A planar metamaterial Lüneburg lens that enables Fourier optics on-a-chip can be implemented in an SOI slab waveguide structure by patterning the silicon core with variable sized holes. The subwavelength patterning of binary nanocomposite material to form the metamaterial offers the major advantage of fabrication by a single etch step while demanding feature sizes that can be accessed by deep UV lithography in addition to e-beam lithography. A numerical calibration procedure is described that is used to find the relation between fill factor and the local homogenised effective refractive index and which improves upon the predictions of analytic effective media theory used by other researchers. The concept and designs were verified by the 2D FDTD simulation of a two lens telescope system with waveguide feeds implemented in a metamaterial that shows a low insertion loss of -0.45 dB with a reliable field profile at exit. A 3D FDTD simulation of the same two lens telescope system that takes full account of the SOI layers, their finite thickness, and the ridge waveguide feeds also predicts a low loss of -0.83 dB. Less reliance however can be placed on this result due to the coarseness of the computational grid that was necessary. Nevertheless both results are encouraging for planned fabrication trials. This structure can be used in optical transpose interconnection systems in optical switching architectures with the advantage of avoiding large number crossover waveguides in optical communication systems.
Optical information processing has traditionally been demonstrated using 3D free-space optical systems employing bulk
optical components. These systems are bulky and unstable due to the stringent alignment tolerances that must be met.
Taking advantage of the alignment accuracy offered by planar light circuits, these issues may be overcome by confining
the light in a planar slab waveguide. The limitation on scaling, consequent on the loss of one dimension is offset by the
nanoscale component footprints attainable in a silicon integration platform. A key component of this free-space-opticson-
a-chip concept is a waveguide lens. Waveguide lenses are of general utility but our specific application is their use to
implement the complex crossover interconnections of a switch fabric.
The graded refractive index of the lens is engineered by patterning the silicon layer of silicon on insulator slab
waveguides into a dense distribution of cylinders; either solid (silicon) or voids (air); using a single etch step. The
cylinders have variable diameters and are placed on a regular square or hexagonal grid with sub-wavelength pitch. In the
case of voids, the patterned silicon may be suspended in air to form the core of a symmetric slab waveguide. Solid
cylinders must be supported by the Si02 layer leading to an asymmetric waveguide of reduced effective index range.
Advantageously, the patterning of the metamaterial region within the slab-waveguide requires only a single etch step.
Photonic wire feeder waveguides at different positions around the lens may be used to launch light into the lenses or
collect light from the lenses. A method is developed to determine the local effective media index of a periodic
metamaterial in terms of the parameters of its unit cell. This method is used as a calibration to lay out a metamaterial
with graded parameters. The operation of a metamaterial Lüneburg lens telescope is verified by FDTD simulations and
shown to be capable of near zero insertion loss and crosstalk. The careful approximation of the graded index of the
Lüneburg lens by a metamaterial introduces minimal impairments.
Advances in silicon photonics motivate the consideration of on-chip switch fabrics that combine switch elements into larger port-count switches. A major challenge is the large number of inter-stage waveguide crossovers. A novel freespace architecture utilising micro-lenses, capable of near zero insertion loss and crosstalk, is described and its principles of operation explained. The architecture is mapped to a planar implementation by the substitution of propagation in a slab-waveguide for free-space propagation and Luneburg lenses for the micro-lenses. Simulations show the careful approximation of the graded index of the Luneburg lens by a metamaterial introduces minimal additional crosstalk.
KEYWORDS: Modulation, Laser sources, Receivers, Radio over Fiber, Heterodyning, Phase shift keying, Signal detection, Radio optics, Oscillators, Laser optics
The deployment of high capacity Radio-over-Fiber (RoF) systems rely, among many aspects, on the capability to efficiently generate, transport, and detect millimeter-wave carriers modulated at high data rates. Photonic approaches based on the heterodyne beating of two free-running laser sources have been proposed as an alternative to generate multi-Gbps quadrature phase modulated signals imposed on millimeter wave carriers. Implementing photonic approaches in the down-link avoids the need for electronic generation of high frequency carriers and decreases the requirements at the base band electronics. In addition, implementing complex modulation formats overcomes some of the typical issues found in intensity modulation direct detection approaches such as non linearity, receiver sensitivity and dynamic range.
In this work, the performance improvement of a coherent RoF system carrying 10 Gbps QPSK signals is numerically analyzed in terms of both the frequency linewidth and the degree of phase correlation between the lasers utilised at the down-link (for the optical heterodyne beating) and at the up-link (for the optical coherent detection). Relative to phase correlated lasers featuring linewidths of 5 MHz, the peak power of the 60 G Hz carrier generated at the down-link is reduced by 8 dB for un-correlated lasers. In addition, the error vector magnitude of the received signal at the up-link is improved from over 20% (for un-correlated lasers and linewidths of 5 MHz) to around 15% (for correlated lasers) at an optical received power of -30 dBm. The results obtained reinforce the idea of using coherent comb laser sources with phase correlated modes located at the Central Office. It also motivates the eventual deployment of techniques to control the degree of phase correlation between the lasers used as signal and local oscillator at the optical coherent receivers.
Optical fields that are periodic in the transverse plane self-image periodically as they propagate along the optical axis: a
phenomenon known as the Talbot effect. A transfer matrix may be defined that relates the amplitude and phase of point
sources placed on a particular grid at the input to their respective multiple images at an image plane. The free-space
Talbot effect may be mapped to the waveguide Talbot effect. Applying this mapping to the transfer matrix enables the
prediction of the phase and amplitude relations between the ports of a Multimode Interference (MMI) coupler– a planar
waveguide device. The transfer matrix approach has not previously been applied to the free-space case and its mapping
to the waveguide case provides greater clarity and physical insight into the phase relationships than previous treatments.
The paper first introduces the underlying physics of the Talbot effect in free space with emphasis on the positions along
the optical axis at which images occur; their multiplicity; and their relative phase relations determined by the Gauss
Quadratic Sum of number theory. The analysis is then adapted to predict the phase relationships between the ports of an
MMI. These phase relationships are critical to planar light circuit (PLC) applications such as 90° optical hybrids for
coherent optical receiver front-ends, external optical I-Q modulators for coherent optical transmitters; and optical phased
array switches. These applications are illustrated by results obtained from devices that have been fabricated and tested by
the PTLab in Si micro-photonic integration platforms.
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