Self-mixing interference measurement system of a fiber ring laser with ultra-narrow linewidth

doi:10.1364/OE.20.008598

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Self-mixing interference measurement system of a fiber ring laser with ultra-narrow linewidth

Liang Lu, Jingyu Yang, Longhua Zhai, Rui Wang, Zhigang Cao, and Benli Yu »View Author Affiliations

Optics Express, Vol. 20, Issue 8, pp. 8598-8607 (2012)
http://dx.doi.org/10.1364/OE.20.008598

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– Abstract
1. Introduction
2. Theoretical simulations
3. Experimental results
4. Conclusions
– References and links

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Abstract

A novel device for self-mixing interference measurement based on the fiber ring laser with ultra-narrow linewidth was investigated for the first time. In order to achieve requirement of our measurement system, a saturable-absorber which consists of a segment un-pumped erbium-doped fiber and a fiber Bragg grating is employed to provide a fine mode selection and guarantee the ultra-narrow linewidth operation. Results demonstrate that the signal-to-noise ratio of the self-mixing interference signal could be enhanced from 18.01 dB to 38.35 dB by inserting a saturable-absorber in the laser cavity. It is in good agreement with the theoretical analysis and proved potential using in self-mixing interference measurement system for high sensitivity and remote measurement.

1. Introduction

Self-mixing interference (SMI), a well-known and viable technique, has attracted more and more attention. In the SMI measurement system, a laser beam emitted from laser is focused on a remote target and reflected or scattered by a target. Then the back-reflected or back-scattered light re-enter the laser cavity and modulate the frequency and the amplitude of the pre-existing lasing field. The SMI signal which carries the information of the irradiated target is suitable for parameters measurement of velocity [1

S. Shinohara, A. Mochizuki, H. Yoshida, and M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25(9), 1417–1419 (1986). [CrossRef] [PubMed]

], vibration [2

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004). [CrossRef]

, 3

K. Otsuka, K. Abe, J.-Y. Ko, and T.-S. Lim, “Real-time nanometer-vibration measurement with a self-mixing microchip solid-state laser,” Opt. Lett. 27(15), 1339–1341 (2002). [CrossRef] [PubMed]

], distance [4

F. Gouaux, N. Servagent, and T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37(28), 6684–6689 (1998). [CrossRef] [PubMed]

] and displacement [5

N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Instrum. Meas. 46(4), 847–850 (1997). [CrossRef]

]. Compared with the traditional Michelson and Mach-Zehnder heterodyne interference measuring technologies, SMI technique has a lot of advantages, such as simplicity and compactness, high accuracy and reliability, and also low cost. In recent decades, the SMI technique based on semiconductor laser [6

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993). [CrossRef] [PubMed]

], solid-state laser [7

K. Otsuka, “Ultrahigh sensitivity laser Doppler velocimetry with a microchip solid-state laser,” Appl. Opt. 33(6), 1111–1114 (1994). [CrossRef] [PubMed]

], Vertical-cavity Surface-Emitting laser (VCSEL) [8

Y. L. Lim, M. Nikolic, K. Bertling, R. Kliese, and A. D. Rakić, “Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 17(7), 5517–5525 (2009). [CrossRef] [PubMed]

], distributed feedback laser (DFB) [9

D. Han, M. Wang, and J. Zhou, “Self-mixing speckle interference in DFB lasers,” Opt. Express 14(8), 3312–3317 (2006). [CrossRef] [PubMed]

, 10

J. Zhou, M. Wang, and D. Han, “Experiment observation of self-mixing interference in distributed feedback laser,” Opt. Express 14(12), 5301–5306 (2006). [CrossRef] [PubMed]

], distributed Bragg reflector (DBR) laser [11

L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er³⁺–Yb³⁺ codoped Distributed Bragg Reflector fiber laser for remote sensing applications up to 20 km,” IEEE Photon. Technol. Lett. 24(5), 392–394 (2012). [CrossRef]

] has been broadly investigated. However, because of the coherence length limitation due to wide linewidth, high performance self-mixing measurement system based on fiber ring laser (FRL) has rarely been reported so far.

The mechanism of linewidth narrowing is desirable in the SMI measurement system based on FRL. For narrow linewidth fiber laser design, both linear and ring cavity configuration have been investigated. The linear cavity will produce spatial hole burning effect in the gain medium and arouse multi-longitudinal modes oscillation inevitably. Several methods, including use of short cavity to enlarge the space of the longitudinal modes have been demonstrated. However, short cavity configuration does not benefit to further improve the output power due to its short gain length. The long traveling-wave ring cavity structure not only allows smaller linewidth as compared to linear cavity but also obtains high lasing power. Unavoidably, there still arouse multi-longitudinal modes oscillation and occur mode hopping because of its densely longitudinal modes spacing resulting from long cavity length.

In this paper, we inserted a segment un-pumped Er³⁺-doped fiber (EDF) which functions as a narrow bandwidth auto tracking filter in laser resonator. The mechanism of linewidth narrowing is to establish a transient Bragg reflection grating by standing-wave saturation effects in the un-pumped EDF. In the section 2, self-mixing model in EDF ring laser was built. In the section 3, the free spectral range (FSR), linewidth of the output power of the FRL with and without saturable absorber were discussed in detail. The SMI signals, the frequency spectrums and the Digital Phosphor (DPX) spectrums of vibration measurement based on the EDF ring laser with narrow linewidth were observed respectively.

2. Theoretical simulations

In this section, we proposed and demonstrated a basic theoretical model of FRL based on amplifier equations of EDF and the steady-state solutions to the rate equations firstly. Then the SMI was simulated based on the one single model FRL. In order to acquire an optimized device for high performance self-mixing measurement, a segment un-pumped EDF (_{${EDF}_{2}$}) which functions as a narrow bandwidth auto tracking filer was inserted in the laser cavity. This induced filer could provide a fine mode selection and observably suppressed frequency hop, to guarantee steady, narrow linewidth and outstanding coherency operation FRL.

Figure 1 shows the setup of the FRL in which two segments EDF is utilized. As shown in Fig. 1, _{${EDF}_{1}$} acts as gain medium of the FRL, and the un-pumped _{${EDF}_{2}$} functions as a narrow bandwidth auto tracking filter. _{$P_{P}^{in}$}and _{$P_{s e e d}$} represent the powers of pump light source and feedback light respectively. _{$P^{i n}$}and _{$P^{o u t}$} are the powers at the input and the output of the _{${EDF}_{1}$}. Pump light is coupled into the cavity through a wavelength-division multiplexer (WDM). The optical isolator is used for preventing unwanted feedback into the laser cavity and ensuring unidirectional laser operation. The coupler with a split ratio of κ is employed to introduce the feedback (_{$P_{s e e d}$}) and the output light (_{$P_{L a s e r}$}). _{$ε_{1}$} and _{$ε_{2}$}are the total attenuation factors including insertion loss of WDM, isolator, splices and other optical components. _{$r_{1}$} is reflectivity of the FBG which acts as a reflector, mode selecting apparatus and with _{${(1-r}_{1})$} launched into the output. In our setup, _{$P_{s e e d 1}$} and _{$P_{s e e d 2}$} are powers of back-scatter light from an external target and back-reflect light from the FBG respectively.

Fig. 1 Fiber ring laser block structure with a segment un-pumped EDF inserted.

According to the expression of output power in FRL [12

P. D. Dragic, “Analytical model for injection-seeded erbium-doped fiber ring lasers,” IEEE Photon. Technol. Lett. 17(8), 1629–1631 (2005). [CrossRef]

], which could be deduced from the well-known amplifier equations for EDF and the steady-state solutions to the rate equations, the power of pump light and the power of signal light with wavelength _{$λ_{i}$} at the output of the _{${EDF}_{1}$} can be written as

P_{p, i (s, i)}^{o u t} = P_{p, i (s, i)}^{i n} \exp (- α_{p, i (s, i)} L + \frac{Δ P_{p, i (s, i)}}{P_{p, i (s, i)}^{s}} + \frac{Δ P_{(p, i) s, i}}{P_{p, i (s, i)}^{s}})

(1)

where the subscripts p and s refer to the pump and laser wavelengths respectively, α is the small signal absorption coefficient, L is the length of _{${EDF}_{1}$}, _{$Δ P$} is the variable value of power, _{$P_{s, i}^{s}$}and _{$P_{p, i}^{s}$} denote saturation powers of signal and pump light at wavelength _{$λ_{i}$} in FRL which could be written as follows.

Δ P_{p, i (s, i)} = P_{p, i (s, i)}^{i n} - P_{p, i (s, i)}^{o u t}

(2)

P_{p, s}^{s} = \frac{h ν A_{p,s}^{eff}}{Γ_{p, s} τ (σ_{p,s}^{e} {+σ}_{p,s}^{a})}

(3)

In Eq. (3), the emission (e) and absorption (a) cross sections are denoted by σ. _$h$is Planck constant, _$ν$is the emission frequency which shifts as a periodic function with respect to the external length, _{$A_{p,s}^{eff}$} is the effective area of the mode, τ is the upper state lifetime, and Г is the optical mode-erbium overlap factor.

According to the steady-state characteristic, we obtain the following expression for power of signal (_{$P_{s}^{i n}$}) at wavelength_{$λ_{i}$}:

P_{s, i}^{i n} = {κε}_{1} P_{s e e d 1, i} + {(1-κ)ε}_{1} P_{s e e d 2, i}

(4)

From the ordinary but tedious calculation, we can gain the following transcendental equation about_{$P_{s, i}^{o u t}$}:

\begin{array}{l} P_{s, i}^{s} {{α}_{s, i} L - \frac{{κε}_{1} P_{s e e d 1, i} + {(1-κ)ε}_{1} P_{s e e d 2, i} - P_{s, i}^{o u t}}{P_{s, i}^{s}} - \ln [\frac{{κε}_{1} P_{s e e d 1, i} + {(1-κ)ε}_{1} P_{s e e d 2, i}}{P_{s, i}^{o u t}}]} \\ = P_{p, i}^{i n} [1 - \exp {- α_{p, i} L + \frac{P_{s, i}^{s}}{P_{p, i}^{s}} {{α}_{s, i} L - [{κε}_{1} P_{s e e d 1, i} + {(1-κ)ε}_{1} P_{s e e d 2, i} - P_{s, i}^{o u t}] / P_{s, i}^{s} \\ - \ln [\frac{{κε}_{1} P_{s e e d 1, i} + {(1-κ)ε}_{1} P_{s e e d 2, i}}{P_{s, i}^{o u t}}]} + \frac{{κε}_{1} P_{s e e d 1, i} + {(1-κ)ε}_{1} P_{s e e d 2, i} - P_{s, i}^{o u t}}{P_{p, i}^{s}}}] \end{array}

(5)

Assumed that the external target is driven by a sinusoidal signal with the angular frequency of _{$ω_{0}$} and amplitude of A, the external cavity length written as following is changed periodically in keeping with the driven signal.

Δ L_{e x t} (t) = {ACos(ω}_{0} t)

(6)

The power of back-scatter light from the target _{$P_{s e e d 1}$} could be written as

P_{s e e d 1, i} = {(1-κ)(r}_{1}^{*})^{2} P_{s, i}^{o u t}

(7)

where _{$r_{1}^{*}$} is the effective reflectivity at the end of FBG, may be written as

r_{1}^{*} {=r}_{1} {+η(1-r}_{1}^{2} {)r}_{2} C o s (2 π L_{e x t} / λ_{i})

(8)

where _{$r_{1}$}and _{$r_{2}$} are the reflectivity of the FBG end and external target face.

The Eq. (5) is solved numerically for _{$P_{s, i}^{o u t}$}and finally the laser output _{$P_{L a s e r, i}$} is given by

P_{L a s e r, i} = ε_{2} {(1-κ)(1-r}_{1}^{2}) P_{s, i}^{o u t}

(9)

In the above analysis, we have neglected both amplified spontaneous emission (ASE) and excited state absorption (ESA). The parameters used in our calculations related the Eqs. (1)–(9) unless stated otherwise, are given in Table 1 .

Table 1 Parameters Used for the Example of Fiber Ring Laser

Parameter	Value
λ_p: the oscillation wavelength of pump	980 nm
λ_s: the oscillation wavelength of signal	1550 nm
σ^a_p: the absorption cross-section when λ = λ_p	0.75 × 10⁻²⁵ m²
σ^e_p: the emission cross-section when λ = λ_p	2.5 × 10⁻²⁵ m²
σ^a_s: the absorption cross-section when λ = λ_s	3 × 10⁻²⁵ m²
σ^e_s (λs): the emission cross-section when λ = λ_s	1 × 10⁻²⁵ m²
α_p: the scattering losses for the pump	0.75 × 10⁻¹ m⁻¹
α_s: the scattering losses for the signal	0.75 × 10⁻³ m⁻¹
Г_p: the power filling factor which represent the fraction of the pump power actually coupled to the active core	0.0012
Г_s: the power filling factor which represent the fraction of the signal amplified in the core	0.82
A^eff: the cross-section area of the core	1.5 × 10⁻¹¹ m²
Pⁱⁿ_p: the power of pump light	0.1W
L: the length of EDF₁	6m
τ₀: spontaneous lifetime	10.8 × 10⁻³ s
ε₁: attenuation factor	0.9
ε₂: attenuation factor	0.9
κ: split ratio of coupler	0.5
r₁: the reflectivity at the end of FBG	0.98
r₂: is the reflectivity of the external target face	0.2
f₀: frequency of driving signal launched on the external target	380 Hz
A: amplitude of driving signal launched on the external target	1.55 × 10⁻⁶ m

In summary, the quasi-analytical model of the FRL has been built. Based on this quasi-analytical model, the output power of SMI signal can be obtained, as shown in Fig. 2 . It is evident that output power is a repetitive function with one period corresponding to half wavelength of optical displacement. This feature of the fringe has already been observed in other lasers self-mixing interference, such as laser diode [13

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994). [CrossRef]

Fig. 2 Simulation results of vibration signal according to self-mixing signal. (Upper traces: vibration signal of external target, Lower traces: self-mixing interference signal.)

One point should be mentioned, we only discuss self-mixing effect based on one single longitude mode operational FRL. Unfortunately, the FBG employed in Fig. 1 is functioned as a filter with considerable band width, so there may arouse multi-longitudinal modes oscillation in the ordinary long traveling-wave ring cavity unavoidably. In this case, the output power of the common FRL could be rewritten as:

P_{Laser} = \sum_{1}^{n} ε_{2} (1- κ {)(1-R)P}_{s, i}^{o u t}

(10)

where n is the number of the modes which is allowed to propagate in the ring cavity. Obviously, there should be phase differences between each mode resulting from distinctive frequency of these modes. When the powers of these modes are superposed, it will lead to unstable laser output because of mode hopping and mode competition. In our optimized device, two waves counter-propagate between coupler and FBG would form interference pattern in_{${EDF}_{2}$}, thus a periodic spatial variation of the intensity will be induced. Such a periodic spatial variation of the intensity is characterized by a grating, which can act as a narrow-band filter. This narrow-band filter provided a fine mode selection and observably suppressed frequency hop, to guarantee steady, narrow linewidth and outstanding coherency operation FRL which could be suitable for high performance self-mixing measurement.

3. Experimental results

In this section, we aimed at studying the performance of the self-mixing signal based on the optimized device. To investigate the effects of the saturable absorber, properties, such as the FSR and linewidth of the ordinary and the optimized FRL were studied in detail. We designed the system shown schematically in Fig. 3 . It consists of a 980/1550nm WDM, two segments EDF, a fiber optical isolator, a FBG with Bragg wavelength of 1549.88 nm acts as a reflector and a mode selecting apparatus, a 2×2 optical coupler with couple ratio 50:50. The optical isolator is utilized to prevent unwanted feedback into the laser cavity and guarantee unidirectional operation of the traveling-wave ring cavity. As shown in Fig. 3, the pump light is coupled into the ring cavity through a WDM and the signal is amplified by the EDF₁. A collimating lens was fusion spliced to the port 4 of the optical coupler to project the laser beam onto the external target and receive the feedback light from target face. At the port 4 of the optical coupler, a segment single mode fiber was inserted between the coupler and the collimating lens to enhance the sensitivity of the measurement system. The feedback light reflected by the target was connected into the system through port 4 of the optical coupler. The external target was fixed on a piezoelectric ceramic transformer (PZT) (MTp200/5*5/7, XMT, Harbin) placed at a distance of 9.5 cm from the end of the collimating lens and driven by a function generator (Tektronix AFG 3102). A reflecting film which can be easily replaced by paper or other reflecting materials was used as the external target and adhered on the PZT. At the port 3 of the optical coupler, 20 m long un-pumped _{${EDF}_{2}$} was inserted between the coupler and the FBG to narrow the linewidth. The un-pumped EDF functions as a saturable absorber capable of forming a self-induced FBG filter with an ultra-narrow bandwidth, which is the key component to guarantee the stable and narrow-linewidth operation FRL. To make the system relative insensitivity to environmental perturbation such as vibration and acoustic noise, the laser cavity was placed in a shielded case during the experimental process.

Fig. 3 Experiment setup of self-mixing vibrometer based on the narrow linewidth FRL.

The entire length of the optimized system cavity is about 60 m giving the corresponding FSR of 3.6 MHz. According to the previous theoretical analysis by A. Othonos [14

A. Othonos and K. Kalli, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Artech House, 1999).

], if we consider the refractive index-change of the induced grating as 3×10⁻⁷, the Bragg wavelength of 1550 nm, the grating length of 20 m, the average index of 1.45. Then the full-width at half maximum of the induced FBG filter is estimated to be less than 0.7216 MHz. The longitudinal modes spacing is visibly greater than the full-width at half maximum of the induced FBG filter. Therefore the single longitudinal mode operation is strongly expected. Based on beat frequency of output laser beam itself, we could get the FSR of fiber ring laser with and without saturable absorber as shown in Fig. 4 . As indicated in Fig. 4(a), without the _{${EDF}_{2}$} inserted in the ring resonator, the frequency spectrum of the output light is extremely unstable and a periodical beat frequency and frequency hop are seen clearly. Contrarily, with the _{${EDF}_{2}$} utilized, the longitudinal modes spacing is up to 3.656 MHz and no frequency hop can be found, as shown in Fig. 4(b), which indicates that the frequency hop is observably suppressed and outstanding coherency of the FRL is successfully realized.

Fig. 4 The free spectral range of the Er³⁺-doped fiber ring laser.

As further proof to discuss the effects of the saturable absorber, the spectral linewidth of the fiber ring laser was investigated by a delayed self-homodyne measurement technique which is an effective method for measuring the spectral linewidth of lasers. The laser beam is split into two beams, and one branch delayed by 20 km single mode fiber. The beat signal generated by the interferometer, which is detected by a photo-receiver and measured by a spectrum analyzer (Tektronix RSA-3408B Real-Time Spectrum Analyzer), is shown in Fig. 5 . The decline at low frequencies is caused by the low-frequency filter in the spectrum analyzer. Curve fitting were used to evaluate the measured value, which are shown in Fig. 5 by the red dotted lines. As shown in Fig. 5(a), without the _{${EDF}_{2}$} inserted, the linewidth of the FRL is about 6400 Hz. However, as shown in Fig. 5(b), the linewidth of the optimized system is 610 Hz, which was drastically narrowed. It is indicates that the employment of _{${EDF}_{2}$} would provide a fine mode restriction and guarantee the narrow linewidth operation.

Fig. 5 The linewidth of the Er³⁺-doped fiber ring laser.

In our experimental setup of self-mixing vibrometer based on the narrow linewidth FRL, a fast InGaAs photodiode connected to the end of the FBG to observe the experimental signal of SMI. In Fig. 6 the driving signal launched to PZT was a sinusoidal signal with the frequency of 380 Hz and driving voltage of 102 V. The amplitude of PZT is proportional to the driving voltage in a range and the amplitude of PZT at 102 V corresponds to 4.196μm. A typical SMI signal was obtained when the target driven by a sinusoidal and reported in Fig. 6. The upper traces are the driven signal applied to achieve the periodic external reflector movement and lower traces are the output signal of the SMI in the Er³⁺-doped FRL which agree to Fig. 2. As that of other SMI, we can easy to observe that the fringe shifting one period corresponds to λ/2 displacements of the target and the abnormality denotes the direction turning of the external target in Fig. 6(b). However, compared with the optimized measurement system, the self-mixing signal shown in Fig. 6(a) is unstable, undecipherable and almost drowned in the noise. The results declared that the optimized system could provide a fine mode selection and observably suppressed frequency hop, to guarantee steady, narrow linewidth and outstanding coherency operation fiber ring laser which could be suitable for high performance self-mixing measurement.

Fig. 6 Self-mixing interference signals when PZT driven by a sinusoidal signal. (Upper traces: vibration signal of the external target, Lower traces: self-mixing interference signal.)

For further study of the self-mixing signal with FRL, the corresponding electric signal which detected by photodiode was delivered to a radio-frequency spectrum analyzer (Tektronix RSA-3408B Real-Time Spectrum Analyzer). Figure 7 shows the frequency spectrum of the signal with the sweep central frequency and the sweep span of the real-time spectrum analyzer were set at 750 Hz and 1.5 kHz respectively. A few of its vibration frequencies (380 Hz) and some FM sidebands: 760 Hz, 1.14 kHz and others are standout in the vibration power spectrum of the self-mixing signal both in Fig. 7(a) and Fig. 7(b). For the sake of contrastive analysis, the same external length, reflectivity of the reflecting film and all the other experimental condition were employed except the _{${EDF}_{2}$}. As shown in Fig. 7(b), we achieved a signal-to-noise ratio (SNR) of 38.35 dB based on the optimized system, which is obviously higher than 18.01 dB in Fig. 7(a).

Fig. 7 Intensity power spectrum of self-mixing interference in fiber ring laser with 50 m delayed fiber.

For observing stability of the vibration measurement system, the Digital Phosphor (DPX) spectrum of the SMI was detected. The DPX spectrum technology enables us to see how traces change over time, displaying transient and intermittent events that cannot be seen on a swept spectrum analyzer. A DPX spectrum indicates how traces change in two ways. First, it uses color grading to show how often a particular signal occurs. Second, it uses persistence to keep events visible in the display, allowing newer events to be compared to older events. Figure 8 shows intensity power DPX spectrums of the self-mixing signal in FRL which can help us to observe the variation of the self-mixing signal power spectrum affected by time. As shown in Fig. 8, the experimental results indicate that the optimized device could provide a fine mode selection and optimize the coherence of laser, thereby improve the stability and the SNR of the SMI signal based on FRL. It is clear that the experimental measurements are in good agreement with the previous theoretical simulation work.

Fig. 8 Intensity power DPX spectrum of self-mixing interference in FRL with 50 m delayed fiber.

4. Conclusions

In this paper, we proposed and demonstrated a novel device for self-mixing interference measurement based on the Er³⁺-doped FRL with a saturable-absorber auto tracking filter. To investigate the effects of the saturable absorber, the free spectral range, linewidth of the FRL with and without _{${EDF}_{2}$} were studied in detail. The SMI signals, the frequency spectrum and the Digital Phosphor (DPX) spectrums of vibration measurement based on the FRL have been experimentally demonstrated. From the experiment results, we have deduced that the optimized system could provide a stable and narrow-width laser light source which could enhance the stability and the SNR of the signal in the SMI interference measurement system. The self-mixing model of EDF ring laser with narrow linewidth we have built has a number of potential applications for high performance in remote self-mixing measurement.

Acknowledgments

This work was supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (grant no. 20103401120001), Key Research Project of Anhui Education Department (grant no. KJ2010A019) and Natural Science Fund of Anhui Province (grant no. 1208085QF110).

References and links

1.	S. Shinohara, A. Mochizuki, H. Yoshida, and M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25(9), 1417–1419 (1986). [CrossRef] [PubMed]
2.	L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004). [CrossRef]
3.	K. Otsuka, K. Abe, J.-Y. Ko, and T.-S. Lim, “Real-time nanometer-vibration measurement with a self-mixing microchip solid-state laser,” Opt. Lett. 27(15), 1339–1341 (2002). [CrossRef] [PubMed]
4.	F. Gouaux, N. Servagent, and T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37(28), 6684–6689 (1998). [CrossRef] [PubMed]
5.	N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Instrum. Meas. 46(4), 847–850 (1997). [CrossRef]
6.	W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993). [CrossRef] [PubMed]
7.	K. Otsuka, “Ultrahigh sensitivity laser Doppler velocimetry with a microchip solid-state laser,” Appl. Opt. 33(6), 1111–1114 (1994). [CrossRef] [PubMed]
8.	Y. L. Lim, M. Nikolic, K. Bertling, R. Kliese, and A. D. Rakić, “Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 17(7), 5517–5525 (2009). [CrossRef] [PubMed]
9.	D. Han, M. Wang, and J. Zhou, “Self-mixing speckle interference in DFB lasers,” Opt. Express 14(8), 3312–3317 (2006). [CrossRef] [PubMed]
10.	J. Zhou, M. Wang, and D. Han, “Experiment observation of self-mixing interference in distributed feedback laser,” Opt. Express 14(12), 5301–5306 (2006). [CrossRef] [PubMed]
11.	L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er³⁺–Yb³⁺ codoped Distributed Bragg Reflector fiber laser for remote sensing applications up to 20 km,” IEEE Photon. Technol. Lett. 24(5), 392–394 (2012). [CrossRef]
12.	P. D. Dragic, “Analytical model for injection-seeded erbium-doped fiber ring lasers,” IEEE Photon. Technol. Lett. 17(8), 1629–1631 (2005). [CrossRef]
13.	W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994). [CrossRef]
14.	A. Othonos and K. Kalli, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Artech House, 1999).

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(140.3560) Lasers and laser optics : Lasers, ring
(280.3420) Remote sensing and sensors : Laser sensors

ToC Category:
Sensors

History
Original Manuscript: February 7, 2012
Revised Manuscript: March 19, 2012
Manuscript Accepted: March 26, 2012
Published: March 28, 2012

Citation
Liang Lu, Jingyu Yang, Longhua Zhai, Rui Wang, Zhigang Cao, and Benli Yu, "Self-mixing interference measurement system of a fiber ring laser with ultra-narrow linewidth," Opt. Express 20, 8598-8607 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-8598

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