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
  • G02B5/00—Optical elements other than lenses
  • G02B5/18—Diffraction 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
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
  • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
  • G02F1/21—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference
  • G02F1/225—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference in an optical waveguide structure
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
  • G02F1/35—Non-linear optics
  • G02F1/355—Non-linear optics characterised by the materials used
  • G02F1/3558—Poled materials, e.g. with periodic poling; Fabrication of domain inverted structures, e.g. for quasi-phase-matching [QPM]
• • 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
  • G02B2006/12083—Constructional arrangements
  • G02B2006/12107—Grating
• • 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
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
  • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
  • G02F1/21—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference
  • G02F1/212—Mach-Zehnder type
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
  • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
  • G02F1/21—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference
  • G02F1/225—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference in an optical waveguide structure
  • G02F1/2252—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference in an optical waveguide structure in optical fibres
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
  • G02F1/29—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the position or the direction of light beams, i.e. deflection
  • G02F1/31—Digital deflection, i.e. optical switching
  • G02F1/313—Digital deflection, i.e. optical switching in an optical waveguide structure
  • G02F1/3136—Digital deflection, i.e. optical switching in an optical waveguide structure of interferometric switch type
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
  • G02F1/35—Non-linear optics
  • G02F1/3515—All-optical modulation, gating, switching, e.g. control of a light beam by another light beam
  • G02F1/3517—All-optical modulation, gating, switching, e.g. control of a light beam by another light beam using an interferometer
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
  • G02F1/35—Non-linear optics
  • G02F1/3515—All-optical modulation, gating, switching, e.g. control of a light beam by another light beam
  • G02F1/3521—All-optical modulation, gating, switching, e.g. control of a light beam by another light beam using a directional coupler
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F2201/00—Constructional arrangements not provided for in groups G02F1/00 - G02F7/00
  • G02F2201/30—Constructional arrangements not provided for in groups G02F1/00 - G02F7/00 grating
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F2201/00—Constructional arrangements not provided for in groups G02F1/00 - G02F7/00
  • G02F2201/30—Constructional arrangements not provided for in groups G02F1/00 - G02F7/00 grating
  • G02F2201/307—Reflective grating, i.e. Bragg grating
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
  • H01S5/00—Semiconductor lasers
  • H01S5/10—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region
  • H01S5/12—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region the resonator having a periodic structure, e.g. in distributed feedback [DFB] lasers
  • H01S5/1206—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region the resonator having a periodic structure, e.g. in distributed feedback [DFB] lasers having a non constant or multiplicity of periods
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
  • H01S5/00—Semiconductor lasers
  • H01S5/10—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region
  • H01S5/12—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region the resonator having a periodic structure, e.g. in distributed feedback [DFB] lasers
  • H01S5/125—Distributed Bragg reflector [DBR] lasers
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
  • H01S5/00—Semiconductor lasers
  • H01S5/10—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region
  • H01S5/18—Surface-emitting [SE] lasers, e.g. having both horizontal and vertical cavities
  • H01S5/183—Surface-emitting [SE] lasers, e.g. having both horizontal and vertical cavities having only vertical cavities, e.g. vertical cavity surface-emitting lasers [VCSEL]
  • H01S5/18361—Structure of the reflectors, e.g. hybrid mirrors

Definitions

• This Application relates to the field of grating structures.
• regular and chirped grating structures to define and/or modify the response characteristics of optical and other devices which utilise the properties of wave-like phenomena such as electromagnetic (EM) waves.
• devices utilising such structures include Fibre Bragg Gratings (FBGs) and apodised FBGs, m whicn a slowly-varying chirp is superposed on the grating.
• FBGs Fibre Bragg Gratings
• apodised FBGs m whicn a slowly-varying chirp is superposed on the grating.
• Periodic grating structures have been the focus of much attention m a very wide range of applications; for example, in photonic crystals, wherein the band structure may be defined by analogy with the well-known (Bloch) periodic lattice analysis of solid-state physics.
• aperiodic grating does not, in general, exhibit a useful band structure, by means of a simple approximate analysis we have found aperiodic structures that exhibit a controllable and useful band structure.
• transforms will belong to the same class of transforms as a Fourier
• material response characteristics result from properties of the atoms making up the material.
• the characteristics may result directly from the properties of the electrons surrounding the atoms or from the atoms' nuclei or from the arrangement of the atoms relative to each other.
• the invention makes possible the selection of properties of a material by the introduction of a suitable variation in the atoms making up the material.
• the variation is in refractive index, which can be related to the response of an atom's electrons to an incident EM field.
• Aperiodic Photonic Band-Gap (APBG) structure.
• Periodic Bragg Grating could also be applied to the structures and has the same acronym.
• Our APBG structures can be classed as fast -varying structures, which differentiates them from slowly-varying aperiodic structures such as a simple chirped-grating. They are also longitudinal aperiodic structures, which differentiates them from holograms employed in transverse situations .
• An APBG grating (defined below as H) is a structure which cannot be expressed as a simple transformation of a regular grating.
• the present invention does not include any of the following gating structures: (1) Chirped gratings
• a chirped grating is described as an aperiodic grating, which is technically correct in the strictest meaning of the term.
• a regular grating can be mathematically described in the following manner:
• T a Grating Transformation/Matrix function
• x spatial dimension.
• the Grating Transformation/Matrix function may be any function which produces a regular grating in the spatial domain.
• a binary regular grating has a unit cell may be of equal mark-space ratio; graphically: 1 So, a binary grating has regions of constant refractive index having one of two possible values.
• a sine wave is another example of a regular grating.
• a chirped grating can be described by a linearly-chirped or stretched regular grating thus:
• the spatial dimension x has undergone a simple, continuous transformation (i.e. it has been squared) . This
• an APBG cannot be so simply expressed as the regular grating transformation function T G operating on some 'simple', continuous function of the spatial dimension f (x) ,
• G t regular grating of i h spatial frequency
• the superposition of two gratings of similar but not identical frequencies will produce a "beat" variation at the difference frequency.
• a similar effect will occur with the superposition of, for example, three or four frequencies.
• an APBG does not include grating derived by taking the superposition of a number of regular gratings and quantising the resultant grating function to a small number of levels, for example, generating a binary grating by thresholding the said resultant grating function.
• the binary grating will typically have regions with few changes of level corresponding to nodes of the envelope of the resultant of the superposition interspersed with regions of regular changes of the level the period of which increases towards the antmodes of the envelope function.
• an APBG grating is a structure which cannot be simply expressed as a set of concatenated regular gratings of varying spatial frequency:
• Each G j is, of course, not infinite in extent but is windowed having a beginning and an end.
• An apodised grating A (x) can be characterised by multiplication of the basic structure with a slowly-varying windowing- function W (x) , such as a raised-cosine, or a
• the resulting apodised grating will often be technically aperiodic, and is mathematically described as:
• A(x) W(x) - G for an apodised regular grating
• A(x) W( ⁇ ) - T c (f(x)) for an apodised slowly-varying grating
• An APBG or longitudinal hologram H requires a special Hologram Transformation/Matrix function T H to produce the aperiodic structure in the spatial domain x, such that in general we have:
• the resulting hologram may be in general characterised as fast -varying.
• A(x) W(x) - H for an APBG structure.
• the Fourier-Transform (FT) of an APBG structure will reveal its spectral distribution; i.e., the spatial period components which make it up.
• spectral distribution i.e., the spatial period components which make it up.
• the transmission function of an APBG be it used, for example, for grating-assisted coupling, as a photonic bandgap crystal, filter, or within Mach-Zehnder configuration, is closely related to its spectral distribution; that is, the Fourier Transform of its spatial structure.
• an APBG is best designed by tailoring its spectral distribution (or the FT of its spatial distribution) to yield the desired spectral response.
• the required spatial distribution is thus merely the inverse FT (which is of course, equivalent to the FT) of the desired spectral response.
• the FT of a spectral distribution function will tend to yield a complex spatial distribution (i.e. containing both real and imaginary components) . That is equivalent to a permittivity distribution containing both absorptive components (i.e. imaginary refractive index) and dielectric components (i.e. real refractive index), which is difficult to realise in practice.
• the present invention arises from the realisation that generally only the modulus of the spectral distribution is of interest (e.g. for power equalisation, filtering, the existence of certain spatial periods etc.) and that its phase characteristic is of negligible importance (N.B. that is not the case for APBGs designed for dispersion compensation, where the dispersion characteristic is given by the second differential of the phase characteristic: see below) .
• N.B. that is not the case for APBGs designed for dispersion compensation, where the dispersion characteristic is given by the second differential of the phase characteristic: see below
• a spatial distribution can be designed, which preferably consists only of a real or an imaginary component .
• the FT of that spatial distribution will yield a spectral distribution with the desired amplitude distribution, but an arbitrary phase distribution.
• One aspect of the invention lies in providing a suitable spatial distribution, which is preferably purely real or purely imaginary, and yields the desired spectral response.
• the two constraints in the calculation are on each side of the FT.
• the first constraint is the actual amplitude characteristic of the spectral distribution
• the second constraint is that the required spatial characteristic is preferably either purely real or purely imaginary. That allows simple fabrication because the real and imaginary material characteristics are usually controlled in different ways. Together, those two constraints make calculation of the required spatial characteristic a non-deterministic problem. It can be solved using optimisation algorithms such as simulated annealing (which is what we have used) , error- diffusion, genetic algorithms etc.
• a binary spatial characteristic has the immediate advantage of being much simpler to fabricate, compared with a continuous spatial characteristic, while still yielding all the desired functionalities inherent to an APBG.
• phase characteristic of the spectral distribution is important, we need to introduce an additional constraint into the calculation. Instead of just desiring a certain magnitude of the spectral distribution response, we are now interested in both the real and imaginary amplitude characteristics respectively, both of which we try to tailor.
• the phase characteristic is not completely specified but is merely constrained to have a particular second derivative.
• the tangent of the phase characteristic is merely the ratio of the imaginary amplitude characteristic to the real amplitude characteristic.
• Fig. 1 shows ((a) to (f ) ) structures of gratings having various single bandgap frequencies
• Fig. 2 shows (i) experimental and (ii) theoretical
• Fig. 3 shows examples of two APBGs ((g), (h) ) designed to exhibit multiple bandgap functionality, at 2.8 GHz and 3.6 GHz.
• Fig. 4 shows experimental and theoretical results for (i) APBG (g) and (ii) APBG (h) , exhibiting multiple bandgaps .
• Fig. 5 is a flowchart illustrating the use of an optimisation algorithm (simulated annealing) to carry out the invention.
• Fig. 6 shows various desirable simple filter characteristics :
• Fig. 7 shows further desirable filters: (a) apodised passband
• Fig. 9 shows an example filter characteristic for multi -wavelength dispersion compensation
• Fig. 10 shows an aperiodic dielectric stack, having: (a) two refractive indices (binary) ; and (b) multiple refractive indices
• Fig. 11 shows an aperiodic fibre Bragg grating, being:
• FIG. 12 shows aperiodic DFB/DBR ribbed waveguiding/stripline structures :
• Fig. 13 shows aperiodic DFB/DBR waveguiding/stripline structures
• FIG. 14 shows programmable APBG structures:
• Fig. 15 shows a magnetic APBG filter, with aperiodically orientated (ferromagnetic) dipoles ;
• Fig. 16 shows aperiodically-poled non-linear material, (for example, aperiodically-poled lithium niobate) :
• Fig. 18 shows an APBG within Mach-Zehnder configurations :
• Fig. 19 shows aperiodic-grating assisted couplers: (a) uni-directional, passive coupling
• FIG. 20 shows a (asymmetric) Fabry-Perot style cavity fibre laser
• Fig. 21 shows a generic fibre ring laser
• Fig. 22 shows a distributed feedback semiconductor laser diode, employing one or more APBG structures in place of regular Bragg grating reflectors;
• Fig. 23 shows a VCSEL employing one or more APBG dielectric stacks
• Fig. 24 shows a generic APBG lattice or superlattice having different atomic/molecular layers or multi -layers
• the smallest spatial period in a grating could thus be a base cell of length 32.5mm, consisting of a unit length of air and a unit length of Perspex. That base cell could then be repeated 10 times within the 325mm length of the transmission line, as shown in figure la.
• a spatial period ⁇ will reflect wavelengths given by
• the grating was made of materials with very different refractive indices and so that formula could not be used directly. Rather, it was necessary to consider
• ⁇ ' 75.2 mm
• bandgap frequency 2.0GHz
• an aperiodic grating does allow this to happen, and the gratings for these intermediate frequencies are shown in figures 1 (b)
• (a) is periodic;
• (b) contains regular region corresponding to granting (a) i.e. it has a repeated unit one mark and one space;
• (c) is periodic and again has the regular one mark and one space unit repeated;
• (d) is an aperiodic APGB;
• (e) is an APGB comprising a concatenation of two identical APGB gratings which are each longer than the wavelengths filtered,
• (f) is a regular grating of twice the period of (a) .
• gratings (b) , (c) , and (e) display some periodicity of a longer period than the period of the regular gratings (a) and (e) .
• Grating (b) comprises two concatenated gratings of form (a) ; grating (c) has a period of 5 elements; and grating (e) has a period of 10 elements.
• Gratings (b) and (c) are thus not fast-varying aperiodic gratings according to our definition.
• the grating of (e) is, in fact, two concatenated aperiodic gratings .
• the reason that a high proportion of the gratings generated in the calculation of Fig. 1 have some degree of periodicity is that the grating consists of only 20 elements, making it likely that those elements will display some periodicity. Larger sets of grating elements will have useful combinations which do not this tendency.
• Figure 2 (i) depicts the measured transmission spectra of the APBG structures depicted in figures la- If.
• Curves (a) and (f) show the transmission spectra for the regular gratings of effective spatial period 37.6mm and 75.2mm respectively.
• the bandgap of curve (a) in figure 2 (i) is very well defined, with a centre frequency of about 4.0GHz, with the bandgap centre frequency of curve (f) predictably being at 2.0GHz, but less well defined as might be expected for a grating with only half the number of periods.
• Curves (b) - (e) show the bandgap being shifted in incremental steps of about 0.4GHz, between 4.0GHz and 2.0Ghz, by using more highly structured Bragg gratings.
• Curve (b) has a bandgap centre frequency of 3.8GHz, while (c) is at 3.4GHz, (d) is at about 2.9GHz, and curve (e) is at about 2.6GHz, agreeing well with the theoretical bandgap frequencies as depicted in figure 2 (ii) .
• the strength of the bandgap for more highly structured Bragg gratings is not as large as for a regular Bragg grating, so that the transmission at the bandgap centre frequency tends to be higher.
• a longer APBG with more segments would ensure a stronger bandgap.
• a Bragg grating can also be designed to exhibit multiple bandgaps .
• FIG 3 Examples of two such APBGs are shown in figure 3, and both have been designed to exhibit bandgaps at 2.8GHz and 3.6GHz.
• Each APBG has been designed to provide the same functionality, as afforded individually by the APBGs shown in figures 1 (b) and 1 (d) .
• the resulting transmission spectra for the two APBGs are depicted in figure 4, and show that the corresponding bandgap centre frequencies lie at about 2.8GHz and 3.7GHz, which while not exactly matching the designed bandgap frequencies of 2.8 GHz and 3.6 GHz, still shows close correspondence.
• the APBG is having to do more 'work', in the sense that it is trying to produce 2 bandgaps, rather than just one, the resulting bandgaps tend to be weaker than those shown in figures 2b and 2d.
• the two APBGs have been designed to ostensibly exhibit the same functionality
• APBGs have the same primary spectral response (i.e. bandgaps at about the designed frequencies of 2.8 and 3.6GHz), but each has slightly different parasitic properties. This illustrates the fact that the solution-space of APBGs is very large and contains many candidate functions, each with a similar Fourier Transform characteristic.
• optimisation algorithm is simulated annealing, which is a well-known optimisation algorithm. Annealing is a process which a material is strengthened by the smoothing out of dislocations m its structure.
• the material is heated up and then slowly cooled down.
• the heating causes atoms forming dislocations in the material to be excited out of local potential energy minima; cooling down slowly causes them to be redistributed smoothly, with minimal dislocations. If the cooling is too fast, dislocations will be "frozen" into the material.
• Simulated annealing mimics the annealing process.
• a cost -function takes the place of potential energy.
• the aim of the process is to locate a global minimum cost space, by randomly “hopping” solutions around (a “hot” system) and then gradually “cooling” the system by reducing the size of the random hops. If the cooling rate is chosen correctly, the solution will hopping into the global minimum whilst the system is hot and be kept there as the system cools.
• the optimisation procedure depicted in Fig. 5 comprises the following steps:
• the FT of the grating structure is compared with the target function, by calculation of the cost function (i.e.,
• the grating is accepted as
• the simulated annealing is "cooled down" slightly, by reducing the temperature T by the factor alpha, and the iteration count is set back to zero.
• the rate of cooling alpha is usually ket constant througout the annealing. If after further loops there is no change in
• the process is stopped (not illustrated) .
• the target function is the reflectivity spectrum and the Fourier transform of grating structure performed in the simulated annealing is in detail as follows:
• n is the average refractive index
• ⁇ r ( z) is the relative permittivity n l ⁇ distribution
• ⁇ is the propagation constant
• z is the spatial coordinate.
• the spatial derivative of the relative permittivity is integrated because it is changes that which scatters light; the tanh function scales the result of the integration appropriately.
• APBG structures can be both 2D and 3D in nature, although many of the applications highlighted tend to only require ID APBG structures.
• a ID APBG structure is one which light emanating from a point sees the structure m one direction (along a line) .
• a 2D APBG structure is one which light emanating from a point sees the structure m all directions m a plane.
• a 3D APBG structure is one m which light emanating from a point sees the structure m all directions in a plane.
• a 3D APBG structure is one in which light emanating from a point sees the structure in all directions in space. "Seeing" the structure means that the light is affected by the structure in its direction of propagation. In wave guides, for example, the light has significant component of the wavevector across the guide as well as along and so in that sense is propagating across as well as along the guide.
• APBGs allow tailored filter responses to be achieved in a far more flexible manner than allowed by existing periodic or "slowly-varying" filter structures.
• desired characteristics are: high-pass, bandpass, notch and low-pass filters (Figs. 6 (a) - (d) ) with particular phase characteristics (e.g. linear-phase, nonlinear phase, phase compensation) ; apodised passbands and passband- flattened passbands (Fig. 7 (a) - (b) ) ; comb-like filters, segmented passbands and non-uniform response segmented passbands ((e.g. for power equalisation) (Fig. 8 (a) - (c) ) ; and single frequency and multiple frequency dispersion compensation (Fig 9) .
• phase characteristics e.g. linear-phase, nonlinear phase, phase compensation
• apodised passbands and passband- flattened passbands e.g. 7 (a) - (b)
• the filter can also be designed to exhibit appropriate combinations of such characteristics.
• Higher dimensioned (i.e. 2D and 3D) APBG structures, such as aperiodic photonic crystals, can be designed to exhibit similar useful filtering properties.
• Dielectric stacks In general, quarter-wavelength dielectric stacks use
• An APBG can be designed for a specific wavelength, where the unit thicknesses are not
• FIG. 10 shows two embodiments of APBG "dielectric stack" filters.
• the first (Fig. 10(a)) is a binary aperiodic dielectric stack where only two different refractive indices are stacked m an aperiodic fashion.
• Figure 10(b) shows a more general APBG dielectric filter consisting of layers of various (more than two) refractive indices where the thickness and refractive index of each layer is designed to yield the overall required filter characteristic.
• APBGs have many applications m guided-wave devices.
• Optical fibre Bragg-grat g ⁇ FBGs have recently received considerable attention.
• the use of APBG structures, (which are by their nature "fast -varying" as opposed to the already demonstrated slowly-varying non-uniform Bragg gratings, such as chirped FBGs and apodised FBGs) permits tailoring of the filter response as described above, e.g. for multi -wavelength applications.
• An APBG structure can be written using UV light into the core and/or the cladding of the fibre, and can consist of either ust a binary structure of two different refractive indices or an APBG of multiple refractive indices, as shown m Figs. 11 (a) - (b) .
• Waveguides can also have APBG structures incorporated in their design.
• the APBG structure is caused by some aperiodic disturbance in the permittivity or refractive index. This can be achieved by ribbed waveguide structures, where the effective refractive index is controlled by the height of the material (which may be a dielectric or a metal) above the waveguide. This can be either binary or multi -level in nature, as shown in Figs. 12 (a) - (b) . Alternatively, different dopants or doping levels can be incorporated into waveguide or strip line to achieve the APBG structure in the refractive index, as shown in Figs. 13 (a) - (b) .
• the APBG structure can also be made dynamic/reconfigurable by causing the refractive index to change due to an applied voltage, via, for example, a thermo- optic or electro-optic effect.
• An inter-digitated set of electrodes, each controlled by an individual voltage can be placed upon the waveguide to create an APBG structure in the refractive index of the waveguide.
• the electrodes could be of different widths.
• the APBG structure could be binary if only 2 different voltages are applied across the ensemble of electrodes, or multi-level if variable voltages are applied to the electrodes, as depicted Fig. 14(a).
• a shaped, comblike electrode with variable thickness arms can be employed to create a fixed APBG structure, which can be turned on or off, or yield variable bandgap strengths, according to the single voltage applied to it Such an arrangement is illustrated m Fig. 14(b)
• Figure 15 depicts a binary APBG structure consisting of an array of dipoles, whose north and south poles are aligned to yield an aperiodic structure. An electromagnetic wave incident on the structure will be filtered according to the APBG designed transfer response.
• Aperiodically-Poled Non-Linear Materials APNLMs
• Periodically-poled Lithium Niobate (PPLN) is now a well established method for enhancing the non-linear effect inherent to Lithium Niobate, via the technique of phase- matching.
• the grating induced by the periodic poling in the non-linear material acts as a photonic bandgap (PBG) for a small range of wavelengths centred on a 'signal' wavelength
• a pump wavelength ⁇ p also travels through the PPLN, but
• the PBG effectively slows the signal wavelength ⁇ s , so
• non-linearities can be used to make optical parametric amplifiers (OPAs) and optical parametric oscillators (OPOs) .
• OPAs optical parametric amplifiers
• OPOs optical parametric oscillators
• There are other non-linearities such as the Kerr effect whose effect can also be enhanced using periodic-poling.
• Aperiodic photonic bandgap structures can also be employed within non-linear materials to quasi -phase-match multiple wavelengths with each other, with multiple generated wavelengths, and with multiple pump wavelengths. Each of the wavelengths within an arbitrarily chosen set of wavelengths can be quasi -phase-matched with each other. Arbitrary, multiple sets of wavelengths can be adopted, and the APBG designed so that each set is essentially independent (i.e. non-phase-matched) with respect to the others.
• the APBG can be designed to have bandgaps and bandpasses at arbitrary multiple wavelengths, it can be used to inhibit/suppress selected wavelengths, such as the pump wavelength (s) , signal wavelength (s) and generated wavelengths.
• selected wavelengths such as the pump wavelength (s) , signal wavelength (s) and generated wavelengths.
• An APBG structure might be used to enhance the 4 -wave-mixing non-linear effect between a pump signal and various signal wavelengths, and to suppress the unwanted generated harmonics .
• Figure 16(a) shows an aperiodically-poled non-linear material, such as aperiodically-poled Lithium Niobate (APLN) ,
• APLN aperiodically-poled Lithium Niobate
• Figure 16(b) shows how an aperiodially-poled non-linear material may be used in a 'bi-directional' manner, as opposed to the 'unidirectional' manner of Figure 16(a).
• Applications include (multi- ) wavelength conversion, optical (multi- ) wavelength regeneration, optical (multi- ) wavelength signal re-timing.
• NOLM non- linear optical loop mirror
• SOA spatially asymmetric semiconductor optical amplifier
• An input signal pulse is split into two equal components within the NOLM, and travel counterwise to each other. In the absence of any perturbing influence, by the principle of reciprocity, they will remain in phase with each other and interfere positively at the coupler, to emerge from the input arm of the NOLM as if it had been reflected.
• a pump (switching) signal pulse is injected into the NOLM from the side, it causes the non-linear Kerr effect to induce a relative phase change in one of the components of the signal, but not the other component. This is due to the spatial asymmetry of the SOA. If the phase change is carefully controlled, the two signal components will interfere destructively at the coupler, and emerge from the alternative arm of the NOLM as a transmitted signal.
• FIG. 17(a) shows a TOAD structure with a spatially- asymmetric (determined by the displacement from symmetry, d aperiodically-poled SOA acting as an APBG with amplification properties.
• the configuration will only allow certain switching wavelengths to pass through the SOA, to cause switching of the input signal pulse. Other wavelengths will be simply reflected.
• This introduces an element of wavelength selectivity within the TOAD, so that only certain wavelengths can be used to switch the signal.
• the APBG structure can be used to reflect the input signal pulse components, so that they are reflected back to the coupler, rather than travelling all the way around the NOLM.
• a combination of aperiodically-poled SOA and APBG i.e. a combination of figures 17(a) and 17 (b) ) can be employed to allow wavelength selectivity in both the switching and input signal pulses.
• Figure 17 (c) shows a TOAD configuration employing an aperiodically-poled non-linear material (APNLM) m place of the SOA.
• Figure 17(d) shows a TOAD configuration employing an APNLM in place of the SOA, conjunction with a passive APBG structure, while figure 17(e) shows 2 passive APBG structures within the NOLM.
• APNLMs these systems have many degrees of freedom, m terms of input, switch g/pump, generated, output wavelengths, and the relative strengths of each of these.
• All of the configurations 17 (a-e) can be used m combination with each other to achieve complex multi -wavelength optical time domain signal processing.
• All APBG structures depicted schematically m figures 17 (a-e) can either be separate components, or written directly into the optical fibre
• the Mach-Zehnder (MZ) interferometer is another important technology for optical switching, and APBGs also find application m it.
• Figure 18(a) shows a simple MZ schematic, with an APBG structure placed within one of its arms.
• the APBG structure can be designed to change the relative phase of wavelengths by slowing the wavelengths down, and/or to reflect the wavelengths. Without any phase changes or reflections, a wavelength would be split equally into the 2 arms of the MZ, and then constructively recombme at the far end to emerge from the 'bar' port.
• MZ Mach-Zehnder
• the APBG can be designed to cause various arbitrary wavelengths to experience the
• the APBG can also be designed to reflect certain wavelengths and impart a relative phase change onto them, so that they emerge either from the original input port, or the alternative input port to the MZ .
• Other intermdiate phase-changes , and degrees of reflectivities will cause the wavelengths to appear at the 4 ports of the device with varying degrees of strength.
• Figure 18(b) shows that such a configuration can also be used bi- directionally.
• Figure 18 (c) shows a MZ configuration with an APBG in each arm.
• Each APBG can be identical, or different to achieve a differential-type filtering operation.
• Figure 18(d) depicts a MZ with a programmable APBG in one of its arms.
• Each element of the programmable APBG can either be individually controlled, such as in figure 14 (a) , or controlled by a single voltage source as in figure 14(b) .
• Figure 18(e) shows a MZ configuration with an APNLM in the arms. Alternatively, there could be just one APNLM in each of the arms, with the second arm plain or containing a passive APBG.
• the APBG/APNLM structures within the MZ configuration can either be discrete components, or written into the integrated-optic waveguides.
• Phase-matching is used in grating assisted couplers to cause cross-coupling, and thus switching to occur.
• a uniform (periodic) grating is written between two closely separated waveguides, each with its own modes of propagation.
• the grating causes coupling to occur between the modes of the first waveguide with the modes of the second waveguide, and coupled mode theory (CMT) can be used to analyse how a mode (associated with a wavelength) in one waveguide can excite a mode (associated with the same wavelength) in the second waveguide. If the parameters of the system are correctly designed (e.g. the correct grating period of the uniform grating) , the power associated with the mode (i.e.
• wavelengths in the first waveguide can be completely resonantly coupled into the second waveguide. Hence switching has occurred. Other wavelengths will not be resonant with the grating, and so will remain unswitched. Generally, a uniform grating will tend to resonantly-couple only one wavelength (as well as weakly coupling higher harmonics of the wavelength) .
• Aperiodic grating structures i.e. APBG structures
• APBG aperiodic grating structure
• the APBG can be considered to consist of multiple spatial periods, each or which resonates with a wavelength to cause cross coupling.
• wavelengths ⁇ 1 enter the aperiodic-grating assisted coupler
• the APBG can also act as a
• Figure 19 (b) shows the aperiodic-grating assisted coupler used in a bidirectional manner.
• Figure 19(c) illustrates that the APBG structure could be made programmable.
• Figure 19(d) indicates that an aperiodically- poled non-linear material (APNLM) could also be used to perform grating-assisted coupling, while generating additional wavelengths in the process, which can be designed to emerge at any one of the 4 possible ports.
• APNLM aperiodically- poled non-linear material
• APBGs have many applications in the field of lasers.
• One or more APBGs can be used to define wavelength selective mirrors, which in turn can be used to define single or composite wavelength-selective resonators.
• greater control of single or multiple laser wavelengths should be achievable than with conventional mirrors. It should be possible to create such mirrors both in bulk material and in waveguiding structures, such as those used, for example, in semiconductor lasers and fibre lasers.
• the APBG can also be designed to function as a suitable filter in optically pumped lasers, e.g. to couple the pump wavelength (s) in and out of the cavity/active medium.
• each wavelength can have the same effective cavity length (or round trip time) .
• the group-velocity/ phase characteristics of each wavelength can be tailored via the APBG to facilitate a/synchronous multi -wavelength modelocking, and to exclude other wavelengths from modelocking, so that they lase in a CW mode .
• two APBGs can be used to create a Fabry- Perot style cavity for a fibre laser (Fig. 20) , with the added functionality that the filter response can be arbitrarily designed (to be high transmission, for example) at single or multiple pump wavelengths and (to have a high-Q, for example) at single or multiple laser wavelengths.
• APBGs can also be advantageously used within other laser configurations, such as rings (single or multiple, Sagnac loops, figure of 8 loops, etc.)
• Figure 21 depicts such a generic fibre ring laser cavity.
• Semiconductor lasers widely employ grating-based wavelength selective feedback, for example in DBR, DFB and VCSEL designs .
• APBGs can usefuly be employed to provide such feedback, with the added functionality as defined above.
• DFB and VCSEL structures incorporating ABPGs are shown in figures 22 & 23 respectively. Further functionality can be achieved, e.g. multi -wavelength conversion, multi - wavelength 3R regeneration, by concatenating suitable
• APBG/APNLM structures with either conventional semiconductor lasers, or APBG-modified semiconductor lasers.
• APBG structures are useful in modifying electronic band-gap of "new" materials, designed to have an aperiodic lattice or superlattice.
• new materials designed to have an aperiodic lattice or superlattice.
• APBG superlattices enhances the possibilities for such designs.
• a generic APBG lattice (or super-lattice) is depicted in figure 24.
• Plane-wave (Fourier) expansions of wavefunctions are often used in current theoretical models of solid-state structures.
• material parameters e.g. location of band minima, effective mass etc. can be tailored to yield new aperiodic materials with desirable band-structure characteristics.
• Other parameters such as conductivity, thermal conductivity and dielectric permittivity or magnetic permeability could also be designed into the material .
• This design technique should also find applications the fabrication of new superconducting materials m which, for example, some of the properties of boson-like Cooper-pairs can be treated m an analogous manner to photons m a photonic crystal .

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