High accuracy dispersion measurements of chirpedfibre gratings

Barcelos, S.; Zervas, M.N.; Laming, R.I.; Payne, D.N.; Reekie, L.; Tucknott, J.A.; Kashyap, Raman; McKee, Paul; Sladen, F.M.E.; Wojciechowicz, B.

doi:10.1049/el:19950847

Cited by 40 publications

(13 citation statements)

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“…Note that since the problem is linear, the reflection coefficient does not depend on the boundary condition . The complex reflection spectrum is often used to characterize gratings, since it can be measured experimentally [3], [15]. It is possible to present the fields in the time domain using a Fourier transform , where is normalized time, is the velocity of light in vacuum, and is time.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The grating structure of the th layer is extracted from the solution to the GLM equation using (8) (17) Note that the extracted grating structure is not used to propagate the reflection coefficient in (15). Therefore, the error in evaluating the grating profile does not accumulate along the grating.…”

Section: The Ilp Algorithmmentioning

confidence: 99%

“…When the width of each layer is short enough, the Born approximation, given in (9), can be accurately used. Substituting (9) into (15) and (16), we obtain a simple equation for propagating the complex reflection coefficient along the grating Equation (18) is the Born approximation to (15). The grating profile is extracted using the connection (20)…”

Section: The Ilp Algorithmmentioning

confidence: 99%

“…We note that although the spectrum contains points, the profile of the whole grating contains only points, due to the casuality of the solution. The complexity of propagating the reflection coefficient from one layer to another using (11), (15), and (16) is equal to . The complexity of calculating the profile of a single layer using (11) and (17) is equal to .…”

Section: Complexity and Numerical Implementationmentioning

confidence: 99%

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Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings

Rosenthal

Horowitz

2003

IEEE J. Quantum Electron.

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We demonstrate a new inverse scattering algorithm for reconstructing the structure of highly reflecting fiber Bragg gratings. The method, called integral layer-peeling (ILP), is based on solving the Gel'fand-Levitan-Marchenko (GLM) integral equation in a layer-peeling procedure. Unlike in previously published layer-peeling algorithms, the structure of each layer in the ILP algorithm can have a nonuniform profile. Moreover, errors due to the limited bandwidth used to sample the reflection coefficient do not rapidly accumulate along the grating. Therefore, the error in the new algorithm is smaller than in previous layer peeling algorithms. The ILP algorithm is compared to two discrete layer-peeling algorithms and to an iterative solution to the GLM equation. The comparison shows that the ILP algorithm enables to solve numerically difficult inverse scattering problems, where previous algorithms failed to give an accurate result. The complexity of the ILP algorithm is on the same order as in previous layer peeling algorithms. When a small error is acceptable, the complexity of the ILP algorithm can be significantly reduced below the complexity of previously published layer-peeling algorithms.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Section: The Ilp Algorithmmentioning

confidence: 99%

Section: The Ilp Algorithmmentioning

confidence: 99%

Section: Complexity and Numerical Implementationmentioning

confidence: 99%

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Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings

Rosenthal

Horowitz

2003

IEEE J. Quantum Electron.

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“…Some of their properties have been studied theoretically and demonstrated in a number of system trials [2]. We have implemented a variablechirp grating using the temperature gradient technique [3] and systematically measured its reflection and dispersion characteristics [4] for a wide range of applied chirp. The results clarify those properties and are in very good agreement with the theoretical predictions, which were calculated using coupled-mode theory applicable to nonuniform aperiodic structures [5,6].…”

Section: Introductionmentioning

confidence: 99%