Explicit formulas for the identification of a small defect in a planar waveguide

Sailing He; Ran Liao; Vladimir Romanov

doi:10.1364/JOSAA.22.001414

Journal of the Optical Society of America A
Vol. 22,
Issue 7,
pp. 1414-1419
(2005)
•https://doi.org/10.1364/JOSAA.22.001414

Explicit formulas for the identification of a small defect in a planar waveguide

Sailing He, Ran Liao, and Vladimir Romanov

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Sailing He, Ran Liao, and Vladimir Romanov, "Explicit formulas for the identification of a small defect in a planar waveguide," J. Opt. Soc. Am. A 22, 1414-1419 (2005)

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Abstract

Nondestructive testing of a small defect (a dust particle or air void) in a strongly confined planar waveguide is considered. Explicit formulas are given for a quick identification of the small defect by use of the distorted fields measured at the two end faces of the planar waveguide for two frequencies. The explicit identification scheme is verified numerically.

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Situations and Parameters	True Value	Reconstructed Value	Reconstruction Error (with clean data) (%)	Reconstruction Error (with 5% noise data) (%)
S1:
$z_{0} (μ m)$	20.0	20.02335346	0.116767	0.425623
$x_{0} (μ m)$	3.0	2.99987674	0.004109	0.001971
A	0.00006942	0.00006958	0.230481	0.632236
$A_{s}$	0.00007299	0.00007316	0.232909	0.633436
S2:
$z_{0} (μ m)$	−195.0	−195.00650497	0.003336	0.167578
$x_{0} (μ m)$	3.0	2.99979145	0.006951	0.235495
A	0.00006942	0.00006960	0.259291	0.576885
$A_{s}$	0.00007299	0.00007318	0.260310	0.809554
S3:
$z_{0} (μ m)$	20.0	19.98057399	0.097130	0.750642
$x_{0} (μ m)$	1.0	1.00085186	0.085186	3.291359
A	0.00004290	0.00004299	0.209790	1.655067
$A_{s}$	0.00007299	0.00007309	0.137005	4.656153

Parameters	True Value	Reconstructed value	Reconstruction Error (with clean data) (%)	Reconstruction Error (with 5%noise data) (%)
$z_{0} (μ m)$	20.0	20.01508708	0.075435	0.806378
$x_{0} (μ m)$	3.0	2.99989739	0.003420	0.115259

Situations and Parameters	True Value	Reconstructed Value	Reconstruction Error (with clean data) (%)	Reconstruction Error (with 5% noise data) (%)
S1:
$z_{0} (μ m)$	20.0	20.02335346	0.116767	0.425623
$x_{0} (μ m)$	3.0	2.99987674	0.004109	0.001971
A	0.00006942	0.00006958	0.230481	0.632236
$A_{s}$	0.00007299	0.00007316	0.232909	0.633436
S2:
$z_{0} (μ m)$	−195.0	−195.00650497	0.003336	0.167578
$x_{0} (μ m)$	3.0	2.99979145	0.006951	0.235495
A	0.00006942	0.00006960	0.259291	0.576885
$A_{s}$	0.00007299	0.00007318	0.260310	0.809554
S3:
$z_{0} (μ m)$	20.0	19.98057399	0.097130	0.750642
$x_{0} (μ m)$	1.0	1.00085186	0.085186	3.291359
A	0.00004290	0.00004299	0.209790	1.655067
$A_{s}$	0.00007299	0.00007309	0.137005	4.656153

Parameters	True Value	Reconstructed value	Reconstruction Error (with clean data) (%)	Reconstruction Error (with 5%noise data) (%)
$z_{0} (μ m)$	20.0	20.01508708	0.075435	0.806378
$x_{0} (μ m)$	3.0	2.99989739	0.003420	0.115259

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Equations (44)

Journal of the Optical Society of America A