Immediate estimation of feedback factor and linewidth enhancement factor from measured self-mixing signals under moderate or strong regime

Abstract

The estimation of self-mixing interferometry (SMI) parameters such as optical feedback factor C and linewidth enhancement factor α is essential to self-mixing (SM) displacement sensors with sub-wavelength resolution. We propose a new method, which is a very simple and fast method to estimate C and α when C > 1 based on an analysis of self-mixing signals (SMSs) in a laser diode. The proposed method is extremely simple, because it takes advantage of analytic relations which enable one to obtain C and α from the simple algebraic operations of the data from SMSs. The simplicity of the method is a great help to developing a compact and low-cost self-mixing (SM) displacement sensor with sub-wavelength resolution which cannot ensure complex operation such as optimization. And the proposed method is highly effective in developing real-time and fast algorithm for the C estimation. This method is applicable when the sensor operates under a moderate or strong feedback regime. The estimation accuracy of C and α are comparable to the results of Yu et al 2004 IEEE Photon. Technol. Lett. 16 990-2; Zabit 2010 PhD Thesis Toulouse; and Fan 2011 MS Thesis University of Wollongong, respectively, and the estimation time of the C parameter is over 30 times faster than Zabit and Fan.

Self-Mixing Interferometer for Acoustic Measurements through Vibrometric Calibration

“…Parameters C and can be estimated from SMI vibrometric signals in air at rest [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ]. Among the different methods, some are only effective in weak feedback [ 23 , 24 , 25 ] and others only in moderate feedback [ 26 , 27 , 28 ].…”

“…For instance, if the distance between the LD and the retro-reflective surface is about 20 cm, an acoustic wave at 112 dB SPL induces an optical path variation of 1.2 nanometers [ 13 ], which is three orders of magnitude below mechanical vibrations of a few micrometers [ 3 ]. For the measurement of C and in strong feedback regime, the methods can be divided into two categories: phase unwrapping methods [ 29 , 30 , 31 , 33 ] and direct SMI signal analysis methods [ 32 , 34 , 35 ].…”

“…As a result, they are faster to implement than phase unwrapping methods. Using a first-order Taylor expansion of the SMI governing equations, Ri et al [ 32 ] have proposed a method to retrieve analytically the values of C and by exploiting the discontinuities in SMI signal. This method can be used to determine C values ranging from 1 to 7 and from 2 to 4.9.…”

Minimizing the linewidth enhancement factor in multiple-quantum-well semiconductor optical amplifiers

“…Appreciable research has been done to enhance the gain-bandwidth product of SOAs [4][5][6][7][8][9][10][11]. The gain of SOAs is known to be intertwined with linewidth enhancement (LWE) due to refractive index fluctuations within the gain bandwidth, which is quantified by a parameter called the linewidth enhancement factor (LWEF) [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Therefore, in the context of enhancing the gain-bandwidth product of SOAs, taking the LWEF of SOAs into consideration is a must to account for the enhanced phase noise that distorts the output signal [18][19][20][21][22][23][24][25].…”

“…The gain of SOAs is known to be intertwined with linewidth enhancement (LWE) due to refractive index fluctuations within the gain bandwidth, which is quantified by a parameter called the linewidth enhancement factor (LWEF) [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Therefore, in the context of enhancing the gain-bandwidth product of SOAs, taking the LWEF of SOAs into consideration is a must to account for the enhanced phase noise that distorts the output signal [18][19][20][21][22][23][24][25]. One example is the case of Fourier domain mode locked lasers where SOA partakes as the most critical element, and the sharp variation of the LWEF introduces significant phase noise in the output intensity pattern [3,26,27].…”