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A new approach for remote reflectivity detecting based on optical feedback effect in distributed feedback (DFB) lasers is presented. A linear dependent relationship between the reflectivity of external target and the signal modulation depth is obtained. The experimental results show a good agreement with the theoretical analysis and the simulation, and indicate that the active sensing based on optical feedback effect in DFB laser is an effective approach for reflectivity detecting. With the advantage of simple and compact structure, this application can easily enhance the development of a new generation of active sensor.
©2007 Optical Society of America
1. Introduction
Laser feedback has demonstrated unique features since it was first reported in the 1960’s to measure changes in the optical length and the behavior of lasers [1]. These features include a simple, single-axis optical arrangement, minimal optical components, and high sensitivity at low light level. Laser feedback effect has been widely used for distance, displacement, and velocity measurement [2–5].
Due to the characteristics of robust single longitudinal mode operation, flexible and accurate wavelength selection in production, narrow line width, small dimensions, and compact in-fiber design, DFB lasers have potential in sensor applications. We have reported the optical feedback effect in DFB lasers in our previous work [6]. Here, we further propose the remote active sensing by combining optical fiber sensing technique and optical feedback effect, because the connection between the DFB laser and the optical fiber is simple and convenient. In recent years, active sensing, which emits radiation directed toward the target, has attracted more and more attention [7–9]. Laser is not only a light source, but also a sensitive element viz. sensing source presented in the active sensing system. This application can satisfy the request of microminiaturized sensing device and the demand of remote detecting, and predigest the structure of sensing system.
In this paper, a new approach for remote reflectivity detecting based on the optical feedback effect in distributed feedback (DFB) lasers has been proposed. The model of optical feedback effect in DFB lasers for remote reflectivity detecting is presented in section 2. In section 3, the feasibility for remote detecting has been analyzed and validated in both simulation and experiment, and the active sensing of reflectivity detecting based on optical feedback effect is discussed. The experimental results show a good agreement with the theoretical analysis and the simulation. It validates the feasibility of active sensing application for remote reflectivity detecting.
2. Model
Figure 1 shows the theoretical illustration for the fiber active sensing application based on the optical feedback interference in DFB laser. Single longitude light emitted from the laser is transferred by an optical fiber (with a collimating lens in its end), then reflected by an external reflector and fed back into the laser cavity. The reentered light, which carries the information of the external reflector, modulates the output of the laser.
Fig. 1. Theoretical illustration for the active sensing application of optical feedback interference in DFB laser.
The output gain variations of the optical feedback interference in DFB lasers with single external cavity can be written as [6]:
where c is the velocity of light in vacuum, n is the equivalent refractive index of the laser, L is the laser cavity length, C r denotes the complex feedback sensitivity which depends only on the proper laser parameters in the limit of a weak feedback level. r is the equivalent reflectivity of external cavity, ω is the laser emission frequency, and the external round-trip time τ=2 L ext, where L ext refers to the equivalent external cavity length.
Considering the influence of feedback light in equivalent cavity, we obtained the equivalent reflectivity as follows:
√R 0 is the initial reflectivity of the fiber end, η fe denotes the coupling efficiency of the fiber end, the external round-trip time between the fiber end and the reflector τ obj=2 L obj/c, where L obj is the cavity length between the fiber end and the reflector.
The power of the reentered light can be obtained as:
here P ff denotes the input light power at the left end of the external fiber, L f is the external fiber length, α i(x) and α s(x) are forward and backward attenuation factors of the fiber, respectively.
Considering the influence of phase variation, the equivalent reflectivity of the laser right-hand facet can be expressed from Eq. (2) and Eq. (3) as:
η lf is the coupling efficiency of reflected light between fiber and the right facet of DFB laser, k 0 refers to the wave number in vacuum, n f denotes the effective refractive index of optical fiber. Posing the initial reflectivity of the right-end of the DFB laser with AR-coated, Eq. (4) can be written in the form:
The equivalent parameters contained external information can be finally derived from Eq. (4) and (5) as:
Because the laser output power is proportional to the output gain, inserting Eq. (6) into (1), we obtain the following relation:
From Eq. (7) we can find that the optical feedback interference signal exhibits a cosine characteristic as the external cavity phase ω τ obj variation. Choosing appropriate parameters, we finally demonstrate that the signal modulation depth is proportional to the reflectivity of the external reflector r obj:
3. Experiment
3.1 Experimental setup
Figure 2 shows the schematic configuration of the remote active sensing system based on optical feedback interference effect, which is mainly composed of a DFB laser. The DFB laser is not only a light source, but also a sensitive element. The others are commercial communication devices for detecting. The power of the DFB laser used in this system is about 0.7mW. The reflected light from the target reenters the laser cavity and causes an optical feedback interference signal which is detected by a PD inside the laser package. The length of external cavity L obj can be modulated by the piezoelectricity (PZT) driven by a PZT driver. After being amplified, the output signal is acquired by a data acquisition card (National Instrument 6024E) where analog-to-digital conversion is performed. Then the digital signal is transferred to a PC.
Fig. 2. Experimental schematic for active sensing application of optical feedback interference in DFB laser.
3.2 The influence of the external fiber attenuation
Figure 3 shows the simulated and experimental results of signal modulation depth δP versus the external fiber length L f from 1m to 2km. From the figure we can find that the δP decreases with the increase of L f. For validating the simulation results, the experimental phenomena in the case of L f≈1m, 173m, 521m, 1170m, and 1691m were observed. We launched the PZT with sinusoidal signal, and acquired five values to get one average modulation depth for each fiber length. The results are denoted by ‘∙’ in Fig. 3. The experimental results show a good agreement with the simulation. The results shown in Fig. 3 are normalized values. For exhibiting the actual attenuation from L f≈1m to L f≈1691m, we illustrated the signal traces in dashed rectangle in Fig. 3. The output presents cosine variation with the linear variation of the external cavity length, and there occurs abnormity when the movement direction of the target changes. The value of the signal modulation depth (peak-peak value) of trace 1 is bigger than that of trace 2. But the variation is too small to be seen in the figure. This result indicates that the attenuation of the external fiber could be neglected in this active sensing application, and shows the feasibility of remote reflectivity detecting based on optical feedback effect in DFB lasers.
3.3 Remote reflectivity detecting
According to Eq. (8), the signal modulation depth δP is proportional to the reflectivity of external reflector r obj. We can perform the noncontact and remote detecting for reflectivity. Figure 4 shows the simulated and experimental results of δP versus the increase of the reflectivity of external target r obj. The symbol ‘-.-’, ‘.+.’, ‘-▫-’, ‘.*.’, and ‘-o-’ in Fig. 4(a) denote the results with the length of external fiber L f=1m, 100m, 500m, 1000m, and 1500m respectively. The reflectivity r obj has a good linearity with the signal modulation depth.
In experiment, corresponded to each reflectivity and length of fiber, 5 values of detected signals are gained, and the average modulation depth can be calculated. For each length of fiber, we get 9 average values corresponding to different reflectivity. The symbol ‘.’, ‘+’, ‘▫’, ‘*’, and ‘o’ in Fig. 4(b) denote the experimental results with the length of external fiber L f=1m, 173m, 521m, 1170m, and 1691m respectively, the continuous and dotted lines are linear fitted. The experimental results show a good agreement with the theoretical analysis and the simulation. The relation between the target reflectivity and the signal modulation shows a good linearity. This indicates that the optical feedback interference in DFB laser is effective for remote reflectivity detecting and it is promising to develop a new generation of active sensor.
Fig. 4. Simulated and experimental results versus different reflectivity of external reflector. (a). Simulation. (b). Experimental results and fitted linear regression lines.
4. Conclusion
In this paper, the active sensing application for remote reflectivity detecting based on the theory of optical feedback interference has been presented. The feasibility has been analyzed and validated through simulation and experiment. The experimental results show a good agreement with the simulation and theoretical analysis, and we get the conclusion that the relationship between the target reflectivity and the signal modulation depth exhibits a good linearity. With the advantage of simple and compact structure, this application can easily enhance the development of a new generation of economic and practical active sensor.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (60578006), the Specialized Research Fund for the Doctoral Program of Higher Education (20050319007),
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