{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T05:01:15Z","timestamp":1775538075055,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,16]],"date-time":"2018-11-16T00:00:00Z","timestamp":1542326400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a new method for measuring the linewidth enhancement factor (alpha factor) by the relaxation oscillation (RO) frequency of a laser with external optical feedback (EOF). A measurement formula for alpha is derived which shows the alpha can be determined by only using the RO frequencies and no need to know any other parameters related to the internal or external parameters associated to the laser. Unlike the existing EOF based alpha measurement methods which require an external target has a symmetric reciprocate movement. The proposed method only needs to move the target to be in a few different positions along the light beam. Furthermore, this method also suits for the case with alpha less than 1. Both simulation and experiment are performed to verify the proposed method.<\/jats:p>","DOI":"10.3390\/s18114004","type":"journal-article","created":{"date-parts":[[2018,11,16]],"date-time":"2018-11-16T11:48:31Z","timestamp":1542368911000},"page":"4004","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3905-7162","authenticated-orcid":false,"given":"Yuxi","family":"Ruan","sequence":"first","affiliation":[{"name":"School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4720-4126","authenticated-orcid":false,"given":"Bin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia"}]},{"given":"Yanguang","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia"}]},{"given":"Jiangtao","family":"Xi","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia"}]},{"given":"Qinghua","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia"}]},{"given":"Jun","family":"Tong","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1109\/JQE.1982.1071522","article-title":"Theory of the linewidth of semiconductor lasers","volume":"18","author":"Henry","year":"1982","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1109\/JQE.1987.1073204","article-title":"Linewidth broadening factor in semiconductor lasers-An overview","volume":"23","author":"Osinski","year":"1987","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/JQE.2006.884583","article-title":"Experiments on the Linewidth-Enhancement Factor of a Vertical-Cavity Surface-Emitting Laser","volume":"43","author":"Fordell","year":"2007","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1049\/el:19830633","article-title":"Measurements of the semiconductor laser linewidth broadening factor","volume":"19","author":"Henning","year":"1983","journal-title":"Electron. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1109\/68.766790","article-title":"A simple and novel method for measuring the chirp parameter of an intensity modulated light source","volume":"11","author":"Kowalski","year":"1999","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1109\/68.920741","article-title":"Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique","volume":"13","author":"Liu","year":"2001","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"990","DOI":"10.1109\/LPT.2004.824631","article-title":"Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect","volume":"16","author":"Yu","year":"2004","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1058","DOI":"10.1109\/JQE.2005.851250","article-title":"Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry","volume":"41","author":"Xi","year":"2005","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/JQE.2007.897862","article-title":"Toward Automatic Measurement of the Linewidth-Enhancement Factor Using Optical Feedback Self-Mixing Interferometry With Weak Optical Feedback","volume":"43","author":"Yu","year":"2007","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1364\/OL.38.001781","article-title":"Influence of external optical feedback on the alpha factor of semiconductor lasers","volume":"38","author":"Yu","year":"2013","journal-title":"Opt. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1109\/3.922778","article-title":"Interferometric measurements of displacement on a diffusing target by a speckle tracking technique","volume":"37","author":"Norgia","year":"2001","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1109\/LPT.2010.2040825","article-title":"A Self-Mixing Displacement Sensor with Fringe-Loss Compensation for Harmonic Vibrations","volume":"22","author":"Zabit","year":"2010","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"053114","DOI":"10.1063\/1.4947494","article-title":"A microchip laser source with stable intensity and frequency used for self-mixing interferometry","volume":"87","author":"Zhang","year":"2016","journal-title":"Rev. Sci. Instrum."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.optlaseng.2016.10.013","article-title":"Self-mixing instrument for simultaneous distance and speed measurement","volume":"99","author":"Norgia","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1109\/TIM.2006.876544","article-title":"Displacement measurements using a self-mixing laser diode under moderate feedback","volume":"55","author":"Bes","year":"2006","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1364\/AOP.7.000570","article-title":"Laser feedback interferometry: A tutorial on the self-mixing effect for coherent sensing","volume":"7","author":"Taimre","year":"2015","journal-title":"Adv. Opt. Photonics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1364\/OPEX.13.001537","article-title":"Self-mixing interferometer based on sinusoidal phase modulating technique","volume":"13","author":"Guo","year":"2005","journal-title":"Opt. Express"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"045505","DOI":"10.1088\/1464-4258\/11\/4\/045505","article-title":"Linewidth enhancement factor measurement based on optical feedback self-mixing effect: A genetic algorithm approach","volume":"11","author":"Wei","year":"2009","journal-title":"J. Opt. A Pure Appl. Opt."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5064","DOI":"10.1364\/AO.50.005064","article-title":"Improving the measurement performance for a self-mixing interferometry-based displacement sensing system","volume":"50","author":"Fan","year":"2011","journal-title":"Appl. Opt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1109\/3.341714","article-title":"Laser diode feedback interferometer for measurement of displacements without ambiguity","volume":"31","author":"Donati","year":"1995","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"043815","DOI":"10.1103\/PhysRevA.64.043815","article-title":"Coherent laser detection by frequency-shifted optical feedback","volume":"64","author":"Lacot","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6962","DOI":"10.1364\/AO.56.006962","article-title":"Displacement sensing using the relaxation oscillation frequency of a laser diode with optical feedback","volume":"56","author":"Liu","year":"2017","journal-title":"Appl. Opt."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1109\/JQE.1980.1070479","article-title":"External optical feedback effects on semiconductor injection laser properties","volume":"16","author":"Lang","year":"1980","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Uchida, A. (2012). Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization, John Wiley & Sons.","DOI":"10.1002\/9783527640331"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2949","DOI":"10.1109\/JLT.2009.2019112","article-title":"Precision Threshold Current Measurement for Semiconductor Lasers Based on Relaxation Oscillation Frequency","volume":"27","author":"Kane","year":"2009","journal-title":"J. Lightwave Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/11\/4004\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:30:15Z","timestamp":1760196615000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/11\/4004"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,16]]},"references-count":25,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["s18114004"],"URL":"https:\/\/doi.org\/10.3390\/s18114004","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,16]]}}}