Finite-Embedded Coordinate Transformations for Reflectionless Beam Shifting
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Solution Overview
Problem
Transformation-optical designs are limited by the inability to transfer electromagnetic field manipulations from the transformation-optical medium to another medium, resulting in local and undesired phenomena, restricting the creation of optical devices with unconventional electromagnetic behavior.
Innovation Solution
The use of finite embedded coordinate transformations allows the transfer of electromagnetic field manipulations from the transformation-optical medium to another medium, enabling the design of reflectionless devices like parallel beam shifters and beam splitters with unconventional behavior by imposing topological criteria on the metric at the interface.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If continuous form-invariant coordinate transformations are used to design transformation-optical devices, then electromagnetic fields can be manipulated within the device region, but the field manipulations cannot be transferred to another medium and the device appears invisible to external observers
Solution Approach 1:
The patent divides the coordinate transformation into two distinct segments: a first coordinate transformation applied within the transformation-optical medium to manipulate electromagnetic fields, and a second coordinate transformation applied in the surrounding medium to transfer and maintain the field manipulations. This segmentation allows the device to both manipulate fields internally and transfer those manipulations externally, resolving the contradiction between design capability and transferability.
2Reliability
If transformation-optical designs are restricted to continuous coordinate transformations, then the electromagnetic properties can be changed within the device region, but the manipulation remains a local phenomenon and cannot affect another medium
Solution Approach 1:
The patent introduces an intermediary coordinate transformation system that acts as a bridge between the transformation-optical medium and the surrounding medium. The first coordinate transformation serves as the intermediary mechanism that transfers electromagnetic field manipulations from the internal medium to the external medium, enabling the device to affect other media while maintaining reliable electromagnetic property control within the device region.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach expands the design capabilities of metamaterials, enabling the creation of devices that can shift or split beams without reflection, achieving electromagnetic behavior not possible with conventional materials, and allowing for tunable optical properties.
Implementation Method 1
Pendry et al., Science 312, 1780 (2006) reported a methodology based on continuous form-invariant coordinate transformations of Maxwell's equations which allows for the manipulation of electromagnetic fields in a previously unknown and unconventional fashion.
Implementation Method 2
Metamaterials offer an enormous degree of freedom for manipulating electromagnetic fields, as independent and nearly arbitrary gradients can be introduced in the components of the effective permittivity and permeability tensors.
Data Source
AI summary
The design method for complex electromagnetic materials is expanded from form-invariant coordinate transformations of Maxwell's equations to finite embedded coordinate transformations. Embedded transformations allow the transfer of electromagnetic field manipulations from the transformation-optical medium to another medium, thereby allowing the design of structures that are not exclusively invisible. A topological criterion for the reflectionless design of complex media is also disclosed and is illustrated in conjunction with the topological criterion to design a parallel beam shifter and a beam splitter with unconventional electromagnetic behavior.