Xochicalco is an archaeological site located in the state of Morelos in central Mexico. It flourished from 600 to 900 a.d. with numerous multicultural elements. There are several underground rooms carved into the hillside In particular, a room with a shaft that has a hole in the roof whose orientation towards the zenith supports its astronomical purpose. Our hypothesis is that the place was used as a tlayohualchieliztli or camera obscura for astronomical observations. This would be the first evidence of a pre-columbian image forming device. To explore the feasibility of this assertion, the conditions required to produce an image were studied. The aperture diameter in the top of the shaft is far too large to be used as a "pinhole" but it may have been covered with a screen containing a smaller bore-hole. We work out the optimum aperture size. The portion of the sky that could be observed due to the orientation of the shaft was also undertaken. The two most intense celestial objects should produce bright enough images thus suggesting that observation of the sun took place during day-time and observation of the moon during night-time. Amate paper or cloth could have been used to directly draw the position of celestial objects.
Propagation of light in stratified media is described with Maxwell's partial differential equations (PDE). Separation of variables allow to decouple the linear PDE's to obtain second order non autonomous linear ODEs for the electric and magnetic fields. In the last decades, the problem has been tackled with matrices whose elements are linearly independent solutions of the fields.
In our approach, although counter-intuitive, the linear differential equations are transformed into a non-linear ODE. To this end, the field is written in terms of amplitude and phase variables. An Ermakov invariant then permits the decoupling of the amplitude and phase nonlinear equations. The amplitude or Milne nonlinear equation is then solved numerically. This method has important advantages: i) initial or final conditions are easily imposed, ii) important physical quantities such as the reflectivity are readily obtained, iii) no further approximations have to be made iv) complex profiles can be modeled with arbitrary degree of precision. The abrupt and adiabatic limits are obtained but most importantly, intermediate more realistic cases can also be tackled, for example, adsorption between thin film layers. Novel effects are addressed such as enhanced reflectivity at derivative discontinuities where the refractive index is continuous.
According to Fresnel formulae, at normal incidence on an abrupt interface, the reflected wave has a phase
difference of zero or π, if the second medium has a lower or larger refractive index than the first. However, what
happens if the refractive indices of two media are the same at the interface but the derivative of the refractive
index varies abruptly? Since the two media are not homogeneous because the refractive index derivative is finite,
the problem cannot be tackled with the Fresnel formalism. In order to deal with this problem the amplitude and
phase representation of plane electromagnetic waves is used. An invariant is obtained that permits the decoupling
of the amplitude and phase equations, both of which, are nonlinear. The amplitude equation is then solved
numerically. No approximations are made regarding how slow or fast refractive index varies compared to the
wavelength. Interpretation of the amplitude equation solutions reveal that surfaces where any of the derivatives
of the refractive index profile is discontinuous, do enhance reflection. At normal incidence, the reflected wave
thus generated will have a phase difference that may be a multiple of π/2, apparently contradicting the Fresnel
equations.
Wave phenomena involve perturbations whose behavior is equivalent in space and time. The perturbations may be of very different nature but they all have to conform with the notion of a field, that is, a scalar or vector quantity defined for all points in space. Some wave phenomena are described in terms of only one field. For example water waves where the perturbation is the level above or below from the equilibrium position. Nonetheless, electromagnetic waves require the existence of two fields. I shall argue that in fact, all wave phenomena involve two fields although we sometimes perform the description in terms of only one field.
To this end, the concept of cyclic or dynamical equilibrium will be put forward where the system continuously moves between two states where it exchanges two forms of energy. In a mechanical system it may be, for example, kinetic and potential energy. Differential equations that form an Ermakov pair require the existence of two linearly independent fields. These equations possess an invariant. For the time dependent harmonic oscillator, such an invariant exists only for time dependent potentials that are physically attainable.
According to this view, two fields must be present in any physical system that exhibits wave behavior. In the case of gravity, if it exhibits wave behavior, there must be a complementary field that also carries energy. It is also interesting that the complex cosmic tension field proposed by Chandrasekar involves a complex field because complex functions formally describe two complementary fields.
The coherence of a Nd:YAG CW laser is analyzed using a Michelson interferometer. Fringe contrast is measured as the path difference is varied by changing the length of one arm. The fringe contrast, as expected, is maximum when there is no path difference between arms. However, the fringe contrast does not decrease monotonically. It decreases and then increases several times before fading away. This behaviour is reminiscent of the fringe contrast depending on aperture and the uncovering of the Fresnel zones. In order to evaluate the mode structure it is necessary to consider the geometric parameters and Q factor of the cavity, the medium gain curve and the type of broadening.
The non interference of waves principle requires that two (or more) modes competition or their interference can only take place though matter non linear interaction. Therefore, and in addition, it is important to consider the setup and type of detectors employed to monitor the frequency and/or time dependence. In as much as speckle is recognized as an interference phenomenon taking place at the detector plane, say the retina, the role of the sensing element in the detection of mode beats should also be decisive.
The reciprocity principle requests that if an observer, say in the laboratory, sees an event with a given velocity,
another observer at rest with the event must see the laboratory observer with minus the same velocity. The
composition of velocities in the Lorentz-Einstein scheme does not fulfill the reciprocity principle because the
composition rule is neither commutative nor associative. In other words, the composition of two non-collinear
Lorentz boosts cannot be expressed as a single Lorentz boost but requires in addition a rotation. The Thomas
precession is a consequence of this composition procedure. Different proposals such as gyro-groups have been
made to fulfill the reciprocity principle.
An alternative velocity addition scheme is proposed consistent with the invariance of the speed of light and
the relativity of inertial frames. An important feature of the present proposal is that the addition of velocities is
commutative and associative. The velocity reciprocity principle is then immediately fulfilled. This representation
is based on a transformation of a hyperbolic scator algebra. The proposed rules become identical with the
special relativity addition of velocities in one dimension. They also reduce to the Galilean transformations in
the low velocity limit. The Thomas gyration needs to be revised in this nonlinear realization of the special
relativity postulates. The deformed Minkowski metric presented here is compared with other deformed relativity
representations.
The sharply peaked comb structure that arises from a mode-locked cavity is usually explained in terms of the
superposition of monochromatic waves with integer wavelength multiples of the round trip of the cavity. However,
the non interaction (or non interference) of waves implies that these wave-fields cannot sum themselves
to reorganize either their amplitudes or their energies. The summation has to be carried out either by a nonlinear
medium whose output involves the wave-mixing and/or it is performed by the detector. The output of
a femtosecond Titanium Sapphire oscillator is analyzed with the above mentioned framework in mind. The
spectrum is obtained in mode-locked and non mode-locked operation via a grating spectrometer for different
cavity detunnings. The time dependence is measured via a fast photo-diode to record the repetition rate. A
frequency resolved optical gating (FROG) device is used to resolve the temporal shape of the femtosecond pulses.
The data is examined from two viewpoints: The superposition process is carried out (a) by the filed amplitudes
themselves, or (b) by some interacting material dipoles.
The Irradiance Transport Equation (ITE), found by Teague, had been used in optics with different applications. One of the field where had been used is in optical testing, for example, with the method developed by Takeda. In this paper following the idea of using different optical and mathematical analysis method, theorical and experimental results are presented.
In the present work Bi thin films were obtained by Pulsed Laser Deposition, using Nd:YAG lasers. The films were characterized by optical microscopy. Raman spectroscopy and X-rays diffraction. It was accomplished the real time spectral emission characterization of the plasma generated during the laser evaporation process. Highly oriented thin films were obtained.
Recent experiments on optical bistability in amorphous Se an GexSe1-x chalcogenide thin films are presented. The results show a strong dependence on the energy density and on the sample composition. The faster responses are for pure selenium as the content of germanium is increased the material response is slower. A simple model is proposed in order to explain the observed results.
Recent experiments regarding the nonlinear optical properties of germanium diselenide glass in thin films and bulk forms are presented. The observed effects are optical bistability without external feedback, laser-induced diffraction patterns, and phase conjugation. These effects are investigated using a 25 mW He-Ne laser at 632.8 nm. The above-mentioned effects show common features, the main one being that they are reversible provided that a certain irradiation power is not reached. Above this threshold the effects are permanent given sufficient exposure time. The recording resolution of the system is diffraction limited below the threshold. The underlying phenomenon responsible for the intensity-dependent refractive index change is believed to be due to photostructural reordering and reorientation of the material.
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