Design of a multiple self-mixing interferometer for a fiber ring laser

Liheng Shi; Dongmei Guo; Yifeng Cui; Hui Hao; Wei Xia; Yiping Wang; Xiaoqi Ni; Ming Wang

doi:10.1364/OL.43.004124

Optics Letters
Vol. 43,
Issue 17,
pp. 4124-4127
(2018)
•https://doi.org/10.1364/OL.43.004124

Design of a multiple self-mixing interferometer for a fiber ring laser

Liheng Shi, Dongmei Guo, Yifeng Cui, Hui Hao, Wei Xia, Yiping Wang, Xiaoqi Ni, and Ming Wang

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Liheng Shi, Dongmei Guo, Yifeng Cui, Hui Hao, Wei Xia, Yiping Wang, Xiaoqi Ni, and Ming Wang, "Design of a multiple self-mixing interferometer for a fiber ring laser," Opt. Lett. 43, 4124-4127 (2018)

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Abstract

In this Letter, a novel multiple self-mixing interferometer for a fiber ring laser (FRL) is designed by introducing a circular feedback cavity. A system model is established based on an injection-seeded erbium-doped FRL proposed by Dragic. Owing to the reflection of the collimating lens, the multiplied fringes have different depths, which shows two Doppler frequencies in the spectrum of the self-mixing signal. A double-peak frequency identification algorithm is proposed to extract the Doppler frequency from the unique signal. This technique has the potential to improve the accuracy of fiber self-mixing measurement systems, particularly in Doppler velocimeters.

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Parameter	Value
$α_{P}$ : small signal absorption coefficient of bump light	0.42
$α_{S}$ : small signal absorption coefficient of signal light	0.611
$P_{p}^{s}$ : saturation power of pump light	0.42 mW
$P_{s}^{s}$ : saturation power of signal light	0.103 mW
$P_{pump}$ : power of pump light	200 mW
$κ$ : split ratio of coupler	0.9
$L$ : length of EDF	5 m
$ϵ_{1}$ : loss factor	0.9
$ϵ_{2}$ : loss factor	0.6
$r_{t}$ : reflectivity of the target	0.8
$λ_{p}$ : the oscillation wavelength of pump	980 nm
$λ_{s}$ : the oscillation wavelength of signal	1550 nm

Step 1	Calculate the absolute value of the STFT spectrogram at time $t$ , remove the DC component, and mark as $S (f)$ .
Step 2	Sort $S (f)$ by value in descending order, and the corresponding frequencies are $f_{s 1}, f_{s 2} \dots$
Step 3	$i = 2$ .
Step 4	In the set [ $f_{s 1}, f_{s 2}, \dots, f_{s (i - 1)}$ ], search for a frequency value $f_{s j}$ sequentially to form a combination of [ $f_{s j}, f_{s i}$ ] that satisfies: $\| f_{s j} - 2 f_{s i} \| \leq d f$ , or $\| f_{s i} - 2 f_{s j} \| \leq d f$ . ( $d f$ is the frequency resolution in the spectrum, related to the rectangular window in the STFT analysis.)
Step 5	If the combination of [ $f_{s j}, f_{s i}$ ] does not exist, $i = i + 1$ , return to step 4; if it exists, go to Step 6.
Step 6	Output $f_{1} (t) = \max (f_{s j}, f_{s i})$ .

Parameter	Value
$α_{P}$ : small signal absorption coefficient of bump light	0.42
$α_{S}$ : small signal absorption coefficient of signal light	0.611
$P_{p}^{s}$ : saturation power of pump light	0.42 mW
$P_{s}^{s}$ : saturation power of signal light	0.103 mW
$P_{pump}$ : power of pump light	200 mW
$κ$ : split ratio of coupler	0.9
$L$ : length of EDF	5 m
$ϵ_{1}$ : loss factor	0.9
$ϵ_{2}$ : loss factor	0.6
$r_{t}$ : reflectivity of the target	0.8
$λ_{p}$ : the oscillation wavelength of pump	980 nm
$λ_{s}$ : the oscillation wavelength of signal	1550 nm

Step 1	Calculate the absolute value of the STFT spectrogram at time $t$ , remove the DC component, and mark as $S (f)$ .
Step 2	Sort $S (f)$ by value in descending order, and the corresponding frequencies are $f_{s 1}, f_{s 2} \dots$
Step 3	$i = 2$ .
Step 4	In the set [ $f_{s 1}, f_{s 2}, \dots, f_{s (i - 1)}$ ], search for a frequency value $f_{s j}$ sequentially to form a combination of [ $f_{s j}, f_{s i}$ ] that satisfies: $\| f_{s j} - 2 f_{s i} \| \leq d f$ , or $\| f_{s i} - 2 f_{s j} \| \leq d f$ . ( $d f$ is the frequency resolution in the spectrum, related to the rectangular window in the STFT analysis.)
Step 5	If the combination of [ $f_{s j}, f_{s i}$ ] does not exist, $i = i + 1$ , return to step 4; if it exists, go to Step 6.
Step 6	Output $f_{1} (t) = \max (f_{s j}, f_{s i})$ .

Abstract

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Equations (8)

Optics Letters