Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/02—Optical fibres with cladding with or without a coating
  • G02B6/02057—Optical fibres with cladding with or without a coating comprising gratings
  • G02B6/02076—Refractive index modulation gratings, e.g. Bragg gratings
  • G02B6/0208—Refractive index modulation gratings, e.g. Bragg gratings characterised by their structure, wavelength response
  • G02B6/02085—Refractive index modulation gratings, e.g. Bragg gratings characterised by their structure, wavelength response characterised by the grating profile, e.g. chirped, apodised, tilted, helical
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/02—Optical fibres with cladding with or without a coating
  • G02B6/02057—Optical fibres with cladding with or without a coating comprising gratings
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
  • G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
  • G02B6/122—Basic optical elements, e.g. light-guiding paths
  • G02B6/124—Geodesic lenses or integrated gratings
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/02—Optical fibres with cladding with or without a coating
  • G02B6/02057—Optical fibres with cladding with or without a coating comprising gratings
  • G02B6/02076—Refractive index modulation gratings, e.g. Bragg gratings
  • G02B6/02123—Refractive index modulation gratings, e.g. Bragg gratings characterised by the method of manufacture of the grating
  • G02B2006/02166—Methods of designing the gratings, i.e. calculating the structure, e.g. algorithms, numerical methods
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/02—Optical fibres with cladding with or without a coating
  • G02B6/02057—Optical fibres with cladding with or without a coating comprising gratings
  • G02B6/02066—Gratings having a surface relief structure, e.g. repetitive variation in diameter of core or cladding

Definitions

• An optical grating can be considered to be a sequence of grating lines.
• the lines modify the reflection and transmission characteristics of an optical transmission medium to which the grating is applied so allowing the characteristics to be tailored, to a greater or lesser degree, to a desired application.
• an optical grating is used in a distributed feedback laser (DFB) to control the wavelength at which the laser is able to lase.
• DFB distributed feedback laser
• an optical grating is used to control the transmission characteristics of an optical waveguide, for example an optical fibre.
• this resonance occurs where the grating period is an integer multiple of half the wavelength, ⁇ /2, divided by the mean effective index n Q .
• the resonance only arises when the period is a odd multiple of ⁇ /(2nr j ).
• the reflection has a characteristic "sin ( ⁇ )/ ⁇ " wavelength response profile of a finite-sized grating. The width of response peak is roughly inversely proportional to the grating length unless the reflectivity is very high. (see Figures 1(a) and 1(b)).
• This characteristic profile is very difficult to change with conventional design methods.
• the periodic change in effective refractive index is fixed by the material properties, then it is not possible to adjust the width of the wavelength response independently of the peak reflec ion.
• the first is to obtain a reflection profile that is flat over a comparatively large wavelength range (greater than about In wide) but with no side lobe reflections in the immediate neighbourhood of this range.
• the peak reflection in this case is not important but it needs to be at least 10%.
• Such an optical grating could be positioned within an optical fibre network so that the connection with a central control could be checked by monitoring the reflections from an interrogation signal sent from the control centre. The wavelength of the peak reflection would then be used to label the position of the grating and hence the integrity of the network could be checked at several places.
• a wide reflection is needed because the wavelength of the interrogation laser could not be accurately specified unless very expensive components were used.
• the side lobes need to be suppressed to prevent interference between different gratings in the network.
• the second requirement is for a high reflection (as close to 100% as possible) in a narrow wavelength region, around 0. lnm wide, with very low side lobes.
• This is for use as a wavelength selective mirror for use with a fibre laser to force it to operate in a narrow wavelength region only.
• Other applications have been identified for non- conventional gratings where the wavelength response of the transmission and reflection properties could be specified.
• DBR distributed Bragg reflectors
• DFB distributed feedback lasers
• K is the effective wavenumber, 2 ⁇ / ⁇
• a 5mm long grating with a pitch of say 0.25 ⁇ m would have 20, 000 steps and therefore the calculation for the scattering matrix would involve 20,000 matrix products. If the matrix were to be calculated at say 100 wavelengths in order to resolve the wavelength response of the grating, then the full scattering matrix of the grating would take several million arithmetic operations to calculate. This is therefore not a trivial calculation but one which would pose no difficulty for a reasonably powerful computer. While the effect of a given sequence of steps in the effective index of the waveguide can easily be calculated, the converse task of designing the sequence to give the required properties to R and T is a different matter entirely. The problem lies in the number of calculations that have to be made.
• the grating has to be defined m terms of some tractable number of parameters and repeated calculations made of how the grating properties change with these parameters.
• This basic idea is known. Simple parameters that have been used are grating pitch which may, for example, vary slowly along the grating' s length to form a chirped grating or gratings that miss out some of the steps in a regular or smoothly varying fashion. See for example T Schrans, M Mitteistein and A Yariv "Tunable Active Chirped-Corrugation Waveguide
• optical gratings are not amenable to approaches of computation that give enough degrees of freedom of device characterisation necessary to achieve the sort of wavelength response that are needed for many applications, for example as identified earlier in this application.
• an optical grating including a sequence of grating lines, the sequence being characterised in that: a) each grating line is centred on a position which is an integer multiple of a line spacing distance from a datum position on the grating; b) the sequence of grating lines is no -periodic; and c) the sequence of grating lines is formed from a multiplicity of N concatenated subsequences, each subsequence comprising a series of one or more instances of a respective grating line pattern.
• the number of subsequences can in effect be reduced by incorporating a number of null sections of zero length. For example, in a preferred embodiment of the present invention, if two adjacent subsequences are found during calculation to be formed from the same grating line pattern they are combined into one larger subsequence for future calculation, the number of subsequences being restored by insertion of a null subsequence.
• the substrate may be an optical waveguide such as an optical fibre having a D-shaped cross-section.
• Other substrates may be used as with known optical gratings.
• the grating lines may be grooves in the substrate, for example, the grooves having a rectangular cross-section or having triangular cross-sections, for example.
• the grating lines may be also be defined by refractive index variations in a substrate or other medium.
• the grating sequence is formed from a multiplicity of subsequences of the type described above in order to give the flexibility of design while allowing tractable calculation of the optical characteristics of a grating.
• the sequence of grating lines is non-periodic so as to allow for non-periodic phase shifts between the grating lines which are necessary to achieve reflection profiles which are ⁇ uaiitativelv different to those that can be achieved by conventional gratings.
• use of a non- periodic sequence of grating lines gives ' flexibility in the design process, while use of subsequences ensures that the design process remains tractable as will be explained below.
• the main consideration in the design algorithm is therefore concerned with providing an efficient method of calculating the total scattering matrix of a grating as efficiently as possible.
• the structure of grating according to the present invention allows such efficient calculation of the scattering matrix.
• the design process of a grating involves determining the values of the parameters of the subsequences, ie the grating line pattern and the number of instances of each pattern in a given subsequence, to obtain desired properties in the resultant optical grating. To do this it is necessary to change these parameters one or a few at a time, and compare the new calculated properties of the grating with the old ones to see if there has been any movement towards the desired characteristics.
• sequence of grating lines of the optical grating is made up of subsequences as described above it is possible to calculate the total scattering matrix of an optical grating more rapidly than if it was necessary to calculate all the properties of the grating from scratch.
• a method of fabricating an optical grating comprises the steps of: calculating the response of an optical grating including a sequence of grating lines, the grating lines being such that: each grating line is centred on a position which is an integer multiple of a line spacing distance from a datum position on the grating; the sequence of grating lines is non-periodic; and the sequence of grating lines is formed from N concatenated subsequences, each subsequence comprising a series of one or more instances of a respective grating line pattern; and subsequently repeatedly altering a subsequence of the grating deciding whether to accept the alteration of the subsequence until some predetermined criterion is achieved; and on achieving the predetermined criterion; forming the resultant optical grating sequence on a substrate.
• the method preferably includes the additional prior steps of: selecting a set of grating line patterns; and calculating the scattering matrix of each member of a set of grating patterns.
• the subsequence is preferably altered by either substituting the respective grating line pattern for a different grating line pattern from the set of grating line patterns or changing the number of instances of the grating line pattern in the subsequence.
• Other operations to change subsequences can be used; the grating line patterns of two subsequences may be interchanged, for example.
• the decision whether to accept an alteration to one of the subsequences is preferably determined by an annealing algorithm.
• an alteration to a subsequence is accepted if the change in a measure of fit of the grating profile to a desired profile is such that exp[-
• T preferably is monotonically decreased between alterations to the sequence of grating lines.
• the grating line patterns may include a null grating pattern of zero length.
• gratings which have reflection profiles that differ qualitatively from known prior art gratings, as discussed above, there have emerged further requirements for gratings whose characteristic profile can be altered in use.
• a tunable laser can be achieved in a known manner by providing means for controlling the refractive index of the grating in a DBR or DFB laser.
• changing the refractive index of a grating means uniformly changing the refractive index across the whole of the grating, or a substantial part thereof, and does not affect the relative index variation which actually constituents the grating itself i. e. the small steps in refractive index which form the grating lines.
• the alteration of the characteristic profile of a grating can be achieved for example, in a grating formed in a semiconductor material, by providing an electrical contact adjacent the grating for injecting current into the grating region so as to alter the refractive index of the material in which the grating is formed.
• a alternative method of altering the characteristic profile of a grating is to physically alter the structure of the grating or a part thereof by for example employing piezo-electric transducers to stress or stretch the grating.
• a grating according to the present invention in addition being more amenable to calculation of a particular desired fixed characteristic profile, is also more amenable to calculation of a characteristic profile which can be varied in a desired manner during use of the grating.
• the present invention also provides a grating in which a plurality of sub-units of the grating, each sub- unit formed from a plurality of subsequences, are separately addressable by means for altering a parameter of each grating sub-unit.
• the multiplicity of sub-sequences from which the grating is formed again give flexibility in the design of, in this case, a variable characteristic profile of the grating, while at the same time enabling the calculation of the profile to be tractable.
• the design process required for such a grating, having a characteristic profile which can be varied in use, can be regarded as an extension of the design process for a grating having a fixed characteristic profile.
• the ability to vary a parameter, for example the refractive index, of a plurality of sub-units of the grating gives an extra degree of freedom in the design process so that any optimisation of the grating design must effectively be two- dimensional, eg the physical structure of the grating sequence comprising the positioning of the grating lines must be optimised in conjunction with the choice of refractive indices for each of the grating sub-units, as will be explained below.
• a grating to be designed which has for example four separately addressable sub-units whose refractive may be varied in use so as to provide a reflection profile which is tunable over a wider range of wavelengths than a conventional periodic grating.
• Figures 1(a) and 1(b) are graphs of the grating responses of prior art optical gratings having grating lines with a flat-triangle section groove;
• Figures 2(a) and 2(b) are graphs of the grating responses of prior art optical gratings having high peak reflectivity;
• Figure 3 is a schematic block diagram of an optical grating according to the present invention.
• Figure 4 is a diagram of a set of grating line patterns suitable for optical gratings that are to be etched on an optical fibre waveguide;
• Figure 5 is a diagram of a grating line patterns suitable for an optical grating for a DFB/DBR laser grating
• Figure 6 is a representation of a grating according to the present invention.
• Figure 7 is a key to the representation of the grating shown in Figure 6 showing the grating line patterns employed
• Figure 8 is a graph of the theoretical response of the optical grating of Figure 6;
• Figure 9 is a graph of the measured response of the optical grating of Figure 6.
• Figure 10 is a scanning electron micrograph of a portion of the grating of Figure 6 at a transition between two subsequences;
• Figure 11 shows a grating in 4 sub-units, the refractive index n of each sub-unit may be varied by current injected via an electrode;
• Figure 12 is a schematic flow diagram showing the stages of the method of designing a grating having a variable reflection response
• Figure 13 is a schematic diagram, similar to that shown in Figure 3, showing the sequence of scattering matrix calculations required when the refractive index of a grating sub-unit is changed.
• Figure 14 a) and b) show the four theoretical reflection responses from a single grating having four sub- units of variable refractive index.
• an optical grating 2 is shown schematically to show its overall subsequence structure.
• Each of the subsequences is formed from a series of one or more instances of a respective grating line pattern.
• the particular grating line pattern and the number of instances of it in a particular subsequence will in general vary from one subsequence to another.
• Figures 4 and 5 show sets of grating line patterns useful for subsequences for an optical fibre grating
• a typical set of grating line patterns comprising grooves 34 having a rectangular cross-section used for optical D-fibre grating designs for fabrication on a silica substrate are shown in Figure 4. This is an exemplary set of grating line patterns - other sets could be chosen instead.
• the fabrication processes force a different type of grating line patterns to be chosen, eg triangular cross-section grooves 36. On these substrates it is very difficult to cut vertical walls, so discreet steps in the refractive index profile cannot be easily achieved.
• the typical groove has a triangular cross- section, in this case with etch angles of around 55°, an exemplary set being shown in Figure 5.
• the optical effect of the subsequences 4 to 18 of the grating is calculated as follows.
• the scattering matrix for each grating line pattern is calculated beforehand in a known manner as described earlier.
• the scattering matrix for a given subsequence 4, 6, 8, 10, 12, 14, 16 and 18 can then be calculated by raising the appropriate grating line pattern scattering matrix to a power equal to the number of instances of that pattern in a subse ⁇ uence. This is carried out for all the subsequences 4 to 18 of the grating line sequence.
• the scattering matrices for consecutive pairs of the subsequences are then calculated by forming the product of the scattering matrices of the subsequences. These products form the second level scattering matrices 20, 22, 24 and 26 of the grating.
• level 2 scattering matrices are paired and the level 1 scattering matrices 28 and 30 are calculated.
• the two, level 1 scattering matrices 28 and 30 are finally combined to form the full, level 0 scattering matrix 32.
• one of the level 3 subsequences is changed during application of an optimization algorithm, for example subsequence 12, then to calculate the new full grating scattering matrix one calculates the matrix product of subsequences 12 and 14 to form a new level 2 matrix, 24, which is then multiplied with the existing level 2 matrix, 26, to form a new level 1 matrix number 30. This finally is multiplied with the other existing level 1 matrix 28 to form the full scattering matrix 32 for this new sequence of grating lines.
• FIG 6 there is shown a particular optical grating calculated according to the method of the present invention comprising ten grating line patterns as shown by the key at Figure 7 and the theoretical response is shown at Figure 8.
• the basic pitch of the grating line patterns of Figure 7 are about 0.5 ⁇ m with a single smallest feature (one line) of about 0.25 ⁇ m.
• the word patterns consist of 4 bits, each word being about l ⁇ m long.
• the total length of the grating of Figure 6 is about 4mm with 64 subsequences including any null subse ⁇ uences that may have been introduced when adjacent subsequences of the same grating line pattern were combined.
• the patterns were etched into a silica substrate to a depth of about 0.25 ⁇ m.
• Figure 9 is a graph of the experimentally measured reflection characteristics of the optical grating of Figure 6 after applying the optical fibre waveguide to the surface of a D-fibre optical fibre waveguide.
• the structure of the grating according to the present invention allows efficient calculation of changes to the scattering matrix and so allows efficient implementation of optimisation algorithms.
• the optimisation algorithm used in the present instance will now be described, by way of example.
• the first step was to choose the shape of the desired reflection characteristics of the grating as a function of wavelength, R ( ⁇ ) and compare the actual reflection R ⁇ ( ⁇ ) obtained from the grating with the desired one.
• the measure of the difference between the two was defined as
• _ is, in effect, a measure of the scale of the reflection and ⁇ a measure of the fit to the desired shape.
• the aim was to minimise ⁇ and maximise ⁇ .
• w is a weighting parameter between 0 and 1.
• a larger value of w means that more weight is being attached to the shape of the refraction profile at the possible expense of the total reflectivity.
• the measure of the value of a particular grating was to some extent arbitrary and other measures of fitness of fit of grating could be used. In particular, if one is interested in the dispersion properties of a grating then one would use the full complex form of the tar ' get response R-.( ⁇ ) and the actual reflection R A ( ⁇ ) and the definitions of ⁇ and ⁇ rather than their moduli.
• the calculated grating sequence was then used to fabricate a grating by forming the grating lines as a sequence of vertically walled, etched steps by electron- beam lithography directly onto a silica substrate.
• the experimentally measured response of the grating of Figure 6 is shown at Figure 9.
• Figure 10 shows a portion of the grating of Figure 6 at a transition between two subsequence 38 and 40.
• a grating line sequence which is made up of a whole number power of 2 subsequence.
• This structure obtains the full benefit of the present invention.
• a grating sequence comprises a small number of concatenated sequences each sequence being as described above. In such a case there will be a small overhead in the calculation as two level 0 scattering matrices will need to be multiplied together.
• a grating comprising a number of grating sequences each having 2 subsequence according to the present invention in series can be calculated with slightly less efficiency than a grating having an exact power of two subsequence.
• Figure 11 shows a grating whose characteristic profile can be altered in use.
• the grating is divided into four sub-units 41, 42, 43, 44, each of which is separately addressable through a electrode.
• the refractive index of each of these sub-units can be controlled between two values which are given, in a known manner, by the properties of the semiconductor material used, by applying a voltage to each of the electrodes.
• the reflection profile of the grating can be switched between a number of different responses by applying different sets of voltages to the sub-units 41-44.
• the design process for this grating must therefore specify a grating sequence, formed from sub-sequences of grating line patterns, and must also specify the particular refractive indices for each of the sub-units required to achieve switching between the desired characteristic responses.
• the design process must optimise both the grating sequence and the four sets of refractive indices n,, n 2 , n 3 , n 4 required to achieve these four responses, so that the grating characteristic is
• n n : , n,, n, ⁇ is ⁇ ⁇ i / &2' ⁇ 2' ⁇ _ i
• n n, n. ⁇ is ⁇ b,, b,, b ; , b 4 ⁇
• n n,, n, ⁇ is 1' 2 7 2' 4 ⁇
• n commute n,, n 4 ⁇ is ⁇ d,, d 2 , d 3 , d. ⁇
• the grating line sequence remains fixed in each case, the only thing that changes is the sequence of refractive indices. This sequence can be changed by applying different voltages through the independent electrodes.
• the design method for a grating having a variable reflection characteristic thus differs from that for a grating having a fixed reflection characteristic in a number of respects.
• variable response grating design method a further difference for the variable response grating design method is that a set of scattering matrices corresponding to each of the different sequences (n.- 4 ) of refractive index for the grating sub-units must be calculated.
• a set of scattering matrices corresponding to each of the different sequences (n.- 4 ) of refractive index for the grating sub-units must be calculated.
• four sets of scattering matrices required to give the four different reflection coefficients as a function of wavelength must be calculated.
• the initialisation stage comprises: - initialising the grating line patterns and R- refractive index sequences in the s sub-units (These could either be random sequences or values read in from a previous calculation) and; pre-calculating the scattering matrices for each of the grating line patterns at each of the allowed values of refractive indices.
• the selection stage 46 comprises choosing at random a grating subsequence or a refractive index sub-unit in one of the switchable sequences (typically with the subsequence being slightly more likely to be chosen). Cycling the subsequence or index value through all the possible choices, until either a change is accepted or all the possibilities are exhausted, and then choosing another subsequence or index sub-unit to change. If a grating subsequence is chosen to be changed then the recalculation stage 47 is the same as for the fixed response grating design method, i. e. only those matrices in the structure shown in Figure 3 which are affected by the change are recalculated. However as mentioned above, the matrices need to be calculated N-times i. e. once for each of the N-target wavelength responses - corresponding to the
• N-switchable refractive index sequences of R-refractive index sections are N-switchable refractive index sequences of R-refractive index sections.
• the recalculating stage 48 must take account of the change in index affecting all the levels in Figure 3 below the level at which the index is changed. This is shown in Figure 13.
• a change to the refractive index value of the sub-unit labelled 1 in level 4 of Figure 13 means that it is necessary to replace all of the scattering matrices affected at level 5 (numbers 8-15). Following this it is necessary to recalculate the matrices (4-7) at level (4) by pairwise multiplication in level (5), recalculate the matrices (2 & 3) at level (3) by pairwise multiplication in level (4), recalculate the matrix 1 at level 2 by multiplication of matrices 2 2. 3 in level (3),
• the next stage 48 is to decide whether to accept this change. This will depend on whether the change gives a better fit to the N-desired or target responses, hence the measure of difference used previously for the fixed grating response design method is modified to account for the R different refractive index sequences for the s sub-units of the grating.
• ⁇ 2 . ⁇ N ⁇ a ⁇ R ⁇ ( ⁇ ,i)l 2 - l* ⁇ ( ⁇ ,0l 2 ) 2 d ⁇ ) SN C /
• » ' - denotes the coefficients corresponding to the i' th refractive index sequence.
• V (1-w). ⁇ -w. ⁇ where w is a weighting parameter.
• V is then used in an optimisation or annealing algorithm in precisely the same way as previously described in order to decide whether to accept the change (in grating subsequence or sub-unit index) or not.
• the result of the design process is one sequence of grating lines and R sequences of refractive indices for the s sub-units.
• refractive index can be replaced by any other parameter which will affect the reflection response of the grating, for example the local stressing or stretching of a sub-unit of the grating.

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