An integrated silicon photonics coupler for fiber to waveguide conversion was designed employing a transformation optics approach. Quasi-conformal mapping was used to obtain achievable material properties, which were realized by a distorted hexagonal lattice of air holes in silicon. The coupler, measuring only 10 μm in length and fabricated with a single-step lithography process, exhibits a peak simulated transmission efficiency of nearly 100% for in-plane mode conversion and a factor of 5 improvement over butt coupling for fiber to waveguide mode conversion in experimental testing.
[Show abstract][Hide abstract] ABSTRACT: We show that every linear optical component can be completely described as a
device that converts one set of orthogonal input modes, one by one, to a
matching set of orthogonal output modes. This result holds for any linear
optical structure with any specific variation in space and/or time of its
structure. There are therefore preferred orthogonal "mode converter" basis sets
of input and output functions for describing any linear optical device, in
terms of which the device can be described by a simple diagonal operator. This
result should help us understand what linear optical devices we can and cannot
make. As illustrations, we use this approach to derive a general expression for
the alignment tolerance of an efficient mode coupler and to prove that
loss-less combining of orthogonal modes is impossible.
[Show abstract][Hide abstract] ABSTRACT: We show how to design an optical device that can perform any linear function or coupling between inputs and outputs. This design method is progressive, requiring no global optimization. We also show how the device can configure itself progressively, avoiding design calculations and allowing the device to stabilize itself against drifts in component properties and to continually adjust itself to changing conditions. This self-configuration operates by training with the desired pairs of orthogonal input and output functions, using sets of detectors and local feedback loops to set individual optical elements within the device, with no global feedback or multiparameter optimization required. Simple mappings, such as spatial mode conversions and polarization control, can be implemented using standard planar integrated optics. In the spirit of a universal machine, we show that other linear operations, including frequency and time mappings, as well as non-reciprocal operation, are possible in principle, even if very challenging in practice, thus proving there is at least one constructive design for any conceivable linear optical component; such a universal device can also be self-configuring. This approach is general for linear waves, and could be applied to microwaves, acoustics and quantum mechanical superpositions.
Photonics Research 06/2013; 1:1 - 15. DOI:10.1364/PRJ.1.000001
[Show abstract][Hide abstract] ABSTRACT: We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap because transformation optics circumvents the need to solve Maxwell's equations at each step. We apply this technique to the design of multimode waveguide bends (realized experimentally in a previous paper) and mode squeezers, in which all modes are transported equally without scattering. In addition to the optimization, a key point is the identification of the correct boundary conditions to ensure reflectionless coupling to untransformed regions while allowing maximum flexibility in the optimization. Many previous authors in transformation optics used a certain kind of quasiconformal map which overconstrained the problem by requiring that the entire boundary shape be specified a priori while at the same time underconstraining the problem by employing "slipping" boundary conditions that permit unwanted interface reflections.
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