the best modes for practicing the present invention will be described in turn with reference to the accompanying drawings . in the following description , the same reference numerals denote components having substantially the same functions and arrangements , and duplicate explanations will be made only where necessary . an important aspect of a high speed electronic interconnection according to a first embodiment is that the microwave loss is reduced by reducing the effective dielectric constant , resulting in increased bandwidth of the interconnection , thereby reaching a signal speed in the interconnection that approaches closer to the source signal speed . according to a second important aspect of the invention , the technique is cost effective and compatible with standard manufacturing technologies known in the art . in an on - chip interconnection between two or more interconnected electronic elements ( such as transistors , ics , etc . ), an electrical signal at a low speed can be communicated through an electrical signal conductor in form of a wire laid on a dielectric medium . however , for communicating an electrical signal at a high - speed , an electrical signal conductor must be a microstrip line type , or a strip line type transmission line . in the following sections , preferred embodiments of the invention will be disclosed , wherein first method ( s ) to reduce effective dielectric constant will be discussed , and later the method ( s ) as applied to preferred embodiments will be presented . fig8 a , 8 b , and 8 c collectively represent a first embodiment of an interconnection according to the principles of the invention , wherein fig8 a is a top view of the interconnection and fig8 b and 8c are cross - sectional views of the interconnection along a line aa ′ shown in fig8 a . more specifically , fig8 a shows a microstrip line type signal line 140 a for carrying an electrical signal , laid on a dielectric system having a periodic dielectric structure 148 , consisting of an array 150 of dielectric spheres or cylinders ( also referred as a periodic dielectric array in the rest of the application ) with a diameter 2 r ( fig8 c ) and a span a ( fig8 a ), and a second dielectric medium 152 ( fig8 b , 8 c ). the combination of elements described above will be collectively referred as an interconnection system in this application . the values 2 r , a , and an operating frequency are carefully selected , such that the electrical field 154 is localized near the signal line , thereby preventing the electrical field 154 from spreading away from the signal line . the periodic dielectric array effectively reduces the dielectric constant and localizes the electric field near the signal line . as a result the microwave loss is substantially reduced . in other words , as compared to a conventional interconnection shown in the prior art example of fig6 , wherein a signal line is laid on to a uniform layer of a dielectric medium , the signal transmission in the interconnection according to the present invention shown in fig8 a is less dispersive , and thereby a higher bandwidth of the interconnection system is achieved . since the electric field is localized near the signal line less cross talk is expected . as shown in fig8 b and 8c , the dielectric medium underlying the signal line may be chosen to be a uniform layer of a dielectric material 156 ( fig8 b ), or a periodic dielectric array 158 ( fig8 c ). as a design choice , the periodic dielectric array as shown in fig8 a , 8 b , and 8 c , may be an array of air holes or any other material having a lower dielectric constant than the surrounding dielectric media . in the exemplary embodiment , although a single signal line is shown , the present invention will be applicable equally well to other types of signal lines such as , a strip - line type transmission line , single and multi electrodes , and a coplanar waveguide configuration . in fig9 frequency responses of the microstrip line type transmission lines of the example shown in the prior art fig6 and the exemplary embodiment shown in fig8 , respectively , are compared . due to a reduction in the microwave loss , the frequency response of the interconnection system according to the principles of the invention is substantially improved as compared to the prior art mircrostrip line type interconnection . fig1 a , 10 b , 10 c , and 10 d collectively represent a second embodiment of the invention , wherein to avoid repeated explanation , like parts are indicated by like reference numerals as used in fig8 a - 8c . more specifically , fig1 a is a top view of an interconnection and fig1 b , 10 c , and 10 d are the enlarged cross - sectional views of an interconnection system along the line aa ′ shown in fig1 a . in fig1 a , 10 b , 10 c , and 10 d , the microstrip line type of transmission line consisting of signal lines 140 c , 140 d , and 140 e and back - side ground lines 144 c , 144 d , and 144 e , laid on to a periodic dielectric structure 168 consisting of dielectric spheres or cylinders 150 , with diameter 2 r ( fig1 d ) and span a ( fig1 a ), similar to the periodic dielectric array described earlier in reference with fig8 a - c , and a backside slot 164 . according to principles of the invention , the effective dielectric constant ( i . e . microwave index ) is substantially reduced , and the electrical field intensity 170 ( fig1 a ) near the signal lines is increased , and localized . fig1 a and 11b are the enlarged cross - sectional views of an interconnection system , in a third preferred embodiment in accordance to the present invention , wherein like parts are indicated by like reference numerals as used in fig8 and 10 so that a repeated explanation is omitted here . more specifically , fig1 a and 11b , each show a microstrip line type transmission line consisting of a signal line 140 f and a back - side ground line 144 f laid on a periodic dielectric structure 172 a ( for fig1 a ) and 172b ( for fig1 b ), respectively , consisting of spheres or cylinders 174 with diameter d and span b , similar to the periodic dielectric array described earlier in reference with fig8 and 10 . each cylinder constitutes a cell 174 ( to be referred as a circular cell hereinafter . each circular cell 174 is arranged in a triangular array 176 , or a square array 178 , shown in insets 180 and 182 of fig1 a and 11b , respectively . the arrangement of the cells forms a lattice . according to the principles of the invention , the circular cells 174 formed inside a dielectric material having a higher dielectric constant , contains air which has a lower dielectric constant . the electric field from the signal line passes through the air cell or air hole 174 , thereby reducing the effective dielectric constant and increasing the bandwidth of the interconnection . the parameters such as diameter d and span b are carefully selected , such that the electrical field distribution away from the signal line is optimized to further increase the interconnection bandwidth . those skilled in the art will appreciate that the circular cells 174 arranged in triangular or square lattice structure shown in the preferred embodiment of fig1 a and 11b , may be replaced by elliptic cells arranged in triangular or square lattice structure without deviating from the principles of the invention . advantageously , the geometrical parameters of the elliptical cells ( lengths of the major and minor axes ) may be additionally selected to further control the proportion of the electrical field passing through the air and through the dielectric material surrounding the elliptical cells . in this case also , the effective dielectric constant (∈ eff ) of the interconnection system is reduced . this adds many features in the interconnection system such as_variable phase velocity ( which is function of ∈ eff ) and variable bandwidth of the interconnection . additionally , it helps in adjusting signal skews within the single signal line of the interconnection system . according to the preferred embodiment , ideally , the electrical signal speed inside the interconnection system can approach closer to the speed of light , provided other losses related to the signal line structure , such as signal line electrode parameters ( resistance , capacitance ) are neglected . the periodic dielectric structure described in the preferred embodiments may also include a photonic crystal structure ( 2d and 3d ) within the periodic dielectric structure and a line defect for the signal line layout . a band - gap is formed due to cylinders of a lower dielectric constant material formed inside a substrate having a relatively higher dielectric constant . fig1 is the cross - sectional view of a periodic dielectric structure comprising 2d photonic crystals for a high - speed interconnection system in a fourth preferred embodiment according to the present invention . the periodic dielectric structure comprises a photonic crystal 184 , consisting of air spheres or cylinders 186 with diameter d ′, height h , and span b ′, in a dielectric substrate , and a line defect 188 on which a signal line is laid . in this structure , the electrical field created from the high - speed signal flows through the signal line ( not shown ) is confined and controlled in the signal - line direction denoted by arrows , by the 2d photonic band gap effect . the electrical field may be completely localized in the air holes along the direction of the signal flow , resulting in a low effective dielectric constant ( low microwave loss ), thereby increasing the bandwidth of the interconnection system . by changing the shape of the cylinder , for example to an ellipse , and its size and span , the electrical field may be localized in a region having a relatively higher effective dielectric constant ( and higher microwave loss ) and the bandwidth of the interconnection reduces . this allows the interconnection systems , to have different bandwidths and the signals therein , to be of a low - speed or a high - speed when required . according to the preferred embodiment , the interconnection can ideally be designed to have a bandwidth substantially close to the bandwidth of an optical fiber so that it can carry the high - speed electronics signal ( even at terahertz frequency ). in the example , the periodic dielectric structure is shown to be comprising a 2d photonic crystal . the present invention also includes the 3d photonic crystal for high - speed interconnection systems , applicable in the on - chip and off - chip interconnections . this also includes the means , such as the connector and cable , used for high - speed connection of electronic elements including transistors . the interconnection systems described in the preferred embodiments , can be fabricated as follows : first , a layer of cylindrical holes is made in a dielectric substrate using one of many methods known in the art . such methods may for example include ic fabrication technology for on - chip interconnections and pcb technology for off - chip interconnections . this is followed by the formation of a signal line . the holes can be made underneath the signal line or the area underneath the signal line may be masked while opening the holes outside the signal line . alternatively , a material with a lower dielectric constant can fill up the holes rather than the dielectric substrate material . fig1 a , 13 b , 13 c , and 13 d are the cross - sectional views of portions of an interconnection system , in a fifth preferred embodiment in accordance with the present invention , wherein like parts are indicated by like reference numerals as used in fig1 and 12 , so that repeated explanation is omitted here . the interconnection system comprising a microstrip line type signal line 140 f and a ground line 144 f as a part of the interconnection is shown therein . in fig1 a and 13b , a periodic dielectric structure comprises single layers of periodic structure 190 and 192 , as described in fig1 . the difference between fig1 a and 13b is that the air holes under the electrical signal line are absent in fig1 a , and the air holes are present in fig1 b . the inset 194 of fig1 shows an exemplary schematic of a periodic dielectric structure with circular cells arranged in a triangular - lattice structure as shown in fig1 c and 13d , periodic dielectric structures 196 and 198 shown therein comprise two layers of dielectrics materials : ( a ) one having a periodic dielectric structure , and ( b ) the other having a uniform dielectric constant located under the periodic dielectric structure . the periodic dielectric structures , mentioned in fig1 a , 13 b , 13 c , and 13 d are substantially similar to those explained in fig1 and 12 , so that related explanation is omitted here . broadband interconnections may be designed by using one or more dielectric layer combinations of photonic crystals and homogeneous dielectric layers . for simplicity , we have shown two layers , however , the present invention also includes interconnection systems with more than two layers having the periodic dielectric structure wherein having a periodic dielectric structure in the inner most dielectric layer contributes to the broadband of the interconnection system the most . in the preferred embodiments , described above in conjunction with fig8 a - 8c , 9 , 10 a - 10 d , 11 a - 11 d , 12 and 13 a - 13 d , single microstrip line type signal lines in different configurations are shown to explain the object of the invention . those skilled in the art will appreciate that these embodiments are only exemplary , and do not exclude other types of transmission lines known in the art , such as single or multiple signal lines in strip - line and coplanar waveguide configurations . advantageously , signal lines in these cases could be single or differential lines . in the preferred embodiments described earlier , such dielectric materials include a wide range of materials known to those skilled in the art , and sold under different trade names . for example , ceramic materials such as duroid ™, fr4 , aln , al 2 o 3 , mullite ( 3al 2 o 3 : 2sio 2 ), sio 2 , silicon nitride , silicon carbide , silicon - oxy - nitride , beo , cordierite ( magnesium alumina silicate ), bn , glass ( with different compositions ), epoxy glass , cao , mno , zro2 , pbo , alkali - halide ( e . g . nabr , nacl ) bn , beo , etc ., and different types of polyimides and benzocyclobutenes ( bcbs ) having desirable dielectric properties are equally applicable . other polymeric dielectric materials also include , but are not limited to , teflon ™, liquid crystal polymer , epoxy , parylene , silicone - polyimide , silicone - gel , fluorinated ethylene propylene copolymer . it also includes elastomers ( e . g . silicone elastomer ), monomers , and gels . dielectric materials , which can be made using high temperature ceramics processing or ic fabrication processing , also are included in this category . all standard polymers can be available from the standard manufacturers for example , dupont ™, hitachi - chemical ™, mitsui ™, and mitsubishi - chemical industries ™. the liquid crystal polymer is marketed by gore - tex ™ of japan . in reference with the preferred embodiments shown in fig8 a - 8c , 10 a - 10 d , 11 a - 11 d , 12 and 13 a - 13 d , the periodic dielectric structures comprising air holes or arrays of spheres or cylinders in the dielectric substrate are described . the spheres in these examples may be made from any dielectric material having a lower dielectric constant than the dielectric substrate . alternatively , the air holes may be filled with a material having a lower dielectric constant than the dielectric constant of the substrate material . alternatively , in the preferred embodiment , the air holes can be filled fully or coated with liquid crystal . in this case the electrical field changes the orientation of the liquid crystals and controls the effective dielectric constant of the periodic dielectric structures . in the preferred embodiments as explained in fig1 a , 10 b , 10 c , and 10 d , a dielectric material having a dielectric constant lower than the dielectric substrate or a liquid crystal polymer material may be filled in the backside slotted portion to effectively provide tunability to the effective dielectric constant of the periodic dielectric structures . according to the present invention , preferred embodiments described earlier may be implemented in applications , including but not limited to ( a ) on - chip interconnections , for example , for connecting two or more electronic devices and / or connecting electrical and optical devices , ( b ) off - chip interconnections , for example , connecting two or more electronics chips on a circuit board , ( c ) high - speed chip ( die ) packaging , ( d ) high - speed electrical cable for connecting multiple electrical modules for example , board - to - board interconnection , rack - to - rack interconnection , etc ., and ( e ) high - speed connectors , used as interface means to connect high - speed electronics elements . some of the different applications of the exemplary interconnection system and their fabrication method ( s ) are described in the following sections . these examples are only representative and are not limited to the specific description provided . fig1 a shows a cross - sectional view of a portion of an on - chip interconnection system in a sixth preferred embodiment of the present invention , wherein like parts are indicated by like reference numerals , so that a repeated explanation is omitted here . fig1 b is a cross - sectional view along the line aa ′ shown in fig1 a . in this example a mos ( metal - oxide semiconductor ) device 224 ( fig1 a ) constructed on a semiconductor substrate 226 ( e . g . silicon , fig1 a ) is connected with other electronic devices ( not shown ) by a signal line 228 a ( fig1 a ). a plurality of other electronic devices ( not shown ) on the semiconductor substrate 226 ( fig1 a ) can be interconnected by signal lines 228 a ( fig1 a ) and 228b ( fig1 b ). the signal lines 228 a ( fig1 a ) and 228b ( fig1 b ) are made on the periodic dielectric structure 230 ( fig1 a ) comprising an array of air holes ( spheres or cylinders ) 232 ( fig1 a ), with predetermined diameter and span , into a dielectric layer 234 ( fig1 a ). the portion of the dielectric layer 236 a ( fig1 a ) and 236b ( fig1 b ) over which the signal line 228 a ( fig1 a ) and 228b ( fig1 a ) is laid is uniform ( without the air holes ). a layer ( not shown ) of the dielectric material used to construct the periodic dielectric structure 230 ( fig1 a ) covers the top of the interconnection . in the exemplary periodic dielectric structure 230 shown in fig1 a and 14b , the dielectric layer 234 ( fig1 a ) is deposited using a standard ic fabrication process including , chemical vapor deposition ( cvd ), sputtering , or evaporation . after making patterns using any standard photolithography technology , the holes 232 ( fig1 a ) are formed into the dielectric layer 234 ( fig1 a ) using a dry - etching ( or wet - etching ) technology , such as reactive ion beam etching ( ribe ), reactive ion etching ( rie ), milling , etc . subsequent patterning and metallization using a lift - off technique is used to make the signal lines which connect the electronic devices on - chip . fig1 a shows a cross - sectional view of a portion of the on - chip interconnection system in a seventh preferred embodiment of the present invention , wherein like parts are indicated by like reference numerals used in fig1 , so a repeated explanation is omitted here . fig1 b is a cross - section view along the line aa ′ shown in fig1 a . in this exemplary embodiment , a mos ( metal - oxide semiconductor )- device 224 ( fig1 a ) on a semiconductor substrate 226 ( e . g . silicon fig1 a ) is connected to another electronic device ( not shown ) by signal line 238 a ( fig1 a ). a plurality of other electronic devices on semiconductor substrate 226 ( fig1 a ) can be interconnected by signal lines 238 a ( fig1 a ) and 238b ( fig1 b ). the signal line 228 a ( fig1 a ) and also 228 b ( fig1 b ) is laid on the periodic dielectric structure 230 ( fig1 a ) comprising an array of air hole ( spheres or cylinder ) 232 with predetermined diameter and span in a dielectric layer 234 ( fig1 a ). the difference between fig1 and fig1 is that the uniform layers of dielectric material 236 a ( and 236 b ) in fig1 a ( and fig1 b ) under the signal lines ( for example 228 a and 228 b in fig1 a and 14b ) is replaced by the periodic dielectric structure 238 a and 238 b in fig1 a and 15b ( i . e . air hole array ). a layer ( not shown ) of the dielectric material used to construct the periodic dielectric structure 230 ( fig1 a ) covers the top of the interconnection . the periodic dielectric structure and signal lines are constructed following substantially the same method as described earlier in reference with fig1 a and 14b . cross - sectional views showing a portion of an on - chip interconnection in fig1 a , 16 b , and 16 c outline a preferred fabrication processes in accordance to the present invention , wherein like parts are indicated by like reference numerals as used in fig1 and 15 , so that repeated explanation is omitted here . for simplicity , a single layer and a single line interconnection is shown . substantially similar techniques may be used for fabricating large scale on - chip interconnection systems as well . following the oxide deposition and subsequent dry - etching steps using ic fabrication technologies such as rie , ribe , or ion - milling etc . air holes 232 ( fig1 a ) are opened into a dielectric layer 234 ( fig1 a ), except in a portion 236 c ( fig1 a ) over which a signal line 228 c ( fig1 c ) will be laid in a later step . the air holes are filled with a polymer material 240 ( fig1 b 1 . after having a pattern for opening 242 ( fig1 b ) for the signal line , metallization for 228 c ( fig1 c ) is formed using a lift - off technique . thus , the dielectric portion 236 c ( fig1 a - 16c ) over which signal line 228 c ( fig1 c ) is laid on is kept without the air holes . according to other preferred embodiments , on - chip interconnection systems may be constructed using one or more periodic dielectric structures ( for reducing the microwave loss ), as explained earlier in reference with fig8 a - 8c , 9 , 10 a - 10 d , 11 a - 11 b , 12 , and 13 a - 13 d . for example , air hole arrays can be used in the periodic dielectric structure . alternatively , the air holes may be filled with a low dielectric constant material or a liquid crystal polymer . for example such low dielectric constant materials include but are not limited to , vapor deposited silicon oxide , silicon nitride , silicon oxynitride , silicon carbide etc . microporous silicon can also be used as dielectric layer 234 . other dielectric materials may also include but are not limited to , vapor deposited or spin - coated polymers such as benzocyclobutene , acrylate based polymer , elastomer or monomer etc . in the preferred embodiments , described in reference with fig1 a - b , 15 a - b and 16 a - 16 c , microstrip line type transmission line is considered for the signal line , however , the principles outline in these examples are applicable equally to other types of signal lines including strip - line , coplanar waveguide line , single or multiple signal lines ( as single or differential ). the signal lines may be additionally covered on top with a layer of ( not shown ) of the same or different dielectric material as the ones used in the periodic dielectric structure . the principles of the on - chip interconnection system described earlier in reference with fig8 a - 8c , 9 , 10 a - 10 d , 11 a - 11 b , 12 , and 13 a - 13 d , are also applicable for multiple chip interconnections on a circuit board ( off - chip ). the circuit board may be made from fr4 material or any other dielectric material as mentioned previously . fig1 shows a flow - chart of a printed circuit board ( pcb ) fabrication process for an off - chip interconnections system in an eighth embodiment in accordance with the principles of the invention , wherein like parts are indicated by like numerals , so that repeated explanation is omitted here . a dielectric sheet ( not shown ) is made using a standard pcb technology , for example a slurry casting process in which the slurry is cast into about 200 μm to 500 μm thick ceramic sheets by a slip cast process . to make the preorder dielectric structure 244 , arrays of air holes are made into the dielectric substrate using processes such as laser drilling , dry - etching , or wet - etching ( following patterning for etching ). via holes are formed through the dielectric sheet with air holes 244 by a punching machine with punches and dies . for example , ceramic sheet 244 may have more than 10 , 000 via holes in a 250 mm square area . a low resistivity conductor paste is applied onto the punch sheet . in this step , via holes are filled with the paste to form the contacts between signal lines to be formed later . as the dielectric system have air holes , additional processes may be necessary to fill the air holes and via holes which are then followed by wet etching to take the excess filler out . the low resistivity conductor material may be the one selected from a group consisting of silver - palladium , gold , molybdenum , and tungsten refractory material . the sheets are then sintered at high temperature , which results in low electrical resistivity . metallization sheet 248 is made using a conventional pcb technology . two or more of such metallized sheets 248 are precisely stacked in a pressing die in sequence by a stacking machine . these sheets 250 are laminated together by a hot press . density heterogeneities in the laminated samples influence any shrinkage in the sintered substrate . therefore , this lamination process is homogenously carried out by means of a correct dimensional die and punch with flat surfaces . burn out and sintering processes for the multilayered pcb board 252 may be necessary after lamination at the temperature suitable to ceramic material used as the sheet . fig1 a , 18 b , and 18 c are the cross - sectional views of two layers of ceramic sheets having the periodic dielectric structure described earlier in reference with fig8 a - 8c , 9 , 10 a - 10 d , 11 a - 11 b , 12 , and 13 a - 13 d , in a ninth embodiment , wherein the like parts are indicated by the like numerals so that repeated explanations are omitted here . the metallization , stacking , and lamination are carried out using the steps described in reference with fig1 . fig1 a is a top view and fig1 b and 19c are cross - sectional views along the lines aa ′ and bb ′, respectively , shown in fig1 a in a tenth preferred embodiment , wherein like parts are indicated by like numerals , so that similar explanations are omitted here . as an example , an interconnection between two chips , a cpu processor 120 and a memory device 130 , is shown . for simplicity , only enlarged portions of the cross - sectional views of high speed chips ( e . g . the processor and the memory ) interconnection is shown . complete pcb with lower speed chips interconnection is not shown . shown in this example is a high speed signal line 254 connected on the top layer of the pcb whereas a low speed signal line ( not shown ) may be connected at the lower layer of the pcb . this arrangement will reduce any possibility of discontinuities , which may arise at the via holes . a high interconnection bandwidth is achieved using the technique described previously thereby individual signal speed of the chips 120 and 130 are preserved . in the preferred embodiment shown in fig1 a , 19 b , and 19 c , as a design choice , either the whole portion of the pcb comprises the periodic dielectric structure or only the portion where the high speed chips are connected , has the periodic dielectric structure , whereas the areas of the pcb where low speed chips are connected has a material having a uniform dielectric constant . fig2 a is a top view and fig2 b and 20c are enlarged cross - sectional views along the lines aa ′ and bb ′ shown in fig2 a , respectively , in an eleventh preferred embodiment of the invention , wherein like parts are indicated by like numerals so that similar explanations are omitted here . in this example , interconnection between two chips is shown wherein high - speed chips are interconnected on a separate board 256 comprising a periodic dielectric structure . in this exemplary embodiment , a circuit board with the periodic dielectric structure fabricated according to the process described earlier in reference with fig1 , is used to connect a processor and a memory device . each board has pins 258 ( fig2 c ) connected on the outside of the pcb board 256 which is mounted on a second conventional pcb board for ground / power lines and other low speed connections . the off - chip interconnection system described earlier may advantageously combine one or more periodic dielectric structures described in fig8 a - 8c , 9 , 10 a - 10 d , 11 a - 11 b , 12 , and 13 a - 13 d for reducing the microwave loss . for example , air hole arrays in the periodic dielectric structures may be used without , or with a low dielectric constant material or a liquid crystal polymer . the low dielectric constant materials may include ceramic materials such as duroid , fr4 , aln , al 2 o 3 , mullite ( 3al 2 o 3 : 2sio 2 ), sic , sio 2 , silicon nitride , silicon - oxy - nitride , beo , cordierite ( magnesium alumina silicate ), bn , glass ( with different compositions ), epoxy glass , cao , mno , zro2 , pbo , alkali - halide ( e . g . nabr , nacl ) etc .) etc . other materials that are used to fill the air holes in a periodic dielectric structures include polyimides and benzocyclobutenes ( bcbs ) having desired dielectric properties . polymer dielectric materials also include , but are not limited to , teflon , liquid crystal polymer , epoxy , parylene , silicone - polyimide , silicone - gel , and fluorinated ethylene propylene copolymer . it also includes materials of elastomers ( e . g . silicone elastomer ), monomers , and gels . all polymer materials listed here are available from the manufacturers known to those skilled in the art , for example , dupont , hitachi - chemical , mitsui , mitsubishi - chemical industries . liquid crystal polymer is marketed by goretex , japan . in the preferred embodiments described earlier in reference with fig1 , 18 a - 18 c , 19 a - 19 c , 20 a - 20 c , the signal lines shown therein are microstrip line type transmission lines . however , the principles of the present invention are applicable to other types of transmission lines such as a strip line type transmission line , or a coplanar waveguide line having a single or multiple signal lines ( as single or differential ). a second layer ( not shown ) of a dielectric material using either same dielectric material as the one used in the periodic dielectric structure , or a different dielectric material , may additionally be used on top of the signal lines . the backside slot of an off - chip high - speed interconnection on a pcb , may additionally have a single layer , or multiple layers of one or more dielectric material including a single or multilayered periodic dielectric structure , as shown in fig1 a - d . the principles of this invention described in reference with fig8 a - 8c , 10 a - 10 d , and 13 a - 13 d are also applicable in designing and constructing high speed connectors and cables for interfacing / transmitting multigigahertz signals . reducing the microwave loss by implementing the periodic dielectric structure in the connector or in the backside slots increases the bandwidth of the connectors and cables . the design may be further extended to single or differential connectors and cables . according to techniques described in reference with fig8 a - 8c , 10 a - 10 d , and 13 a - 13 d , high - speed chip packaging can be designed . reducing the microwave loss by implementing the periodic dielectric structure described previously increases the bandwidth of the interconnection that connects the chip to its package . single or differential pair lines can be designed using the periodic dielectric structure having the lower dielectric loss and dielectric constant . according to the principles of the invention the high - speed interconnection system may be designed , such that high - speed signals flowing through the interconnection are made to flow some portion into the high dielectric constant region and some portion flow through the lower dielectric constant region of the interconnection , for example into air , resulting in a significantly higher interconnection bandwidth . several preferred embodiments for high - speed on - chip and off - chip interconnection systems are described to merely illustrate the principles of the invention . more specifically , the interconnection systems described in the exemplary embodiments comprise a microstrip line type transmission lines laid on a periodic dielectric structure . however , strip - line type and coplanar waveguide type transmission lines in single or multiple signal lines ( including differential line ) configuration are included within the scope of the invention . the periodic dielectric structure comprises arrays of spherical or cylindrical air holes , or cells in a dielectric material substrate . the shape of each cell could be any type such as square , or any polynomial shape , and may optionally be filled with a second dielectric material having lower dielectric constant than the dielectric substrate . the effective dielectric constant and dielectric loss tangent of periodic dielectric structure are lower as compared to a uniform dielectric material . therefore microwave loss of the interconnection system is substantially reduced , resulting in higher bandwidth of the interconnection system . in some other preferred embodiments described in reference with fig1 a - 13d , the periodic dielectric structure may be based on a 2 - d or a 3 - d photonic or an crystal . alternatively , the periodic dielectric structure could be based on a fully photonic crystal ( where full photonic band - gap effect may be used ), or a quasi - photonic crystal . in the preferred embodiments described , an electrical signal is considered in the signal line of the interconnection system . the interconnections system with certain modification can also be used for controlling and transmitting optical signals , electrical signals , or a combination of both . the present invention has been described by way of its embodiments . however , those skilled in the art while practicing the invention may affect various changes and modifications that are within the scope of the present invention . therefore , it must be understood that such changes and modifications are included without departing from the scope and spirit of the invention . the present invention will find application in high - speed on - chip and off - chip interconnections , where signal speeds of 5 gb / s and higher are necessary . according to the principles of the invention using conventional materials , the signal speed in the interconnections can ideally be made substantially equal to the speed of light for no - loss transmission lines . the present invention can also be implemented in the high - speed , single or multiple signal connectors , and high - speed cables ( not shown ). applications of the invention also include , on - chip interconnections where high - speed electronic chips or electronic chips with optical chips need to be connected . as the bandwidth of the interconnection system can ideally be made close to the bandwidth of optical fiber , future monolithic ( and also hybrid in the near future ) integration of electronic and optical chips can also be realized without significantly sacrificing the signal speed within the chip . the application of the invention may be extended to include high speed multichip module interconnection , 3 - d chip or memory interconnection , high speed parallel system for computer animation and graphics for high speed 2 - d or 3 - d video transmission , high bandwidth image display , and high speed routers , where high speed electronic switches ( or ic ) need to be interconnected . other applications may include high speed ( 5 gb / s and higher speed ) connectors and cables for high speed board - to - board , rack - to - rack interconnection , and single or multiple high - density signal connections . it will be understood by those skilled in the art that the foregoing preferred embodiments in the specification are merely illustrative examples to describe the principles of this invention , and that various modifications can be made by those skilled in the art without departing from the scope and spirit of the invention . although the invention has been described with respect to specific embodiments for complete and clear disclosure , the appended claims are not to be thus limited but are to be construed as embodying all modifications and alternative constructions that may occurred to one skilled in the art which fairly fall within the basic teaching set forth here .