This work presents a research in which a Twin Core Fiber (TCF) has been employed for designing a Mach- Zehnder
interferometer and its behavior under the effect of thermal gradients has been regarded. From the coupled modes theory
can be deduced that under the phase-matched condition-that is similar propagation constants in both cores of a TCF,
the energy transported in the cores is the same, which is fundamental for developing this interferometer. This research
required to design a thermal cavity and an automation circuit for applying thermal cycles to a segment of the TCF. The
temperature was recorded by means of a thermocouple placed inside the thermal cavity and its signal was introduced into
the computer where an instrumentation software (Lab View) designed for monitoring and controlling variables used this
signal for controlling the on-off states of a power resistor and a refrigeration system for raising and lowering the
temperature, respectively. It was observed that the optical power variations in a point of the interference pattern
presented a weak dependence with the thermal cycles.
The spatial coherence wavelets theory provides more insight into the understanding of interference and diffraction
because they are the primary carriers of power and correlation of light. In this context, novel keys for analyzing the
physical properties of light are revealed by these wavelets, as discussed in the present work. Particularly, the bright and
the dark rays and related features as the energy flux vectors - parallel and anti-parallel to the Poynting vector, and the
transverse energy transference, provide insight into the mechanism of energy distribution of a wavefield after diffraction
and its dependence on spatial coherence properties of the field. These properties could be experimentally controlled by
modulating the spatial coherence of the light, offering new possibilities of technological applications in subjects
involving beam shaping.
Previous researches have shown that spatial coherence wavelets provide the phase-space representation for optical fields
in any state of coherence and polarization and can represent the radiometric properties of optical sources. In this paper,
we have developed a research about their holographic features and particularly we have found the cross-spectral density
at the observation plane should be regarded as the second-order wave reconstructed from the Fourier hologram of the
marginal power spectrum, where the power spectrum corresponds to the zeroth-order of the reconstruction and the
characteristic hermiticity of the cross-spectral density determines the twin images. In a similar way, the holographic
reconstruction of the cross-spectral density at the aperture plane has been stated, taking the marginal power spectrum as
its Fourier hologram, the power spectrum at the aperture plane related to its zeroth-order, and its twin images determined
by the hermiticity of the cross-spectral density at aperture plane. After realizing that spatial coherence wavelets can be
regarded as Wigner distribution functions with similar morphology to the hologram diagrams recently proposed for
formulating holography in the phase-space by Lohmann and Testorf, we recognized their power for providing a precise
and wide physical interpretation of optical signals in phase space which enables us to apply these holographic features in
many fields like optical coherence modulation and beam shaping.
The concept of spatial coherence wavelet has been introduced some years ago with very productive results. It has given
new insight on the fundamental optical phenomena, and has predicted novel light characteristics like polarizations
domain and transverse energy transference. The concept of marginal power spectrum emerges as the amplitude of the
wavelet and provides a phase-space representation of the optical field in any state of spatial coherence. Its values have
energy units and are carried by the spatial coherence wavelets along specific paths or rays. Some of them, called carrier
rays, are corresponding to the radiant energy of the field, but the rest, called dark (or tamasic) rays, do not contribute to
the radiant energy, i.e. they take on positive and negative values, symmetrically distributed, which are responsible for the
constructive and destructive interference after redistributing the radiant energy of the field. This description of
interference is illustrated by analyzing the Young experiment, gratings and one-dimensional apertures. Furthermore, the
principle of spatial coherence modulation is introduced, showing its feasibility for practical applications in beam
shaping.
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