Waveguide and method for producing a waveguide
A waveguide is provided for transmitting electromagnetic waves, in particular for transmitting image information, from a proximal end to a distal end, along a transport direction running between the ends and a via a cross-section running transversely to the transport direction. The waveguide has a plurality of structural elements, wherein at least two different types of structural elements have a first type with a first refractive index and a second type with a second refractive index. Each of the structural dements extends along the transport direction and over a part of the cross-section of the waveguide such that a plurality of cross-sectional regions are defined in the cross-section of the waveguide, each cross-sectional region corresponding to the cross-section of an individual structural element.
1 . A waveguide for transmitting electromagnetic waves from a proximal end to a distal end along a transport direction and over a cross section running transversely with respect to the transport direction, the waveguide comprising:
a first multiplicity, the first multiplicity comprising a plurality of structural elements having at least two different types of structural elements, the at least two different types of structural elements comprises a first type with a first refractive index and a second type with a second refractive index that is different than the first refractive index,
wherein the first multiplicity extends along the transport direction and partly over the cross section in such a way that a multiplicity of cross-sectional regions are defined in the cross section, each of which correspond to the cross section of an individual structural element, and
wherein the plurality of structural elements are configured in the first multiplicity nonuniformly but in a way which is uniquely established by a predetermined rule such that transverse Anderson localization occurs in the first multiplicity, wherein the predetermined rule contains detailed information for describing and/or constructing the waveguide in its structure formed by the multiplicity of structural elements.
2 . The waveguide of claim 1 , wherein the plurality of structural elements have a feature selected from a group consisting of a nonuniform arrangement, nonuniform cross sectional geometries, nonuniform diameters, nonuniform refractive indices, and any combinations thereof.
3 . The waveguide of claim 1 , wherein the plurality of structural elements are configured nonuniformly in the first multiplicity such that transmitted electromagnetic waves remain localized in a direction running transversely with respect to the transport direction.
4 . The waveguide of claim 1 , wherein the plurality of structural elements are configured in such a way that the first multiplicity has a reproducible structure.
5 . The waveguide of claim 1 , wherein the plurality of structural elements are invariant along the transport direction.
6 . The waveguide of claim 1 , wherein the predetermined rule comprises indicating a characteristic parameter for each plurality of structural element of the area of the cross-sectional region or of the refractive index of the respective structural element, according to a deterministic specification.
7 . The waveguide of claim 1 , wherein the predetermined rule comprises a mathematical series of fixed values configured as a series selected from a group consisting of a low discrepancy series, a deterministic series, a Halton series, a Sobol series, a Niederreiter series, a Hammersley series, a Faure series, and any combinations thereof.
8 . The waveguide of claim 1 , wherein the predetermined rule comprises:
picking a particular value of a deterministic series in order to indicate a characteristic parameter for a particular structural element,
picking a further value of the deterministic series in order to indicate a characteristic parameter for a further structural element,
checking whether the value or the characteristic parameter for the further structural element violates a defined condition, and if the defined condition is violated, and
discarding the further value and picking yet another value of the deterministic series in order to indicate a characteristic parameter for the further structural element, or modifying the further value in a predefined way such that the defined condition is satisfied or no longer violated.
9 . The waveguide of claim 8 , wherein the defined condition is configured as a fixed minimum difference of the values or characteristic parameters.
10 . The waveguide of claim 1 , wherein the distribution of the area contents of Voronoi cells with respect to the positions of the cross-sectional areas of the structural elements of at least one type fulfills at least one of the following conditions:
(1) variance V d of the distribution is less than the variance V z of a corresponding distribution for random positions of the cross-sectional areas, the ratio V z /V d lying between 0 and 10, and/or
(2) variance Va of the distribution is less than 0.38/N 2.033 , where N denotes the number of structural elements of the at least one type, and/or
(3) variance Va of the distribution is greater than the variance of a corresponding distribution for periodic positions of the cross-sectional areas, the variance V d being greater than 0.
11 . The waveguide of claim 1 , further comprising a ratio of the total area of the cross-sectional regions of the structural elements of the first type and the total area of the cross-sectional regions of the structural elements of the second type lies in a range of between 1:9 and 9:1, and/or
wherein the total area of the cross-sectional regions of the structural elements for each type is at least 1/(10*T), where T denotes the number of types, and/or
wherein the first refractive index of the structural elements of the first type and the second refractive index of the structural elements of the second type differ by at least 10 −4 .
12 . The waveguide of claim 1 , wherein at least one cross-sectional region has a diameter of from 100 nm to 50 μm, and/or
wherein at least one cross-sectional region has a diameter which lies between 0.1 times and 10 times the average wavelength, and/or
wherein at least one cross-sectional region has a polygonal geometry.
13 . The waveguide of claim 1 , wherein one structural element of the first type is configured as a base body comprising a first medium having the first refractive index and the structural elements of the second type are configured as cavities in the base body, wherein the cavities form the second refractive index.
14 . The waveguide of claim 13 , wherein the cavities are configured as filamentary channels introduced into the base body by a laser beam of an ultrashort-pulse laser and are chemically finished by etching to smooth the contours of the channels.
15 . The waveguide of claim 13 , wherein the cavities are formed by additive construction of the base body and/or are introduced subtractively into the base body as mechanical bores.
16 . The waveguide of claim 13 , wherein the cavities are filled with a second medium, the second medium having the second refractive index.
17 . The waveguide of claim 1 , comprising an area of at least 4 square millimeters in cross section, and/or comprising an extent in cross section which is at least 2 times greater than the extent along the transport direction.
18 . The waveguide of claim 1 , comprising an extent of less than 10 millimeters along the transport direction and configured as a faceplate.
19 . The waveguide of claim 1 , comprising an extent of greater than 10 millimeters along the transport direction.
20 . The waveguide of claim 1 , wherein the predetermined rule comprises detailed information for describing and/or constructing the first multiplicity.
21 . The waveguide of claim 1 , wherein the predetermined rule comprises detailed information for describing and/or constructing each of the cross-sectional regions of the first multiplicity.
22 . The waveguide of claim 1 , wherein the predetermined rule comprises a deterministic rule.
23 . The waveguide of claim 1 , further comprising:
a second multiplicity, the second multiplicity comprising a plurality of second structural elements having at least two different types of second structural elements,
wherein the second multiplicity extends along the transport direction and partly over the cross section, and
wherein the plurality of second structural elements are configured in the second multiplicity nonuniformly but in a way which is uniquely established by the predetermined rule such that transverse Anderson localization occurs in the second-multiplicity.
24 . The waveguide of claim 23 , wherein the first and second multiplicity are the same or different.
25 . A waveguide for transmitting electromagnetic waves from a proximal end to a distal end along a transport direction and over a cross section running transversely with respect to the transport direction, the waveguide comprising:
a first multiplicity, the first multiplicity comprising a plurality of structural elements having at least two different types of structural elements configured such that transverse Anderson localization occurs in the first multiplicity,
wherein the first multiplicity extends along the transport direction and partly over the cross section in such a way that a multiplicity of cross-sectional regions are defined in the cross section, each of which correspond to the cross section of an individual structural element,
wherein the plurality of structural elements are configured aperiodically within the first multiplicity in such a way which is uniquely established by a predetermined rule, wherein the predetermined rule contains detailed information for describing and/or constructing the waveguide in its structure formed by the multiplicity of structural elements.
26 . The waveguide of claim 25 , further comprising:
a second multiplicity, the second multiplicity comprising a plurality of second structural elements having at least two different types of second structural elements,
wherein the second multiplicity extends along the transport direction and partly over the cross section, and
wherein the plurality of second structural elements are configured aperiodically within the second multiplicity in such a way which is uniquely established the predetermined rule.
27 . The waveguide of claim 26 , wherein the first and second multiplicity are the same or different.
28 . A waveguide for transmitting electromagnetic waves from a proximal end to a distal end along a transport direction and over a cross section running transversely with respect to the transport direction, the waveguide comprising:
a first multiplicity, the first multiplicity comprising a plurality of structural elements having at least two different types of structural elements configured such that transverse Anderson localization occurs in the first multiplicity,
wherein the first multiplicity extends along the transport direction and partly over the cross section in such a way that a multiplicity of cross-sectional regions are defined in the cross section, each of which correspond to the cross section of an individual structural element,
wherein the plurality of structural elements deviate from symmetry within the first multiplicity in such a way that is uniquely established by a predetermined rule, wherein the predetermined rule contains detailed information for describing and/or constructing the waveguide in its structure formed by the multiplicity of structural elements.
29 . The waveguide of claim 28 , further comprising:
a second multiplicity, the second multiplicity comprising a plurality of second structural elements having at least two different types of second structural elements,
wherein the second multiplicity extends along the transport direction and partly over the cross section, and
wherein the plurality of second structural elements deviate from symmetry within the second multiplicity in such a way that is uniquely established by the predetermined rule.
30 . The waveguide of claim 29 , wherein the first and second multiplicity are the same or different.