Patent Publication Number: US-11387529-B2

Title: Waveguides interconnected by flanges having glide symmetrically positioned holes disposed therein

Description:
BACKGROUND 
     A waveguide is a device or a guide through which electromagnetic currents are guided. The waveguide typically comprises a hollow tube or pipe, and is therefore also referred to as a “hollow waveguide”. The hollow tube may be circular, rectangular or have any other suitable shape. The waveguide has a hollow centre and conductive walls defining the centre of the waveguide. The diameter of the waveguide and the wavelength of the electromagnetic wave traveling in the waveguide are closely related such that if the frequency of the wave is too low, then the electromagnetic wave cannot propagate through the waveguide. 
     Hollow waveguides have been widely used as a hardware standard technology for the design of passive microwave components and antenna arrays. Such hollow waveguides are entirely made of metal and exhibit attractive features like low loss, good isolation properties and high power handling capability. A common application of hollow waveguides is to be used as a standard interconnection interface of high frequency circuits for lab testing purposes. In such cases, the waveguide typically comprises a flange. There are different types of waveguide flanges, and some of them will be described below. The surface of a waveguide flange (e.g., made of metal) should be smooth and clean in order to let the electromagnetic currents suitably flow along the two waveguides joined together without any leakage or reflection. Additional versions of waveguide flanges provide a texture pattern around the waveguide opening to facilitate the flow of electromagnetic currents between the waveguide joints without leaking energy. One example is the choke flange that contains a corrugation that establishes a high impedance condition at the contact point between the flanges that is transformed into a short-circuit at the side-edges of the waveguide opening by using a Ag/4 section. Ag represents the guided (g) wavelength (A) of the wave propagating in the parallel plate waveguide region between the two flanges. Therefore, the current flows smoothly across the joint between two waveguides without leaking. Another waveguide flange type is the so-called pin-flange adapter where a pin surface surrounding the waveguide opening in one of the flanges avoids any possible power loss when screwed together with a smooth waveguide flange in the presence of a gap between the pin-flange and the smooth flange. See S. Rahiminejad, E. Pucci, S. Haasl, and P. Enoksson, “Micromachined contactless pin-flange adapter for robust high-frequency measurements”, Journal of Micromachining and Microengineering, vol. 24, no. 8, 2014. 
     An example of a traditional flange of a rectangular waveguide for measurement purposes is illustrated in  FIG. 1 . The waveguide is referred to as a rectangular waveguide because the opening has a rectangular shape. The left part of  FIG. 1  illustrates a waveguide assembly where three waveguides  1101   a,    1101   b,    1101   c  are connected together, and the right part of  FIG. 1  provides a more detailed illustration of some of the flanges comprised in the waveguide assembly.  FIG. 1  illustrates an example where the three waveguides  101   a,    101   b,    101   c  are rectangular tubes. As seen in  FIG. 1 , a first waveguide  101   a  comprises a first flange  103   a  surrounding an end opening  105   a  in one end of the first waveguide  101   a.  A second waveguide  101   b  comprises a second flange  103   b  surrounding an end opening  105   b  in one end of the second waveguide  101   b.  The first waveguide  101   a  is connected to the second waveguide  101   b  by connecting the first flange  103   a  to the second flange  103   b  so that the end openings  105   a,    105   b  face each other. The first and second flange  103   a,    103   b  may be connected to each other by using for example screws or other suitable connecting means. Furthermore,  FIG. 1  illustrates that the second waveguide  101   b  comprises a third flange  103   c  surrounding an end opening in the opposite end of the second waveguide  101   b  as compared to the second flange  103   b.  The second waveguide  101   b  may be a Device Under Test (DUT). A third waveguide  101   c  comprises a fourth flange  103   d  surrounding an end opening of the third waveguide  101   c.  The third waveguide  101   c  is connected to the second waveguide  101   b  by connecting the fourth flange  103   d  to the third flange  103   c.  The end openings  105   a,    105   b  are illustrated as a rectangular openings due to that the waveguide is formed as a rectangular tube. 
     As seen in the right part of  FIG. 1 , each flange  103   a,    103   b,    103   c,    103   d  are circular flat disks having a smooth surface and having a respective end opening  105   a,    105   b  in the center of the disk. Each flange  103   a,    103   b,    103   c,    103   d  is located around the outer circumference of the end part of the respective waveguide  101   a,    101   b,    101   c.  The surface of the waveguide flange (e.g. made of metal) should be smooth and clean in order to let the electromagnetic currents suitably flow along the two waveguides joined together without any leakage or reflection. Tolerances or errors when mating to flanges  103   a  and  103   b  and mating flanges  103   c  and  103   d  can cause gaps  112  between the flange surfaces. The errors and gaps  112  can be created by screwing the flanges carelessly or not tightening them well. The gaps  112  may cause leakage, reflections, and measurement uncertainties. 
     Both the flat flange and the choke flange need to be carefully mated to ensure a good electrical contact. The term mated may also be described as connected, joined, coupled etc. This is usually done by screwing, which is time consuming and laborious. The pin flange and the choke flange both need very accurate fabrication methods, which limits their use at higher frequencies since the dimensions of the corrugations and the pins become very small. Therefore, there is a need to at least mitigate or solve this issue. 
     SUMMARY OF THE INVENTION 
     An objective of embodiments herein is therefore to obviate at least one of the above disadvantages and to provide an improved waveguide interconnection. 
     According to a first aspect, the object is achieved by a first waveguide comprising a first flange surrounding an end opening of the first waveguide. The first flange comprises at least two holes which are periodically distributed around the end opening. The first waveguide is arranged to be connected to a second waveguide by connecting the first flange to a second flange of the second waveguide such that the end opening of the first waveguide faces an end opening of the second waveguide and such that the holes in the first flange are at least partly glide symmetrically positioned with respect to holes which are periodically distributed around the end opening of the second flange. 
     According to a second aspect, the object is achieved by a waveguide assembly for waveguides. The waveguide assembly comprises a first waveguide comprising a first flange surrounding an end opening of the first waveguide. The waveguide assembly further comprises a second waveguide comprising a second flange surrounding an end opening of the second waveguide. Each flange comprises at least two holes which are periodically distributed around the respective end opening. The first and second waveguides are arranged to be connected to each other by connecting the first flange to the second flanges such that the end openings face each other and such that the holes in the first flange are at least partly glide symmetrically positioned with respect to the holes in the second flange. 
     According to a third aspect, the object is achieved by a method for manufacturing a first waveguide. The method comprises providing a first flange surrounding an end opening to the first waveguide. The first flange comprises at least two holes which are periodically distributed around the end opening. The first waveguide is arranged to be connected to a second waveguide by connecting the first flange to a second flange of the second waveguide such that the end opening of the first waveguide face an end opening of the second waveguide and such that the holes in the first flange are at least partly glide symmetrically positioned with respect to holes which are periodically distributed around the end opening of the second flange. 
     According to a fourth aspect, the object is achieved by a method for manufacturing a waveguide assembly for waveguides. The method comprises providing a first waveguide comprising a first flange surrounding an end opening of the first waveguide. The method further comprises providing a second waveguide comprising a second flange surrounding an end opening of the second waveguide. Each flange comprises at least two holes which are periodically distributed around the respective end opening. The method further comprises connecting the first and second waveguides to each other by connecting the first flange to the second flanges such that the end openings face each other and such that the holes in the first flange are at least partly glide symmetrically positioned with respect to the holes in the second flange. 
     An improved waveguide interconnection is provided since each flange comprises at least two holes which are periodically distributed around the respective end opening, and since the first and second waveguides are configured to be connected to each other by connecting the first flange to the second flanges such that the end openings face each other and such that the holes in the first flange are at least partly glide symmetrically positioned with respect to the holes in the second flange. 
     Embodiments herein afford many advantages, of which a non-exhaustive list of examples follows: 
     A glide symmetric structure is a periodic pattern generated by two geometrical transformations: a translation and a reflection with respect to a certain reference plane. It has been found that by using holes as unit cell of this glide symmetric structure, a wideband stopband where all higher-order modes are avoided is achieved. When this structure is integrated surrounding a waveguide flange opening, an advantage of the embodiments herein is that any possible leakage of signals with frequencies within the stop band due to a gap between the flange joints is eliminated and a smooth transition is achieved. 
     Only one row of holes surrounding the waveguide opening is enough to prevent leakage and provides almost perfect transmission, thereby the embodiments herein haVE an advantage of simplifying the waveguide since it is not necessary to apply several rows of holes in the holey flange configuration as compared to a pin-type flange which has several rows of pins. 
     Another advantage of the embodiments herein is that the holes can be made by just drilling, which is much simpler and cost-effective than milling pins or corrugations. 
     There is a minimum required depth of the holes but as long as the depth is larger than the minimum required depth, the depth does not affect the stopband. This provides an advantage of a non-sensitivity tolerance to the depth of the hole. Moreover, the depth of the hole is smaller than the pin height in the pin-flange, which should be around λ/4 (λ represents the wavelength) in order to create an open boundary condition, so the holey flange can be made smaller (thinner) than the pin flange. 
     A further advantage of the embodiments herein is that the performance of the at least partly glide symmetric holey structure is insensitive to the flatness of the bottom of the hole, which provides manufacturing flexibility since the drill could have a conical shape and the holey flange still performs as expected. 
     The period and hole dimensions in the embodiments herein are larger than the required ones in a pin-type Electromagnetic bandgap (EBG) structure for operating at the same center frequency. A larger period means an advantage of less sensitivity to manufacturing tolerances and misalignments. For example, at a center frequency of 60 GHz, it has been seen that misalignments of 0.2 mm do not affect its performance. 
     If the number of holes surrounding the waveguide is even, the holes can be placed in an anti-symmetric topology so that the need of fabricating two different male and female holey flange adapters is avoided. In this way, the embodiments herein have an advantage of that both flanges are manufactured identical and when the flanges are joined together the geometry is built-up at least partly glide symmetrical. This fact simplifies the manufacturing and use since there is only one variant of flange. 
     The embodiments herein provide the additional advantage of that the at least partly glide symmetric holey flange reduces leakage independently of if the surface of the flange is flat or if the surface of the flange has a bulge. 
     Furthermore, the embodiments herein provide the advantage of that the at least partly glide symmetric holey pattern reduces any leakage independently on how the holes are distributed around the waveguide opening (the hole topology can be rounded, elliptical, square etc.). 
     The embodiments herein are not limited to the features and advantages mentioned above. A person skilled in the art will recognize additional features and advantages upon reading the following detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The embodiments herein will now be further described in more detail in the following detailed description by reference to the appended drawings illustrating the embodiments and in which: 
         FIG. 1  is a schematic drawing illustrating an example embodiment of a waveguide assembly. 
         FIG. 2  is a schematic drawing illustrating an example embodiment of a waveguide assembly. 
         FIG. 3  is a schematic drawing illustrating an example embodiment of the flange. 
         FIG. 4  is a schematic drawing illustrating an example embodiment of the flange. 
         FIG. 5  is a schematic drawing illustrating an example embodiment of the flange. 
         FIG. 6  is a schematic drawing illustrating an example embodiment of the flange. 
         FIG. 7  is a schematic drawing illustrating an example embodiment of the flange. 
         FIG. 8  is an example illustration of a holey unit cell and corresponding stopband. 
         FIG. 9  is a graph illustrating the effect in the stopband for gap variations. 
         FIG. 10  is a graph illustrating the transmission in a prior art flange and a flange with a glide symmetric pattern. 
         FIG. 11  is a flow chart illustrating embodiments of a method. 
     
    
    
     The drawings are not necessarily to scale and the dimensions of certain features may have been exaggerated for the sake of clarity. Emphasis is instead placed upon illustrating the principle of the embodiments herein. 
     DETAILED DESCRIPTION OF THE INVENTIOIN 
     The embodiments herein relates to a waveguide with an at least partly glide symmetric holey pattern surrounding the waveguide end opening. 
       FIG. 2  illustrates an example embodiment of a waveguide assembly. A waveguide assembly may be described as waveguides connected to each other via flanges. The left part of  FIG. 2  illustrates a waveguide assembly where three waveguides  101   a,    101   b,    101   c  are connected together, and the right part of  FIG. 2  provides a more detailed illustration of some of the flanges comprised in the waveguide assembly.  FIG. 2  illustrates an example where the three waveguides  101   a,    101   b,    101   c  are hollow tubes having a rectangular form, thus the waveguide can be referred to as a “hollow waveguide”. 
     As seen in  FIG. 2 , a first waveguide  101   a  comprises a first flange  103   a  surrounding an end opening  105   a  in one end of the first waveguide  101   a.  A second waveguide  101   b  comprises a second flange  103   b  surrounding an end opening  105   b  in one end of the second waveguide  101   b.  The first waveguide  101   a  is connected to the second waveguide  101   b  by connecting the first flange  103   a  to the second flange  103   b  so that the end openings face each other. Furthermore,  FIG. 2  illustrates that the second waveguide  101   b  comprises a third flange  103   c  surrounding an end opening in the opposite end of the second waveguide  101   b  as compared to the second flange  103   b.  The second waveguide  101   b  may be a DUT. A third waveguide  101   c  comprises a fourth flange  103   d  surrounding and end opening (not shown) of the third waveguide  101   c.  The third waveguide  101   c  is connected to the second waveguide  101   b  by connecting the fourth flange  103   d  to the third flange  103   c.  The end openings  105   a,    105   b  are illustrated as a rectangular opening due to the fact that the waveguides  101   a,    101   b,    101   c  are formed as rectangular tubes. However, any other suitable shape of the waveguide is applicable such as e.g. a circular tube. The end openings  105   a,    105   b  have a shape which corresponds to the shape of the waveguide (i.e., the tube which comprises the waveguide). 
     When the reference number  101  is used without the letters a, b or c, it refers to any of the waveguides in the assembly. When the reference number  103  is used without the letters a, b, c or d, it refers to any of the flanges in any of the waveguides  101 . Similarly, when the reference number  105  is used without the letters a or b, it refers to any of the end openings in any of the waveguides  101 . 
     Considering an example where two waveguides  101  are connected to each other (e.g. the first waveguide  101   a  and the second waveguide  101   b ) in an at least partly glide symmetrical way. This means the holes  110  in the first flange  103   a  are at least partly glide symmetrically positioned with respect to the holes  110  in the second flange  103   b.  The holes  110  in the first flange  103   a  are not necessarily directly placed opposite to the holes  110  in the second flange  103   b  when the flanges  103   a ,  103   b  are connected, but the holes  110  in the first flange  103   a  at least partly overlap with the holes  110  in the second flange  103   b.  In other words, the holes  110  in one flange  103  can glide a certain amount with respect to the holes  110  in the other flange  103  when the flanges  103   a ,  103   b  are connected, e.g., they can glide by up to half a period. The term “at least partly glide symmetric” refers to the fact that the structure may be completely glide symmetric, or quasi glide symmetric. The term “quasi glide symmetric” refers to having a small deviation from the exact glide symmetric structure, for example quasi glide symmetric refers to the case that one flange  103  has moved slightly more than half periodicity. “Quasi periodic structure” refers to the case that the periodicity of the next rows or the dimensions of the holes  110  in next row change slightly. A quasi periodic structure may be described as a structure where the dimensions of the holes  110  changes slightly from flange  103  to flange  103 . A quasi periodic structure is a structure that is ordered but not periodic. Thus, the at least partly glide symmetric structure may be referred to as an “at least partly quasi periodic structure having complementary holes”  110 . 
     Note that the waveguide assembly illustrated in  FIG. 2  which comprises three connected waveguides  101   a,    101   b,    101   c  is only an example. A waveguide assembly can comprise any other suitable number of waveguides from two and upwards. For example, the waveguide assembly may comprise the first and second waveguides  101   a,    101   b  where the first flange  103   a  is arranged to be connected to the second flange  103   b.    
     As seen in the right part of  FIG. 2 , each flange  103  surrounds the end opening  105  of the respective waveguide  101 . The end opening  105  may be located substantially in the center of the flanges  103 . 
     Each flange  103  is provided with at least two holes  110  which surround the respective end opening  105 . The at least two holes  110  are periodically distributed around the respective end opening  105 . Each flange  103  is located around the outer circumference of the end part of the respective waveguide  101 . A hole  110  may also be referred to as a “groove”, “recess”, “aperture”, “opening”, “orifice”, “perforation”or “slit”. The hole has any suitable diameter and depth, and these parameters may be in relation to the frequency band in which the waveguide operates. 
       FIG. 2  illustrates that there may be a gap  112  between the flanges  103  when the flanges  103  are connected to each other. In other examples, there is no gap between the connected flanges  103 . The gap  112  may be of any length, e.g., zero or more. By embedding an end opening  105  with one row of holes  110 , there is no need to worry about the presence of a small gap  112  when screwing the two flanges  103  together. Nevertheless, those of skill in the art will note that the smaller the gap  112 , the wider operating bandwidth of the at least partly glide symmetric holey structure is achieved (see  FIG. 9  which is described below). 
     There can be any number of holes  110  from two and upwards and at any distance from the end opening  105 .  FIG. 3  illustrates an example of a flange  103  having six holes  110 . However, each flange  103  may have any other (even or odd) number of holes  110  greater than two. The holes  110  drawn with continuous lines are the holes  110  located on the flange  103  which is seen in the figure, and the holes  110  drawn with dotted lines are the holes  110  located on the other flange  103 , i.e. the flange  103  on the other waveguide  101  which is not shown in the figure. The continuous and dotted drawn holes also apply to  FIGS. 4-7  described below. The periodicity of the holes  110  may be dependent on the stopband. 
     The left part of  FIG. 3  illustrates an example of the position of the holes  110 , and the right part of  FIG. 3  illustrates how the holes  110  in the two mating flanges  103  are placed relative to each other. The holes  110  in  FIG. 3  are placed around a circle with diameter D of 9 mm. Note that 9 mm is only an example diameter and is for an example frequency of 60 GHz. The diameter can be scaled to any other frequency by scaling the relevant parameters, such as hold diameter, hole depth, periodicity of a unit cell, gap width, and the like. Another example may be in the U band. See also M. Ebrahimpouri, O. Quevedo-Teruel and E. Rajo-Iglesias, “Design guidelines for gap waveguide technology based on glide symmetric holey structures,” in IEEE Microwave and Wireless Component Letters, vol. 27, no. 6, 2017 for additional details regarding the diameter and frequency. The holes  110  can be positioned at any angle from the center, i.e. the end opening  105 .  FIG. 3  illustrates an example where the holes  110  are positioned at an angle of 15° from the end opening  105  and where the angle between two neighboring holes  110  is 60°. Specifically, they can be drilled in symmetric topology so that it is possible to avoid fabricating two different topologies to have complementary holes  110  on different flanges  103 . In this way, both flanges  103  are manufactured identically and when the flanges  103  are joined together the geometry is built-up at least partly glide symmetrically (see the right part of  FIG. 3 ). This fact simplifies the manufacturing process. 
     The holes  110  can be placed in a circular geometry, as exemplified in  FIG. 3 , but generally, along any closed shape surrounding the end opening  105 , e.g., a rectangle, hexagon, or any polygon.  FIG. 4  illustrates an example with N=9 circular holes  110  on each flange  103 , and where the holes  110  are placed in a hexagonal closed shape surrounding the end opening  105 . 
       FIG. 5  illustrates an example where each flange  103  comprises  18  holes  110 .  FIG. 5  also shows an example of the position of the holes  110  on the flanges  103 . The rotation angle (i.e. the rotation angle is the angle between the center of one hole  110  and the center of another hole  110  on the same flange  103 ) and the deviation angle (i.e. the deviation angle is the angle from the center of the flange  103  and the center of a hole  110 ) associated with the holes  110  can be calculated using the following formulas: 
     
       
         
           
             
               Rotation 
               ⁢ 
               
                   
               
               ⁢ 
               angle 
             
             = 
             
               
                 360 
                 ⁢ 
                 ° 
               
               
                 Number 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 holes 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 on 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 each 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 flange 
               
             
           
         
       
       
         
           
             
               Deviation 
               ⁢ 
               
                   
               
               ⁢ 
               angle 
             
             = 
             
               
                 
                   360 
                   ⁢ 
                   ° 
                 
                 
                   Number 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   of 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   holes 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   on 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   each 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   flange 
                 
               
               4 
             
           
         
       
     
     For 8 holes  110  on each flange  103 , the angles may be calculated as follows: 
     
       
         
           
             
               Rotation 
               ⁢ 
               
                   
               
               ⁢ 
               angle 
             
             = 
             
               
                 
                   3 
                   ⁢ 
                   6 
                   ⁢ 
                   
                     0 
                     ° 
                   
                 
                 8 
               
               = 
               
                 4 
                 ⁢ 
                 
                   5 
                   ° 
                 
               
             
           
         
       
       
         
           
             
               Deviation 
               ⁢ 
               
                   
               
               ⁢ 
               angle 
             
             = 
             
               
                 
                   
                     3 
                     ⁢ 
                     6 
                     ⁢ 
                     
                       0 
                       ° 
                     
                   
                   8 
                 
                 4 
               
               = 
               
                 
                   
                     4 
                     ⁢ 
                     
                       5 
                       ° 
                     
                   
                   4 
                 
                 = 
                 
                   11.25 
                   ⁢ 
                   ° 
                 
               
             
           
         
       
     
     For 6 holes  110  on each flange  103 , the angles may be calculated as follows: 
     
       
         
           
             
               Rotation 
               ⁢ 
               
                   
               
               ⁢ 
               angle 
             
             = 
             
               
                 
                   3 
                   ⁢ 
                   6 
                   ⁢ 
                   
                     0 
                     ° 
                   
                 
                 6 
               
               = 
               
                 60 
                 ° 
               
             
           
         
       
       
         
           
             
               Deviation 
               ⁢ 
               
                   
               
               ⁢ 
               angle 
             
             = 
             
               
                 
                   
                     3 
                     ⁢ 
                     6 
                     ⁢ 
                     
                       0 
                       ° 
                     
                   
                   6 
                 
                 4 
               
               = 
               
                 
                   
                     60 
                     ° 
                   
                   4 
                 
                 = 
                 
                   15 
                   ⁢ 
                   ° 
                 
               
             
           
         
       
     
     The holes  110  may have any suitable shape.  FIGS. 3, 4 and 5  illustrate examples with circular holes  110  and  FIG. 6  illustrate an example flange  103 with hexagonal shaped holes  110 . However, the holes  110  may also be triangular, rectangular etc. In  FIG. 6 , the example number of holes  110  is 6. 
     The at least two holes  110  may be distributed in one, two or more rows around the end opening  105 .  FIGS. 3-6  described above illustrates an example where the holes  110  are distributed in one row around the end opening  105 .  FIG. 7  illustrates an example where the holes  110  are distributed in two rows around the end opening  105 . The inner row (the row being closest to the end opening  105 ) comprises 16 holes  110  and the outer row (the row being further away from the end opening  105  compared to the inner row) comprises  19  holes  110 . Note that two rows of holes  110  is only an example, and that a flange  103  may comprise any suitable number of rows of holes  110  and also number of holes  110 . 
     The holes  110  may be provided to each flange  103  using any suitable method such as drilling, molding etc. 
     Each flange  103  may have any suitable shape, for example circular, rectangular, triangular, hexagonal etc. The flanges  103  on each waveguide  101  are preferably of the same shape. For example, the flanges  103  may be a circular disk having at least two holes  110  on each flange  103 . 
     Each flange  103  may be of any suitable material such as metal, copper, aluminum, brass, gold, silver, metallized plastic or any other suitable material having sufficient electrical conductivity. 
     The two waveguides  101  are arranged to be connected to each other by connecting e.g., the first flange  103   a  to the second flanges  103   b , such that the end openings  105   a,    105   b  face each other and such that the holes  110  in the first flange  103   a  are at least partly glide symmetrically positioned with respect to the holes  110  in the second flange  103   b.  The connected first and second flanges  103   a,    103   b  may then be described as mating flanges  103 . 
     The joined flanges  103  having at least two holes  110  that are periodically distributed around the opening may form an EBG structure. 
     The embodiments herein use an at least partly glide symmetric periodic structure composed of for example a holey-unit cell as exemplified in  FIG. 8 . A unit-cell may be described as a part of the structure, that when repeated periodically, builds up the complete waveguide. For example, the unit cell can be one hole in the first flange plus two halves of two different holes in the second flange. The left part of  FIG. 8  illustrates an example of a holey unit cell when a=3.5 mm, 2r=2.8 mm, h=1.5 mm and gap (g) is 0.05 mm. The right part of  FIG. 8  illustrates a graph (i.e., a dispersion diagram) with the stopband corresponding to the holey unit cell in the left part. In particular, the lower and upper bounds of the stop band correspond to the Lower Layer and Upper Layer depicted in the left side of  FIG. 8 , respectively. The x-axis of the graph represents the boundaries of a Brillouin zone and the y-axis of the graph represents the frequency measured in GHz. The X, M, and gamma Γ in the x-axis correspond to the points shown in the holey unit-cell at the left side of  FIG. 8  (X, M, and Γ are corners of a Brillouin zone). As seen in  FIG. 8 , the stopband is between 40 and 77 GHz. The stopband is the band between the dotted lines in  FIG. 8 . The solid lines in  FIG. 8  represent propagating modes (i.e., different orientation of fields), the x-axis is different directions, and it is seen that there exists a frequency band (i.e., the stop band) where no modes can propagate in any direction. As seen, no wave can propagate inside the stop-band. 
     A stopband may be described as a band of frequencies, between specified limits, through which currents are not allowed to pass. 
       FIG. 9  is a graph illustrating the effect in the stopband for different gap size variations. The x-axis of  FIG. 9  represents the gap measured in pm and the y-axis represents the frequency measured in GHz. With the previous example hole dimensions (i.e., the ones seen in  FIG. 8 ), it is possible to achieve a stopband from 40 to 77 GHz where no waves are allowed to propagate within that air gap. 
       FIG. 10  is a graph illustrating a comparison of the transmission in a prior art flange having a smooth surface and a flange with at least partly glide symmetric holes as in the embodiments herein in case of having a gap of 0.05 mm between the first flange and the second flange. The x-axis of  FIG. 10  represents the frequency measured in GHz and the y-axis represents transmission parameter (S 21 ) measured in dB. S 21  represents the power transmitted from one waveguide  101  to the other (i.e., not through the gap between the flanges). The transmission in the prior art (normal) flange is illustrated with a dotted line and the transmission in the flange with the at least partly glide symmetric holes is illustrated with a continuous line. 
     Simulations of the scattering parameters of the at least partly glide symmetric flange design will now be described. The performance of the at least partly glide symmetric flange design has been compared with a prior art rectangular waveguide flange. A gap  112  of 0.05 mm between the two flanges  103  is allowed and it is possible to observe in  FIG. 10  how the mismatch obtained for the prior art flange is avoided when using the at least partly glide symmetric holey flange  103 . The at least partly glide symmetric holey flange  103  creates a smooth transition and all energy between the ports is transmitted without disturbances. Surface roughness caused by manufacturing or assembly tolerances would not affect the performance of the at least partly glide symmetric flange  103  but the operating bandwidth will increase as the gap  112  tends to zero, as it is shown in  FIG. 9 . 
     The method for manufacturing a first waveguide  101   a  according to some embodiments will now be described. The method comprises at least one of the following steps, which steps may as well be carried out in another suitable order than described below: 
     A first flange  103   a  surrounding an end opening  105   a  to the first waveguide  101   a  is provided. The first flange  103   a  comprises at least two holes  110  which are periodically distributed around the end opening  105   a.  The first waveguide  101   a  is arranged to be connected to a second waveguide  101   b  by connecting the first flange  103   a  to a second flange  103   b  of the second waveguide  101   b  such that the end opening  105   a  of the first waveguide  101   a  face an end opening  105   b  of the second waveguide  101   b  and such that the holes  110  in the first flange  103   a  are at least partly glide symmetrically positioned with respect to holes  110  which are periodically distributed around the end opening  105   b  of the second flange  103   b.    
     As shown in  FIG. 2-7 , at least two holes  110  comprised in the first flange  103   a  may constitute a holey and at least partly glide symmetric EBG structure integrated within the first flange  103   a.  The at least two holes  110  in the first flange  103   a  may be placed in a closed shape around the end opening  105   a  of the first flange  103   a.  The at least two holes  110  in the first flange  103   a  may be periodically distributed around the end opening  105   a  of the first flange  103   a  in at least one row. Each of the at least two holes  110  on the first flange  103   a  are at least one of circular, squared or hexagonal shaped. 
     The at least two holes  110  on the first flange  103   a  are periodically distributed around the end opening  105   a  in a circular, a hexagonal or a polygonal form. 
     The first flange  103   a  may be located around an outer circumference of the first waveguide  101   a.    
     The first waveguide  101   a  may be arranged to be connected to a second waveguide  101   b  such that a gap that is either zero or more than zero is located between the first flange  103   a  and the second flange  103   b  when they are connected. 
     The method for manufacturing a waveguide assembly for waveguides  101 , according to some embodiments will now be described with reference to the flowchart depicted in  FIG. 11 . The method comprises at least one of the following steps, which steps may as well be carried out in another suitable order than described below: 
     Step  1101   
     A first waveguide comprising a first flange surrounding an end opening of the first waveguide is provided. 
     Step  1102   
     A second waveguide comprising a second flange surrounding an end opening of the second waveguide is provided. Each flange comprises at least two holes which are periodically distributed around the respective end opening. 
     Step  1103   
     The first and second waveguides  101   a,    101   b  are connected to each other by connecting the first flange  103   a  to the second flange  103   b  such that the end openings  105   a,    105   b  face each other and such that the holes  110  in the first flange  103   a  are at least partly glide symmetrically positioned with respect to the holes  110  in the second flange  103   b.    
     The at least two holes comprised in each flange may constitutes a holey and at least partly glide symmetric EBG structure integrated within each of the first and second flange. The at least two holes in each flange are placed in a closed shape around the respective end opening. The at least two holes in each flange may be periodically distributed around the respective end opening in at least one row. The at least two holes on each flange may be at least one of: circular, squared or hexagonal shaped. The at least two holes on each flange may be periodically distributed around each end opening in a circular, a hexagonal or a polygonal form. 
     The first flange may be located around an outer circumference of the first waveguide and the second flange may be located around an outer circumference of the second waveguide. 
     A gap that is either zero or more than zero may be located between the first flange and the second flange when the first and second flanges are connected. 
     Some embodiments described herein may be summarised in the following manner: A waveguide flange where a holey at least partly glide symmetric EBG structure is integrated within a waveguide flange  103 . Thus, the flange  103  may be referred to as a “holey and at least partly glide symmetric flange”  103 . The holey at least partly glide symmetric flange  103  is placed surrounding the waveguide end opening  105  and significantly reduces the leakage, should there be a gap  112  between the mated flanges  103 . This waveguide  101  is easier to manufacture than the pin surface applied in the pin-flange since it just requires drilling holes which is much faster and easier than milling, casting, moulding, or die-sinking pins. 
     The embodiments herein are not limited to the above described embodiments. Various alternatives, modifications and equivalents may be used. Therefore, the above embodiments should not be taken as limiting the scope of the embodiments, which is defined by the appending claims. A feature from one embodiment may be combined with one or more features of any other embodiment. 
     It should be emphasized that the term “comprises/comprising” when used in this specification is taken to specify the presence of stated features, integers, steps or components, but does not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof. It should also be noted that the words “a” or “an” preceding an element do not exclude the presence of a plurality of such elements. The terms “consisting of” or “consisting essentially of” may be used instead of the term comprising. 
     The term “configured to” used herein may also be referred to as “arranged to”, “adapted to”, “capable of” or “operative to”. 
     It should also be emphasised that the steps of the methods defined in the appended claims may, without departing from the embodiments herein, be performed in another order than the order in which they appear in the claims.