fig2 shows the cross section of an optical fiber 1 of a first embodiment of the present invention , in which a plurality of holes 3 , which are sub medium regions , are arranged in silica glass 2 , which is a main medium . the cross section has an inner region 11 and an outer region 12 surrounding the inner region . the arrangement of the holes is substantially a hexagonal lattice . in the outer region , the centers of the holes 32 substantially coincide with the outer lattice points 42 , which are a part of the lattice points 4 of a hexagonal lattice and are located in the outer region . on the other hand , in the inner region , the centers of the holes 31 are apart from the inner lattice points 41 by approximately 0 . 1 lattice period outward . the inner lattice points are a part of the lattice points 4 of the hexagonal lattice and are located in the inner region . the diameters of the holes 31 and 32 are substantially uniform in the cross section . for each lattice cell of the lattice point 41 or 42 , a single hole 31 or 32 has its center in the cell . in describing the present invention , the hole located in a lattice cell of a lattice point is called the hole corresponding to the lattice point . the outer region is further surrounded by a jacket region 13 composed of silica glass . although the jacket region is not essential for guidance of lightwave in the core of the optical fiber , it has effects to improve the mechanical strength of the optical fiber and to reduce microbending loss , which is one of the causes of transmission loss . because of the arrangement of the holes described above , the area of the main medium region 21 between the holes 31 in the inner region 11 becomes larger than that of the main medium region 22 between the holes 32 in the outer region 12 . as a result , the inner region has a higher average refractive index than that of the outer region , and it becomes possible to localize a lightwave in the main medium region 21 in the inner region 11 by total reflection and guide it over the optical fiber . investigation of optical characteristics has been done on three structures ha8 , ha7 and ha6 of the present invention and three structures hb8 , hb7 and hb6 of the prior art . relative hole diameters of these structures are given in the following table . fig3 - 5 show various fiber characteristics for each of the listed fibers . fig3 shows the chromatic dispersion at 1550 nm wavelength as a function of the hole diameter . as shown in the figure , the increase in the relative hole diameter results in an increase in the hole diameter below which zero or negative dispersion can be obtained . the hole diameter below which zero or negative dispersion can be obtained is larger for the fibers of the present invention than in the prior art fibers having the same relative hole diameters . fig4 shows the chromatic dispersion slope at 1550 nm wavelength as a function of the hole diameter . as shown in the figure , the increase in the relative hole diameter results in an increase in the hole diameter below which zero or negative dispersion slope can be obtained . the hole diameter below which zero or negative dispersion slope can be obtained is larger for the fibers of the present invention than in the prior art fibers having the same relative hole diameters . fig5 shows the effective core area at 1550 nm wavelength as a function of the hole diameter . as shown in the figure , the increase in the relative hole diameter results in an increase in the hole diameter below which small ( less than 5 μm 2 ) effective core area can be obtained . the hole diameter below which small ( less than 5 μm 2 ) effective core area can be obtained is larger for the fibers of the present invention than in the prior art fibers having the same relative hole diameters . these graphs demonstrate advantages obtained with fibers of the present invention . it is also preferable to add dopants such as germanium and fluorine to the main medium in the main medium region 21 in the inner region 11 , and decrease the viscosity therein . as a result , it becomes possible to reduce the concentration of the drawing tension to the main medium region in the inner region , in which a guided lightwave is to be localized , and reduce excess transmission loss due to residual tension . it is also preferable to add 1 - 35 mol % of germanium to the main medium in the main medium region 21 in the inner region 11 , and form a fiber grating by varying the refractive index along the fiber length by exposing the optical fiber to uv radiation . as a result , it becomes possible to realize a wavelength - selective transmission and a wavelength - selective directional coupler . it is also preferable to vary the cross - sectional structure along the fiber length . as a result , it becomes possible to change chromatic dispersion along the fiber length and form a dispersion - managed transmission line . it is also preferable to form a length of section in which no holes are included . by providing such sections in the fiber ends , it becomes possible to prevent the entrance of contaminants into the holes . it is also preferable to employ compound glass or polymer as main medium , or to fill the holes with gases or metals having optical amplifying properties . as a result , it becomes possible to enhance the efficiency of nonlinear optical effects , and / or to realize an optical amplifying function . fig6 shows the cross section of an optical fiber 1 a of a second embodiment of the present invention . in this structure , a plurality of holes 3 a are arranged in silica glass 2 a , and the holes 32 a in the outer region 12 a are arranged so that there centers coincide with respective lattice points 42 a , which are a part of the lattice points 4 a of a hexagonal lattice and located in the outer region , and consequently the arrangement possesses a two - dimensional translational symmetry . other media having appropriate refractive indices may be used in lieu of holes . because of the two - dimensional translational symmetry , it is possible to localize a lightwave in the inner region 11 a by bragg reflection and guide it over the fiber . since the arrangement of the holes 32 a is periodical in the outer region 12 a , the outer region 12 a can reflect a lightwave belonging to a certain range of frequencies and propagation constant by bragg reflection . although such a lightwave cannot propagate in the outer region 12 a , since the structural periodicity is broken in the inner region 11 a , it localizes and propagates in the inner region 11 a . a waveguiding mechanism known as guidance by bragg reflection , or guidance by photonic bandgap , is described in stig e . barkou et al ., ofc &# 39 ; 99 fg5 , and j . a . west et al ., ecoc &# 39 ; 01 th . a . 2 . 2 . however , these prior art disclosures do not recognize that it is possible to break the structural periodicity by offsetting the holes from the corresponding lattice points . as a result , although a dispersion with a positive dispersion slope was disclosed by j . a . west , a dispersion with a negative dispersion slope has not been known . in the present invention , a dispersion with a negative dispersion slope is realized by forming a region in which a lightwave is guided by offsetting the holes from the corresponding lattice points . fig7 shows the dispersion and mode field diameter ( mfd ) of the optical fiber 1 a shown in fig6 . in this example , the pitch of the hexagonal lattice is 1 . 68 μm , the hole diameter 0 . 84 μm . the holes 35 a in the inner region 11 a is located 0 . 15 lattice period outward from the inner lattice points 41 a . the hole 31 a at the center of the inner region 11 a is located on the inner lattice point 41 a . as in this example , it is also preferable to provide in the inner region holes having centers that are located apart from the corresponding lattice points in addition to holes whose centers are located on the corresponding lattice points . as shown in fig7 , the lightwave from 1540 nm wavelength to 1570 nm is localized in the inner region 11 a and has a small mode field diameter ( mfd ). in addition , the dispersion slope is negative in this wavelength range , which is favorable for application to compensation of dispersion with a positive slope . it is also possible to use the optical fiber 1 a as a band - pass filter because bragg reflection occurs in a finite frequency range and hence a wavelength - dependent transmission can be realized . fig8 shows the cross section of an optical fiber 1 c of a third embodiment of the invention . in the optical fiber 1 c , a plurality of holes 3 c are arranged in silica glass 2 c . the cross section has an inner region 11 c and an outer region 12 c surrounding the inner region . in this embodiment , the arrangement of the holes is substantially a square lattice . in the outer region 12 c , the centers of holes 32 c are located at the outer lattice points 42 c , which are a part of lattice points 4 c of the square lattice and are located in the outer region 12 c . on the other hand , in the inner region 11 c , the centers of holes 31 c are located apart from the inner lattice points 41 c by approximately 0 . 1 lattice period outward . the inner lattice points 41 c are a part of lattice points 4 c of square lattice and are located in the inner region 11 c . for each lattice cell of the lattice point 41 c or 42 c , a single hole 31 c or 32 c has its center in the cell . the outer region 12 c is further surrounded by a jacket region 13 c . although the jacket region 13 c is not essential for waveguiding , it has effects to improve the mechanical strength of the optical fiber 1 c and to reduce microbending loss , which is a cause of transmission loss . because of the arrangement of the holes described above , the area of the main medium region 21 c between the holes 31 c in the inner region 11 c is larger than that of the main medium region 22 c between the holes 32 c in the outer region 12 c . as a result , the inner region has a higher average refractive index than that of the outer region , and it becomes possible to localize a lightwave in the main medium region 21 c in the inner region 11 c by total reflection and guide it over the optical fiber . an investigation has been made comparing optical characteristics of fibers having structures such as illustrated in fig8 with microstructure fibers having holes whose centers substantially coincide with all lattice points a square lattice but lack a hole in the center of the fiber , thereby being provided with a higher average refractive index in the center than that of the surrounding region . relative hole diameters are given in the following table , wherein structures ra8 , ra7 and ra6 represent fiber structures of the present invention as illustrated in fig8 and the structures rb8 , rb7 and rb6 have no holes offset from the lattice . fig9 - 11 show various fiber characteristics for each of the listed fibers . fig9 shows the chromatic dispersion at 1550 nm wavelength as a function of the hole diameter . as shown in the figure , the increase in the relative hole diameter results in an increase in the hole diameter below which zero or negative dispersion can be obtained . the hole diameter below which zero or negative dispersion can be obtained is larger for the fibers of the present invention than in the other fibers having the same relative hole diameter . fig1 shows the chromatic dispersion slope at 1550 nm wavelength as a function of the hole diameter . as shown in the figure , the increase in the relative hole diameter results in an increase in the hole diameter below which zero or negative dispersion slope can be obtained . the hole diameter below which zero or negative dispersion slope can be obtained is larger for the fibers of the present invention than in the other fibers having the same relative hole diameter . fig1 shows the effective core area at 1550 nm wavelength as a function of the hole diameter . as shown in the figure , the increase in the relative hole diameter results in an increase in the hole diameter below which small ( less than 5 or 6 μm 2 ) effective core area can be obtained . the hole diameter below which small ( less than 5 or 6 μm 2 ) effective core area can be obtained is larger for the fibers of the present invention than in the other fibers that have the same relative hole diameters . these graphs demonstrate advantages obtained with fibers of the present invention . the optical fibers of the embodiments of the invention described above can be fabricated as illustrated in fig1 . first , a preform with a column shape and made of silica glass is fabricated by well - known methods such as vad method , mcvd method , and ovd method . the silica glass for the preform can be free from impurities , or can include dopants such as germanium , fluorine , chlorine , boron , aluminum , phosphorus , rare earth elements , and transition metals . by appropriately choosing the kind and concentration of the dopants , it is possible to enhance the efficiency of nonlinear optical effects or to realize optical amplifying characteristics . second , a plurality of holes 64 extending along the preform length are formed by a boring means 63 in the preform 61 , which is secured by grabbing means 62 . the arrangement of the holes should be made proportional to that of the holes in the fiber to be made , such as those in fig2 , 6 and 8 . it is preferable that the tip 65 of the boring means 63 is made of an alloy including diamond particles or of metal with a surface equipped with diamond particles . it is also possible to enhance the efficiency of boring holes by applying an ultrasonic wave to the boring means 63 . although the holes 64 can penetrate through the preform , it is also possible to end the holes in the midst of the preform so that enough length of the original preform length can be retained for handling in the later steps . shortening the boring length also shortens the time for the boring step . the holes 64 may be bored , either by rotating the boring means 63 around the axis of a hole 64 , or by rotating the preform 61 around the axis of a hole 64 , or by rotating both the boring means and the preform . after the boring step , further processing steps comprise elongating the preform 61 , inserting the elongated preform 61 in a glass tube with an inner diameter slightly larger than the outer diameter of the elongated preform 61 , and heating and collapsing the glass tube onto the elongated preform 61 . also , it is possible to deposit soot of silica glass onto the outer surface of the preform 61 by vapor phase deposition , and heat and sinter the deposited soot . by employing such steps , it becomes possible to reduce the ratio of the hole diameter to the whole preform diameter , and to equivalently form holes with small diameter that are difficult to form by boring . it is also possible to etch the inner surface of the holes 64 by hydrofluoric acid solution or sf 6 gas . as a result , it becomes possible to eliminate impurities such as hydroxyl group and transition metals on the surface or in the glass near the surface , and to reduce the surface roughness , resulting in a low transmission loss . finally , the preform 61 is drawn into an optical fiber as illustrated in fig1 . the preform 61 is grabbed by a grabbing means ( not shown ). an end of the preform 61 having the holes 64 is connected to a pressure adjusting means 72 via a connecting means 71 , and thereby the pressure in the holes 64 is adjusted . the arrangement of the holes is same or proportional to that in the preform - febrication step shown in fig1 or 15 given below . from the other end , the preform is fed into a heating means 73 at a predetermined velocity . from the heated and softened portion of the preform , an optical fiber 76 is drawn . the optical fiber is pulled by a pulling means ( not shown ). the hole diameter in the optical fiber can be controlled by controlling the pressure of the pressure adjusting means 72 . it is also possible to draw an optical fiber from the preform 61 in which the holes 64 are sealed , as shown in fig1 . as a result , it becomes easier to prevent contaminants to enter into the holes 64 . the arrangement of the holes is same or proportional to that in the preform - febrication step shown in fig1 or 15 given below . it is also possible to form the holes 64 in the preform 61 not by boring as in fig1 . fig1 is illustrative of preform fabrication to obtain optical fibers using several different materials . a preform 61 a can be formed by arranging a plurality of silica capillaries 67 around a silica rod 66 into a bundle , and insert the bundle into a silica jacket tube 68 . the silica rod 66 has a smaller diameter than the silica capillaries 67 . then , the preform 61 a is drawn in the step as shown in fig1 or 14 . the drawing temperature is chosen so that the interstitial gaps between the silica capillaries 67 shrink and / or close by surface tension . since the flow amount of softened glass accompanying the shrink of the gap is small where the silica rod 66 exists , the distance between the holes becomes larger there than elsewhere in the cross section . as a result , an optical fiber with a cross section that is similar to that in embodiment 1 can be obtained . the preform fabrication method of fig1 is suited to fabricate optical fibers using several different materials . for example , by employing silica with more than 10 mol % of germanium as the material of the silica rod 66 , the efficiency of the nonlinear optical effects can be enhanced . also , by employing a silica rod 66 doped with rare earth elements , an optical fiber with optical amplifying characteristics can be obtained . while this invention has been described in connection with what is presently considered to be the most practical and preferred embodiments , the invention is not limited to the disclosed embodiments , but on the contrary , is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims .