Silica is the ideal material for a wide range of optical applications on account of its many desirable linear properties. For many important non-linear optical applications, such as second harmonic generation (SHG), silica cannot be used as it doesn’t possess an even ordered optical non-linearity. For some time now thermal poling has been used to create an artificial second order non-linearity in silica. While early results suggested that the resulting non-linearity was not large (less than 1 pm/V) or extensive enough (only 5 microns penetration into the substrate) to be practical, there has been a concerted effort to find new ways to improve upon and harness this ‘artificial’ non-linearity. In this presentation, we will show our recent results in SHG in both poled and unpoled multi-layer silica structures. We believe that these structures, of alternating doped and undoped silica, can be used to increase the size of the non-linear region in glass and improve the efficiency of poled devices. The second harmonic generated in our samples is compared to that produced in both a silica substrate and quartz. We show that a non-zero second order non-linearity is intrinsic to multi-layer structures and study the impact of varying the number of layers and doped/un-doped duty cycle. We then investigate impact of poling on the SHG in these samples. For un-poled samples we study the effect of using different dopants or varying the concentration. We conclude by discussing applications of these structures.
Maxwell’s wave equations can be solved using different techniques in order to extract optical properties of a variety
of dielectric structures. For structures that contain an extended axis which serve for the reference for cylindrical
symmetry, we have shown that an expansion of the fields and inverse of the relative dielectric profile using a
simplified and complete set of basis functions of Fourier-Bessel terms provide access to an eigenvalue formulation
from which the eigen-states can be computed. We review the steps used to convert Maxwell’s equation into an
eigenvalue formulation, and then proceed to discuss several applications of the technique. For cylindrically
symmetric structures, the computational technique provides a significantly reduced matrix order to be populated.
New target structure for the presentation consists of cylindrical space slot channel waveguide in which the channel
extends in azimuthal (ϕ) direction. The channel is provided by considering the etching of external side walls of
“Bragg fiber”. The configuration is similar to a structure that can support whispering-gallery modes, except that the
modes highest field locations are within the ambient medium of the channel. Optical properties of this structure can
be best examined through field component which is discontinuous by ratio of relative dielectric constants when
passing air–Bragg interfaces. The ability to select Bragg dielectric properties and to introduce non-uniformities in
Bragg plane spacing provides access to tuning slot channel waveguide properties and design several novel
configurations.
The plane wave expansion (PWM) technique applied to Maxwell’s wave equations provides researchers with a
supply of information regarding the optical properties of dielectric structures. The technique is well suited for
structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that
lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case
of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis
functions have been employed to cast Maxwell’s wave equations into an eigen-matrix formulation from which the
resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and
field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier-
Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical
development details will be presented indicating how certain mathematical complications in the process have been
overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM,
FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z
axis component of propagation constant makes the technique applicable to photonic crystal fibers and other
waveguide structures. Computational results will be presented for a number of different dielectric geometries
including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further
enhance the computation process will be reported.
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