Dielectric-filled metamaterial filter

Abstract

A dielectric-filled metamaterial filter includes a waveguide, a plurality of metamaterial resonant elements, an input port, and an output port. The waveguide is filled with a dielectric material. The plurality of metamaterial resonant elements are arranged inside the waveguide. Each of the plurality of metamaterial resonant elements is electromagnetically coupled to at least one adjacent metamaterial resonant element. The input port is configured to receive an input electromagnetic wave and couple the input electromagnetic wave to the waveguide. The output port is configured to receive an output electromagnetic wave from the waveguide and transmit the output electromagnetic wave to outside of the dielectric-filled metamaterial filter. The output electromagnetic wave is generated by the plurality of metamaterial resonant elements through filtering the input electromagnetic wave.

Description

DIELECTRIC-FILLED METAMATERIAL FILTERTECHNICAL FIELD

[0001] The present disclosure generally relates to metamaterials, and particularly, to metamaterial filters.BACKGROUND ART

[0002] Various technologies have emerged for the development of microwave and millimeter wave (mmWave) filters. They can be briefly categorized into two types of planar and volumetric designs. Planar filters for microwave and mmWave applications are notable for their small size and packaging capabilities. They are composed of either lumped or distributed elements, enabling efficient integration and miniaturization. On the other hand, volumetric filters, such as waveguide filters, provide much lower loss but may have large footprints, due to the use of large cavities. Therefore, the size of waveguide filters may exceed the requirements of modem devices. Although waveguide filters exhibit lower insertion loss, they may be still larger than planar competitors.

[0003] Metamaterials are artificial and exhibit negative permittivity and / or permeability. Metamaterials may also be inherently resonant, i.e., they may strongly shape the electromagnetic radiation at a certain range of frequencies. Due to the ability in subwavelength manipulation of electromagnetic radiation, metamaterials have been utilized for designing electromagnetic radiation filters [US Patents no. 10,620,343 B2 and 10,996,385 B2], However, metamaterial filters may demonstrate a very narrowband transmission, high loss, and high group velocity dispersion (GVD) around a resonance frequency. Moreover, a guided mode that may be created inside a bandgap of resonant metamaterials may limit a passband and / or rejection band of designed filters to the bandgap of resonant metamaterials.

[0004] There is, therefore, a need for a microwave and millimeter wave filter that may be easily fabricated with a low loss and highly miniaturized size. There is also a need for a microwave and millimeter wave filter that may demonstrate a wideband transmission and high selectivity with low insertion loss.SUMMARY OF THE DISCLOSURE

[0005] This summary is intended to provide an overview of the subject matter of this patent, and is not intended to identify essential elements or key elements of the subject matter, nor is it intended to be used to determine the scope of the claimed implementations. The proper scope of this patent may be ascertained from the claims set forth below in view of the detailed description below and the drawings.

[0006] In one general aspect, the present disclosure describes an exemplary dielectric-filled metamaterial filter. An exemplary dielectric-filled metamaterial filter may include a primary waveguide, a plurality of metamaterial resonant elements, an input port, and an output port. An exemplary primary waveguide may be filled with a dielectric material. In an exemplary embodiment, the dielectric material may include multiple layers of ceramics. In an exemplary embodiment, each of the multiple layers may include a different dielectric constant and a different loss tangent. An exemplary primary waveguide may include one of a rectangular cuboid shape, a triangular prism shape, a cylindrical shape, a 180 ° bent tube, or a 90 ° bent tube .

[0007] An exemplary plurality of metamaterial resonant elements may be arranged inside the primary waveguide. In an exemplary embodiment, each of the plurality of metamaterial resonant elements may be electromagnetically coupled to at least one adjacent metamaterial resonant element of the plurality of metamaterial resonant elements by being placed at a subwavelength distance from at least one adjacent metamaterial resonant element. An exemplary input port may be coupled to a first side of the primary waveguide. In an exemplary embodiment, the input port may be configured to receive an input electromagnetic wave and couple the input electromagnetic wave to the primary waveguide. An exemplary output port may be coupled to a second side of the primary waveguide. In an exemplary embodiment, the output port may be configured to receive an output electromagnetic wave from the primary waveguide and transmit the output electromagnetic wave to outside of the dielectric-filled metamaterial filter. An exemplary output electromagnetic wave may be generated by the plurality of metamaterial resonant elements through filtering the input electromagnetic wave.

[0008] An exemplary dielectric-filled metamaterial filter may further include a first network of metamaterial resonant elements and a second network of metamaterial resonant elements. An exemplary first network of metamaterial resonant elements may be successively arranged in one or more rows inside the primary waveguide between the plurality of metamaterial resonant elements and a third side of the primary waveguide. In an exemplary embodiment,each two successive metamaterial resonant elements in the first network of metamaterial resonant elements may be configured to be electromagnetically coupled to each other by being placed at a subwavelength distance from each other. An exemplary second network of metamaterial resonant elements may be successively arranged in one or more rows inside the primary waveguide between the plurality of metamaterial resonant elements and a fourth side of the primary waveguide. In an exemplary embodiment, each two successive metamaterial resonant elements in the second network of metamaterial resonant elements may be configured to be electromagnetically coupled to each other by being placed at a subwavelength distance from each other. An exemplary height of each metamaterial resonant element in the first network or the second network may be larger than an exemplary height of each of plurality of metamaterial resonant elements.

[0009] An exemplary dielectric-filled metamaterial filter may further include a first transition region and a second transition region. An exemplary first transition region may be integrally attached between the input port and the first side. An exemplary second transition region may be integrally attached between the output port and the second side. In an exemplary embodiment, each of the first transition region and the second transition region may include a respective waveguide and a respective plurality of metamaterial resonant elements. An exemplary respective waveguide may be filled with the dielectric material. An exemplary respective plurality of metamaterial resonant elements arranged inside the respective waveguide. In an exemplary embodiment, each of the respective plurality of metamaterial resonant elements may be configured to be electromagnetically coupled to at least one adjacent metamaterial resonant element of the respective plurality of metamaterial resonant elements by being placed at a subwavelength distance from at least one adjacent metamaterial resonant element of the respective plurality of metamaterial resonant elements. In an exemplary embodiment, at least one of the respective plurality of metamaterial resonant elements may be configured to be electromagnetically coupled to at least one of the plurality of metamaterial resonant elements by being placed at a subwavelength distance from at least one of the plurality of metamaterial resonant elements.

[0010] In an exemplary embodiment, each of the input port and the output port may include a respective secondary waveguide. An exemplary respective secondary waveguide may be filled with the dielectric material. An exemplary dielectric-filled metamaterial filter may further include an input coaxial connector and an output coaxial connector. An exemplary inputcoaxial connector may be connected to the input port. An exemplary output coaxial connector may be connected to the output port. In an exemplary embodiment, each of the input port and the output port may include a respective coaxial connector.

[0011] An exemplary input port may include an input metal patch that may be printed on a dielectric substrate. An exemplary output port may include an output metal patch that may be printed on the dielectric substrate. An exemplary first side of the primary waveguide may be mounted on the input metal patch. An exemplary second side of the primary waveguide may be mounted on the output metal patch. In an exemplary embodiment, each of a bottom side of the primary waveguide and a top side of the primary waveguide may include a respective semi- cylindrical surface. In an exemplary embodiment, each of the first side and the second side may include a respective rectangular surface that may be enclosed between respective ends of the top side and the bottom side. In an exemplary embodiment, each of the plurality of metamaterial resonant elements may include a cylindrical metallic pin.

[0012] In an exemplary embodiment, the plurality of metamaterial resonant elements may be attached perpendicular to a third side of the primary waveguide towards a fourth side of the primary waveguide and may be arranged along a semi-circular path. In an exemplary embodiment, each of the third side and the fourth side may include a respective two- dimensional surface that may be enclosed between and perpendicular to respective semi- cylindrical surfaces of the top side and the bottom side.

[0013] In an exemplary embodiment, the plurality of metamaterial resonant elements may be attached perpendicular to the top side of the primary waveguide towards the bottom side of the primary waveguide and may be arranged along a semi-circular path. In an exemplary embodiment, the plurality of metamaterial resonant elements may be attached perpendicular to the bottom side of the primary waveguide towards the top side of the primary waveguide and may be arranged along a semi-circular path.

[0014] An exemplary shape of the primary waveguide may include a rectangular cuboid. An exemplary bottom surface of the rectangular cuboid may be mounted on the dielectric substrate. In an exemplary embodiment, each of the plurality of metamaterial resonant elements may include a cylindrical metallic pin that may be attached perpendicular to a top surface of the rectangular cuboid towards the bottom surface of the rectangular cuboid. An exemplary plurality of metamaterial resonant elements may be arranged along a straight line. In an exemplary embodiment, each of the input port and the output port may further include arespective metamaterial resonator element that may be coupled to a respective metal patch of one of the input metal patch and the output metal patch. An exemplary respective metamaterial resonator element may be mounted on the dielectric substrate perpendicular to the bottom surface towards the top surface and may be configured to be electromagnetically coupled to at least one of the plurality of metamaterial resonant elements.

[0015] In an exemplary embodiment, the respective metamaterial resonator element may include a cylindrical metallic rod that may be placed at a subwavelength distance from the at least one of the plurality of metamaterial resonant elements. In an exemplary embodiment, each of the input metal patch and the output metal patch may include a respective circular arc shaped patch that may be etched on the dielectric substrate around the respective metamaterial resonator element.

[0016] In an exemplary embodiment, the respective metamaterial resonator element may include a metallic semi-loop. An exemplary metallic semi-loop may include a first metallic rod, a second metallic rod, and a third metallic rod. An exemplary first metallic rod may be mounted on the dielectric substrate perpendicular to the bottom surface towards the top surface and may be configured to be electromagnetically coupled to at least one of the plurality of metamaterial resonant elements by being placed at a subwavelength distance from at least one of the plurality of metamaterial resonant elements. An exemplary second metallic rod may be perpendicularly attached to a top end of the first metallic rod. An exemplary third metallic rod may be attached between the second metallic rod and the dielectric substrate perpendicular to the bottom surface. In an exemplary embodiment, the third metallic rod may be connected to the respective metal patch.

[0017] An exemplary dielectric-filled metamaterial filter may further include a first conductive transmission line, a first coaxial connecter, a second conductive transmission line, and a second coaxial connecter. An exemplary first conductive transmission line may be printed on the dielectric substrate. An exemplary proximal end of the first conductive transmission line may be connected to the input metal patch. An exemplary first coaxial connecter may be connected to a distal end of the first conductive transmission line. An exemplary second conductive transmission line may be printed on the dielectric substrate. An exemplary proximal end of the second conductive transmission line may be connected to the output metal patch. An exemplary second coaxial connecter may be connected to a distal end of the second conductive transmission line.

[0018] Other exemplary systems, methods, features and advantages of the implementations will be, or will become, apparent to one of ordinary skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description and this summary, be within the scope of the implementations, and be protected by the claims herein.BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawing figures depict one or more implementations in accord with the present teachings, by way of example only, not by way of limitation. In the figures, like reference numerals refer to the same or similar elements.

[0020] FIG. 1A shows a schematic of a dielectric -filled metamaterial filter, consistent with one or more exemplary embodiments of the present disclosure.

[0021] FIG. IB shows a schematic of different implementations of a dielectric-filled metamaterial filter with different shapes of a primary waveguide, consistent with one or more exemplary embodiments of the present disclosure.

[0022] FIG. 1C shows a schematic of a vertical cross-section (side-view) of a dielectric -filled metamaterial filter, consistent with one or more exemplary embodiments of the present disclosure.

[0023] FIG. ID shows a schematic of a horizontal cross-section (top view) of a dielectric- filled metamaterial filter, consistent with one or more exemplary embodiments of the present disclosure.

[0024] FIG. IE shows a schematic of a top view of different pluralities of metamaterial resonant elements, consistent with one or more exemplary embodiments of the present disclosure.

[0025] FIG. 2A shows a schematic of a dielectric-filled metamaterial filter with coaxial connectors connected to respective sides of input and output ports, consistent with one or more exemplary embodiments of the present disclosure.

[0026] FIG. 2B shows a schematic of a dielectric-filled metamaterial filter with coaxial connectors connected to top surfaces of input and output ports, consistent with one or more exemplary embodiments of the present disclosure.

[0027] FIG. 3A shows a schematic of a dielectric-filled metamaterial filter with coaxial connectors as input and output ports, consistent with one or more exemplary embodiments of the present disclosure.

[0028] FIG. 3B shows a schematic of a three-dimensional (3D) cross-section of a dielectric- filled metamaterial filter with additional metamaterial resonant elements coupled to coaxial connectors, consistent with one or more exemplary embodiments of the present disclosure.

[0029] FIG. 4A shows a schematic of a dielectric-filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0030] FIG. 4B shows a schematic of a vertical cross-section (side view) of a dielectric-filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0031] FIG. 4C shows a schematic of a horizontal cross-section (top view) of a dielectric- filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0032] FIG. 5A shows a schematic of a 3D cross-section of an E-bent dielectric-filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0033] FIG. 5B shows a schematic of a vertical cross-section (side view) of an E-bent dielectric-filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0034] FIG. 6A shows a schematic of a 3D cross-section of a first implementation of an H- bent dielectric -filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0035] FIG. 6B shows a schematic of a vertical cross-section (side view) of a first implementation of an H-bent dielectric-filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0036] FIG. 7A shows a schematic of a 3D cross-section of a second implementation of an H- bent dielectric -filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0037] FIG. 7B shows a schematic of a vertical cross-section (side view) of a second implementation of an H-bent dielectric -fdled metamaterial fdter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0038] FIG. 8A shows a schematic of a dielectric -fdled metamaterial fdter with a rectangular cuboid shape waveguide mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0039] FIG. 8B shows a schematic of a vertical cross-section (side view) of a dielectric-fdled metamaterial fdter with a rectangular cuboid shape waveguide mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0040] FIG. 8C shows a schematic of a horizontal cross-section (top view) 828 of a dielectric- fdled metamaterial fdter with a rectangular cuboid shape waveguide mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0041] FIG. 9 shows a schematic of a dielectric-fdled metamaterial fdter with loop shaped metamaterial resonator elements inside a rectangular cuboid shape waveguide mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure.

[0042] FIG. 10 shows a full band frequency response of a dielectric-fdled metamaterial fdter, consistent with one or more exemplary embodiments of the present disclosure.DESCRIPTION OF EMBODIMENTS

[0043] In the following detailed description, numerous specific details are set forth by way of examples in order to provide a thorough understanding of the relevant teachings. However, it should be apparent that the present teachings may be practiced without such details. In other instances, well known methods, procedures, components, and / or circuitry have been described at a relatively high-level, without detail, in order to avoid unnecessarily obscuring aspects of the present teachings.

[0044] The following detailed description is presented to enable a person skilled in the art to make and use the methods and devices disclosed in exemplary embodiments of the present disclosure . For purposes of explanation, specific nomenclature is set forth to provide a thorough understanding of the present disclosure. However, it will be apparent to one skilled in the art that these specific details are not required to practice the disclosed exemplary embodiments. Descriptions of specific exemplary embodiments are provided only as representative examples.Various modifications to the exemplary implementations will be readily apparent to one skilled in the art, and the general principles defined herein may be applied to other implementations and applications without departing from the scope of the present disclosure. The present disclosure is not intended to be limited to the implementations shown, but is to be accorded the widest possible scope consistent with the principles and features disclosed herein.

[0045] Herein is disclosed an exemplary dielectric-filled metamaterial filter. An exemplary filter may include a primary (or host) metamaterial waveguide that is attached to an input port and an output port. An exemplary input port may deliver an input signal or electromagnetic wave to the host waveguide to be filtered and be sent outside the filter through the output port. An exemplary host waveguide may include a number of metamaterial resonant elements that may be arranged inside a waveguide in several different patterns so that a metamaterial structure with an exemplary passband and stopband may be obtained. An exemplary bandwidth of the filter may be tuned by changing the specifications of the host waveguide (such as width) and the metamaterial resonant elements (such as arrangement, height, inter-distance, etc.).

[0046] Exemplary input and output ports may include secondary waveguides and / or coaxial connectors. Additional metamaterial resonant elements may also be placed between exemplary ports and the host waveguide and also between along the sides of the host waveguide to improve selectivity of the metamaterial filter. Exemplary primary and secondary waveguides may be filled with a dielectric material (such as silicon and / or silicon dioxide) that may allow for fabricating the metamaterial filter at a highly miniaturized size without losing efficiency of the filter. Unique properties of a low-loss dielectric may allow for overcoming size, loss, and integration challenges of conventional waveguide filters. An exemplary dielectric-filled metamaterial filter may also be mounted on a dielectric substrate so that it may be integrated with conventional electronic elements on a printed circuit board (PCB) via a metal transmission line (for example, a microstrip or a stripline) that may be printed on the dielectric substrate.

[0047] FIG. 1A shows a schematic of a dielectric-filled metamaterial filter, consistent with one or more exemplary embodiments of the present disclosure. An exemplary dielectric-filled metamaterial filter 100 may include a primary waveguide 102, an input port 104, and an output port 106. In an exemplary embodiment, primary waveguide 102 may be filled with a dielectric material. An exemplary width 107 of primary waveguide 102 may be smaller thanOI , where Aois an operating wavelength of dielectric-filled metamaterial filter 100. In an exemplary embodiment, operating wavelength Aomay be equal to c / (Ve o) where c is the speed of light,6 is a permitivity of the dielectric material, and f0an operating frequency of dielectric-filled metamaterial filter 100.

[0048] In an exemplary embodiment, the dielectric material may include multiple layers of ceramics. Exemplary multiple layers may be arranged in vertical and / or horizontal directions. In an exemplary embodiment, each of the multiple layers may include a different dielectric constant and a different loss tangent. In an exemplary embodiment, a “dielectric constant” of a layer may refer to a ratio of a permitivity of that layer to the permitivity of free space. In an exemplary embodiment, a “loss tangent” of a layer may refer to the layer’ s inherent dissipation of electromagnetic energy.

[0049] FIG. IB shows a schematic of different implementations of a dielectric-filled metamaterial fdter with different shapes of a primary waveguide, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, primary waveguide 102 may have a rectangular cuboid shape 102A, a triangular prism shape 102B, a cylindrical shape 102C, 180° bent tube 102D, a 90° bent tube 102E, etc. In an exemplary embodiment, a “primary” waveguide may also be referred to as a “host” waveguide.

[0050] FIG. 1C shows a schematic of a vertical cross-section (side-view) 108 of a dielectric- filled metamaterial filter, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, each of input port 104 and output port 106 may include a respective secondary waveguide. For example, input port 104 may include a secondary waveguide 109A. In an exemplary embodiment, secondary waveguide 109A may be filled with the dielectric material. In an exemplary embodiment, output port 106 may include a secondary waveguide 109B. In an exemplary embodiment, secondary waveguide 109B may be filled with the dielectric material.

[0051] In an exemplary embodiment, secondary waveguides 109A and 109B may allow for improving a matching efficiency with dielectric-filled metamaterial filter 100 compared to other couplers / connectors such as a conventional waveguide. In an exemplary embodiment, secondary waveguides 109A and 109B may allow for efficiently coupling an electromagnetic wave from, for example, a standard waveguide, to dielectric-filled metamaterial filter 100. In an exemplary embodiment, secondary waveguides 109A and 109B may implement a low-pass or a band-pass filter that tailors a frequency profile of a signal to assure a low insertion loss and a sharp roll-off.

[0052] In an exemplary embodiment, dielectric-filled metamaterial filter 100 may further include a plurality of metamaterial resonant elements 110. In an exemplary embodiment, plurality of metamaterial resonant elements 110 may be arranged inside primary waveguide 102. In an exemplary embodiment, plurality of metamaterial resonant elements 110 may locally resonate in primary waveguide 102 which may create a passband and a stopband. Each exemplary resonance may generate a high unloaded Q pole and deep zero with critical coupling to an adjacent metamaterial resonant element. In an exemplary embodiment, plurality of metamaterial resonant elements 110 may make a bandgap artificial material that may provide a deep and sharp metamaterial bandgap (that is, negative permittivity) right after a passband of the filter. In an exemplary embodiment, each of plurality of metamaterial resonant elements 110 may be electromagnetically coupled to at least one adjacent metamaterial resonant element of plurality of metamaterial resonant elements 110 by being placed at a microwave or a millimeter wave subwavelength distance (for example, less than about A / 4 where A is a wavelength of a microwave or a millimeter wave) from at least one adjacent metamaterial resonant element. For example, a metamaterial resonant element 112 may be placed at a subwavelength distance 114 from an adjacent metamaterial resonant element 116. In an exemplary embodiment, a “metamaterial resonant element” may refer to a subwavelength component within a metamaterial structure designed to exhibit resonance at specific frequencies, enabling wave manipulation. Exemplary metamaterial resonant elements may interact by propagating waves and radiations since they are open resonators.

[0053] In an exemplary embodiment, plurality of metamaterial resonant elements 110 may be coupled via electric and magnetic fields (or modal electric and magnetic fields) generated by plurality of metamaterial resonant elements 110. In an exemplary embodiment, energy may be coupled between or from one metamaterial resonant element to another by this coupling. In an exemplary embodiment, primary waveguide 102 may be configured to support evanescent modes or waves of a microwave or a millimeter electromagnetic wave. In an exemplary embodiment, primary waveguide 102 may be a single-mode waveguide. In an exemplary embodiment, primary waveguide 102 may have a waveguide cut-off frequency fcbelow which primary waveguide 102 may not support a propagating mode or wave. For example, no transverse electric TE mode of a microwave or a millimeter electromagnetic wave may be propagated in primary waveguide 102 below cut-off frequency fc. In an exemplary embodiment, cut-off frequency fcmay refer to a lowest cutoff frequency of primary waveguide102 in an absence of any metamaterial resonant element inside primary waveguide 102. An exemplary resonance frequency frof each of plurality of metamaterial resonant elements 110 may be less than cut-off frequency fc.

[0054] In an exemplary embodiment, input port 104 may be coupled to a first side 118 of primary waveguide 102. In an exemplary embodiment, input port 104 may be configured to receive an input electromagnetic wave and couple the input electromagnetic wave to primary waveguide 102. In an exemplary embodiment, output port 106 may be coupled to a second side 120 of primary waveguide 102. In an exemplary embodiment, output port 106 may be configured to receive an output electromagnetic wave from primary waveguide 102 and transmit the output electromagnetic wave to outside dielectric-filled metamaterial filter 100. An exemplary output electromagnetic wave may be generated by plurality of metamaterial resonant elements 110 through filtering the input electromagnetic wave.

[0055] In an exemplary embodiment, input port 104 and output port 106 may assure filtering of a microwave or millimeter wave signal passing or propagating through dielectric-filled metamaterial filter 100 and may function to implement a low-pass or a band-pass filter. In an exemplary embodiment, input port 104 and output port 106 may provide a medium that may induce some poles (transmission band peak) in a passband of dielectric-filled metamaterial filter 100 and some zeros (transmission band minimum) in a rejection band of dielectric-filled metamaterial filter 100. Near or around exemplary poles’ frequency, energy may efficiently couple from a conventional waveguide to dielectric-filled metamaterial filter 100 via input port 104 and output port 106. An exemplary size of each of plurality of metamaterial resonant elements 110 and their inter-distances may be adjusted to place one or more poles at a desired frequency to be passed through and place zeros in a rejection band to filter out undesired frequencies.

[0056] In an exemplary embodiment, a height hrof each of plurality of metamaterial resonant elements 110 may satisfy a condition defined by the following:0.15Ao< hr< 0.25AoInequation (1)

[0057] In an exemplary embodiment, a difference hgbetween a height 122 of primary waveguide 102 and height hrmay be larger than Ao / 10.

[0058] FIG. ID shows a schematic of a horizontal cross-section (top view) 124 of a dielectric- filled metamaterial filter, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, dielectric-filled metamaterial filter 100 may furtherinclude a first network 126 of metamaterial resonant elements and a second network 128 of metamaterial resonant elements. In an exemplary embodiment, first network 126 may be successively arranged in one or more rows inside primary waveguide 102 between plurality of metamaterial resonant elements 110 and a third side 130 of primary waveguide 102. In an exemplary embodiment, each two successive metamaterial resonant elements in first network 126 (similar to successive metamaterial resonant elements 112 and 116 of FIG. 1C) may be configured to be electromagnetically coupled to each other by being placed at a subwavelength distance from each other. In an exemplary embodiment, second network 128 may be successively arranged in one or more rows inside primary waveguide 102 between plurality of metamaterial resonant elements 110 and a fourth side 132 of primary waveguide 102. In an exemplary embodiment, each two successive metamaterial resonant elements in second network 128 (similar to successive metamaterial resonant elements 112 and 116 of FIG. 1C) may be configured to be electromagnetically coupled to each other by being placed at a subwavelength distance from each other. An exemplary height of each metamaterial resonant element in first network 126 or second network 128 may be larger than height hrof each of plurality of metamaterial resonant elements 110. In an exemplary embodiment, first network 126 and second network 128 may introduce extra transmission zeros on a left side of a passband of dielectric-filled metamaterial filter 100 to increase selectivity of dielectric-filled metamaterial filter 100.

[0059] In an exemplary embodiment, dielectric-filled metamaterial filter 100 may further include a first transition region 134 and a second transition region 136. In an exemplary embodiment, first transition region 134 may be integrally attached between input port 104 and first side 118. In an exemplary embodiment, second transition region 136 may be integrally attached between output port and the second side. In an exemplary embodiment, each of first transition region 134 and second transition region 136 may include a respective waveguide and a respective plurality of metamaterial resonant elements. For example, first transition region 134 may include a waveguide 138 and a plurality of metamaterial resonant elements 140. In an exemplary embodiment, waveguide 138 may be integrally attached to secondary waveguide 109A. An exemplary width 141 of secondary waveguide 109A and waveguide 138 may be smaller than Ao / 2. Similarly, in an exemplary embodiment, second transition region 136 may include a waveguide 142 and a plurality of metamaterial resonant elements 144. In an exemplary embodiment, waveguide 142 may be integrally attached to secondary waveguide109B. An exemplary width 145 of secondary waveguide 109B and waveguide 142 may be smaller than Ao / 2. In an exemplary embodiment, waveguides 138 and 142 may be filled with the dielectric material. In an exemplary embodiment, plurality of metamaterial resonant elements 140 may be arranged inside waveguide 138 and plurality of metamaterial resonant elements 144 may be arranged inside waveguide 142.

[0060] In an exemplary embodiment, plurality of metamaterial resonant elements 140 and 144 may function as locally resonant metamaterials and may have a resonance frequency that may be higher than resonance frequency frand a cut-off frequency of secondary waveguides 109A and 109B. An exemplary height of each metamaterial resonant element of plurality of metamaterial resonant elements 140 and 144 may be less than height hr. This may allow a desired frequency range or band to be passed through dielectric-filled metamaterial fdter 100. In an exemplary embodiment, resonance frequency frmay be in a frequency range in which secondary waveguides 109A and 109B may support propagating transverse electric TE mode or single propagating transverse electric TE mode.

[0061] In further detail with respect to arrangements of pluralities of metamaterial resonant elements 140 and 144, FIG. IE shows a schematic of atop view 146 of different pluralities of metamaterial resonant elements, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, each of plurality of metamaterial resonant elements 140 may be configured to be electromagnetically coupled to at least one adjacent metamaterial resonant element of plurality of metamaterial resonant elements 140 by being placed at a subwavelength distance from at least one adjacent metamaterial resonant element of plurality of metamaterial resonant elements 140. For example, metamaterial resonant element 148 may be placed a subwavelength distance from adjacent metamaterial resonant elements 150 and 152. In an exemplary embodiment, each of plurality of metamaterial resonant elements 144 may be configured to be electromagnetically coupled to at least one adjacent metamaterial resonant element of plurality of metamaterial resonant elements 144 by being placed at a subwavelength distance from at least one adjacent metamaterial resonant element of plurality of metamaterial resonant elements 144. For example, metamaterial resonant element 154 may be placed at a subwavelength distance from adjacent metamaterial resonant elements 156 and 158.

[0062] In an exemplary embodiment, at least one of plurality of metamaterial resonant elements 140 may be configured to be electromagnetically coupled to at least one of pluralityof metamaterial resonant elements 110 by being placed at a subwavelength distance from at least one of plurality of metamaterial resonant elements 110. For example, metamaterial resonant elements 150 and 159 of plurality of metamaterial resonant elements 140 may be placed at a subwavelength distance from a metamaterial resonant element 160 of plurality of metamaterial resonant elements 110. In an exemplary embodiment, at least one of plurality of metamaterial resonant elements 144 may be configured to be electromagnetically coupled to at least one of plurality of metamaterial resonant elements 110 by being placed at a subwavelength distance from at least one of plurality of metamaterial resonant elements 110. For example, metamaterial resonant elements 156, 162, and 164 of plurality of metamaterial resonant elements 144 may be placed at a subwavelength distance from a metamaterial resonant element 166 of plurality of metamaterial resonant elements 110.

[0063] FIG. 2A shows a schematic of a dielectric-filled metamaterial fdter with coaxial connectors connected to respective sides of input and output ports, consistent with one or more exemplary embodiments of the present disclosure. FIG. 2B shows a schematic of a dielectric- filled metamaterial fdter with coaxial connectors connected to top surfaces of input and output ports, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, dielectric-filled metamaterial fdter may further include an input coaxial connector 202 and an output coaxial connector 204. In an exemplary embodiment, input coaxial connector 202 may be connected to input port 104. For example, input coaxial connector 202 may be connected to a left side 206 or a top surface 208 of input port 104. In an exemplary embodiment, output coaxial connector 204 may be connected to output port 106. For example, output coaxial connector 204 may be connected to a right side 210 or atop surface 212 of output port 106.

[0064] FIG. 3A shows a schematic of a dielectric-filled metamaterial filter with coaxial connectors as input and output ports, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1A and 3A, an exemplary dielectric-filled metamaterial fdter 300 may be similar to dielectric-filled metamaterial fdter 100. In an exemplary embodiment, plurality of metamaterial resonant elements 110 may be arranged inside a waveguide 301 (that may be similar to waveguide 102). In an exemplary embodiment, each of the input port and the output port of dielectric-filled metamaterial fdter 300 may include a respective coaxial connector. An exemplary coaxial connector 302 may serve as an input portof dielectric-filled metamaterial filter 300 and an exemplary coaxial connector 304 may serve as an output port of dielectric-filled metamaterial filter 300.

[0065] FIG. 3B shows a schematic of a three-dimensional (3D) cross-section of a dielectric- filled metamaterial filter with additional metamaterial resonant elements coupled to coaxial connectors, consistent with one or more exemplary embodiments of the present disclosure. An exemplary dielectric -filled metamaterial filter 306 may be similar to dielectric-filled metamaterial filter 300 and may include similar elements. In an exemplary embodiment, dielectric-filled metamaterial filter 306 may further include a network 308 of metamaterial resonant elements. In an exemplary embodiment, network 308 may be successively arranged in one or more rows inside primary waveguide 301 similar to networks 126 and 128 of FIG. ID

[0066] In an exemplary embodiment, dielectric-filled metamaterial filter 306 may also include a plurality of metamaterial resonant elements 310. In an exemplary embodiment, plurality of metamaterial resonant elements 310 may be arranged inside waveguide 301 between plurality of metamaterial resonant elements 110 and coaxial connector 302. In an exemplary embodiment, plurality of metamaterial resonant elements 310 may be configured to be coupled to plurality of metamaterial resonant elements 110 (similar to plurality of metamaterial resonant elements 140 of FIG. ID). In an exemplary embodiment, plurality of metamaterial resonant elements 310 may be placed around a pin of coaxial connector 302 to be coupled to coaxial connector 302.

[0067] In an exemplary embodiment, dielectric-filled metamaterial filter 306 may further include a plurality of metamaterial resonant elements 312. In an exemplary embodiment, plurality of metamaterial resonant elements 312 may be arranged inside waveguide 301 between plurality of metamaterial resonant elements 110 and coaxial connector 304. In an exemplary embodiment, plurality of metamaterial resonant elements 312 may be configured to be coupled to plurality of metamaterial resonant elements 110 (similar to plurality of metamaterial resonant elements 144 of FIG. ID). In an exemplary embodiment, plurality of metamaterial resonant elements 312 may be placed around a pin of coaxial connector 304 to be coupled to coaxial connector 304.

[0068] FIG. 4A shows a schematic of a dielectric-filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1A, 1C, and 4A, an exemplary dielectric-filled metamaterialfilter 400 may be similar to dielectric-filled metamaterial filter 100 and may have similar elements. For example, dielectric-filled metamaterial filter 400 may include a primary waveguide 402 (similar to primary waveguide 102), an input port 404 (similar to input port 104), and an output port 406 (similar to output port 106). In an exemplary embodiment, dielectric-filled metamaterial filter 400 may also include a first transition region 408 (similar to first transition region 134) and a second transition region 410 (similar to second transition region 136). In an exemplary embodiment, dielectric-filled metamaterial filter 400 may be mounted on a dielectric substrate 412.

[0069] FIG. 4B shows a schematic of a vertical cross-section (side view) 414 of a dielectric- filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. FIG. 4C shows a schematic of a horizontal cross-section (top view) 416 of a dielectric-filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. ID, and 4A-4C, in an exemplary embodiment, input port 404 may include a secondary waveguide 417A (similar to secondary waveguide 109A) that may be filled with the dielectric material. In an exemplary embodiment, output port 406 may include a secondary waveguide 417B (similar to secondary waveguide 109B) that may be filled with the dielectric material.

[0070] In an exemplary embodiment, dielectric-filled metamaterial filter 400 may further include a plurality of metamaterial resonant elements 418 (similar to plurality of metamaterial resonant elements 110) that may be arranged inside primary waveguide 402 similar to arrangement of plurality of metamaterial resonant elements 110 inside primary waveguide 102. In an exemplary embodiment, dielectric-filled metamaterial filter 400 may also include a first network 420 of metamaterial resonant elements (similar to first network 126) that may that may be arranged inside primary waveguide 402 similar to arrangement of first network 126 inside primary waveguide 102. In an exemplary embodiment, dielectric-filled metamaterial filter 400 may further include a second network 422 of metamaterial resonant elements (similar to second network 128) that may that may be arranged inside primary waveguide 402 similar to arrangement of second network 128 inside primary waveguide 102.

[0071] In an exemplary embodiment, first transition region 408 may include a waveguide 424 (similar to waveguide 138) and a plurality of metamaterial resonant elements 426 (similar to plurality of metamaterial resonant elements 140). Similarly, in an exemplary embodiment,second transition region 410 may include a waveguide 428 (similar to waveguide 142) and a plurality of metamaterial resonant elements 430 (similar to plurality of metamaterial resonant elements 144). In an exemplary embodiment, waveguides 424 and 428 may be filled with the dielectric material. In an exemplary embodiment, plurality of metamaterial resonant elements 426 may be arranged inside waveguide 424 (similar to arrangement of plurality of metamaterial resonant elements 140 inside waveguide 138) and plurality of metamaterial resonant elements 430 may be arranged inside waveguide 428 (similar to arrangement of plurality of metamaterial resonant elements 144 inside waveguide 142).

[0072] In an exemplary embodiment, input port 404 may include an input metal patch 432 that may be printed on dielectric substrate 412. In an exemplary embodiment, output port 406 may include an output metal patch 434 that may be printed on dielectric substrate 412. In an exemplary embodiment, dielectric -fdled metamaterial fdter 400 may further include a first conductive transmission line 436, a first coaxial connecter 438, a second conductive transmission line 440, and a second coaxial connecter 442. In an exemplary embodiment, first conductive transmission line 436 may be printed on dielectric substrate 412. In an exemplary embodiment, a “conductive transmission line” printed on a dielectric substrate may also be referred to as a microstrip transmission line. An exemplary proximal end 444 of first conductive transmission line 436 may be connected to input metal patch 432. In an exemplary embodiment, first coaxial connecter 438 may be connected to a distal end 446 of first conductive transmission line 436. In an exemplary embodiment, second conductive transmission line 440 may be printed on dielectric substrate 412. An exemplary proximal end 448 of second conductive transmission line 440 may be connected to output metal patch 434. In an exemplary embodiment, second coaxial connecter 442 may be connected to a distal end 450 of second conductive transmission line 440.

[0073] FIG. 5A shows a schematic of a 3D cross-section of an E-bent dielectric-filled metamaterial filter 500 mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. FIG. 5B shows a schematic of a vertical cross-section (side view) 502 of an E-bent dielectric-filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1A, 1C, and 5A, in an exemplary embodiment, dielectric-filled metamaterial filter 500 may be similar to dielectric -filled metamaterial filter 100 and may have similar elements. For example, dielectric -filled metamaterial filter 500 may include a primarywaveguide 504 (similar to primary waveguide 102), an input port 506 (similar to input port 104), an output port 508 (similar to output port 106), and a plurality of metamaterial resonant elements 510 that may be arranged inside primary waveguide 504 (similar to arrangement of plurality of metamaterial resonant elements 110 inside primary waveguide 102). In an exemplary embodiment, each of plurality of metamaterial resonant elements 510 may be a cylindrical metallic pin (for example, cylindrical metallic pin 511).

[0074] In an exemplary embodiment, input port 506 may include an input metal patch (similar to input metal patch 432 of FIG. 4C) that may be printed on a dielectric substrate 512 (similar to dielectric substrate 412). In an exemplary embodiment, output port 508 may include an output metal patch (similar to output metal patch 434 of FIG. 4C) that may be printed on dielectric substrate 512. An exemplary first side 513 of primary waveguide 504 may be mounted on an exemplary input metal patch. An exemplary second side 514 of primary waveguide 504 may be mounted on an exemplary output metal patch. In an exemplary embodiment, each of a bottom side 516 of primary waveguide 504 and a top side 518 of primary waveguide 504 may include a respective semi-cylindrical surface. In an exemplary embodiment, each of first side 513 and second side 514 may include a respective rectangular surface that may be enclosed between respective ends of top side 518 and bottom side 516.

[0075] In an exemplary embodiment, plurality of metamaterial resonant elements 510 may be attached perpendicular to a third side 520 of the primary waveguide towards a fourth side 522 of primary waveguide 504 and may be arranged along a semi-circular path 524. In an exemplary embodiment, each of third side 520 and fourth side 522 may include a respective two-dimensional surface that may be enclosed between and perpendicular to respective semi- cylindrical surfaces of top side 518 and bottom side 516. In an exemplary embodiment, a difference between a thickness 526 of primary waveguide 504 and a length of the cylindrical metallic pin 511 (similar to height hr) may be larger than Ao / 10. In an exemplary embodiment, thickness 526 may be defined as a distance between third side 520 and fourth side 522. In an exemplary embodiment, primary waveguide 504 in dielectric-filled metamaterial filter 500 may be an E-bend waveguide, that is, bending of primary waveguide 504 may alter an electric field of signals propagating through primary waveguide 504.

[0076] In an exemplary embodiment, dielectric-filled metamaterial filter 500 may further include a first conductive transmission line 528, a first coaxial connecter 530, a second conductive transmission line 532, and a second coaxial connecter 534. In an exemplaryembodiment, first conductive transmission line 528 may be printed on dielectric substrate 512. An exemplary proximal end 536 of first conductive transmission line 528 may be connected to an exemplary input metal patch of input port 506. In an exemplary embodiment, first coaxial connecter 530 may be connected to a distal end 538 of first conductive transmission line 528. In an exemplary embodiment, second conductive transmission line 532 may be printed on dielectric substrate 512. An exemplary proximal end 540 of second conductive transmission line 532 may be connected to an exemplary output metal patch of output port 508. In an exemplary embodiment, second coaxial connecter 534 may be connected to a distal end 542 of second conductive transmission line 532.

[0077] FIG. 6A shows a schematic of a 3D cross-section of a first implementation of an H- bent dielectric-filled metamaterial filter 600 mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. FIG. 6B shows a schematic of a vertical cross-section (side view) 602 of a first implementation of an H-bent dielectric-filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1A, 1C, and 6A, in an exemplary embodiment, dielectric-filled metamaterial filter 600 may be similar to dielectric-filled metamaterial filter 100 and may have similar elements. For example, dielectric-filled metamaterial filter 600 may include a primary waveguide 604 (similar to primary waveguide 102), an input port 606 (similar to input port 104), an output port 608 (similar to output port 106), and a plurality of metamaterial resonant elements 610 that may be arranged inside primary waveguide 604 (similar to arrangement of plurality of metamaterial resonant elements 110 inside primary waveguide 102). In an exemplary embodiment, each of plurality of metamaterial resonant elements 610 may be a cylindrical metallic pin (for example, cylindrical metallic pin 611).

[0078] In an exemplary embodiment, input port 606 may include an input metal patch (similar to input metal patch 432 of FIG. 4C) that may be printed on a dielectric substrate 612 (similar to dielectric substrate 412). In an exemplary embodiment, output port 608 may include an output metal patch (similar to output metal patch 434 of FIG. 4C) that may be printed on dielectric substrate 612. An exemplary first side 613 of primary waveguide 604 may be mounted on an exemplary input metal patch. An exemplary second side 614 of primary waveguide 604 may be mounted on an exemplary output metal patch. In an exemplary embodiment, each of a bottom side 616 of primary waveguide 604 and a top side 618 of primarywaveguide 604 may include a respective semi-cylindrical surface. In an exemplary embodiment, each of first side 613 and second side 614 may include a respective rectangular surface that may be enclosed between respective ends of top side 618 and bottom side 616.

[0079] In an exemplary embodiment, plurality of metamaterial resonant elements 610 may be attached perpendicular to top side 618 towards bottom side of 616 and may be arranged along a semi-circular path 620. In an exemplary embodiment, primary waveguide 604 in dielectric- filled metamaterial filter 600 may be an H-bend waveguide, that is, bending of primary waveguide 604 may alter a magnetic field of signals propagating through primary waveguide 604.

[0080] In an exemplary embodiment, dielectric-filled metamaterial filter 600 may further include a first conductive transmission line 622, a first coaxial connecter 624, a second conductive transmission line 626, and a second coaxial connecter 628. In an exemplary embodiment, first conductive transmission line 622 may be printed on dielectric substrate 612. An exemplary proximal end 630 of first conductive transmission line 622 may be connected to an exemplary input metal patch of input port 606. In an exemplary embodiment, first coaxial connecter 624 may be connected to a distal end 632 of first conductive transmission line 622. In an exemplary embodiment, second conductive transmission line 626 may be printed on dielectric substrate 612. An exemplary proximal end 634 of second conductive transmission line 626 may be connected to an exemplary output metal patch of output port 608. In an exemplary embodiment, second coaxial connecter 628 may be connected to a distal end 636 of second conductive transmission line 626.

[0081] FIG. 7A shows a schematic of a 3D cross-section of a second implementation of an H- bent dielectric-filled metamaterial filter 700 mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. FIG. 7B shows a schematic of a vertical cross-section (side view) 702 of a second implementation of an H-bent dielectric- filled metamaterial filter mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1A, 1C, and 7A, in an exemplary embodiment, dielectric-filled metamaterial filter 700 may be similar to dielectric- filled metamaterial filter 100 and may have similar elements. For example, dielectric-filled metamaterial filter 700 may include a primary waveguide 704 (similar to primary waveguide 102), an input port 706 (similar to input port 104), an output port 708 (similar to output port 106), and a plurality of metamaterial resonant elements 710 that may be arranged insideprimary waveguide 704 (similar to arrangement of plurality of metamaterial resonant elements 110 inside primary waveguide 102). In an exemplary embodiment, each of plurality of metamaterial resonant elements 710 may be a cylindrical metallic pin (for example, cylindrical metallic pin 711).

[0082] In an exemplary embodiment, input port 706 may include an input metal patch (similar to input metal patch 432 of FIG. 4C) that may be printed on a dielectric substrate 712 (similar to dielectric substrate 412). In an exemplary embodiment, output port 708 may include an output metal patch (similar to output metal patch 434 of FIG. 4C) that may be printed on dielectric substrate 712. An exemplary first side 713 of primary waveguide 704 may be mounted on an exemplary input metal patch. An exemplary second side 714 of primary waveguide 704 may be mounted on an exemplary output metal patch. In an exemplary embodiment, each of abottom side 716 of primary waveguide 704 and atop side 718 ofprimary waveguide 704 may include a respective semi-cylindrical surface. In an exemplary embodiment, each of first side 713 and second side 714 may include a respective rectangular surface that may be enclosed between respective ends of top side 718 and bottom side 716.

[0083] In an exemplary embodiment, plurality of metamaterial resonant elements 710 may be attached perpendicular to bottom side 716 towards top side 718 and may be arranged along a semi-circular path 720. In an exemplary embodiment, primary waveguide 704 in dielectric- filled metamaterial filter 700 may be an H-bend waveguide, that is, bending of primary waveguide 704 may alter a magnetic field of signals propagating through primary waveguide 704.

[0084] In an exemplary embodiment, dielectric-filled metamaterial filter 700 may further include a first conductive transmission line 722, a first coaxial connecter 724, a second conductive transmission line 726, and a second coaxial connecter 728. In an exemplary embodiment, first conductive transmission line 722 may be printed on dielectric substrate 712. An exemplary proximal end 730 of first conductive transmission line 722 may be connected to an exemplary input metal patch of input port 706. In an exemplary embodiment, first coaxial connecter 724 may be connected to a distal end 732 of first conductive transmission line 722. In an exemplary embodiment, second conductive transmission line 726 may be printed on dielectric substrate 712. An exemplary proximal end 734 of second conductive transmission line 726 may be connected to an exemplary output metal patch of output port 708. In anexemplary embodiment, second coaxial connecter 728 may be connected to a distal end 736 of second conductive transmission line 726.

[0085] FIG. 8A shows a schematic of a dielectric -fdled metamaterial fdter with a rectangular cuboid shape waveguide mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1A, 1C, and 8A, an exemplary dielectric -fdled metamaterial fdter 800 may be similar to dielectric-fdled metamaterial fdter 100 and may have similar elements. For example, dielectric-fdled metamaterial fdter 800 may include a primary waveguide 802 (similar to primary waveguide 102), an input port 804 (similar to input port 104), an output port 806 (similar to output port 106), and a plurality of metamaterial resonant elements 808 that may be arranged inside primary waveguide 802 (similar to arrangement of plurality of metamaterial resonant elements 110 inside primary waveguide 102).

[0086] In an exemplary embodiment, input port 804 may include an input metal patch 810 (similar to input metal patch 432 of FIG. 4C) that may be printed on a dielectric substrate 812 (similar to dielectric substrate 412). In an exemplary embodiment, output port 806 may include an output metal patch 814 (similar to output metal patch 434 of FIG. 4C) that may be printed on dielectric substrate 812. In an exemplary embodiment, a shape of primary waveguide 802 may be a rectangular cuboid 816. An exemplary bottom surface of rectangular cuboid 816 may be mounted on dielectric substrate 812.

[0087] FIG. 8B shows a schematic of a vertical cross-section (side view) 818 of a dielectric- fdled metamaterial fdter with a rectangular cuboid shape waveguide mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, each of plurality of metamaterial resonant elements 808 may include a cylindrical metallic pin (for example, a cylindrical metallic pin 820) that may be attached perpendicular to a top surface 822 of rectangular cuboid 816 towards a bottom surface 824 of rectangular cuboid 816. In an exemplary embodiment, a distance between bottom surface 824 to top surface 822 (that is, a height of rectangular cuboid 816) may be about 1.14 mm. An exemplary height of cylindrical metallic pin 820 may be about 0.65-0.69 mm. An exemplary diameter of cylindrical metallic pin 820 may be about 0.3 mm. In an exemplary embodiment, plurality of metamaterial resonant elements 808 may be arranged along a straight line 826.

[0088] FIG. 8C shows a schematic of a horizontal cross-section (top view) 828 of a dielectric- fdled metamaterial fdter with a rectangular cuboid shape waveguide mounted on a dielectricsubstrate, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, a width 829A and a length 829B of rectangular cuboid 816 may be about 0.96 mm and 3.02 mm, respectively. In an exemplary embodiment, each of input port 804 and output port 806 may further include a respective metamaterial resonator element that may be coupled to a respective metal patch of input metal patch 810 or output metal patch 814. For example, input port 804 may further include a metamaterial resonator element 830 that may be coupled to input metal patch 810. In an exemplary embodiment, a “metamaterial resonator element” may refer to a subwavelength component within a metamaterial structure designed to exhibit resonance at specific frequencies, enabling wave manipulation. In an exemplary embodiment, metamaterial resonator element 830 may be mounted on dielectric substrate 812 perpendicular to bottom surface 824 towards top surface 822 and may be configured to be electromagnetically coupled to at least one of plurality of metamaterial resonant elements 808 (for example, a metamaterial resonant element 832). For this purpose, in an exemplary embodiment, metamaterial resonator element 830 may include a cylindrical metallic rod that may be placed at a subwavelength distance from metamaterial resonant element 832. An exemplary height of the cylindrical metallic rod may be about 1.01 mm. In an exemplary embodiment, input metal patch 810 may include a circular arc shaped patch that may be etched on dielectric substrate 812 around metamaterial resonator element 830.

[0089] In an exemplary embodiment, output port 806 may further include a metamaterial resonator element 834 that may be coupled to output metal patch 814. In an exemplary embodiment, metamaterial resonator element 834 may be mounted on dielectric substrate 812 perpendicular to bottom surface 824 towards top surface 822 and may be configured to be electromagnetically coupled to at least one of plurality of metamaterial resonant elements 808 (for example, a metamaterial resonant element 836). For this purpose, in an exemplary embodiment, metamaterial resonator element 834 may include a cylindrical metallic rod that may be placed at a subwavelength distance from metamaterial resonant element 836. An exemplary height of the cylindrical metallic rod may be about 1.01 mm. In an exemplary embodiment, output metal patch 814 may include a circular arc shaped patch that may be etched on dielectric substrate 812 around metamaterial resonator element 834.

[0090] In an exemplary embodiment, dielectric-filled metamaterial fdter 800 may further include a first conductive transmission line 838 and a second conductive transmission line 840. In an exemplary embodiment, first conductive transmission line 838 may be printed ondielectric substrate 812 and may be connected to input metal patch 810. In an exemplary embodiment, second conductive transmission line 840 may be printed on dielectric substrate 812 and may be connected to output metal patch 834.

[0091] FIG. 9 shows a schematic of a dielectric-filled metamaterial fdter with loop shaped metamaterial resonator elements inside a rectangular cuboid shape waveguide mounted on a dielectric substrate, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1A, 1C, and 9, an exemplary dielectric-filled metamaterial filter 900 may be similar to dielectric-filled metamaterial filter 100 and may have similar elements. For example, dielectric-filled metamaterial filter 900 may include a primary waveguide 902 (similar to primary waveguide 102), an input port 904 (similar to input port 104), an output port 906 (similar to output port 106), and a plurality of metamaterial resonant elements 908 that may be arranged inside primary waveguide 902 (similar to arrangement of plurality of metamaterial resonant elements 110 inside primary waveguide 102).

[0092] In an exemplary embodiment, input port 904 may include an input metal patch 910 (similar to input metal patch 432 of FIG. 4C) that may be printed on a dielectric substrate 912 (similar to dielectric substrate 412). In an exemplary embodiment, output port 906 may include an output metal patch 914 (similar to output metal patch 434 of FIG. 4C) that may be printed on dielectric substrate 912. In an exemplary embodiment, a shape of primary waveguide 902 may be a rectangular cuboid 916. An exemplary bottom surface 918 of rectangular cuboid 916 may be mounted on dielectric substrate 912.

[0093] In an exemplary embodiment, each of plurality of metamaterial resonant elements 908 may include a cylindrical metallic pin (similar to cylindrical metallic pin 820 of FIG. 8B) that may be attached perpendicular to a top surface 920 of rectangular cuboid 916 towards bottom surface 918 of rectangular cuboid 916. In an exemplary embodiment, plurality of metamaterial resonant elements 908 may be arranged along a straight line (similar to straight line 826 of FIG. 8B)

[0094] In an exemplary embodiment, each of input port 904 and output port 906 may further include a respective metamaterial resonator element that may be coupled to a respective metal patch of input metal patch 910 or output metal patch 914. For example, input port 904 may further include a metamaterial resonator element 922 that may be coupled to input metal patch 910. In an exemplary embodiment, metamaterial resonator element 922 may be mounted on dielectric substrate 912 perpendicular to bottom surface 918 towards top surface 920. In anexemplary embodiment, metamaterial resonator element 922 may include a metallic semi-loop. An exemplary metallic semi-loop may include a first metallic rod 924, a second metallic rod 926, and a third metallic rod 928. In an exemplary embodiment, first metallic rod 924 may be mounted on dielectric substrate 912 perpendicular to bottom surface 918 towards top surface 920 and may be configured to be electromagnetically coupled to at least one of plurality of metamaterial resonant elements 908 by being placed at a subwavelength distance from at least one of plurality of metamaterial resonant elements 908. For example, first metallic rod 924 may be placed at a subwavelength distance from a metamaterial resonant element 930 of plurality of metamaterial resonant elements 908. In an exemplary embodiment, second metallic rod 926 may be perpendicularly attached to atop end of first metallic rod 924. In an exemplary embodiment, third metallic rod 928 may be attached between second metallic rod 926 and dielectric substrate 912 perpendicular to bottom surface 918. In an exemplary embodiment, third metallic rod 928 may be connected to input metal patch 910.

[0095] In an exemplary embodiment, output port 906 may further include a metamaterial resonator element 932 that may be coupled to output metal patch 914. In an exemplary embodiment, metamaterial resonator element 932 may be mounted on dielectric substrate 912 perpendicular to bottom surface 918 towards top surface 920. In an exemplary embodiment, metamaterial resonator element 932 may include a metallic semi -loop. An exemplary metallic semi-loop may include a first metallic rod 934, a second metallic rod 936, and a third metallic rod 938. In an exemplary embodiment, first metallic rod 934 may be mounted on dielectric substrate 912 perpendicular to bottom surface 918 towards top surface 920 and may be configured to be electromagnetically coupled to at least one of plurality of metamaterial resonant elements 908 by being placed at a subwavelength distance from at least one of plurality of metamaterial resonant elements 908. For example, first metallic rod 934 may be placed at a subwavelength distance from a metamaterial resonant element 940 of plurality of metamaterial resonant elements 908. In an exemplary embodiment, second metallic rod 936 may be perpendicularly attached to a top end of first metallic rod 934. In an exemplary embodiment, third metallic rod 938 may be attached between second metallic rod 936 and dielectric substrate 912 perpendicular to bottom surface 918. In an exemplary embodiment, third metallic rod 938 may be connected to output metal patch 914.

[0096] In an exemplary embodiment, dielectric-filled metamaterial filter 900 may further include a first conductive transmission line 942 and a second conductive transmission line 944.In an exemplary embodiment, first conductive transmission line 942 may be printed on dielectric substrate 912 and may be connected to input metal patch 910. In an exemplary embodiment, second conductive transmission line 944 may be printed on dielectric substrate 912 and may be connected to output metal patch 914.EXAMPLE

[0097] In this example, performance of different dielectric-filled metamaterial filters similar to dielectric-filled metamaterial filter 800 of FIGs. 8A-8C is demonstrated. Table 1 shows specifications of exemplary dielectric-filled metamaterial filters. FIG. 10 shows a full band frequency response 1000 of a dielectric-filled metamaterial filter, consistent with one or more exemplary embodiments of the present disclosure. Frequency response 1000 includes variations 1002 and 1004 of S-parameters S21and Slt, respectively, with respect to frequency at a center frequency of about 28 GHz for an exemplary dielectric-filled metamaterial filter. Results of Table 1 and diagrams 1002 and 1004 highlight promising capabilities of the exemplary dielectric-filled metamaterial filter in terms of wide bandwidth, sharp selectivity, low loss, and deep rejection. Frequency response 1000 shows that the target frequency range of the exemplary dielectric-filled metamaterial filter is about 5-100 GHz, with a special focus on about 20-40 GHz. The size (<5 mm2for 28 GHz) and RF performance (IL<0.5 dB for 15% bandwidth) of exemplary dielectric-filled metamaterial filters of Table 1 promise unlocking new possibilities for efficient and high-throughput mmWave communication systems.Table 1. specifications of different exemplary dielectric-filled metamaterial filters

[0098] While the foregoing has described what are considered to be the best mode and / or other examples, it is understood that various modifications may be made therein and that the subject matter disclosed herein may be implemented in various forms and examples, and that the teachings may be applied in numerous applications, only some of which have been described herein. It is intended by the following claims to claim any and all applications, modifications, and variations that fall within the true scope of the present teachings.

[0099] Unless otherwise stated, all measurements, values, ratings, positions, magnitudes, sizes, and other specifications that are set forth in this specification, including in the claims that follow, are approximate, not exact. They are intended to have a reasonable range that is consistent with the functions to which they relate and with what is customary in the art to which they pertain.

[0100] The scope of protection is limited solely by the claims that now follow. That scope is intended and should be interpreted to be as broad as is consistent with the ordinary meaning of the language that is used in the claims when interpreted in light of this specification and the prosecution history that follows and to encompass all structural and functional equivalents.

[0101] Except as stated immediately above, nothing that has been stated or illustrated is intended or should be interpreted to cause a dedication of any component, step, feature, object, benefit, advantage, or equivalent to the public, regardless of whether it is or is not recited in the claims.

[0102] It will be understood that the terms and expressions used herein have the ordinary meaning as is accorded to such terms and expressions with respect to their corresponding respective areas of inquiry and study except where specific meanings have otherwise been set forth herein. Relational terms such as first and second and the like may be used solely to distinguish one entity or action from another without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent tosuch process, method, article, or apparatus. An element proceeded by “a” or “an” does not, without further constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0103] The Abstract of the Disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, it can be seen that various features are grouped together in various implementations. This is for purposes of streamlining the disclosure, and is not to be interpreted as reflecting an intention that the claimed implementations require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed implementation. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separately claimed subject matter.

[0104] While various implementations have been described, the description is intended to be exemplary, rather than limiting and it will be apparent to those of ordinary skill in the art that many more implementations and implementations are possible that are within the scope of the implementations. Although many possible combinations of features are shown in the accompanying figures and discussed in this detailed description, many other combinations of the disclosed features are possible. Any feature of any implementation may be used in combination with or substituted for any other feature or element in any other implementation unless specifically restricted. Therefore, it will be understood that any of the features shown and / or discussed in the present disclosure may be implemented together in any suitable combination. Accordingly, the implementations are not to be restricted except in light of the attached claims and their equivalents. Also, various modifications and changes may be made within the scope of the attached claims.

Claims

What is claimed is:

1. A dielectric-filled metamaterial filter, comprising: a primary waveguide filled with a dielectric material, a width of the primary waveguide being smaller than Ao / 2 where Aois wavelength associated with an operating frequency of the dielectric- filled metamaterial filter; a plurality of metamaterial resonant elements arranged inside the primary waveguide, each of the plurality of metamaterial resonant elements configured to be electromagnetically coupled to at least one adjacent metamaterial resonant element of the plurality of metamaterial resonant elements by being placed at a subwavelength distance from the at least one adjacent metamaterial resonant element; an input port coupled to a first side of the primary waveguide and configured to: receive an input electromagnetic wave; and couple the input electromagnetic wave to the primary waveguide; and an output port coupled to a second side of the primary waveguide and configured to: receive an output electromagnetic wave from the primary waveguide, the output electromagnetic wave generated by the plurality of metamaterial resonant elements through filtering the input electromagnetic wave; and transmit the output electromagnetic wave to outside of the dielectric-filled metamaterial filter.

2. The dielectric-filled metamaterial filter of claim 1, wherein a height hrof each of the plurality of metamaterial resonant elements satisfies a condition defined by the following:0.15Ao< hr< 0.25Ao.

3. The dielectric- filled metamaterial filter of claim 2, wherein a difference hgbetween a height of the primary waveguide and the height hris larger than Ao / 10.

4. The dielectric-filled metamaterial filter of claim 2, further comprising: a first network of metamaterial resonant elements successively arranged in one or more rows inside the primary waveguide between thp nlnr lity of metamaterial resonant elements and a third side of the primary waveguide, each t ;ssive metamaterial resonant elements in thefirst network of metamaterial resonant elements configured to be electromagnetically coupled to each other by being placed at a subwavelength distance from each other; and a second network of metamaterial resonant elements successively arranged in one or more rows inside the primary waveguide between the plurality of metamaterial resonant elements and a fourth side of the primary waveguide, each two successive metamaterial resonant elements in the second network of metamaterial resonant elements configured to be electromagnetically coupled to each other by being placed at a subwavelength distance from each other.

5. The dielectric-filled metamaterial filter of claim 4, wherein a height of each metamaterial resonant element in the first network of metamaterial resonant elements or the second network of metamaterial resonant elements is larger than the heightr.

6. The dielectric-filled metamaterial filter of claim 1 , further comprising a first transition region integrally attached between the input port and the first side and a second transition region integrally attached between the output port and the second side, each of the first transition region and the second transition region comprising: a respective waveguide filled with the dielectric material, a width of the respective waveguide being smaller than oi!'., ' and a respective plurality of metamaterial resonant elements arranged inside the respective waveguide, wherein: each of the respective plurality of metamaterial resonant elements configured to be electromagnetically coupled to at least one adjacent metamaterial resonant element of the respective plurality of metamaterial resonant elements by being placed at a subwavelength distance from the at least one adjacent metamaterial resonant element of the respective plurality of metamaterial resonant elements; and at least one of the respective plurality of metamaterial resonant elements configured to be electromagnetically coupled to at least one of the plurality of metamaterial resonant elements by being placed at a subwavelength distance from the at least one of the plurality of metamaterial resonant elements.

7. The dielectric-filled metamaterial filter of claim 1, wherein each of the input port and the output port comprises a respective secondary waveguide filled with the dielectric material, a width of the respective secondary waveguide being smaller than Ao / 2.

8. The dielectric-filled metamaterial filter of claim 1, further comprising: an input coaxial connector connected to the input port; and an output coaxial connector connected to the output port.

9. The dielectric-filled metamaterial filter of claim 1, wherein each of the input port and the output port comprises a respective coaxial connector.

10. The dielectric-filled metamaterial filter of claim 1, wherein the primary waveguide comprises one of a rectangular cuboid shape, a triangular prism shape, a cylindrical shape, a 180° bent tube, or a 90° bent tube.

11. The dielectric-filled metamaterial fdter of claim 1 , wherein: the input port comprises an input metal patch printed on a dielectric substrate; and the output port comprises an output metal patch printed on the dielectric substrate.

12. The dielectric-filled metamaterial filter of claim 11, wherein: the first side of the primary waveguide is mounted on the input metal patch; the second side of the primary waveguide is mounted on the output metal patch; each of a bottom side of the primary waveguide and a top side of the primary waveguide comprises a respective semi-cylindrical surface; each of the first side and the second side comprises a respective rectangular surface enclosed between respective ends of the top side and the bottom side; and each of the plurality of metamaterial resonant elements comprises a cylindrical metallic pin.

13. The dielectric-filled metamaterial filter of claim 12, wherein the plurality of metamaterial resonant elements are attached perpendicular to a third side of the primary waveguide towards a fourth side of the primary waveguide and are arranged along a semi-circular path, wherein: each of the third side and the fourth side comprises a respective two-dimensional surface enclosed between and perpendicular to respective semi-cylindrical surfaces of the top side and the bottom side; and a difference between a thickness of the primary waveguide and a length of the cylindrical metallic pin is larger than Ao / 10, the thickness comprising a distance between the third side and the fourth side.

14. The dielectric-filled metamaterial filter of claim 12, wherein the plurality of metamaterial resonant elements are attached perpendicular to the top side of the primary waveguide towards the bottom side of the primary waveguide and are arranged along a semi-circular path.

15. The dielectric-filled metamaterial filter of claim 12, wherein the plurality of metamaterial resonant elements are attached perpendicular to the bottom side of the primary waveguide towards the top side of the primary waveguide and are arranged along a semi-circular path.

16. The dielectric-filled metamaterial fdter of claim 11, wherein: a shape of the primary waveguide comprises a rectangular cuboid, a bottom surface of the rectangular cuboid mounted on the dielectric substrate; each of the plurality of metamaterial resonant elements comprises a cylindrical metallic pin attached perpendicular to a top surface of the rectangular cuboid towards the bottom surface of the rectangular cuboid; the plurality of metamaterial resonant elements are arranged along a straight line; each of the input port and the output port further comprises a respective metamaterial resonator element coupled to a respective metal patch of one of the input metal patch and the output metal patch, the respective metamaterial resonator element mounted on the dielectric substrate perpendicular to the bottom surface towards the top surface and configured to be electromagnetically coupled to at least one of the plurality of metamaterial resonant elements.

17. The dielectric-filled metamaterial fdter of claim 16, wherein: the respective metamaterial resonator element comprises a cylindrical metallic rod placed at a subwavelength distance from the at least one of the plurality of metamaterial resonant elements; and each of the input metal patch and the output metal patch comprises a respective circular arc shaped patch etched on the dielectric substrate around the respective metamaterial resonator element.

18. The dielectric-filled metamaterial filter of claim 16, wherein the respective metamaterial resonator element comprises a metallic semi-loop, the metallic semi-loop comprising: a first metallic rod mounted on the dielectric substrate perpendicular to the bottom surface towards the top surface and configured to be electromagnetically coupled to at least one of the plurality of metamaterial resonant elements by being placed at a subwavelength distance from the at least one of the plurality of metamaterial resonant elements; a second metallic rod perpendicularly attached to a top end of the first metallic rod; and a third metallic rod attached between the second metallic rod and the dielectric substrate perpendicular to the bottom surface, the third metallic rod connected to the respective metal patch.

19. The dielectric-filled metamaterial fdter of claim 11, further comprising: a first conductive transmission line printed on the dielectric substrate, a proximal end of the first conductive transmission line connected to the input metal patch; a first coaxial connecter connected to a distal end of the first conductive transmission line; a second conductive transmission line printed on the dielectric substrate, a proximal end of the second conductive transmission line connected to the output metal patch; and a second coaxial connecter connected to a distal end of the second conductive transmission line.

20. The di electric- filled metamaterial filter of claim 1, wherein the dielectric material comprises multiple layers of ceramics, each of the multiple layers comprising a different dielectric constant and a different loss tangent.

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