmethane derivatives and one boroxine derivative were characterized, in solid state, at infrared wavelengths comprising telecommunication bands \mbox{(900 - 1600 nm).} At these wavelengths, for which there is practically an absence of reports about cubic nonlinearities in octupolar compounds, we measured third-order susceptibilities $\chi^{(3)}$ of the order of $10^{-12}$ esu, the latter partially enhanced by multiphoton resonances. As the molecules studied were prototypes of octupolar systems, our results correlate the magnitude of the observed nonlinearities with the molecular structure, thus providing helpful information for the design of new molecules with improved nonlinearities. On the other hand, we discuss how polymer films functionalized with these molecules can be useful for applications involving the conversion of optical frequencies. Such films produce frequency-converted signals sensitive enough that they can be employed in ultra-fast optical correlators.
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  • Estructura electrónica de superficies: estados de superficie y estados resonantes del calcio

    H. Herrera, César Mora.
    534-0
    Abstract:
    In this paper we present a detailed study of the electronic band structure of the (001) and (110) surface of the face centered cubic Ca. For our study we use the tight-binding approach and the surface Green function matching method. We use tigth-binding Hamiltonians in the Slater Koster formalism (SK). First, we use an orthogonal atomic basis of nine \emph{spd} atomic orbitals, for each atom in the unitary cell. For the study of the surfaces we use the surface Green function matching method. We find that our results compare acceptably well with the previous published values, and we make the prediction of new different states not yet reported in the literature.
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  • Self-focusing in chromium-doped potassium niobate single ceramic crystal

    J. Castillo-Torres, J. Hernández A., S. Gonzalez-Martínez, A. Aguirre-López, M. B, J.A. Aguilar-Martínez
    540-0
    Abstract:
    The self-focusing and nonlinear optical absorption in a chromium-doped potassium niobate single ceramic crystal have been investigated. The third-order electric susceptibility $\chi$$^{(3)}$ at continuous 532 nm radiation is estimated based on a band transport model describing photorefractive properties for this electro-optic material. An anisotropic behavior on its nonlinear optical absorption properties has also been observed due to the presence of chromium ions.
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  • Irradiance transport equation from geometrical optics considerations

    M. Campos-García, R. Díaz-Uribe
    546-0
    Abstract:
    A general equation for the propagation of phase and irradiance is derived within the geometrical optics regime. The starting point is Poynting's theorem together with the representation of the Poynting vector in the eikonal approximation. It is shown that the irradiance transport equation is a particular case of a more general conservation equation and is valid in the paraxial regime. An analysis of the range of validity of the irradiance transport equation is performed.
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  • Noise measurements on optical detectors

    F.J. González
    550-0
    Abstract:
    The main figure of merit for detectors whose output consists of an electrical signal that is proportional to the radiant signal power is the normalized detectivity $D^{\ast }$, which is directly proportional to the signal-to-noise ratio ($SNR)$. In order to have an accurate value for the signal-to-noise ratio of an optical detector, the noise level of the measurement system and the bias circuit should be small compared to the noise of the device under test. In this paper a low-noise setup to make noise measurements on optical detectors is analyzed and characterized for the specific case of an antenna-coupled microbolometer. The noise floor of the setup was calculated and measured at about 1.3 $\mathrm{nV}/\sqrt{\mathrm{Hz}}$, which gives detector-noise-limited measurements for microbolometers with resistances as low as 200 $\Omega.$ This measurement setup was used to characterize the noise of a 200 $\Omega $ antenna-coupled microbolometer made out of chrome. Measurements showed two $1/f^{k}$ components in this particular device.
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  • \phantom{Errata}

    555-0