Abstract

A high-accuracy fiber optical microphone (FOM) is first applied by self-mixing technique in a DBR fiber laser based on a nanothick silver diaphragm. The nanothick silver diaphragm fabricated by the convenient and low cost electroless plating method is functioned as sensing diaphragm due to critically susceptible to the air vibration. Simultaneously, micro-vibration theory model of self-mixing interference fiber optical microphone is deduced based on quasi-analytical method. The dynamic property to frequencies and amplitudes are experimentally carried out to characterize the fabricated FOM and also the reproduced sound of news and music can clearly meet the ear of the people which shows the technique proposed in this paper guarantee steady, high signal-noise ratio operation and outstanding accuracy in the DBR fiber laser which is potential to medical and security applications such as real-time voice reproduction for throat and voiceprint verification.

© 2013 Optical Society of America

1. Introduction

Interest on fiber optical microphone (FOM) [1, 2] is related to the advantages that an optical sensor has over conventional sensors, such as intrinsic safety, electromagnetic interference immunity, capability for remote control and low transmission loss. Furthermore, the microphone itself does not emit any electromagnetic radiation and thus it is explosion proof. Additionally long distances between electronic devices and optical head are possible due to low losses in transmission by using glass fiber optics. These characteristics facilitate new applications in measurement, surveillance and medicine, e.g. for EMI labs, RFI testing labs, and MRI application.

In the last years several transduction mechanisms [3, 4] for optical microphone technology have been developed. Mostly traditional heterodyne or homodyne technique has been applied to FOM by the way of mixing the scattered light with the light of a constant frequency close to or equal to the original laser frequency. Compared to the heterodyne or homodyne interference measuring technology, self-mixing interference (SMI) [5, 6] technique has a lot of advantages, such as sensitivity and compactness, high accuracy and reliability, self-aligned and simple to implement. Among the many applications of SMI, ultrahigh sensitivity response to external optical feedback light in the short cavity configuration of DBR fiber laser has led to self-aligned optical sensing applications, such as laser Doppler velocimetry [7], vibrometry [8]. The key idea is the efficient intensity modulation of DBR fiber lasers through the interference between the pre-existing lasing field and the coherent component of the back-reflected light scattered from the measured object. The enhanced sensitivity of self-mixing approach results from the low ratio of fluorescence to photon lifetime especially in DBR fiber lasers. As the gain medium in the cavity plays the key important role to amplify the demodulated SMI signal greatly, the signal-to-noise ratio (SNR) is limited only by the laser quantum noise of spontaneous emission in the gain medium.

Most recently, we have demonstrated nanothick silver diaphragm fabricated by the electroless plating method which is more convenient and less costly compared with the micro-electromechanical fabrication process. The measured thickness of diaphragm is uniform in a few hundreds of nanometers which is the thinnest diaphragm that currently exists in the literature. The sketch of extrinsic Fabry–Perot interferometric sensor constructed by our team [9] demonstrates a higher pressure sensitivity of 70.5 nm/kPa compared to silica diaphragm sensors (typically 11 nm/kPa) due to extremely high sensitivity critically susceptible to the air pressure resulting from the thin size and the small residual stress of the sensing diaphragm.

In this paper, we employ the nanothick diaphragm as sensing diaphragm of fiber optical microphone by the self-mixing technique in short cavity DBR fiber laser to obtain a steady and outstanding accuracy real-time voice reproduction. Section2 describes some theoretical works primarily on the micro-vibration of self-mixing interference. In Section 3, the experimental setup and results are presented in detail that dynamic property to frequencies and amplitudes are carried out to characterize the fabricated FOM and also the reproduced sound of news and music can clearly meet the ear of the people which is potential to medical and security applications. Finally, the conclusions are drawn in Section 4.

2. Theory model of micro-vibration in self-mixing interference

In this section, we propose and demonstrate a basic theoretical SMI model of micro-vibration in the DBR fiber laser based on amplifier equations for EYDF [10, 11] and the quasi-analytical method results of steady-state equations in the DBR fiber laser [12] firstly. On account of the boundary conditional equations, we introduce the feedback light from the silver diaphragm in the form of seed light, so the output power of micro-vibration SMI can be deduced.

We build the model of DBR fiber laser with optical feedback presented in Fig. 1 to get the results of SMI output power based on quasi-analytical solutions to the rate equations. The pump light with wavelength 980 nm is coupled into the DBR fiber laser cavity by a wavelength-division multiplexer (WDM). The Fabry–Pérot cavity of the DBR fiber laser incorporates with a pair of wavelength matched fiber gratings in which Erbium: Ytterbiuum (Er:Yb) codoped fiber is efficient gain medium. Ytterbium sensitization to Er ions allows short laser cavity construction critical for output power stability of fiber laser and high sensitivity to the sensing application due to efficient pump absorption, high peak absorption cross-section, and efficient energy transfer. Here the lasing light PLaseroutscattered by the silver diaphragm reenters into the lasing cavity in the form ofPseed.

 figure: Fig. 1

Fig. 1 The principle of SMI output power based on the Boundary conditional equations.

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As shown in Fig. 1, Pin and Pout denote the powers at the input and output of the EYDF. The subscripts p, s and L, R refer to the pump, lasing light and left, right respectively. Pseed represents feedback light from external object. 1-ε1and 1-ε2are the total attenuation factor considering the insertion loss of WDM, connection of fibers and coupling efficiencies. Ri and ri are corresponding to the reflectivity and reflection coefficient of related apparatus.

Lasing light is scattered from the silver diaphragm influenced by the weak change of sound pressure and coupled into the laser cavity, then the SMI phenomena occurs. According to the amplifier equations for EYDF and boundary conditions, we build the following equations that the expression of output power can be theoretically deduced.

PLout=PLine-αsL+Psabs/Pss+Ppabs/Pss
PRout=PRine-αsL+Psabs/Pss+Ppabs/Pss
PLin=ε2[ε2R2PRout+(1R2)Pseed]
PRin=ε12R1PLout

Where P, α are presented the power and small signal absorption coefficient respectively. The index of abs and ss are powers of the absorbed in one round trip and saturation respectively. L is the length of the doped fiber.

The transcendental equation for the power PRout in the DBR system is deduced through iteration from Eq. (1-4) where the scatted light is introduced as the seed light.

PRout=ε12R1ε2[ε2R2PRout+(1R2)Pseed]e-2αsL+2Psabs/Pss+2Ppabs/Pss

WithPss=hνsaeffΓsτEr(σseEY+σsaEY),Pseed=(1-R2)(r2*)2PRout, r2=r2+(1-r22)r3cos(2πLext/λ) is the effective reflectivity at the end of FBG2. νs is the frequency of the signal light, гs is the optical mode-erbium overlap factor, τEr is the upper level lifetime of erbium ions, σseEY and σsaEY are the equivalent cross section of signal light stimulated absorption and stimulated emission of EYDF, aeff is the effective core area of signal light. Equation (5) is a transcendental equation of PRout, which can be solved by numerical simulation.

In case of the silver diaphragm is influenced by a sinusoidal change of sound pressure with the angular frequency of ω0 and amplitude of A, the vibration of the diaphragm is changed in keeping with the sinusoidal change of sound pressure.

Lext(t)=L0+Acos0t)

The Eq. (5) is solved numerically for PRoutand finally the laser output PLaser is given by

PLaser=ε1(1-R1)PRoute-(-sL+Psabs/Pss+Ppabs/Pss)

The parameters used in our calculations related to the Eqs. (1)-(7) unless stated otherwise, are given in Table 1. According to the above calculation, we simulate the modulated signal of micro-vibrations in self-mixing interference system in the follow. The waveform of output power is shown in Fig. 2.

Tables Icon

Table 1. The parameters used for the DBR fiber laser

 figure: Fig. 2

Fig. 2 The typical simulated result by quasi-analytical method (Upper trace: vibration signal of external target, Lower trace: self-mixing interference signal).

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Figure 2 shows the simulated output power of the nanothick silver diaphragm micro-vibration in DBR fiber laser based on the results of quasi-analytical solutions to the rate equations. In the simulation process, we present a procedure to solve numerically transcendental equation problem with standard root-finding technique, and obtain the emitted power of the laser in the self-mixing system. For a small value of A = 1.55 × 10−10 m less than 1/8 wavelength, the simulated output power (lower trace) of micro-vibration approximates to the driven signal (upper trace) when a sinusoidal waveform is launched on the external reflector. As the sound signals can be decomposed into the combinations of the sinusoidal signals, thus the sound signals can be real-time reproduced on the occasion of micro-vibration.

3. Experimental results and discussions

Based on the theoretical analysis and numerical simulation, we built a set of the self-mixing sound reproduction system based on a DBR fiber laser with short lasing cavity which is the key important to the high sensitivity and remote sensing [13]. The scattered light causing self-mixing interference is from the optical head that consists a reflector functioned as an external cavity. The optical head includes an APC patchcord and a ceramic pipe butt-coupled with silver diaphragm. And we experimentally get the real-time sound reproduction from micro-vibration vibrations of the nanothick silver diaphragm based on self-mixing interference in the DBR fiber laser. The experimental setup of microphone measurement is shown in Fig. 3.

 figure: Fig. 3

Fig. 3 Experimental setup of fiber optical microphone based on self-mixing in DBR fiber laser.

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As shown in Fig. 3, a Wavelength Division Multiplex (WDM) coupler is employed to couple the pump power into the gain medium with 3.9cm length. A pair of fiber Bragg gratings with Bragg wavelength of 1549.77nm and 1549.66nm which are supplied commercially functioned as short laser resonator and mode selecting apparatus. The short cavity of the laser with 9.8cm length is preferable to eliminate the multi-longitudinal modes oscillation and suppress the mode hopping. That is because based on the longitudinal mode spacing expression (Δvq=c2nl), we can get the value of longitudinal mode spacing (Δvq=1.05×109 Hz), where the speed of light in vacuum (c) is 3*108 m/s and the refractive index of optical fiber (n) is 1.45. However, the 3dB linewidth is 0.0161nm measured by envelope analysis patterns with 0.020nm resolution in the spectrum analyzer shown in Fig. 4. Moreover, the lasing modes’ range (Δν=cλ2Δλ) is 2.01×109 Hz based on the equationΔν=cλ2Δλ.

 figure: Fig. 4

Fig. 4 The linewidth of DBR fiber laser measured by optical analyzer.

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To further discuss the effect of the short cavity in the DBR fiber laser, the spectrum shown in Fig. 5 is recorded every 5 minutes. The signal-to-noise ratio (SNR) is up to 60dB and the output power difference of oscillate modes is 0.019dBm which illustrates the stable operating fiber laser of DBR.

 figure: Fig. 5

Fig. 5 The power spectrum of DBR fiber laser at different times.

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On account for the FBGs applied in our setup, the bandwidth and grating diffraction efficiency reflectance of FBG1 and FBG2 are 0.285nm and 0.213nm, 87% and 90% respectively. The stimulated gain medium amplifies the signals of λ and the lasing light is projected to the silver diaphragm which the thickness is 130 nm and the diameter is 1.25 mm, through an optical APC patchcord which is spliced to the other port of the WDM coupler. Between the DBR fiber laser and the APC pathcord, a segment of single mode fiber (SMF) is inserted to segregate the optical sensing part from the electronic devices that is significant to intrinsic safety, electromagnetic interference immunity, capability for remote control, low transmission loss and explosion proof. The nano-sickness silver diaphragm in optical head is critically susceptible to the air vibration caused by the acoustic wave and the reflectivity of the diaphragm is at the scope from 10% to 90% within the near and intermediate infrared range of lasing light by changing the reaction time. The thickness and reflectivity of the diaphragm at a reaction time of 15 min at room temperature are typically 130 nm and 15% reflectivity [9]. So, the diaphragm is a good candidate for fiber optical microphone. The technique of the silver diaphragm is processed by the chemical coating method which is convenient, low cost and easy to industrialized manufacturing. The other port of lasing light is fed through the photo diode (PD) to convert the acoustic SMI signal into the photocurrent. For the sake of the processing circuit, the SMI photocurrent is demodulated to the sound voltage which can meet the ear by the louder speaker. To quantify the performance of the fiber optical microphone in this paper, the results of self-mixing sound reproduction system based on a DBR fiber laser are given in the following part.

Proof-of-principle experiments are carried out to characterize the fabricated FOM. To identify the property of the FOM carried out in the paper, the Brüel & Kjær anechoic test system is exploited as shown in Fig. 6. The application program of Pulse is installed in PC which connects the “Panel of 2ch Input 2ch output Generator Module” (Type 3160-A-022, Module Panel) by a cable with the green line. The Module Panel output signal regulated by the generator in the Pulse program feeds through the “Power amplifier” (Type 2716C) to amplify the signal and drive the speaker in the “Anechoic Test Box” (Type 4232) by the Bayonet Nut Connector (BNC) in blue. In the Test Box, the reference microphone (RM) and the optical head composed by an APC patchcord and a ceramic pipe butt-coupled with silver diaphragm are laydown, so we can confirm the ultra merits of FOM utilizing the self-mixing interference (SMI-FOM) in a DBR fiber laser by the comparison to the RM which is a commercially manufactured with 20uPa/Hz minimum detectable acoustic pressure. The RM semaphores and the signals of SMI-FOM are jointed to the Panel Input1 and Input2 respectively. Therefore the effects of SMI-FOM can be gained by the Pulse system.

 figure: Fig. 6

Fig. 6 Schematic of the test setup for characterization of the fiber optical microphone by self-mixing technique.

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To measure the response of the proposed SMI-FOM, a sinusoidal signal launched to the speaker in the “Anechoic Test Box” is applied to mobilize the silver diaphragm. In our experimental setup of fiber optical microphone based on self-mixing, a fast InGaAs photodiode connects to the output port of the WDM to observe the experimental signal of SMI-FOM. A typical SMI-FOM signal is obtained in Fig. 7 at the condition of the driven signal with single frequency of 820 Hz and driving voltage of 1mVrms (mill voltage root-mean-square) with the 0dB magnification of “Power amplifier”. Left curve from the reference microphone links to the input1 of the Module Panel and right curve from the fiber optical microphone refers to the input2. The peaks at frequency of 820Hz illustrate the measured values of reference microphone and SMI-FOM and the results declare the correspondent SNR with each other. At the same time, the peaks with frequency less than 200 Hz associate with environmental perturbation and noise of electric supply (fundamental frequency and its sidebands). But other than that, the noises of RM is generated by the Brüel & Kjær anechoic test system itself at low frequency, especially lower than 200 Hz. Compared with the reference measurement system, the self-mixing signal of fiber optical microphone with silver diaphragm as the optical head shown in Fig. 7 is accurate, stable with low noise. The results declare that the SMI-FOM system could provide a fine response to the single frequency at 820 Hz and the silver diaphragm is sensitive to micro-vibration referred to the sound source.

 figure: Fig. 7

Fig. 7 Measured signal at 820 Hz with 1mVrms. Left curve from the reference microphone links to the input1 of the Module Panel and right curve from the fiber optical microphone refers to the input2.

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To seek for dynamic property of the FOM to frequencies, the range from 120Hz to1020 Hz is mounted on the speaker with 1mVrms amplitude and 0dB gain. The output signals SNR of RM and SMI-FOM are recorded by the signal analyzer in the Pulse program through the “2ch Input Module”. Along with the dynamic frequencies of sinusoidal excitation, the SNR is separately labeled with red solid dot and black hollow circles in polygonal lines. It can be observed that the SMI-FOM is in the same order of RM on SNR aspect shown in Fig. 8. To learn more property about SMI-FOM, we obtain the minimum detectable acoustic pressure with 20uPa/Hz based on the same SNR value with the RM. Thus the minimum detectable acoustic pressure by self-mixing technique is typical less than the existing fiber optic microphone [14] with180uPa/Hz. The difference of SNR is derived from the different measurement points and the amplitude-frequency response of their circuits. Additionally, the signal processing circuit is the simple O/E conversion electric circuit with eliminator which needs to lucubrate.

 figure: Fig. 8

Fig. 8 Measured SNR-frequency response of SMI-FOM and RM.

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As a further proof to discuss the effects of the SMI-FOM, the SNR of the fiber optical microphone and the reference microphone are investigated by different amplitude of the speaker in the Test Box. The signal generated by the Pulse program is at the frequency of 1020 Hz with an initial voltage of 1mVrms. The different magnifications of the “Power Amplifier” are load on the speaker with 5 points of the arithmetic sequence at the adjustable extent, so the SNR to amplitude response of the SMI-FOM is shown in Fig. 9. The hollow points in black and the solid red dots refer to the measured SMI-FOM and RM respectively. The red dots are approximately linear dependence on the amplification factor due to the linearly-reinforced sound pressure, while the SNR of SMI-FOM is not a linear process resulted from the stimulation of multiple frequencies. The phenomenon is on account of amplitude-frequency response by the self-mixing interference. In terms of the amplitude of the vibration larger than 1/8 wavelength, the SMI signal is not a monofrequency signal but with multiple frequencies. Thus the signals of SMI-FOM can be reproduced with a high signal-to-noise ratio at different vibration amplitudes of silver diaphragm when a tracking filter is carried on the signal processing circuit.

 figure: Fig. 9

Fig. 9 Measured SNR-amplitude response of SMI-FOM and RM at different gain amplitude.

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In the sound reproduction experiment, the signal launched on the speaker is replaced by a sound fragment through editing the generator in Pulse program. The experimental setup is the same with the measured system as shown in Fig. 6 and the real-time sound reproduction can be obtained by the loud speaker followed with the signal processing circuit. To fully comprehend the dynamic sound reproduction of the fiber optical microphone in a DBR fiber laser at a period of time, we would like to give three examples of the power spectrums shown in Fig. 10. The upper figures are the power spectrums of SMI-FOM measured by Brüel & Kjær measurement system at different times, the lower diagrams trace the performance of RM at the same measured time of the SMI-FOM. By the frequency components comparison of the lower diagraphs to the upper ones, we achieve the closest propinquity power spectrums between the SMI-FOM and RM except for the frequencies around 100 Hz originated from Brüel & Kjær anechoic test system itself noise. The tiny difference of amplitude observed in the diagrams is resulted from not only the amplitude-frequency response of the circuits applied to the dual microphones, the frequency distinguishability generated by the sampling rate of the “2ch Input Module” but also the asynchronized suspension time of the dual Input channel in the Module. On the other hand, the original music produced directly from the speaker in the Test Box can be regressed by the loudspeaker and the reversion of the loudspeaker can clearly meet the ear of the people. In our experiments, the news broadcast and music are regenerated by the SMI-FOM technique. By the multi-dimensional comparison between the performance of SMI-FOM and the RM in Brüel & Kjær system, the technique proposed in this paper guarantees steady, high signal-noise ratio operation and outstanding accuracy sound reproduction in the DBR fiber laser .

 figure: Fig. 10

Fig. 10 the power spectrums of SMI-FOM and RM at different times.

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In this paper we achieve the micro-vibration of the silver diaphragm caused by the sound source with the technique of the self-mixing interference. The self-mixing interference occurs due to the scattered light reentering into the laser. In the condition, the SMI-FOM can be applied to the remote spatial sound transducer which can be used in spy system to guard the public security. As the stuff of daily essentials could function as the scattered light such as boxes of paper, mental, slice of paper influenced by the acoustic waves, the self-mixing model of FOM in DBR fiber laser with outstanding accuracy we have built has a number of potential applications for high performance in remote spatial sound sensor.

4. Conclusion

We demonstrate a theory analysis and experimental results of self-mixing sound reproduction system based on a DBR fiber laser with short lasing cavity which is the key important to the high sensitivity and remote sensing which has never been studied. To investigate the optical head of the SMI-FOM, the silver diaphragm is applied to scatter the light into the laser cavity fabricated by the electroless plating method which is convenient and low cost. The nano-sickness silver diaphragm is critically susceptible to the air vibration caused by the acoustic wave. Different movements of the silver diaphragm can be detected from the self-mixing interference system based on DBR fiber laser and the experimental results of the SMI-FOM guarantee the outstanding accuracy and steady operation coinciding with the RM results. On the other hand, the reproduced sound of news and music can clearly meet the ear of the people. The presented technique may find medical and security applications such as real-time voice reproduction for throat and voiceprint verification.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61307098, 61275165), the Natural Science Fund of Anhui Province (Grant No. 1208085QF110) and the open foundation of Key Laboratory of Environmental Optics and Technology of Chinese Academy of Sciences (Grant No. 2005DP173065-2013-2).

References and links

1. L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

2. J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).

3. H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

4. J. H. Churnside, “Laser Doppler velocimetry by modulating a CO2 laser with backscattered light,” Appl. Opt. 23(1), 61–66 (1984). [CrossRef]   [PubMed]  

5. L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

6. W. M. Wang, W. J. Boyle, K. T. 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. Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

8. L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011). [CrossRef]  

9. F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012). [CrossRef]   [PubMed]  

10. E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003). [CrossRef]  

11. I. Kelson and A. Hardy, “Optimization of strongly pumped fiber lasers,” J. Lightwave Technol. 17(5), 891–897 (1999). [CrossRef]  

12. M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997). [CrossRef]  

13. 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 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012). [CrossRef]  

14. J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005). [CrossRef]  

References

  • View by:

  1. L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).
  2. J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).
  3. H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).
  4. J. H. Churnside, “Laser Doppler velocimetry by modulating a CO2 laser with backscattered light,” Appl. Opt. 23(1), 61–66 (1984).
    [Crossref] [PubMed]
  5. L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).
  6. W. M. Wang, W. J. Boyle, K. T. 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. Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).
  8. L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
    [Crossref]
  9. F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
    [Crossref] [PubMed]
  10. E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
    [Crossref]
  11. I. Kelson and A. Hardy, “Optimization of strongly pumped fiber lasers,” J. Lightwave Technol. 17(5), 891–897 (1999).
    [Crossref]
  12. M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997).
    [Crossref]
  13. 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 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
    [Crossref]
  14. J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
    [Crossref]

2013 (1)

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

2012 (3)

2011 (1)

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

2010 (2)

J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

2006 (1)

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

2005 (1)

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

2003 (1)

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
[Crossref]

1999 (1)

1997 (1)

M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997).
[Crossref]

1993 (1)

1984 (1)

Boyle, W. J.

Bucaro, J. A.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Cao, Z.

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 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

Churnside, J. H.

Dai, J.

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 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

Du, K. Z.

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Du, Z.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Grattan, K. T.

Gui, H.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Hardy, A.

Hardy, A. A.

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
[Crossref]

Houston, B. H.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Jarzynski, J.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Karasek, M.

M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997).
[Crossref]

Kelson, I.

Koh, L. M.

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

Konle, H. J.

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

Lagakos, N.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Li, C.

Lu, L.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

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 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Lu, W.

Mohanty, L.

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

Pacheco, G. M.

J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).

Palmer, A. W.

Paschereit, C. O.

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

Ren, D.

Rohle, I. R.

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

Sakamoto, J. M. S.

J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).

Shi, X.

Tjin, S. C.

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

Wang, R.

Wang, W. M.

Xu, F.

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

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 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

Yahel, E.

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
[Crossref]

Yang, B.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Yang, J.

Yu, B.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

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 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Zalalutdinov, M.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Zhai, L.

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Zhang, W.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Appl. Opt. (2)

Appl. Phys. B (1)

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Appl. Phys. Lett. (1)

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

IEEE J. Quantum Electron. (2)

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
[Crossref]

M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997).
[Crossref]

IEEE Photonics Technol. Lett. (1)

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 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

J. Acoust. Soc. Am. (1)

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

J. Lightwave Technol. (1)

Meas. Sci. Technol. (1)

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

Opt. Commun. (1)

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Proc. (1)

J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).

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Figures (10)

Fig. 1
Fig. 1 The principle of SMI output power based on the Boundary conditional equations.
Fig. 2
Fig. 2 The typical simulated result by quasi-analytical method (Upper trace: vibration signal of external target, Lower trace: self-mixing interference signal).
Fig. 3
Fig. 3 Experimental setup of fiber optical microphone based on self-mixing in DBR fiber laser.
Fig. 4
Fig. 4 The linewidth of DBR fiber laser measured by optical analyzer.
Fig. 5
Fig. 5 The power spectrum of DBR fiber laser at different times.
Fig. 6
Fig. 6 Schematic of the test setup for characterization of the fiber optical microphone by self-mixing technique.
Fig. 7
Fig. 7 Measured signal at 820 Hz with 1mVrms. Left curve from the reference microphone links to the input1 of the Module Panel and right curve from the fiber optical microphone refers to the input2.
Fig. 8
Fig. 8 Measured SNR-frequency response of SMI-FOM and RM.
Fig. 9
Fig. 9 Measured SNR-amplitude response of SMI-FOM and RM at different gain amplitude.
Fig. 10
Fig. 10 the power spectrums of SMI-FOM and RM at different times.

Tables (1)

Tables Icon

Table 1 The parameters used for the DBR fiber laser

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

P L out = P L in e - α s L+ P s abs / P ss + P p abs / P ss
P R out = P R in e - α s L+ P s abs / P ss + P p abs / P ss
P L in = ε 2 [ ε 2 R 2 P R out +(1 R 2 ) P seed ]
P R in = ε 1 2 R 1 P L out
P R out = ε 1 2 R 1 ε 2 [ ε 2 R 2 P R out +(1 R 2 ) P seed ] e -2 α s L+2 P s abs / P ss +2 P p abs / P ss
L ext (t)= L 0 +Acos 0 t)
P Laser = ε 1 (1-R 1 ) P R out e -(- s L+ P s abs / P ss + P p abs / P ss )

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