WO2003079083A1 - Improved multi channel grating design - Google Patents
Improved multi channel grating design Download PDFInfo
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- WO2003079083A1 WO2003079083A1 PCT/AU2003/000319 AU0300319W WO03079083A1 WO 2003079083 A1 WO2003079083 A1 WO 2003079083A1 AU 0300319 W AU0300319 W AU 0300319W WO 03079083 A1 WO03079083 A1 WO 03079083A1
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- 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
- 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
- G02B6/02133—Refractive index modulation gratings, e.g. Bragg gratings characterised by the method of manufacture of the grating using beam interference
-
- 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
- G02B6/24—Coupling light guides
- G02B6/26—Optical coupling means
- G02B6/28—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
- G02B6/293—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means
- G02B6/29304—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by diffraction, e.g. grating
- G02B6/29305—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by diffraction, e.g. grating as bulk element, i.e. free space arrangement external to a light guide
- G02B6/29307—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by diffraction, e.g. grating as bulk element, i.e. free space arrangement external to a light guide components assembled in or forming a solid transparent unitary block, e.g. for facilitating component alignment
-
- 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
Abstract
A method of calculating a sampling function for fabricating an N-channel grating, the method comprising the steps of forming a summation of N+n periodic seeding functions each describing a refractive index variation, wherein each periodic function includes a phase shift with respect to the other functions, and wherein at least one of the phase shift values is non-zero, and wherein the total number of the periodic seeding functions N+n is smaller than an upper limit given by a resolution limitation in the fabrication of the grating.
Description
Improved Multi Channel Grating Design
Field of the invention
The present invention relates broadly to a multi-channel grating design method and to multi-channel grating structures.
Background of the invention
Multi-channel grating structures are typically written into photosensitive waveguides. The grating structure comprises refractive index variations induced in the photosensitive waveguide, which in turn determines the optical characteristics such as the reflection, transmission, and group delay characteristics of the resulting grating structure.
One approach to induce a multi-channel grating structure is to impose a periodic amplitude modulation to a given single-channel grating profile. The resulting periodic profile of the refractive index is typically achieved by exposing the photosensitive waveguide to an appropriate light beam emerging from e.g. a suitable phase mask or other method.
In a vast majority of previously reported work on multi-channel gratings, a so-called sine-sampling (amplitude modulation) design has been used. For the sine-sampling approach, an N-channel grating design q z) can be obtained by a direct in-phase summation of N identical seeding gratings [with the amplitude of the grating κ(z) and the grating phase θ (z)] equally spaced in the frequency space:
q(z) = ∑ rølκβI+β+( 2 -/v-.,Δ»/2] = κe^^ssinc (z) , (1)
where sampling function is
Ssinc (z) = N ∑smc[N(Akz - 2πn)/ 2], sinc(; )=sin( ) / , (2) π=-co
and Δk is the inter-channel spacing. This design will be referred to as "in-phase" grating design herein after by the applicant.
An example of the "in-phase" design is shown in Figures 7 (a) and (c) with corresponding spectral characteristics as shown in Figures 7 (b) and (d). The peak of the refractive index change required to implement this design is given by expression:
AnN = NAns , (3)
where Δw. is the peak refractive index change of the single-channel grating. Since photosensitive fibers used to fabricate Bragg gratings have material limits on the maximum achievable refractive index change AnN , Eq. (3) represents a limitation on the maximum number of channels that can be recorded in a given fiber. Thus it is highly desirable to reduce a required AnN as much as possible.
In a phase modulation approach, the theoretical peak of the refractive index change required to implement a multi-channel grating is reduced compared to the sine-sampling approach, AnN = VNΔ«_ . In one of the realisations, it has been proposed to use a numerical optimisation method in which a grating in a waveguide is divided into sections, where the grating pitch and depth are assumed to be uniform, and only the grating phase θt depends on section i. The relative phases θt of all sections were used as parameters to minimise the mean square deviation of the calculated spectral characteristics of the grating from target characteristics. This proposed numerical optimisation method results in the presence of a large number of sidebands in the spectral characteristic of the calculated (and measured) grating. That in turn, both diminishes the quality of the spectral characteristics achievable and leads to steep requirements for the spatial resolution of a grating fabrication method.
At least preferred embodiments of the present invention seek to provide an alternative multi-channel grating design in which the maximum refractive index change required as a function of number of channels is reduced, but also deterioration of the grating spectral characteristics is reduced when compared with the prior art grating designs discussed above.
Summary of the invention
In accordance with a first aspect of the present invention there is provided a method of calculating a sampling function for fabricating an N-channel grating, the method comprising the steps of forming a summation of N+n periodic seeding functions each describing a refractive index variation, wherein each periodic function includes a phase shift with respect to the other functions, and wherein at least one of the phase shift values is non-zero, and wherein the total number of the periodic seeding functions N+n is smaller than an upper limit given by a resolution limitation in the fabrication of the grating.
For a given N, the number of side channels n may be chosen such that the peak amplitude of the resulting sampling function falls within a local minimum region of a function representing the peak amplitude of the sampling function versus n.
In other embodiments, n may be chosen based on a selected generic formula. The formula may be: n=2(N+J).
The summation of the N+n periodic functions may comprise a Fourier analysis. This may result in the following expression for a multi-channel design:
= / BH o,+,',-S,(z), (4)
where , is a phase shift of the Eth periodic function, S(z) is a complex sampling function.
The Fourier analysis advantageously comprises defining N high-amplitude periodic functions (central channels) out of the N+w periodic functions (the total number of channels).
The method may comprise the step of forming a summation of N periodic functions to calculate an initial sampling function.
The step of calculating the initial sampling function may comprise the step of determining a set of the phase shifts for which the peak amplitude of initial sampling function S(z) is minimised.
Alternatively, the step of calculating the initial sampling function may comprise the step of determining a set of the phase shifts for which a difference between the peak and the minimum amplitude of initial sampling function S(z) is minimised.
Alternatively, the step of calculating the initial sampling function may comprise the step of determining a set of the phase shifts for which the mean square deviation of the amplitude \S(z)\ of the initial sampling function from average is minimised.
The step of determining the set of phase shifts may comprise direct scanning through all combinations or conducting a variational (functional) analysis, or using other forms of extremum search numerical techniques, or a simulated annealing (Monte Carlo) approach.
The method may further comprise the steps of (a) modifying the initial sampling function, (b) decomposing the modified initial sampling function into the summation of N+w periodic functions, (c) modifying the decomposition coefficients in the summation of the N+n
periodic functions, and (d) applying an inverse Fourier transformation to the summation of the N+n periodic functions with the modified decomposition coefficients to calculate the sampling function.
Preferably, steps (a)-(d) are iterated until a selected quality criterion has been reached. The iteration may be stopped when a variation in the maximum sampling function amplitude between iterations falls below a predetermined value.
Step (a) may comprise replacing nontrivial amplitude dependence in the initial sampling function with a constant value for a given N. The constant value may be N .
Step (b) may comprise decomposing the modified initial sampling function into a Fourier series.
Step (c) may comprise replacing N decomposition coefficients and setting all decomposition coefficients outside the band / € [1 - n 12, N + n 12] to zero.
The replacement of the N decomposition coefficients may be based on a variable function.
The absolute value of the N decomposition coefficients may be replaced by a constant C. C may be based on a normalisation condition.
The grating may be multi-dimensional, wherein the periodic seeding functions are multidimensional.
In accordance with a second aspect of the present invention, there is provided a method for fabricating a multi-channel grating comprising the step of calculating a sampling function in accordance with a method as defined in the first aspect.
The multi-channel grating may e.g. be fabricated utilising photo-induced refractive index changes in a photosensitive waveguide material, etching techniques, or epitaxial techniques, or a developing technique such as a photo polymerisation process.
In accordance with a third aspect of the present invention, there is provided a multichannel grating structure fabricated utilising a method of fabrication as defined in the second aspect.
In accordance with a fourth aspect of the present invention, there is provided an N- channel grating structure having a spectral response characterised by N central channels and n
side bands, wherein N+n is smaller than an upper limit given by a resolution limitation in the fabrication of the grating.
For a given N, the number of side channels n may be chosen such that the peak amplitude of the sampling function required for the formation of the grating structure falls within a local minimum region of a function representing the peak amplitude of the sampling function for the given N versus n.
In other embodiments, n may be chosen based on a selected formula. The formula may be: n=2(N+l).
Brief description of the drawings
Preferred forms of the present invention will now be described with reference to the accompanying drawings.
Figure 1 shows the maximum and minimum values of the sampling function amplitude for different number of channels obtained using the difference minimisation approach.
Figure 2 shows a 16-channel initial grating design using the difference minimization approach.
Figure 3 shows a 16-channel grating design using the unlimited extended difference minimization approach.
Figure 4 shows a 16-channel grating design using the limited extended difference minimization approach embodying the present invention.
Figure 5 shows plots of normalised sampling function amplitude required for 8 and 16- channel grating designs as a function of the number of side channels.
Figure 6 shows an experimental set up for writing a multi-channel grating structure of a multi-channel grating design embodying the present invention.
Figure 7 shows a prior art 4-channel "in-phase" grating design.
Detailed description of the embodiments
The preferred embodiment described provides a multi-channel grating design in which the maximum refractive index change is less than directly proportional to the number of
channels N, and which reduces deterioration of the grating spectral characteristics as a result of side bands in the spectral characteristics of the resulting grating, thereby improving on prior art multi-channel grating designs.
In the preferred embodiment, an initial sampling function, which periodically modulates the amplitude of a given single-channel grating (seeding grating), is utilised, similar to prior art multi-channel grating designs. In addition to the periodic modulation of the amplitude of the seeding grating, a periodic modulation of the phase of the seeding grating is also introduced. Accordingly, the resulting initial sampling function S(z) for an N-channel grating in the preferred embodiment may be expressed as:
S(z) = rø lκ."*+("-"-υ °'2+Λ] = K-e'(K°z+ S(z), (5)
where the phase of the sampling function, ^,(z) = arg{S'(z)}, and the amplitude, |S(z)|, are given by:
By direct calculations it is straightforward to show that
£ |S(z)| dz = 2πN/ Ak (8)
for any ψι. This expression, in turn, leads to an asymptotic formula for the achievable minimum peak AnN corresponding to an "ideal" optimisation when |S(z)|=VN and only the grating phase is nontrivially modulated [by addition of an appropriately chosen phase of the sampling function ψ{z) \.
In one of the preferred embodiments, the stage of calculating the preliminary sampling function comprises reduction of the difference between the maximum and minimum values of the sampling function amplitude. Mathematically this may be formulated as finding
SdΛz;Φ °p,)) or which
max{Srfm} - min{Sdm} = min[max{S(z;^)} - min{S(z;^)}]. (10) z z φl z z
This approach may be implemented by using a simulated annealing algorithm, a Monte Carlo method for minimization of multi-variable functions. This statistical method samples the search space in such a way that there is a high probability of finding an optimal or near-optimal solution in a reasonable time. The term "simulated annealing" is derived from the analogy to physical process of heating and then slowly cooling a substance to obtain a crystalline structure.
The corresponding results are given in Fig. 1. An example of this version of optimal (difference minimisation) "out-of-phase" initial design and spectral characteristics for a 16- channel grating is shown in Fig. 2(a)-(d). This initial sampling function design already reduces the maximum AnN of the "in-phase" design, as can be seen from a comparison with the prior art design and spectral characteristics shown in Figures 7(a) to (d).
Another embodiment of the calculating the preliminary sampling function comprises the functional minimisation (variational approach). The key property of this embodiment is that it relies on estimate of some integral functional rather than time-consuming numerical scanning through continuous variable z. Quantitatively, proximity of |S(z)| to the theoretical limit VN can be characterised by the mean-square-deviation,
ΔS = ^{S(z)| - |S|^ , (11)
where (/(z)) ≡ / = Ak/2π I f(z)dz . Due to expression (8), the best optimisation of |S(z)|
corresponds to the achievement of the zero mean square deviation from average |S| = VN . Assuming a sufficiently good initial optimisation, ΔS « 1 , and that the amplitude of the sampling function is close to VN for any z, the second term under square root (7) is considered
to be small. Expansion of |S(z)| into the Taylor series followed by the averaging the result over the period results in estimate,
E = - m+l.p )cos(a, + β, - a, - βp + βm - βm+l-P ), (13)
and a, ≡ ( . + φN+ _,) / 2 , β, ≡ (φ, - φN+i_,)/ 2.
The major advantage of the optimisation strategy based on the functional minimisation when compared to direct scanning is the speed of calculations: integration over z is carried out analytically which efficiently reduces the computational time.
Simulated annealing has proven to be one of the most efficient methods for finding a set of phase shifts that minimises mean square deviation ΔS .
It is noted that points with the best optimisation quality may be used to get reasonable (but not exactly the best) optimisation for some higher channel numbers using a block scheme (convolution of sampling functions). For example, the point N=9 with the particularly good optimisation quality provides us with an effortless optimisation for N=81=9x9.
In the preferred embodiment, the results of the calculating of the preliminary sampling function are extended further. The second stage of optimisation comprises the following iterative steps.
The best set of N dephasing angles φι (l ≤ l ≤ N) is taken and the initial sampling function S(z)=|S(z)| e'^z) is constructed on a period 2ττ/Δk, in accordance to expression (5). Then a nontrivial |S(z)| dependence is replaced by the asymptotic value VN and the resulting intermediate sampling function (with only phase sampling present) is decomposed into the Fourier series to find complex decomposition coefficients a, and the corresponding new set of dephasing angles
= arg(α/ ) . This procedure leads to a change in partial grating amplitude values in sum (5). In addition, extra small higher order harmonics (corresponding to additional small partial gratings) arise.
Next step comprises modification of the sampling function in the Fourier domain. This includes coefficients α for N high- amplitude partial gratings being replaced by Ce ' , where a constant C is found from the normalisation condition
N 2
∑|β,| = KC2 (14)
1=1 and all coefficients ai outside the band / e [l - n /2,N + n /2] being set to zero. These modified N+n amplitudes are used to construct a new sampling function
via inverse Fourier transformation. Significantly, the side-band coefficients ai (for which / e [1 - n 12,0], / e [N + 1, N + n 12] ) are maintained from the sampling function in the Fourier domain.
The procedure is continued in an iterative fashion until a selected quality criterion has been reached. In the example embodiment, the iteration is stopped when a variation in the maximum sampling function amplitude between iterations falls below 10"6.
As a result of an extended minimisation, the obtained sampling function S(z) is characterised by amplitude which is close to the theoretical limit VN . Finally, S(z) is multiplied by 1/C factor (with C corresponding to amplitude of any equal central channel partial gratings) to compensate for the central gratings strength reduction due to appearance of the additional small partial gratings. If the optimisation quality achieved prior to the iteration procedure is reasonably good then this factor is close to one.
The extended iterative procedure for an infinite number of side channels n translates all nontrivial amplitude modulation of the sampling function into its phase ψ z). As a price for doing that, about ION additional partial gratings (higher order harmonics with |α/|> 0.001) appear in S(z) decomposition, which means that phase dependence ψ(z) has a very fine structure. However, for practical applications the scale of the fine structure should always be larger than the size of the laser beam used for grating writing. An estimate for the upper limit for the maximum total number of nonzero partial gratings can be given as
I2
N + n = °- , (15)
2z0Aλ0n0
where λo is the central wavelength, zø is the minimal laser beam size, Δλ is the neighbouring channel spacing, and no is the FBG average refractive index. Estimate (15) is based on the Nyquist theorem requiring at leat 2 grid points to describe a period of the function cos(z) well enough. For the purpose of this description, the upper limit for the maximum total number given by the resolution limitation in the fabrication of the grating [estimate (15)] will be referred to as un-limited in the context of the preferred embodiment of the present invention, as it relates to a given experimental limitation.
The un-limited extended difference minimisation design and spectral characteristics of this step for a 16-channel grating design is shown in Figures 3(a) to (d). It was found that as a result of this restriction on the resolution, numerically calculated spectral characteristics became worse than for difference minimization or variational minimization alone [compare Figures 3(b) and (d) with Figures 2(b) and (d)]. Thus, it has been recognised that it is important to limit the number of additional small amplitude partial gratings to a number smaller than that determined by the resolution limitation [estimate (15)]. It was found that selecting n=2(N+l) channels yields good results in preferred embodiments of the invention.
The limited extended difference minimization grating design and spectral characteristics of the preferred embodiment is shown in Figures 4(a) to (d). Although the peak amplitude of the sampling function is slightly increased when compared to the un-limited extended difference minimization design [compare Figure 4(a) and Figure 3(a)], the quality of the spectral characteristics are significantly improved [compare Figures 4(b), (d) and Figure 3 (b), (d)]. At the same time, the achievable peak amplitude of the sampling function is still significantly reduced when compared to the initial difference minimization design [compare Figures 4(a) and 1(a)], and the "in-phase" approach [compare Figures 4(a) and 7(a)].
Figure 5 shows normalised maximum amplitude of the sampling function versus the number of side channels for 8 and 16 central channels designs, solid and dash lines respectively. The limitation n=2(N+7) side channels is marked by squares. As can be seen, the limitation of the preferred embodiment falls into regions of local minima, thus providing further support for the selection of the limitation of the preferred embodiment.
The implementation of the multi-channel grating design of the preferred embodiment in a grating structure requires grating writing apparatus with high spatial resolution to be utilised. Therefore, in a grating writing apparatus relying on photoinduced refractive index changes, the
apparatus preferably comprises a beam focusing means to reduce the size of the beam in the core of the photosensitive waveguide.
Figure 6 shows an example experimental set up 50 for writing a multi-channel grating 52 into an optical fibre 54. The experimental set up 50 comprises an interferometer 56 which includes a first acousto-optic modulation 58 being operated under an acousto-optic wave at a first frequency Ωi, as indicated by arrow 14. An incoming light beam 60 is incident on the first acousto-optic modulator 58 at a first order Bragg angle. The operating conditions of the acousto-optic modulator 58 are chosen such that the modulator 58 is under driven, whereby approximately 50% of the incoming beam 60 is diffracted into a first order beam 62, and 50% passing through the acousto-optic modulator 58 as an un-diffracted beam 64. The un-diffracted beam 64 is incident on a second acousto-optic modulator 66 of the interferometer 56 at a first order Bragg angle, whereas the beam 62 is not. Accordingly, the beam 62 passes through the second acousto-optic modulator 66 without any significant loss.
The second acousto-optic modulator 66 is operated under an acousto-optic wave at a frequency Ω2, which propagates in a direction opposing the direction of the acousto-optic wave in the first modulator 58 as indicated by arrow 68. After the second acousto-optic modulator 66 the first order diffracted beam 70 and the beam 62 are frequency shifted in the same direction (e.g. higher frequency), but by different amounts i.e. Ω\ v Ω2.
The beams 62, 70 are then brought to interfere utilising an optical lens 72, and the resulting interference pattern (at numeral 74) induces refractive index changes in the photosensitive optical fibre 54, whereby a refractive index profile, i.e. grating structure 52, is induced in the optical fibre 54.
In Figure 6, the optical fibre 54 is translated along the interferometer at a speed v, as indicated by arrow 74.
It will be appreciated by a person skilled in the art that the experimental set up 50 shown in Figure 6 can be utilised to write a multi-channel grating structure of a multi-channel grating design embodying the present invention through suitable control of the first and second acousto- optic modulators 58, 66, in conjunction with a suitable control of the speed v at which the optical fibre 54 is translated along the interferometer 56 at any particular time. The high spatial resolution required to implement the multi-channel design of the preferred embodiment is
achieved in the set up shown in Figure 6 by utilising the optical lens 72, with the practical limit of the beam size in the focal plane preferably being of the order of the waveguide core size.
It will be appreciated by a person skilled in the art that numerous variations and/or modifications may be made to the present invention as shown in the specific embodiments without departing from the spirit of scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects to be illustrative and not restrictive.
For example, multi-channel gratings can be fabricated on the basis of the multi-channel grating design of the present invention using various known grating writing techniques, including one or more of the group of photo-induced refractive index variation in photo sensitive waveguide materials, etching techniques including etching techniques utilising a phasemask, and epitaxial techniques. Furthermore, while the preferred embodiments have been described in the context of 1 -dimensional Bragg gratings, the present invention does extend to multi-dimensional multi-channel gratings. Such gratings have applications e.g. as photonic bandgap structures.
In the claims that follow and in the summary of the invention, except where the context requires otherwise due to express language or necessary implication the word "comprising" is used in the sense of "including", i.e. the features specified may be associated with further features in various embodiments of the invention.
Claims
1. A method of calculating a sampling function for fabricating an N-channel grating, the method comprising the steps of:
- forming a summation of N+n periodic seeding functions each describing a refractive index variation, wherein each periodic function includes a phase shift with respect to the other functions, and wherein at least one of the phase shift values is non-zero, and
- wherein the total number of the periodic seeding functions N+n is smaller than an upper limit given by a resolution limitation in the fabrication of the grating.
2. A method as claimed in claim 1, wherein for a given N, n is chosen such that the peak amplitude of the resulting sampling function falls within a local minimum region of a function representing the peak amplitude of the sampling function for the given N as a function of n.
3. A method as claimed in claim 1, wherein n is chosen based on a selected formula.
4. A method as claimed in claim 3, wherein the formula is: n=2(N+l).
5. A method as claimed in any one of the preceding claims, wherein the summation of the N+n periodic functions comprises a Fourier analysis.
6. A method as claimed in claim 5, wherein the result of the analysis leads to the grating design expressed as:
N+n 12 q(z) = ∑ rø'lK^÷(«- V-.-l)Δ« /2+Λ] = „_** +* S(z),
/=!-«/ 2 where φ, is a phase shift of the /-th periodic function, S(z) is a complex sampling function with the phase ψ(z) = arg{S(z)}.
7. A method as claimed in claims 5 or 6, wherein the Fourier analysis comprises defining N high-amplitude periodic functions out of the N+n periodic functions.
8. A method as claimed in any one of the preceding claims, wherein the method comprises the step of forming a summation of N periodic functions to calculate an initial sampling function.
9. A method as claimed in claim 8, wherein the step of calculating the initial sampling function comprises the step of determining a set of the phase shifts for which the peak amplitude of the initial sampling function S(z) is minimised.
10. A method as claimed in claim 8, wherein the step of calculating the initial sampling function comprises the step of determining a set of the phase shifts for which a difference between the peak and minimum amplitude of the initial sampling function is minimised.
11. A method as claimed in claim 8, wherein the step of calculating the initial sampling function comprises the step of determining a set of the phase shifts for which the mean square deviation of the initial sampling function amplitude |S(z)| from average is minimised.
12. A method as claimed in any one of claims 9 to 11, wherein the step of determining the set of phase shifts may comprise direct scanning through all combinations or conducting a variational analysis, or using other forms of extremum search numerical techniques, or a simulated annealing (Monte Carlo) approach.
13. A method as claimed in any one of claims 8 to 12, wherein the method further comprises the steps of:
(a) modifying the initial sampling function,
(b) decomposing the modified initial sampling function into the summation of N+n periodic functions,
(c) modifying the decomposition coefficients in the summation of the N+n periodic functions, and
(d) applying an inverse Fourier transformation to the modified decomposition coefficients to calculate the sampling function.
14. A method as claimed in claim 13, wherein steps (a)-(d) are iterated until a selected quality criteria has been reached.
15. A method as claimed in claim 14, wherein the iteration is stopped when a variation in the maximum sampling function amplitude between iterations falls below a predetermined value.
16. A method as claimed in any one of claims 13 to 15, wherein step (a) comprises replacing nontrivial amplitude dependence in the initial sampling function with a constant value for a given N. The constant value may be VN .
17. A method as claimed in any one of claims 13 to 16, wherein step (b) comprises decomposing the modified initial sampling function into a Fourier series.
18. A method as claimed in any one of claims 13 to 17, wherein step (c) comprises replacing N decomposition coefficients and setting all decomposition coefficients outside the band / e [l - n / 2,N + n /2] to zero.
19. A method as claimed in claim 18, wherein the replacement of the N decomposition coefficients is based on a variable function.
20. A method as claimed in claim 18, wherein a constant C replaces the absolute values of the Ν decomposition coefficients.
21. A method as claimed in claim 20, wherein C is based on a normalisiation condition.
22. A method as claimed in any one of the preceding claims, wherein the grating is multi-dimensional, wherein the periodic seeding functions are multi-dimensional.
23. A method for fabricating a multi-channel grating comprising the step of calculating a sampling function in accordance with a method as claimed in any one of the preceding claims.
24. A method as claimed in claim 23, wherein the multi-channel grating is fabricated utilising photo-induced refractive index changes in a photosensitive waveguide material, etching techniques, or epitaxial techniques, or a developing technique such as a photo polymerisation process.
25. A multi-channel grating structure fabricated utilising a method of fabrication as claimed in claims 23 or 24.
26. A N-channel grating structure having a spectral response characterised by N central channels and n side bands, wherein N+n is smaller than an upper limit given by a resolution limitation in the fabrication of the grating.
27. A grating structure as claimed in claim 26, wherein, for a given N, n is chosen such that a peaks amplitude of the sampling function required for the formation of the grating structure falls within a local minimum region of a function representing the peak amplitude of the sampling function for the given N versus n.
28. A grating structure as claimed in claim 25, wherein n is chosen based on a selected formula.
29. A grating structure as claimed in claim 28, wherein the formula is: n=2(N+l).
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|---|---|
| AU (1) | AUPS113102A0 (en) |
| WO (1) | WO2003079083A1 (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6317539B1 (en) * | 1999-09-17 | 2001-11-13 | Jds Uniphase Corporation | Interleaved sampled and chirped optical waveguide gratings for WDM channel operations and resulting devices |
| US6345135B1 (en) * | 1998-05-06 | 2002-02-05 | Douglas Charles John Reid | Multi-wavelength optical reflector |
| WO2002069006A1 (en) * | 2001-02-26 | 2002-09-06 | Redfern Optical Components Pty Ltd | Multi channel grating design |
-
2002
- 2002-03-15 AU AUPS1131A patent/AUPS113102A0/en not_active Abandoned
-
2003
- 2003-03-17 WO PCT/AU2003/000319 patent/WO2003079083A1/en not_active Application Discontinuation
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6345135B1 (en) * | 1998-05-06 | 2002-02-05 | Douglas Charles John Reid | Multi-wavelength optical reflector |
| US6317539B1 (en) * | 1999-09-17 | 2001-11-13 | Jds Uniphase Corporation | Interleaved sampled and chirped optical waveguide gratings for WDM channel operations and resulting devices |
| WO2002069006A1 (en) * | 2001-02-26 | 2002-09-06 | Redfern Optical Components Pty Ltd | Multi channel grating design |
Also Published As
| Publication number | Publication date |
|---|---|
| AUPS113102A0 (en) | 2002-04-18 |
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