Transfer function analysis of measured transfer matrices

Shao Yang; I. P. Vayshenker; Dag R. Hjelme; Alan R. Mickelson

doi:10.1364/AO.28.003148

Applied Optics
Vol. 28,
Issue 15,
pp. 3148-3157
(1989)
•https://doi.org/10.1364/AO.28.003148

Transfer function analysis of measured transfer matrices

Shao Yang, I. P. Vayshenker, Dag R. Hjelme, and Alan R. Mickelson

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Shao Yang, I. P. Vayshenker, Dag R. Hjelme, and Alan R. Mickelson, "Transfer function analysis of measured transfer matrices," Appl. Opt. 28, 3148-3157 (1989)

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Abstract

Measurements of mode transfer matrices of various multimode fiber optic connectors are presented. To analyze the accuracy and repeatability of such measurements, a theoretical framework which employs mode transmission functions is derived. It is shown that the transfer function can be used to find transfer matrices for any set of launches. A procedure for determination of the mode transfer function is given.

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		1	2	3	4	5	6	Total
$K 1 (\overset{i}{P 11} / \overset{i}{P 21})$		2.41	4.46	2.96	2.92	0.06	2.1
$K 2 (\overset{i}{P} 22 / \overset{i}{P 12})$		4.55	4.21	6.40	2.26	2.27	1.05
T11	D	.0139	.0059	.0008	−.0293	.0084	.0127	0
T11	S	.0302	.0059	.0537	.037	.027	.0156	.0358
T12	D	−.0068	−.0043	−.0064	.0021	.0069	.0168	0
T12	S	.0076	.0052	.0118	.02	.0078	.0357	.0153
T21	D	−.0082	−.0144	−.018	.0045	.0201	.0192	0
T21	S	.0252	.0162	.0495	.0246	.023	.043	.0325
T22	D	.0064	−.0039	.0097	−.012	.0053	−.0241	0
T22	S	.0202	.0214	.0379	.0234	.0106	.0591	.0286

	T₁₁	T₁₂	T₂₁	T₂₂
T_m	.9710	.0020	.0410	.9270
T^(m)	.9904	−.0058	.0154	.9601
T⁽¹⁾	.9870	.0083	.0063	.9978
T⁽²⁾	.9451	.0046	.0163	.9588
$\begin{array}{l} (a) & L = . 067 dB & τ = . 055 \\ k_{1} = 4.15 & k_{2} = 4.35 \end{array}$
	T₁₁	T₁₂	T₂₁	T₂₂
T_m	.9380	−.0130	.0870	.9240
T^(m)	.9769	−.0012	.0374	.9218
T⁽¹⁾	.9683	.0170	.0204	.9580
T⁽²⁾	.9203	.0108	.0389	.9215
$\begin{array}{l} (b) & L = . 19 dB & τ = . 07 \\ k_{1} = 2.13 & k_{2} = 4.72 \end{array}$
	T₁₁	T₁₂	T₂₁	T₂₂
T_m	.9730	−.0380	.0360	.9500
T^(m)	.9722	.0004	.0398	.9011
T⁽¹⁾	.9643	.0243	.0258	.9437
T⁽²⁾	.9046	.0150	.0531	.8982
$\begin{array}{l} (c) & L = . 27 dB & τ = . 075 \\ k_{1} = 3.04 & k_{2} = 4.63 \end{array}$

		1	2	3	4	5	6	Total
$K 1 (\overset{i}{P 11} / \overset{i}{P 21})$		2.41	4.46	2.96	2.92	0.06	2.1
$K 2 (\overset{i}{P} 22 / \overset{i}{P 12})$		4.55	4.21	6.40	2.26	2.27	1.05
T11	D	.0139	.0059	.0008	−.0293	.0084	.0127	0
T11	S	.0302	.0059	.0537	.037	.027	.0156	.0358
T12	D	−.0068	−.0043	−.0064	.0021	.0069	.0168	0
T12	S	.0076	.0052	.0118	.02	.0078	.0357	.0153
T21	D	−.0082	−.0144	−.018	.0045	.0201	.0192	0
T21	S	.0252	.0162	.0495	.0246	.023	.043	.0325
T22	D	.0064	−.0039	.0097	−.012	.0053	−.0241	0
T22	S	.0202	.0214	.0379	.0234	.0106	.0591	.0286

	T₁₁	T₁₂	T₂₁	T₂₂
T_m	.9710	.0020	.0410	.9270
T^(m)	.9904	−.0058	.0154	.9601
T⁽¹⁾	.9870	.0083	.0063	.9978
T⁽²⁾	.9451	.0046	.0163	.9588
$\begin{array}{l} (a) & L = . 067 dB & τ = . 055 \\ k_{1} = 4.15 & k_{2} = 4.35 \end{array}$
	T₁₁	T₁₂	T₂₁	T₂₂
T_m	.9380	−.0130	.0870	.9240
T^(m)	.9769	−.0012	.0374	.9218
T⁽¹⁾	.9683	.0170	.0204	.9580
T⁽²⁾	.9203	.0108	.0389	.9215
$\begin{array}{l} (b) & L = . 19 dB & τ = . 07 \\ k_{1} = 2.13 & k_{2} = 4.72 \end{array}$
	T₁₁	T₁₂	T₂₁	T₂₂
T_m	.9730	−.0380	.0360	.9500
T^(m)	.9722	.0004	.0398	.9011
T⁽¹⁾	.9643	.0243	.0258	.9437
T⁽²⁾	.9046	.0150	.0531	.8982
$\begin{array}{l} (c) & L = . 27 dB & τ = . 075 \\ k_{1} = 3.04 & k_{2} = 4.63 \end{array}$

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Applied Optics