Intensity-independent wavelength locking of diode lasers to a spectral slope of a fiber-optic sensor for ultrasonic detection

Lingling Hu; Ming Han

doi:10.1364/OE.25.031017

1. Introduction

Fiber-optic ultrasonic sensors, particularly those based on various kinds of fiber Bragg gratings (FBGs), have been considered as an attractive ultrasonic sensing technology due to their many advantages such as small size, light weight, immunity to electrical magnetic interference, and ability for multiplexing [1–6]. A simple demodulation technique for FBG-based ultrasonic sensors is to use a laser whose wavelength is set in the linear range of the spectral slope of the sensor. As a result, the ultrasound-induced spectral shifts are converted into laser intensity variations that can be detected by a photodetector (PD). In many practical applications, both the laser and the FBG sensors can be subject to low-frequency environmental perturbations such as thermal fluctuations and mechanical vibrations, which may knock the laser wavelength out of the linear range. Laser wavelength locking techniques are needed to keep the operating point in the linear range [7–9]. Figure 1(a) shows a typical configuration for laser wavelength locking used in a FBG-based ultrasonic sensor system, where the laser intensity reflected by the sensor is measured and fed back to the laser controller to hold this intensity constant. This simple method, however, has a drawback that it cannot distinguish between the wavelength shift and the changes in the laser intensity. As schematically shown in Fig. 1(b), the change of the light intensity influences the operation point of the sensor and, consequently, the responsivity of the sensor system that is proportional to the spectral slope at the operating point. In addition, when the light intensity drops below the value that the system is locked to, the laser wavelength can no longer be locked. Large laser intensity variations are possible for locking of distributed-feedback (DFB) diode lasers using injection current wavelength modulation where the wavelength tuning is associated with intensity modulations [10]. For FBG-based resonators in single-mode fibers where fiber birefringence can be induced from FBG inscription [11], laser locking point can also change significantly due to the changes of light polarization. Pond-Drever-Hall (PDH) locking technique is intensive to laser intensity variations by locking the laser wavelength to the resonance of an interferometer [7]. Its error signal is proportional to the difference between the laser wavelength and the resonance wavelength, which can be adapted for ultrasonic detection using FBG-based resonators [12]. However, the sensor responsivity is dependent on the spectral width of the resonance. For sensors with multiple resonances of different widths [10, 13] the amplitude of the sensor output cannot be directly related to the shift of the resonant wavelength.

Fig. 1 Schematic of a conventional method to lock the laser wavelength to the spectral slope of the sensor using the reflection from the ultrasonic sensor. (b) The error signal vs. wavelength for intensity-based wavelength locking.

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In this paper, we propose and demonstrate a novel laser-wavelength locking method for diode lasers that is independent on the laser intensity variations and can lock the laser wavelength to a particular normalized spectral slope of a sensing resonator regardless of the spectral width of the resonance. Conceptually, this locking method is achieved by simultaneously and independently modulating the laser wavelength and laser intensity. On the spectral slope of the resonator, the wavelength modulation is also converted to intensity modification, which is superimposed on the direct intensity modulation. The modulations are designed in such way that, at a particular spectral slope, the intensity variation from the wavelength modulation cancels out the directly laser intensity modulation. The difference between the intensity variations caused by these two mechanisms is used as the error signal, which is fed back to the laser controller to hold the error signal at zero. As a result, the laser wavelength is locked to the point with a given spectral slope, independent upon the spectral width of the resonance and the fluctuations in the laser intensity.

2. Theoretical analysis

A detailed quantitative illustration of the proposed locking method is given as follows. As schematically shown in Fig. 2(a), the current injected to a diode laser is modulated by a sinusoidal signal, which in turn cause proportional modulations to both the laser wavelength and laser intensity [14, 15]. The intensity of the laser output is modulated by an external intensity modulator driven by a sinusoidal signal of the same frequency and appropriate amplitude and phase relative to the current modulation signal. The light is then directed to a sensor resonator (here a π-phase shifted FBG or πFBG is used as an example) through a circulator. The light reflected back from the sensor resonator is directed to a PD by the same circulator to measure its intensity which can be expressed as:

I (t) = I_{0} (1 + a \cos Ω t) (1 + b \cos Ω t) (R + k λ_{m} \cos Ω t)

where

I_{0}

is the laser output intensity,

Ω

is the modulation frequency,

a

and

b

are the intensity modulation depth due, respectively, to the injection current modulation and the intensity modulator,

λ_{m}

is the amplitude of the wavelength modulation,

k

is the value of the slope of the normalized resonance spectrum, and

R

is the reflection coefficient of the resonator at the laser wavelength. If we assume small modulations,

a ≪ 1

or,

b ≪ 1

, and

k λ_{m} ≪ 1

, Eq. (1) can be approximated by

I (t) \approx I_{0} {R + [R (a + b) + k λ_{m}] \cos Ω t}

Note that the

\cos Ω t

term describes the superimposed intensity variations from the direct intensity modulation and the current injection modulation. Its amplitude will be used as the error signal for laser wavelength locking, which is given by

Fig. 2 Layout of the proposed method for locking the laser wavelength to a spectral slope of the sensor. (a) is the optical part of the system; (b) shows the diagram to retrieve the error signal from the PD output.

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ϵ \propto I_{0} [R (a + b) + k λ_{m}]

The error signal of Eq. (3) can be obtained from the ouput of the PD [Eq. (2)] using a frequency mixer followed by a low-pass filter, as shown in Fig. 2(b). After mixing Eq. (2) with the same modulation signal, $\cos Ω t$ , the output of the mixer contains a dc component, which happens to be the error signal, and two ac components at frequencies of $Ω$ and $2 Ω$ . The error signal is then isolated by applying the low-pass filter to filter out the ac component. From Eq. (3), the amplitude of the error signal is related to the modulation depth, $b$ , of the intensity modulator. Later, we will show that the value of the spectral slope the laser wavelength is locked to can be conveniently adjusted by changing $b$ .

As an example, we assume that the normalized reflection spectrum of the sensing resonator has a Gaussian shape given by

R = 1 - e^{- {(\frac{λ - λ_{0}}{δ λ})}^{2}}

where

λ

is the wavelength,

λ_{0}

is the resonant wavelength, and

δ λ

specifies the spectral width of the resonance. The spectral slope is expressed as

k = \frac{d R}{d λ} = \frac{2 (λ - λ_{0})}{δ λ} e^{- {(\frac{λ - λ_{0}}{δ λ})}^{2}}

Inserting Eqs. (4) and (5) into Eq. (3) gives the error signal as

ϵ \propto [1 - e^{- {(\frac{λ - λ_{0}}{δ λ})}^{2}}] (a + b) + \frac{2 (λ - λ_{0}) λ_{m}}{δ λ^{2}} e^{- {(\frac{λ - λ_{0}}{δ λ})}^{2}}

Defining

x = (λ - λ_{0}) / δ λ

y = \frac{λ_{m} / δ λ}{a + b}

the error signal can be simplified to

ϵ \propto [1 + (2 x y - 1) e^{- x^{2}}]

In Eqs. (7) and (8),

x

is the normalized relative wavelength and

y

is a parameter determined by the intensity modulation depths and the amplitude of the wavelength modulation relative to the spectral width of the resonance, which, as mentioned previously, can be used to tune the locking point by adjusting the intensity modulation depth,

b

. Figure 3(a) shows the resonant spectrum and the error signals for different values of

y

. For each error signal, there are two zero points. One of them locates at the resonant wavelength where the slope (

k

) and the reflectivity (

R

) vanish; the other is located on the slope at the shorter-wavelength side of the resonator spectrum. The laser wavelength can be locked to either of them. Here, we focus on the one on the slope. It is also shown that, by changing

y

(through tuning

b

), the locking point can be tuned to an arbitrary position on the shorter wavelength side of resonance spectrum. The laser wavelength can also be locked on the other side with a positive slope simply by introducing a π-phase shift between the intensity modulation and the wavelength modulation, in which case the intensity measured by the PD becomes

I (t) = I_{0} (1 + a \cos Ω t) (1 + b \cos Ω t) (R - k λ_{m} \cos Ω t)

The corresponding error signal is given by

Fig. 3 Error signal vs. normalized relative wavelength when the laser is locked to (a) the side with negative spectrum slope and (b) the side with positive spectrum slope.

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ϵ \propto [1 - (2 x y + 1) e^{- x^{2}}]

Figure 3(b) shows the corresponding error signal relative to the resonant spectrum for different values of $y$ , indicating that the locking points are now locked at the longer-wavelength side of the spectrum.

3. Experiment

The locking method and its application in fiber-optic ultrasonic sensing were experimentally demonstrated using a setup schematically shown in Fig. 4. The sensing resonator is a 7-mm long πFBG centered at 1545 nm fabricated on a regular single-mode fiber by using a 193 nm excimer laser and a phasemask [11]. The 3-dB spectral width of the center notch of the reflection spectrum was 3 pm. The πFBG was glued on an aluminum plate to detect ultrasonic pulses centered at 200 kHz, which was generated from a piezoelectric transducer (HD50, Physical Acoustic Corp.) powered by a function generator. The light source was a distributed-feedback (DFB) laser (1905LMI, Avanex) diode with a nominal linewidth of 2 MHz. The current controller (D2-105, Vescent Photonics) driving the DFB laser had a nominal current modulation bandwidth > 10 MHz. The light intensity was modulated by a 10 GHz external intensity modulator (Model: OC-192, JDS Uniphase). Another function generator provided two synchronized 5 MHz sinusoidal modulation signals with tunable relative phase to drive the current controller and the intensity modulator. After the intensity modulator, a tunable attenuator was used to adjust the intensity of the light before it was divided into two paths by a coupler with 5% of the light reserved for monitoring the laser intensity and the other 95% of the light was directed to the πFBG by a circulator. The use of the tunable attenuator is to prevent the photodetector from saturation and provide laser intensity variations for the testing of the locking method. A polarization controller (PC) was inserted before the πFBG to align the laser polarization to one polarization mode of the πFBG. The reflected light from the πFBG was collected by a PD with a build-in wide-band amplifier. The signal was then sent to a 500 kHz low-pass filter to monitor the ultrasonic signal. It was also sent to a 500 kHz high-pass filter to obtain the modulated signal, which was then mixed with the 5 MHz oscillation signal. Another low-pass filter (500 Hz) was used after the mixer to provide the error signal to tune the laser wavelength through a servo controller (Model: LB1005, Newport). The bandwidth of the feedback loop was limited to 500 Hz by the low-pass filter, which was sufficient to compensate for the spectral drift of the πFBG caused by thermal changes and vibrations in our experiment. However, much higher bandwidth can be achieved by simply using a filter with higher cut-off frequency. Note that the frequency of the modulation signal (5 MHz) was far above the frequency range of the ultrasonic signal (~200 kHz).

Fig. 4 Schematics of the experiment setup for demonstration of laser wavelength locking and ultrasonic detection.

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First, we demonstrate that the locking point is independent on the laser intensity. In this experiment, the light intensity was reduced to several different levels by the attenuator, and, at each level, the error signal as well as the resonant spectrum were recorded as the laser wavelength was scanned around the resonant wavelength. The recorded error signal relative to the resonant spectrum is shown in Fig. 5(a) and 5(b). All the error signals crossed zero at the same wavelengths relative to the resonant spectrum regardless of the light intensity, proving that the laser wavelength can be locked to the same normalized slope independent upon light intensity. Even when the light intensity reduces to more than 50% of the initial value, the error signal still cross the zero voltage line and thus the laser output wavelength can still be locked to the same operation point on the sharp slope of the $π$ FBG sensor.

Fig. 5 The reflection spectrum of the sensor at different light intensity levels (a) and the corresponding error signal vs. wavelength (b).

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We then demonstrated that the locking point can be tuned by changing the modulation depth of the intensity modulator, $b$ . In this study, the wavelength modulation was kept at a constant level and the error signal was recorded at different intensity modulation depths. Figure 6(a) shows the results when the wavelength modulation corresponded to $a = 0.04$ . Figure 6(b) shows the results for a larger wavelength modulation depth corresponding to $a = 0.05$ . As the intensity depth increased, the locking point moved from the center resonant wavelength toward shoulder of the spectrum. A larger wavelength modulation depth also led to a larger peak-to-peak value of the error signal. In this experiment, the laser wavelength was locked on the longer-wavelength side of the resonant spectrum. As described early, it can also be locked to the shorter wavelength by an appropriate relative phase shift between the intensity and wavelength modulation signals.

Fig. 6 Error signal at different intensity modulation depths relative to the sensor reflection spectrum when the wavelength modulation depth from (a) a = 0.04 (b) a = 0.05.

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Finally, we demonstrate the application of the proposed locking method for ultrasonic signal detection. The wavelength of the laser diode was locked to the point with maximum normalized slope on the πFBG spectrum using the proposed locking method. Ultrasonic pulses centered at 200 kHz were monitored by the sensor system when the light intensity was attenuated to different levels. As described previously, the light intensity was measured through the 5% port of the fiber coupler shown in Fig. 4. The detected ultrasonic waveforms at several light intensity levels are shown in Fig. 7(a). Figure 7(b) shows the root-mean-square (rms) values of the measured ultrasonic signal, which represent the signal strength, at these different light intensity levels, as well as the linear fitting of the data. The good linear relationship between the signal strength and the light intensity is another indication that the laser wavelength was locked to the same normalized spectral slope at all light intensity levels.

Fig. 7 (a) The strength of the detected ultrasonic signals (represented by the rms value of the signal) vs. light intensity. (b) Detected ultrasonic signals at different light intensity levels.

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We note that a 10 GHz external intensity modulator with relatively high cost was used for demonstration. Because modulation frequency only needs to be a few MHz, lasers with integrated electro-absorption modulator may be used that can significantly reduce the cost of the locking system. In addition to the applications in fiber-optic ultrasonic sensor system, the locking method can also be used for laser frequency stabilization and is particularly useful in situations where the wavelength of the free-running laser is not perfectly aligned with the resonant wavelength of the reference cavity.

4. Conclusion

In conclusion, we have proposed and demonstrated a method to lock the laser wavelength to a particular normalized spectral slope. In this method, the laser wavelength and intensity are simultaneously and independently modulated and, at a particular normalized spectral slope, the wavelength modulation is converted to intensity variations that cancel out the direct laser intensity modulation. The amplitude of the overall intensity modulation is used as the error signal to control the wavelength. We demonstrated that the locking point is independent on the light intensity variations and the operation point on slope of the sensor spectrum can be conveniently tuned by adjusting the intensity modulation depth. The laser wavelength can be locked to both sides of the spectrum. Finally, we demonstrated the application of this locking method for ultrasonic detection when the laser intensity varies over a large range. Although we only demonstrated the case where the ultrasound frequency is much smaller than the laser modulation frequency, the approach is also applicable for detection of ultrasonic waves whose frequency is much higher than the modulation frequency.

Funding

Office of Naval Research (ONR) (N000141410456, N000141613185, N000141712819)

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Intensity-independent wavelength locking of diode lasers to a spectral slope of a fiber-optic sensor for ultrasonic detection

Abstract

1. Introduction

2. Theoretical analysis

3. Experiment

4. Conclusion

Funding

References and links

Cited By

Figures (7)

Equations (11)

Optics Express