fig1 a shows a digital phase grating 1 comprising four steps per grating period g . the height of the steps is designated d , and the surfaces of the steps extend perpendicular to the plane of the drawing and either perpendicular or parallel to the grating plane . the grating is provided with a reflecting coating on its upper side . such a regular digital reflection phase - grating diffracts light of the wavelength l q in the q th diffraction order if the relationship is met . in this equation , d is the step height , q the number of the diffraction order ( positive for positive diffraction orders and negative for negative diffraction orders and zero for the zero diffraction order ), k is either a positive integer or zero ( zero only if q differs from zero ), and p is the number of steps per grating period . it has been found that the diffraction efficiency for the central diffraction orders ( q =+ 1 , 0 or - 1 ) is particularly high , and that the efficiencies for the non - zero diffraction orders increase as the number of steps , p , per grating period increases . β being expressed in degrees of arc and g being the grating period . the diffraction angle is the angle of the relevant diffraction direction to the normal to the grating plane or the steps . if β = 0 ( zeroth diffraction order ) the direction of diffraction in fig1 a ( in the case of light incident perpendicularly ) extends perpendicularly upwards . if β ≧ 0 the light is diffracted to the top right and for β & lt ; 0 a diffraction to the top left is obtained . a practical embodiment of the reflection phase - grating shown in fig1 a has a grating period g = 25 , 000 nm and a step height d = 1600 nm . equation ( 1 ) then yields the wavelength l + 1 = 753 nm for the + 1st diffraction order , the wavelength l 0 = 800 nm for the zeroth diffraction order and the wavelength l - 1 = 853 nm for the - 1st diffraction order . the efficiency for the + 1st and the - 1st diffraction orders is approximately 81 %, as calculated using equation ( 2 ). the efficiency for the zeroth diffraction order is 100 %, so that light of wavelength l 0 will not appear in + 1st or the - 1st diffraction order . moreover , the theory ( cf . dammann , physik in unserer zeit , supra at page 88 ) shows that light of the wavelength l + 1 cannot appear in the - 1st diffraction order and in the zeroth diffraction order , and that light of the wavelength l - 1 cannot appear in the + 1st diffraction order and in the zeroth diffraction order . it also follows from theory that these conclusions also apply to narrow spectral bands around the specified wavelengths . fig1 b shows an optical wavelength demultiplexer which employs the phase grating described with reference to fig1 a for separating the various wavelengths . the grating direction extends perpendicular to the plane of the drawing . the step height decreases from top to bottom within the grating period shown in fig1 a . light of the wavelengths l + 1 , l 0 and l - 1 which emanates from a fiber f is incident on the grating 1 . fiber f and three other fibers f - 1 , f 0 , f + 1 ( component light guides ) are disposed in one plane as shown in fig1 b . a lens 2 is arranged at a distance from the end faces of the fibers , which distance is equal to its focal length f . the lens 2 converts the diverging light from the fiber f into a parallel light beam which is incident on the reflection phase - grating 1 . this grating reflects the diffracted parallel light beams back to the lens which converges the light . the focal plane of lens 2 coincides with the plane of the end faces of the glass fibers f - 1 , f 0 and f + 1 . the grating 1 is arranged so that in its zeroth diffraction order , for which the grating acts as a mirror , the light from the fiber f is coupled into the glass fiber f 0 . this can be achieved by arranging the grating not exactly perpendicular to the optical axis , but tilted through a small angle about an axis which is perpendicular to the plane of drawing of fig1 b . fig1 b shows one ray which emerges from the end face of the fiber f . after reflection from the grating ( slightly off the optical axis ), the ray is diverted into the fiber f 0 . in reality , a diverging beam emerges from f , which beam illuminates a comparatively large part of the grating area , from which it is reflected back to the lens 2 . the light of the wavelength l - 1 which issues from the fiber f is deviated upward through a small angle β - 1 ( cf . equation ( 3 )) by the grating 1 . this beam is focussed by the lens 2 and is coupled into the fiber f - 1 , which is situated between the fiber f and the fiber f 0 . the light of the wavelength l + 1 from fiber f is deviated downward through the angle β + 1 and coupled into the fiber f + 1 . the positions of the individual fibers are shown in fig1 c . the spacing of the fibers f - 1 and f + 1 from the fibre f 0 ( which is the spacing between the central axis of these fibers ) is determined by the product of the focal length f of the lens 2 and the diffraction angle β - 1 or β + 1 according to the equation ( 3 ). for the specified values of f , p and d , the distances will be 0 . 17 mm and 0 . 15 mm respectively . in the manner described above , the device shown in fig1 b operates as a demultiplexer . it may be used as a multiplexer if the optical paths are reversed . light of the wavelength l - 1 from the fiber f - 1 , light of the wavelength l 0 from the fiber f 0 , and light of the wavelength l + 1 from the fiber f + 1 is then coupled into the fiber f 0 . when a second set of fibers is used the grating 1 and the lens 2 may also be used as part of a combination of a multiplexer and a demultiplexer which are operated independently of each other . fig2 a shows a digital reflection phase - grating comprising six steps per grating period . the grating period g is 48 , 000 nm and the step height d is 4 , 000 nm . the demultiplexer shown in fig2 b and 2c , which is constructed by means of this phase grating , differs from the demultiplexer shown in fig1 b and 1c one difference is in that the fiber f transmits light of five different wavelengths , which is divided among five fibers 3 . . . 7 . moreover , the fiber f of fig2 b and 2c , as distinct from that in fig1 b and 1c , is not arranged in the same plane as the fibers 3 . . . 7 which transmit monochromatic light . the fiber f is arranged above the central fiber 5 in such a way that the plane through the central axes of fibers f and 5 extends perpendicular to the plane defined by the central axes of the fibers 3 . . . 7 . the fiber f transmits light of the wavelengths 787 nm , 800 nm , 813 nm , 1297 nm and 1371 nm . the light of the wavelength 800 nm propagates in the 0th diffraction order and is coupled into the fiber 5 via the lens 2 . in order to achieve this the grating 1 is inclined slightly relative to an axis which is disposed in the plane of the drawing and which is perpendicular to the optical axis 0 . the grating 1 which acts as a mirror for this diffraction order . it follows from equation ( 1 ) that it is also possible to transmit light of the wavelength 1333 nm in the 0th diffraction order . the light of the wavelength 787 nm from the fiber f is diffracted in the + 1st diffraction order and coupled into the fiber 6 . fiber 0 is situated at a distance of 0 . 23 mm from the fiber 5 ( if the lens 2 has a focal length of 14 mm ). in addition to the light of the wavelength 787 nm the light of the wavelength 1297 nm is also diffracted in the 1st diffraction order , as can be demonstrated by equation ( 1 ), if k = 3 instead of k = 5 . the wavelengths in the + 1st diffraction order are spaced so far apart that in spite of its high grating period of 48 , 000 nm the dispersion of the grating is sufficient to separate the two wavelengths spatially from each other . thus , the light of the wavelength of 1297 nm is coupled into the fiber 7 which is situated at a distance of 0 . 378 mm from the fiber 5 . the wavelengths 813 nm and 1371 nm are both diffracted in the - 1st diffraction order . the light of the wavelength 813 nm is coupled into the fiber 4 , which is spaced 0 . 237 nm from the fiber 5 . the light of the wavelength 1371 nm is coupled into the fiber 3 which is spaced approximately 400 nm from the fiber 5 . by means of the phase grating shown in fig2 b , it is in principle possible to separate wavelengths in the 2nd diffraction order . however , the diffraction efficiency ( approximately 68 % is then substantially smaller than in the 1st diffraction order ( approximately 91 %). the wavelengths in a range around 800 nm are substantially closer to each other than in the multiplexer described with reference to fig1 a to 1c . this is caused by the greater number of steps and the greater step height . such small differences in wavelengths ( 13 nm in the case of two adjacent fibers ) cannot be processed by means of the known demultiplexers . on the other hand , the demultiplexer shown in fig2 a to 2c processes wavelengths which are situated in the range around 800 nm and in the range around 1300 nm . this may be advantageous in various cases because these wavelength ranges are of practical interest . light sources ( laser diodes or light - emitting diodes ) are available for these wavelengths , and the attenuation in the fibers is very low for these wavelengths . multiple , wavelengths , some of which are close to each other and others which are far from each other cannot be processed with known demultiplexers . for known demultiplexers the wavelength differences must be substantially constant . a further advantage of the demultiplexer according to the invention is that as a result of the comparatively high grating constant their operation is not adversely affected by polarization effects , in contrast to the known demultiplexers which are so affected . the digital phase gratings in the multiplexers and / or demultiplexers according to the invention need not be regular as the gratings shown in fig1 a and 2a . within a grating period they may comprise steps of different height and / or width . the exactly rectangular shape of the steps shown in the drawing cannot be achieved in practice , so that the profile of digital phase gratings which can be manufactured in practice differs slightly from this ideal shape . however , this does not affect the operation of the demultiplexers and / or multiplexers constructed by means of such gratings . if the reflection grating is curved ( concave ) the lens 2 may be dispensed with .