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Register a new userReflectionless excitation of arbitrary photonic structures: A general theory
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We outline a recently developed theory of impedance-matching, or reflectionless excitation of arbitrary finite photonic structures in any dimension. It describes the necessary and sufficient conditions for perfectly reflectionless excitation to be possible, and specifies how many physical parameters must be tuned to achieve this. In the absence of geometric symmetries the tuning of at least one structural parameter will be necessary to achieve reflectionless excitation. The theory employs a recently identified set of complex-frequency solutions of the Maxwell equations as a starting point, which are defined by having zero reflection into a chosen set of input channels, and which are referred to as R-zeros. Tuning is generically necessary in order to move an R-zero to the real-frequency axis, where it becomes a physical steady-state solution, referred to as a Reflectionless Scattering Mode (RSM). Except in single-channel systems, the RSM corresponds to a particular input wavefront, and any other wavefront will generally not be reflectionless. In a structure with parity and time-reversal symmmetry or with parity-time symmetry, generically a subset of R-zeros is real, and reflectionless states exist without structural tuning. Such systems can exhibit symmetry-breaking transitions when two RSMs meet, which corresponds to a recently identified kind of exceptional point at which the shape of the reflection and transmission resonance lineshape is flattened.
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We develop the theory of a special type of scattering state in which a set of asymptotic channels are chosen as inputs and the complementary set as outputs, and there is zero reflection back into the input channels. In general an infinite number of such solutions exist at discrete complex frequencies. Our results apply to linear electromagnetic and acoustic wave scattering and also to quantum scattering, in all dimensions, for arbitrary geometries including scatterers in free space, and for any choice of the input/output sets. We refer to such a state as reflection-zero (R-zero) when it occurs off the real-frequency axis and as an Reflectionless Scattering Mode (RSM) when it is tuned to a real frequency as a steady-state solution. Such reflectionless behavior requires a specific monochromatic input wavefront, given by the eigenvector of a filtered scattering matrix with eigenvalue zero. Steady-state RSMs may be realized by index tuning which do not break flux conservation or by gain-loss tuning. RSMs of flux-conserving cavities are bidirectional while those of non-flux-conserving cavities are generically unidirectional. Cavities with ${cal PT}$-symmetry have unidirectional R-zeros in complex-conjugate pairs, implying that reflectionless states naturally arise at real frequencies for small gain-loss parameter but move into the complex-frequency plane after a spontaneous ${cal PT}$-breaking transition. Numerical examples of RSMs are given for one-dimensional cavities with and without gain/loss, a ${cal PT}$ cavity, a two-dimensional multiwaveguide junction, and a two-dimensional deformed dielectric cavity in free space. We outline and implement a general technique for solving such problems, which shows promise for designing photonic structures which are perfectly impedance-matched for specific inputs, or can perfectly convert inputs from one set of modes to a complementary set.
We investigate the use of a Genetic Algorithm (GA) to design a set of photonic crystals (PCs) in one and two dimensions. Our flexible design methodology allows us to optimize PC structures which are optimized for specific objectives. In this paper, we report the results of several such GA-based PC optimizations. We show that the GA performs well even in very complex design spaces, and therefore has great potential for use as a robust design tool in present and future applications.
Unidirectional reflectionless propagation (or transmission) is an interesting wave phenomenon observed in many $mathcal{PT}$-symmetric optical structures. Theoretical studies on unidirectional reflectionless transmission often use simple coupled-mode models. The coupled-mode theory can reveal the most important physical mechanism for this wave phenomenon, but it is only an approximate theory, and it does not provide accurate quantitative predictions with respect to geometric and material parameters of the structure. In this paper, we rigorously study unidirectional reflectionless transmission for two-dimensional (2D) $mathcal{PT}$-symmetric periodic structures sandwiched between two homogeneous media. Using a scattering matrix formalism and a perturbation method, we show that real zero-reflection frequencies are robust under $mathcal{PT}$-symmetric perturbations, and unidirectional reflectionless transmission is guaranteed to occur if the perturbation (of the dielectric function) satisfies a simple condition. Numerical examples are presented to validate the analytical results, and to demonstrate unidirectional invisibility by tuning the amplitude of balanced gain and loss.
Nature features a plethora of extraordinary photonic architectures that have been optimized through natural evolution. While numerical optimization is increasingly and successfully used in photonics, it has yet to replicate any of these complex naturally occurring structures. Using evolutionary algorithms directly inspired by natural evolution, we have retrieved emblematic natural photonic structures, indicating how such regular structures might have spontaneously emerged in nature and to which precise optical or fabrication constraints they respond. Comparisons between algorithms show that recombination between individuals inspired by sexual reproduction confers a clear advantage in this context of modular problems and suggest further ways to improve the algorithms. Such an in silico evolution can also suggest original and elegant solutions to practical problems, as illustrated by the design of counter-intuitive anti-reflective coating for solar cells.
The transformation media concept based on the form-invariant Maxwells equations under coordinate transformations has opened up new possibilities to manipulate the electromagnetic fields. In this paper we report on applying the finite-embedded coordinate transformation method to design electromagnetic beam modulating devices both in the Cartesian coordinates and in the cylindrical coordinates. By designing the material constitutive tensors of the transformation optical structures through different kinds of coordinate transformations, either the beam width of an incident Gaussian plane wave could be modulated by a slab, or the wave propagating direction of an omni-directional source could be modulated through a cylindrical shell. We present the design procedures and the full wave electromagnetic simulations that clearly confirm the performance of the proposed beam modulating devices.
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