Researching | SNR improvement of 8.2 dB in a self-mixing laser diode interferometer by using the difference signal at the output mirrors [Invited]

Journals >Chinese Optics Letters >Volume 19 >Issue 9 >Page 092502 > Article

Chinese Optics Letters
Vol. 19, Issue 9, 092502 (2021)

SNR improvement of 8.2 dB in a self-mixing laser diode interferometer by using the difference signal at the output mirrors [Invited] | Editors' Pick

Silvano Donati^1、* and Michele Norgia²

Author Affiliations

¹Department of Industrial and Information Engineering, University of Pavia, 27100 Pavia, Italy

²Department of Electronics, Informatics and Bioengineering, 20133 Milano, Italy

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DOI: 10.3788/COL202119.092502 Cite this Article Set citation alerts

Silvano Donati, Michele Norgia. SNR improvement of 8.2 dB in a self-mixing laser diode interferometer by using the difference signal at the output mirrors [Invited][J]. Chinese Optics Letters, 2021, 19(9): 092502 Copy Citation Text

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Abstract

At the mirrors of a laser diode self-mixing interferometer, the output beams carry anti-correlated (i.e., in phase opposition) interferometric signals, whereas the superposed noise fluctuations are (partially) correlated. Therefore, by using an instrumental output of the interferometer as the difference of the two, we double the amplitude of the self-mixing useful signal, while the superposed noise is reduced. To validate the idea, we first calculate the noise reduction by means of a second-quantization model, finding that in a laser diode the signal-to-noise ratio (SNR) can be improved by 8.2 dB, typically. Then, we also carry out an experimental measurement of SNR and find very good agreement with the theoretical result.

Keywords

interferometry laser diodes noise self-mixing

E_{1} = t_{1} E_{0} {1 - (t_{1}^{2} / r_{1}) (A \cos ϕ) [{(2 γ L + \ln R_{1} R_{2})}^{- 1} - R_{1} / T_{1}]},

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E_{2} = \sqrt (r_{1} / r_{2}) t_{2} E_{0} [1 - (t_{1}^{2} / r_{1}) (A \cos ϕ) {(2 γ L + \ln R_{1} R_{2})}^{- 1}],

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m_{1} = (t_{1}^{2} / r_{1}) (A \cos ϕ) [{(2 γ L + \ln R_{1} R_{2})}^{- 1} - R_{1} / T_{1}],

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m_{2} = (t_{1}^{2} / r_{1}) (A \cos ϕ) {(2 γ L + \ln R_{1} R_{2})}^{- 1};

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m_{1} / m_{2} = 1 - (R_{1} / T_{1}) (2 γ L + \ln R_{1} R_{2}) .

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E_{1} = t (E_{0} + Δ E_{coh}) + i r Δ E_{vac 1},

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〈 Δ E_{coh} 〉 = 〈 Δ E_{vac 1} 〉 = 0, and σ_{E}^{2} = 〈 Δ E_{coh}^{2} 〉 = 〈 Δ E_{vac 1}^{2} 〉 = ½ h ν B .

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P_{1} = 〈 | E_{1}^{2} | 〉 - 〈 Δ E_{vac 1}^{2} 〉 .

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P_{1} = t^{2} E_{0}^{2} + t^{2} 〈 Δ E_{coh}^{2} 〉 + r^{2} 〈 Δ E_{vac 1}^{2} 〉 + {2 t}^{2} 〈 E_{0} E_{coh}^{2} 〉 + 2 t r 〈 E_{0} E_{vac 1} 〉 + 2 t r 〈 E_{coh} E_{vac 1} 〉 - 〈 Δ E_{vac 1}^{2} 〉,

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〈 P_{1} 〉 = t^{2} E_{0}^{2} = T P_{0},

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σ_{P 1}^{2} = 4 T^{2} E_{0}^{2} 〈 E_{coh}^{2} 〉 + 4 T R E_{0}^{2} 〈 E_{vac 1}^{2} 〉,

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σ_{P 1}^{2} = 2 T P_{1} h ν B + 2 R P_{1} h ν B .

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P_{2} = P_{1}, σ_{P 2}^{2} = 4 T^{2} E_{0}^{2} 〈 E_{coh}^{2} 〉 + 4 T R E_{0}^{2} 〈 E_{vac 2}^{2} 〉 = 2 T P_{2} h ν B + 2 R P_{2} h ν B .

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σ_{P 2 - P 1}^{2} = 4 T R E_{0}^{2} 〈 E_{vac 1}^{2} 〉 + 4 T R E_{0}^{2} 〈 E_{vac 2}^{2} 〉 = 8 T R P_{0} ½ h ν B = 4 R P_{1} h ν B

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σ_{P 2 - P 1}^{2} / σ_{P 1}^{2} = 2 R,

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F = {({SNR}_{P 2 - P 1} / {SNR}_{P 1})}^{2} = (4 / 2 R) / 1 = 2 / R .

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σ_{P 2 - P 1}^{2} / s_{P 1 or 2}^{2} = (R_{2} T_{1} + R_{1} T_{2}) / \sqrt T_{1} T_{2},

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P_{1 B S} = {(r_{B S} t)}^{2} E_{0}^{2} = R_{B S} P_{1} = T R_{B S} P_{0},

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σ_{P 1 B S}^{2} = 2 T R_{B S} P_{1 B S} h ν B + 2 (R R_{B S} + T_{B S}) P_{1 B S} h ν B = 2 T R_{B S}^{2} P_{1} h ν B + 2 R_{B S} (R R_{B S} + T_{B S}) P_{1} h ν B .

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σ_{P 1 B S (eq)}^{2} = σ_{P 1 B S}^{2} / R_{B S}^{2} = [2 T R_{B S}^{2} P_{1} h ν B + 2 R_{B S} (R R_{B S} + T_{B S}) P_{1} h ν B] / R_{B S}^{2} = 2 T P_{1} h ν B + 2 (R + T_{B S} / R_{B S}) P_{1} h ν B

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σ_{P 2 - P 1}^{2} = 2 (2 R + T_{B S} / R_{B S}) P_{1} h ν B, and {SNR}_{P 1 - P 2}^{2} = [4 / 2 (2 R + T_{B S} / R_{B S})] (P_{1} h ν B) = [2 / (2 R + T_{B S} / R_{B S})] (P_{1} h ν B)

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F = {({SNR}_{P 2 - P 1} / {SNR}_{P 1})}^{2} = 2 / (R + T_{B S} / 2 R_{B S}) .

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Silvano Donati, Michele Norgia. SNR improvement of 8.2 dB in a self-mixing laser diode interferometer by using the difference signal at the output mirrors [Invited][J]. Chinese Optics Letters, 2021, 19(9): 092502

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