Open Access
Add to BibSonomy
Abstract
An extended range dual wavelength differential detection technique for interrogating fiber Bragg grating sensors is implemented for the measurement of tilted fiber Bragg gratings. The dynamic chirp of a single DFB laser diode modulated with a square wave is used to generate two pairs of wavelengths, in the high and low modulation states, with a separation approximately equal to the bandwidth of the TFBG, resulting in a doubling of the range of the DWDD measurement. A spectral resolution of 0.08 pm and a refractive index resolution of 9.9 × 10−6 are obtained over a range of refractive index of 3.7 × 10−2, corresponding to 11.9 bits of resolution.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The use of optical fiber for chemical, biochemical and biological sensing has been studied extensively in the past few years [1–6], as an alternative to the widely used surface plasmon resonance (SPR) instruments that are bulky, delicate and expensive [7–9]. While optical fiber has been used as the light guiding medium for surface plasmon resonance analysis via a metallic coating [5], fibre gratings, due to their ease of fabrication and compactness, have also been investigated by many groups, either as a coupling means to the SPR [10–14], or for their own sensitivity to the surrounding medium [1,2,15–18]. A standard fiber Bragg grating (FBG) reflects light from the core of the fiber back along the same path, and is therefore not suited for probing the external environment. Hence other types of gratings, such as long period fiber gratings (LPFGs) [3,19], and tilted fiber Bragg gratings (TFBGs) [1], have been used instead, because they involve cladding modes with electric fields extending outside the fiber itself. While much work has focused on LPFGs, those have some drawbacks, such as relatively long devices, large bandwidths, and also relatively high sensitivity to fabrication conditions. TFBGs, on the other hand, are more compact (typically less than 10 mm long), and their fabrication has a high degree of repeatability, as is attested by the industrial production and wide commercial availability of FBGs for telecommunications or sensing applications.
Despite the large amount of published work on LPFG or TFBG sensors, the instruments used to monitor such gratings, such as optical spectrum analyzers and swept-wavelength sources, are also typically bulky and expensive, and a resolution limited to a few pm or more. To overcome this limited resolution, a lot of effort has been made to increase the sensitivity of the sensors themselves, as defined by the spectral shift of a given resonance per refractive index unit. This was achieved, for example, by etching the cladding around a fiber grating, making fiber interferometers with very small fiber diameters, or using a D-shaped fiber to increase the overlap of the mode with the external environment [20–24]. Adding a metallic or high index overlay on the fiber [13,14,24–30] also increases the sensitivity. However, those schemes inevitably increase fabrication complexity, and often result in fragile devices, while not solving the problem of expensive, bulky, and low resolution interrogation apparatus. The limited resolution can also be overcome by using sophisticated algorithms for peak tracking, or determination of the TFBG cutoff wavelength [31–34]. Most of these techniques nevertheless still require a knowledge of the entire spectrum, or at least one entire resonance.
We describe here an inexpensive, yet high-resolution instrument to measure TFBG sensors that uses the recently developed dual wavelength differential detection technique (DWDD) [35–39]. This technique uses measurements of the grating reflectivity at two fixed, slightly different wavelengths to provide a signal that is linearly proportional to the grating central wavelength. To generate such a wavelength pair, we take advantage of the dynamic chirp of a single square-wave modulated DFB laser diode. We also show how the measurement range, which for DWDD is normally limited to about one grating bandwidth, can be doubled by using two such wavelength pairs, one in each of the modulation states, with their average wavelengths separated by one grating bandwidth.
The DWDD technique is entirely different from standard peak location techniques in that it does not require a measurement of the entire spectrum but rather makes a measurement of the slope of the spectrum around the two fixed, probing wavelengths. Since the slope at any point across the spectrum is a single-valued function of the position of the peak, it will change as the grating spectrum shifts. Therefore, the source does not need to cover or scan the entire resonance, nor the full TFBG spectrum. The usual concept of spectral resolution cannot be used. As shown in the next section, the effective equivalent spectral resolution only depends on the signal-to-noise ratio of the detected signal, and the wavelength stability of the laser diode. The latter can, however, be improved with the use of an external, stable reference, such as another grating.
The sensor’s performance is best described by the range-to-resolution ratio $R$. We demonstrate here a ratio of over 3700, or 11.9 bits of resolution, with the potential to reach 13 bits or more. While the short- and long-term precision can be limited by the wavelength stability of the DFB laser diode, we show that the use of a reference grating is an effective way to overcome this limitation. In our demonstration, an effective spectral resolution of 0.08 pm is achieved, but we estimate that a resolution of 0.01 to 0.05 pm is attainable. Using the instrument for refractive index measurements of an NaCl solution, we demonstrate a refractive index resolution of $9.9\times 10^{-6}$ over a range of $3.7\times 10^{-2}$. Nearly three times better resolution could be achieved by using a TFBG resonance closer to cutoff. This outperforms other demonstrations involving bare TFBGs without any coating or treatment, that have shown resolutions in the range $10^{-5}-10^{-4}$ [2,17,18].
2. Dual wavelength differential detection: theory and sensitivity analysis
The dual-wavelength differential detection technique (DWDD) was recently demonstrated by a few groups for the interrogation of fiber Bragg gratings [35–39], though an early version of the concept can be found in [40]. As we use it here, the technique is illustrated in Fig. 1. A DFB laser diode is made to emit light at two slightly different wavelengths $\lambda _{-}$ and $\lambda _{+}$, both within the spectrum of the grating, but with a separation $\delta =\left ( \lambda _{+} - \lambda _{-}\right )$ that is a fraction of the grating full width at half maximum (FWHM) $w_{B}$. The different reflected signal provides a measure of the slope, which provides information on the position of the peak. Previous authors used different implementations of a similar concept. Wilson et al. [40] used a single laser diode, that emitted light simultaneously in two longitudinal modes, positioned on either side of the grating spectrum. They used a monochromator to recover the reflected light at those two wavelengths. The range in their case was limited to one half of the grating bandwidth. Cheng and Xia [37] used a single tunable laser switched between two wavelengths, electro-optically modulated over a swept frequency range, and retrieved the signals from multiple gratings with a vector network analyzer. Rohollahnejad et al. [39] used three separate lasers launched simultaneously and externally modulated. The three wavelengths were discriminated at the detection end by Fabry-Perot filters. Li et al. [38] used two separate lasers pulsed in sequence by switched semiconductor optical amplifiers, amplified by an EDFA. While those previous works use a similar principle, their implementation is much more complex and expensive than ours. The algorithm that we use to compute the DWDD signal is simpler than in those previous works, though it is essentially the same as used by Wilson et al. [40].
Fig. 1. Schematic of the extended range DWDD measurement scheme: two pairs of wavelengths interrogate the grating over 2 bandwidths $w_{B}$.
In a previous work [36], we showed a much simpler implementation that used two successive short pulses from a single DFB laser diode with a different driving current to generate the two wavelengths. In this work, we rather take advantage of the dynamic chirp of the laser when it is modulated with a square wave. During one modulation state (upper or lower), the laser actually emits light over a narrow spectrum typical of a DFB laser, but the central wavelength is swept in a continuous manner, due to the thermalization of the diode chip. By digitizing the transmitted light, and chosing the digitized samples around specific times, we can effectively select a probing wavelength at will within the range covered by this dynamic chirp. For the extended-range technique that we demonstrate here, the extent of the dynamic chirp was such that two such pairs of wavelengths could be selected in this way : $\lambda _{+u}$ and $\lambda _{-u}$ during the upper modulation state, $\lambda _{+l}$ and $\lambda _{-l}$ during the lower state, separated by one grating bandwidth.
The dynamic chirp of DFB laser diodes has been studied in detail by Shalom et al. [41], who have found that it is governed by up to four different time constants, in addition to instantaneous change related to carrier density in the junction. The four time constants are widely different, with values ranging from 16 ns, to 50 $\mu$s. The chirp coefficient at each time scale was of the order of 1-10 pm/mA, which is suitable for our application, since it is of the order of a typical TFBG spectral bandwidth for modulation amplitudes around 10 mA. In our experiments, we observed a total chirp of 238 pm for 8.93 mA modulation amplitude (17.8 mA peak-to-peak).
The difference between the reflected power at each wavelength for a given pair gives a measurement of the slope of the spectrum at the average of the two probing wavelengths $\lambda _{av}=\left ( \lambda _{+}+\lambda _{-}\right ) /2$. On the other hand, the average of the two reflected powers in each pair is proportional to the reflectivity of the grating at $\lambda _{av}$. The ratio of these two quantities therefore gives a dimensionless, self-referenced signal $S$ that is insensitive to the transmission loss between the source and the grating. Figure 1 shows how the difference between the reflected powers evolves as the spectrum of the grating shifts to longer wavelengths. Assuming that a significant signal is generated when the average power is above half of the maximum reflected power, initially only the upper state pair generates a useful signal, over one grating bandwidth. When the grating has shifted by one bandwidth, the second pair now starts to generate a useful signal over another grating bandwidth.
Assuming that the spectrum has a Gaussian shape, the reflected powers $P_{+}$ and $P_{-}$ at wavelengths $\lambda _{+}$ and $\lambda _{-}$ are given by:
Normalizing this difference to the sum of $P_{+}$ and $P_{-}$ gets rid of the Gaussian function dependence, leaving a signal $S$ that is a linear function of the difference between $\lambda _{av}$ and $\lambda _{B}$, and can therefore be used to determine the state of the sensor:
This linear response is a result of the Gaussian shape of the spectrum and the small wavelength separation $\delta$. In actual fact, an almost purely linear response ($r^{2} \ge 0.9998$) is obtained over a range at least as large as $w_{B}$ for ratios of $\delta /w_{B}$ up to 0.4. The signal $S$, which is dimensionless, varies from positive to negative as $\lambda _{B}$ shifts from shorter wavelengths to longer ones, reflecting the change of sign of the slope. The measurement range is proportional to $w_{B}$, since the denominator in Eq. (3) becomes very small at low reflectivity, eventually increasing the measurement error to unacceptable values. But this means that the range can be tailored by making the grating longer or shorter. The simple algorithm of Eq. (3) can be performed in real time even on ns time scales by a fast electronic processor, such as an FPGA chip, as we demonstrated recently [36].
The slope of Eq. (3) gives the sensitivity of $S$ to the Bragg wavelength shift. It is linearly related to the wavelength separation $\delta$ and inversely proportional to the square of the grating bandwidth. It is therefore advantageous to use a smaller $w_{B}$, and to maximize $\delta$. On the other hand, the range is limited by, and proportional to $w_{B}$. The effective spectral resolution then depends on the smallest power difference that can be detected, which is limited by photodetector noise, laser power noise, and ADC quantizing noise. Given an rms noise $\sigma _{p}$ on the measured, digitized power, we find that the measured value $S_{m}$ is related to the true value $S$ by:
The error is minimum at the center of the grating, where $S=0$, and increases with the detuning between the laser wavelength and the Bragg wavelength $\Delta = \left | \lambda _{av}-\lambda _{B} \right | /w_{B}$. Taking the maximum number of bits of resolution in the measured power as $B_{p} =\log _{2}(P_{max}/\sigma _{p})$, we can find a general expression for the number of bits lost with increased detuning . The smallest change in Bragg wavelength that can be detected $\Delta \lambda _{B}^{min}$ corresponds to twice the error on $S$, so considering a measurement range $w_{B}$, and from Eqs. (3) and (4), we can express the resolution on $S$ as:
One bit is always lost from $B_{p}$ because the calculation involves twice the error on the power. For the largest detuning $\Delta = 1/2$, and taking $\delta /w_{B} =0.4$ as a maximum practical value, we find that a maximum of about 2 bits are lost. On the other hand, bits are gained by averaging and oversampling. For example, averaging over more than 64 samples ($4^{3}$) gains 3 additonal bits. Since we operate at 5 kHz, and applications such as chemical and biochemical sensing typically only require a 1 s response time or more, such averaging is readily achievable. In our case, with a detected power of a few mW, we estimated a noise-equivalent-power of $2\times 10^{-5}$ mW, which would give more than 17 bits, while the ADC has a 14-bit resolution, though the positive-only signal only uses 13 bits. Most of the noise was found to be from the laser diode driver, at about 0.01%, or more than 13 bits, which gives a minimum resolution $B_{S}=11$ bits. Therefore, with enough averaging to restore an effective 14-bit resolution, a DWDD measurement should be able to achieve $<0.01$ pm resolution for a grating with a FWHM $w_{B}\le 150$pm. This is more than 100 times better than spectral instruments.
In practice, while the instrumental resolution can be very high, the precision is limited by the fluctuations and drift of the laser diode wavelength on time scales of seconds to minutes. While temperature controllers can provide stability down to 1 mK, which should result in a $< 0.1$ pm stability, we found that the true temperature of the laser chip often deviates from that measured by the internal thermistance,which is never exactly co-located with the laser chip. Those fluctuations and drift are very small, typically less than 0.5 pm, but nevertheless easily detectable when the resolution is itself sub-pm. As we will show below, a practical solution to increase the precision is to use another FBG or TFBG as a reference. Since FBGs and TFBGs have a ten times smaller wavelength dependence on temperature than typical DFB laser diodes, and are not generating any heat by themselves, maintaining them with a temperature stability of 5 mK is readily achievable, which should guarantee a stability $\le 0.05$pm. Having this temperature-controlled reference grating further mounted on a temperature-compensated package [42] could also improve the stability to $\le 0.005$pm. In our demonstration, simply maintaining a reference TFBG at the same (room) temperature as the signal TFBG, we could achieve RMS fluctuations of 0.06 pm or less over many minutes in stable laboratory conditions. Therefore a practical limit to the resolution appears to be in the range $0.01 - 0.05$ pm. We consider this extremely high resolution to be the main advantage of the DWDD method, together with its simplicity and very low cost.
The measurement of the DWDD signal is different for a TFBG than for an un-tilted reflective FBG in that the reflected light is not accessible, as it is coupled to strongly attenuated cladding modes, unless one uses complicated ways to retrieve it [43]. The reflectivity can only be calculated with a knowledge of the maximum transmitted power outside of the grating spectrum $P_{max}$. In our case, the DFB laser diode can be temperature tuned over more than 20 degrees, corresponding to more than 2 nm, whereas the typical separation between TFBG resonances is about 1 nm. Thus it is possible to tune the laser diode to a wavelength between two resonances where transmission is not affected by the grating, and determine the value of the maximum transmission $P_{max}$. One can then use the following modified algorithm to calculate the signal S:
In this case, the additional requirement for accurate and repeatable measurements is that the transmission loss between the source and the detector not vary significantly during the time of the measurement. Many chemical or biochemical measurements are concerned with the analysis of a given sample performed over a few minutes or less, and in such cases that requirement is not very difficult to meet. Long term stability is also achievable with a suitable, stable mechanical design. For long term monitoring instruments, periodic recalibration can also be performed automatically, which only requires a few seconds. Fluctuations in the power emitted by the laser diode can be measured independently via a coupler branch, or from the photodiode internal to the laser. A correction factor can then be applied to $P_{max}$ in Eq. (6). We performed such a correction in many of our measurements, though we found that over short measurement times, it did not significantly improve the precision and stability.
3. Experimental setup
Our experimental setup is shown in Fig. 2. The light source was a commercial DFB laser diode (Allwave Photonics) with internal isolator and monitor photodiode, emitting a power up to 10 mW at a wavelength of about 1550 nm. The laser was driven by a laser driver and temperature controller (Thorlabs CLD1015), and modulated with a 5 kHz square wave, with an amplitude of about $\pm 9$ mA, and a bias current of 75 mA. For modulation as well as signal digitization, we used a simple, inexpensive Red Pitaya board, that has two input and two output channels, and performs 14 bit analog-to-digital conversion at 125 Msps. The modulation and acquisition parameters were controlled with a Labview interface, that also acted as an oscilloscope to visualize the detected signals, and performed the computation of the DWDD signal. The same setup and interface was used both to characterize the dynamic chirp and to perform the DWDD measurements.
The DFB laser light was split by a 3 dB coupler and sent either to two separate TFBGs (one for signal and one used as reference as described below), or to a signal TFBG in one branch and a power reference in the other. The section of fiber containing the TFBG was connected via an FC/APC connector, and a polarization controller was placed in the short, straight fiber section between the connector and the TFBG (about 40 cm). Each TFBG resonance actually consists of two distinct lines for the two orthogonal polarizations, with a wavelength separation that was measured as 34 pm for the TFBG resonance that we used, when immersed in water. Thus for consistent and stable results, the fibre section from the laser to the sensor was kept as short and straight as possible (about one meter) to avoid a drift in the polarization state. The polarization state was then chosen by adjusting the polarization controller to either maximize or minimize the value of $S$ at a given temperature-tuned laser diode wavelength.
The TFBGs themselves were written in standard, previously hydrogenated, SMF28 fiber, using a standard process as described in [1]. They had a tilt angle of 10 degrees and a 10 mm length, with a nominal Bragg wavelength of about 1608 nm. We used the TFBG resonance at about 1550 nm, close to, but above the cutoff when the TFBG is immersed in water, which we found to be at about 1542 nm. Previously, we had performed measurements of its shift with refractive index, using an optical spectrum analyzer, showing a typical sensitivity of about 10 nm/RIU, and a linear response. Resonances closer to cutoff, for example at 1543 nm, showed an expected higher sensitivity of about 25 nm/RIU and a more nonlinear behaviour.
Two free-space photodetectors (Thorlabs model PDA20CS2) were used to measure the transmitted power in both arms. The angle-cleaved fiber ends were placed directly in front of the detectors. The two TFBGs were simply taped on microscope glass plates with minimal strain, and immersed in a water solution in separate Petri dishes, that were at substantially the same (room) temperature. A digital thermometer was used to monitor temperature in either of the Petri dishes, which confirmed that there was no significant temperature difference in normal conditions.
The signals from the photodetectors were digitized by the Red Pitaya board, using a decimation of 8, meaning that each sample is the average of the 8 samples at the basic rate of 125 Msps. Each acquired trace had 16284 samples, each sample covering 64 ns. Thus each trace was enough to acquire 5 modulation cycles at 5 kHz. The Labview interface could analyze three such acquisitions per second. Furthermore, the values of $S$ were calculated using a moving average over 12 measurements. Thus each value represents an average over 180 modulation cycles.
4. Measurement and analysis of the dynamic chirp
To visualize and measure the dynamic chirp of DFB lasers, Shalom et al. [41] used an all-fiber Mach-Zehnder interferometer as a frequency discriminator. In our case, we used the TFBG itself as the frequency dependent transmissive element. Knowing the grating spectral shape, we could determine the wavelength at any given time from the temporal transmission measurement. This way, we determined the major time constants and chirp coefficients involved in our experiment.
Figure 3 shows the evolution of the shape of the modulated signal when transmitted through the TFBG for different laser diode temperatures, corresponding to different average wavelengths. Such curves are similar to those obtained by Shalom et al. [41]. The laser diode bias was 75 mA, the modulation amplitude was 8.93 mA, and the frequency was 5 kHz. The average wavelength dependence on temperature had been previously measured with an optical spectrum analyzer to be 111 pm/°C. The first trace was taken at 25.5 °C, in between two resonances of the TFBG spectrum, and shows the emitted square wave without any distortion. At 28.2 °C, the leading edge of the upper state, which has the longest wavelength, has entered the short wavelength side of the TFBG spectrum and shows a lower transmission. At 29.2 °C, it has past the center of the spectrum, and its transmission is higher, while the trailing edge now has a lower transmission. At 29.7 °C, the lower modulation state begins to be affected by the grating, in a reverse way: the trailing edge is first affected as it has a longer wavelength and shows a lower transmission. As it moves past the spectrum center (31.1 °C), the trailing edge now has the lower transmission. For still higher temperatures (not shown), the transmitted shape reverts back to that of the incident square wave seen at 25.2 °C.
Knowing the TFBG shape and bandwidth, we simulated this behaviour using a model for the thermal behaviour of the laser diode chip similar to that of Shalom et al. [41]. In our case, we bundled all the fast behavior ($\le 0.5 \mu$s), into one instantaneous, current-dependent chirp, and all slow behaviour ($\ge 200\mu$s) into a linear time-dependent chirp with positive and negative slopes during the upper and lower cycle, respectively. Over the time scale of one modulation cycle, the thermal response was modeled with two time constants $\tau _{1}$ and $\tau _{2}$. The total themal response is:
To model the traces of Fig. 3, the current pulse shape (including its 1$\mu$s rise and fall time) was convoluted with the thermal response of Eq. (7) to give the wavelength as a function of time. The diode laser power was calculated using the threshold and the slope of the power vs current curve that had previously been measured. The transmission was then calculated using the wavelength at any given time from a fit of the spectrum shown in Fig. 4 . The spectrum was modeled as a Gaussian with FWHM of 172 pm, and 60.5% maximum reflection. To better account for the unapodized spectrum, we also added two small sidelobes of 3% reflectivity each, with the same FWHM, at $\pm$210 pm on each side. That fit is shown in Fig. 5. Once one trace was properly fit to the data with one set of parameters, all other traces were fitted with the same parameters, changing only the central wavelength, using the coefficient of thermal shift (111 pm/°C). Only small changes of the constant $\tau _{2}$ of about $\pm$ 0.5 $\mu$s were required to optimize the fits at each temperature.
Fig. 4. Chirp of the laser diode wavelength over one modulation cycle obtained from the trace fits of Fig. 3. Two proposed sets of sampling points for the DWDD measurement are shown at 13 $\mu$s and 75 $\mu$s for the upper state (blue), 113 $\mu$s and 175 $\mu$s for the lower state (red). The corresponding wavelength shifts (in pm) are shown on the right. The bottom graph shows the square-wave modulated power.
From our results, we extracted the following coefficients: $A=$ 1.40 pm/mA for the instantaneous change, $B=$ 9.79 pm/mA with a time constant $\tau _{1} =1.9 \mu$s, $C=$ 1.02 pm/mA with $\tau _{2} =15.9 \pm 0.8 \mu$s. The linear chirp during each state was $\pm$20 pm. The total chirp was 238 pm. The resulting temporal behavior of the wavelength over one modulation period is shown in Fig. 4.
5. DWDD measurements over an extended range
For a DWDD measurement, a wavelength separation of 30% of the grating FWHM provides a good resolution while still resulting in a linear response. For 172 pm FWHM, this would require a wavelength separation of 52 pm. From Fig. 4, it is seen that this can be obtained by selecting samples around 13 $\mu$s and 75 $\mu$s in the upper state. Moreover, by selecting samples at 113 $\mu$s and 175 $\mu$s in the lower state, we find that we can get another DWDD signal, with the average wavelength being 172 pm away from that of the upper cycle. This means that as the DWDD signal from the upper cycle becomes unmeasurable, we can still get a signal from the lower cycle, and extend the measurement range for another FWHM, as illustrated in Fig. 1.
To illustrate this further, Fig. 5 shows the transmission spectrum of the TFBG obtained by measuring the transmitted power at four such times (named start-hi, end-hi, start-lo, and end-lo), as the laser diode temperature was scanned in 0.1°C steps, knowing that the wavelength shifts at a rate of 111 pm/°C. The difference in central wavelengths of the otherwise identical spectra is therefore indicative of the wavelength difference between those time intervals. The scans are normalized to the maximum power measured during the upper state, so the lower state scans reflect the lower power in that modulation state. Instead of using just one sample at a given time, we averaged the transmission over a range of samples to further reduce the noise. For the start-hi points, we averaged a range of samples centered at 7.1 $\mu$s after the start of the pulse, and spanning 3.8 $\mu$s, for a total of 60 samples. The end-hi samples were centered at 69.2 $\mu$s, and spanned 12.8 $\mu$s, for a total of 500 samples. The samples in the lower state were taken at similar times with respect to the start of the state. The values of $S$ were simultaneously calculated using those measured values, and are shown in Fig. 6. The wavelength axis is centered on the spectrum for the time sample at the beginning of the upper state (start-hi). Also shown superimposed with the start-hi spectrum is the Gaussian fit used for fitting the traces of Fig. 3. The same fit was used to find the centers of the three other spectra. Those were found at 68 pm (end-hi), −87 pm (start-lo), and −149 pm (end-lo). Thus there is a 68 pm separation for the two upper state sample ranges, and 62 pm for those in the lower state ranges. The arrows indicate the direction of the chirp in each state. The different wavelength separation in each cycle hints at a thermal behaviour that is more complex than the model we used. The separation between the average wavelength in each state is 152 pm. Figure 6 shows the values of $S$ over the ranges where they have significance (the error is too large outside of those ranges). Since we are aiming at resolutions of 14 bits or more, we applied a multiplier of 10,000 to $S$, which is otherwise $<1$, so that the resulting integer value has all the significant digits. The values of $S$ show relatively good linearity with $r^{2}=0.997$ for each state, limited mostly by the non-gaussian shape of the spectrum. The deviation from a perfect Gaussian shape is readily seen in Fig. 5, with a slightly flattened bottom, which leads to a slightly smaller slope in the center of the spectrum. This is due to the relatively high reflection of that particular resonance (60%). A resonance with a maximum reflectivity of 30% or lower would be closer to a true Gaussian shape, and give a better linearity. It is also possible to use a third-degree polynomial to improve the fit.
Fig. 6. Values of $S$ as a function of the laser diode wavelength, as measured in the upper (High state) and lower (Low state) modulation states.
As expected, we obtained two significant sets of $S$, overlapping over about 33 pm (or 0.3°C), as shown by the two vertical dotted lines. The slope was slightly different for both sets, which is a consequence of the different wavelength separation that we found in the upper and lower states. Other than the different slope and despite their imperfect linear behaviour, the two sets of $S$ are remarkably similar, reflecting the fact that both are a function of the same grating shape, and have a very low noise. It would be possible to adjust the sampling times independently for each state to obtain an identical slope, but here we just chose the same sampling intervals with respect to the start of each modulation state. This way we could measure $S$ over a total of 327 pm, which is close to twice the FWHM. Each set of $S$ (upper and lower cycle) covers a range of about 10,000 units. Given that the short term (<10 s) rms value of fluctuations of $S$ was about 5 units, which would be the effective resolution, the actual range-to-resolution ratio $R$ for each cycle is $>$ 2000. Considering the overlap of the two sets, the total ratio $R > 3700$, which is close to 12-bit resolution. The actual spectral resolution is thus found to be about 0.08 pm, far lower than typical optical spectrum analyzers, and representative of the short term stability of the laser diode wavelength.
While the signal $S$ was stable to better than 5 units over a short time span, the most important source of fluctuation and drift was found to come from the laser diode itself, as discussed above. Hence using a reference TFBG is necessary to reduce the effect of those fluctuations, since they affect both signal and reference TFBGs in the same way.
To demonstrate the efficacy of a reference scheme, Fig. 7 shows the parallel measurement of $S$ for a signal ($S_{sig}$) and reference ($S_{ref}$) TFBG over a period of 8 minutes, along with a compensated signal $S_{comp}$. The latter was obtained by first measuring the slope of the two TFBG signals with temperature, obtained from taking the values of $S$ at two laser temperatures separated by $\pm 0.05\circ$C. Since the two TFBGs were not perfectly identical, they had a different slope for $S$ as a function of temperature. Then the compensated value $S _{comp}$ was obtained by calculating:
where $a_{ref}$ and $a_{sig} $ are the respective slopes for the reference and signal TFBGs respectively. Short term fluctuations were found to be reduced this way: the RMS fluctuations of the signal over the first minutes had a value of 5 units for both TFBGs, and 4 units for the compensated signal, for a reduction of about 20%. But the most dramatic effect of the compensation can be seen as the diode temperature was shifted by 0.03°C at the 163 seconds time, which is about 3.3 pm. Both $S_{sig}$ and $S_{ref}$ made a more than 200 unit jump, while no observable change in $S_{comp}$ can be seen. Even the slow drift following the temperature jump, which is due to the relatively long settling time of the laser diode temperature, is mostly eliminated. The remaining fluctuations were found to be mostly due to a small mechanical instability in the free-space coupling of light onto the photodetectors while those measurements were made, affecting the value of $P_{max}$.Fig. 7. Signal, reference, and compensated values of $S$. A temperature step of 0.03 °C was performed at about 163 s
In order to assess the performance of the system for refractometry, we performed measurements of $S$ when adding NaCl to the water. The dependence of the refractive index of the NaCl solution as a function of concentration was obtained from the literature [44].
Figure 8(a) shows the real-time measurement of $S$ relative to the value $S0$ at time $0$, while the NaCl concentration was changed in $\approx 1.5\%$ steps. For this, a high concentration solution was deposited with a 20 ml pipette around the Petri dish surface. No magnetic stirrer could be used because of space constraints, so the solution was stirred by hand with a small metal spoon. There is actually only a very small change when the solution is deposited, but as soon as it is stirred, the signal jumps, and then gradually comes down and settles to a higher $S$, reflecting the actual dynamic mixing of the solution with the water, as is indicated in the figure. The final value of $S$ was taken after the measurement had become stable to better than 5 units, as indicated by the short vertical arrows. The result is shown in Fig. 8(b). A regression coefficient $r^{2}=0.998$ is obtained, which is actually the same as that of the $S$ curve in Fig. 6, indicating that the imperfect linearity of the $S$ curve is the main factor limiting the accuracy of our measurement. Using 5 units of $S$ as the resolution, we obtain a refractive index resolution of $9.9\times 10^{-6}$ RIU, and a total measurement range of $3.7\times 10^{-2}$, for a range-to-resolution ratio of 3700, or nearly 12-bit, as in the measurements above. Using a wavelength closer to the 1542 nm cutoff would increase the sensitivity by a factor close to 3, as we measured a sensitivity of about 27 nm/RIU at that wavelength. This would result in a correspondingly smaller range, but keep the same nearly 12-bit resolution. Therefore, we estimate that slight improvements should bring the refractive index resolution to $\le 4\times 10^{-6}$, making our simple and inexpensive instrument on par with much more expensive SPR instruments, without requiring any coating or special treatment to the fiber to enhance its sensitivity.
Fig. 8. (a) Change in $S$ while NaCl was added by steps. The period required for mixing the new solution is indicated, while the measurement time is approximately shown by the short vertical arrows; (b) $S-S _{0}$ vs Refractive index change
6. Discussion and conclusion
Despite our good preliminary results, our instrument has not yet reached its optimal performance, and many improvements remain to be implemented. For example, the communication between the Red Pitaya and the Labview interface is rather slow, and thus only about 15 modulation cycles are analyzed every second. Since the modulation rate is 5 kHz, 5000 cycles could in principle be measured and averaged every second, thus further reducing the overall noise. This could be done by directly programming the FPGA on the Red Pitaya to compute and average the signal $S$ in real time. Short term power fluctuations from the laser diode could be monitored by the internal photodiode, which was not done here because the Red Pitaya board only has two input ports. Such fluctuations can then be used as a correction factor in the calculation of $S$.
For our demonstration, we used a 5 kHz modulation frequency, somewhat limited by the 1 $\mu$s rise time of the laser driver that we used. However, as seen from our thermal response measurements, most of the chirp occurs with a time constant of 1.9 $\mu$s. More than 138 pm of chirp occured within the first 5 $\mu$s, and more can be obtained simply with a larger modulation amplitude. Thus our instrument could work just as well with modulation frequencies of 50 kHz, which would allow even more averaging. It would also probably be more immune to thermal changes in the macro environment around the laser diode that govern the slower thermal response. For example, we have demonstrated elsewhere [36] the use of 5 ns pulses for DWDD measurement of reflective FBGs, and measured dynamic chirp of as much as 110 pm over 40 mA. Such fast interrogation allowed us to average over more than 100,000 pulses every second. By compensating for both power and wavelength fluctuations (with a reference grating), we expect the signal fluctuations to be reduced down to about 1 unit of $S$, and a sensitivity over 13 bits to be attained.
One further aspect to consider for long-term accuracy is the aging of the laser diode. Any shift in wavelength can be compensated by the reference grating. A well-annealed grating can have a very good long term stability, and periodic calibration of the instrument can be made using a so-called golden standard. On the other hand, the amount of dynamic chirp can also change over time, which changes the slope in Eq. (3). Thus two reference signals are required to monitor both the position and slope of the $S$ curve. In our case, this can be readily achieved if the reference grating is positioned to give two $S$ signals, as in the overlap region shown in Fig. 6. Their relative movement, either in the same or in opposite direction, provides the required information. In our short-term experiments, however, we found that this was not required.
In conclusion, we have demonstrated a high-resolution, extended-range instrument to measure TFBG sensors using the dual-wavelength differential detection method with a single, square-wave modulated DFB laser diode, taking advantage of its large dynamic chirp. By selecting both the modulation amplitude and the sampling intervals, the sensitivity and range can be adjusted, with the potential to reach 14-bit resolution. The resolution and precision are ultimately limited by the stability of a reference grating sensor with respect to the signal sensor. Refractive index measurements of an NaCl solution with varied concentration showed a resolution of $9.9\times 10^{-6}$, and a range of $3.7\times 10^{-2}$, for a range-to-resolution ratio $R=3700$ or 11.9 bits. The instrument has the potential to reach a refractive index resolution of $\le 4\times 10^{-6}$, which would make it on par with high performance commercial SPR instruments, while bringing the convenience of compact fiber-based sensors that don’t require the bulkiness, alignment precision and stability of free space SPR angle measurements.
In a more general way, our results and analysis demonstrate that the DWDD technique has the potential to replace current, spectral measurement based instruments for measuring FBG-type sensors. The simple instrument that we described has the potential to reach an effective resolution of 0.01-0.05 pm, which is 10-100 times better than current commercial instruments, while still having up to 14-bit resolution, and finally a much lower cost. This is possible because the DWDD technique reverses the traditional approach to spectral measurement, so that the effective resolution depends solely on the signal-to-noise ratio at detection, and the stability of the wavelength reference. Both these quantities can be made very high at low cost using simple, well established techniques (such as TEC temperature control) and widely available, high-performance and low cost electronic and opto-electronic components (such as high resolution ADCs and standard DFB laser diodes and drivers).
Funding
Sichuan Province Science and Technology Support Program (2019YFH0091), National Natural Science Foundation of China (61307102, 61327004).
Disclosures
The authors declare no conflicts of interest.
References
1. J. J. Albert, L.-Y. Shao, and C. Caucheteur, “Tilted fiber bragg grating sensors,” Laser Photonics Rev. 7(1), 83–108 (2013). [CrossRef]
2. C. A. J. Gouveia, J. M. Baptista, and P. A. Jorge, Current Developments in Optical Fiber Technology (InTech, 2013), chap. Refractometric Optical Fiber Platforms for Label Free Sensing, pp. 345–373.
3. X.-D. Wang and O. S. Wolfbeis, “Fiber-optic chemical sensors and biosensors (2013–2015),” Anal. Chem. 88(1), 203–227 (2016). [CrossRef]
4. T. Guo, F. Liu, B.-O. Guan, and J. Albert, “Tilted fiber grating mechanical and biochemical sensors,” Opt. Laser Technol. 78, 19–33 (2016). [CrossRef]
5. H. E.-H. Klantsataya, P. Jia, T. Monro, and A. François, “Plasmonic fiber optic refractometric sensors: From conventional architectures to recent design trends,” Sensors 17(12), 12 (2016). [CrossRef]
6. F. Chiavaioli, S. T. Francesco Baldini, C. Trono, and A. Giannetti, “Biosensing with optical fiber gratings,” Nanophotonics 6(4), 663–679 (2017). [CrossRef]
7. J. H. Luong, K. B. Male, and J. D. Glennon, “Biosensor technology: Technology push versus market pull,” Biotechnol. Adv. 26(5), 492–500 (2008). [CrossRef]
8. A. H. P. Ho, S. Y. Wu, S. K. Kong, S. Zeng, and K. T. Yong, Handbook of Photonics for Biomedical Engineering (Springer, Dordrecht, 2017), chap. SPR Biosensors.
9. M. Piliarik and J. Homola, “Surface plasmon resonance (spr) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009). [CrossRef]
10. Y. Y. Shevchenko and J. Albert, “Plasmon resonances in gold-coated tilted fiber bragg gratings,” Opt. Lett. 32(3), 211–213 (2007). [CrossRef]
11. J. Albert, S. Lepinay, C. Caucheteur, and M. C. DeRosa, “High resolution grating-assisted surface plasmon resonance fiber optic aptasensor,” Methods 63(3), 239–254 (2013). [CrossRef]
12. C. Caucheteur, Y. Shevchenko, L.-Y. Shao, M. Wuilpart, and J. Albert, “High resolution interrogation of tilted fiber grating spr sensors from polarization properties measurement,” Opt. Express 19(2), 1656–1664 (2011). [CrossRef]
13. C. Caucheteur, T. Guo, and J. Albert, “Review of plasmonic fiber optic biochemical sensors: improving the limit of detection,” Anal. Bioanal. Chem. 407(14), 3883–3897 (2015). [CrossRef]
14. C. Caucheteur, V. Voisin, and J. Albert, “Near-infrared grating-assisted spr optical fiber sensors: design rules for ultimate refractometric sensitivity,” Opt. Express 23(3), 2918–2932 (2015). [CrossRef]
15. C.-F. Chan, C. Chen, A. Jafari, A. Laronche, D. J. Thomson, and J. Albert, “Optical fiber refractometer using narrowband cladding-mode resonance shifts,” Appl. Opt. 46(7), 1142–1149 (2007). [CrossRef]
16. S. Maguis, G. Laffont, P. Ferdinand, B. Carbonnier, K. Kham, T. Mekhalif, and M.-C. Millot, “Biofunctionalized tilted fiber bragg gratings for label-free immunosensing,” Opt. Express 16(23), 19049–19062 (2008). [CrossRef]
17. W. Zhou, D. J. Mandia, S. T. Barry, and J. Albert, “Absolute near-infrared refractometry with a calibrated tilted fiber bragg grating,” Opt. Lett. 40(8), 1713–1716 (2015). [CrossRef]
18. B. Jiang, K. Zhou, C. Wang, Y. Zhao, J. Zhao, and L. Zhang, “Temperature-calibrated high-precision refractometer using a tilted fiber bragg grating,” Opt. Express 25(21), 25910–25918 (2017). [CrossRef]
19. S.-Y. Tan, Y.-T. Yong, S.-C. Lee, and F. A. Rahman, “Review on an arc-induced long-period fiber grating and its sensor applications,” J. Electromagn. Waves Appl. 29(6), 703–726 (2015). [CrossRef]
20. A. Chryssis, S. Lee, S. Lee, S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber bragg grating sensor,” IEEE Photonics Technol. Lett. 17(6), 1253–1255 (2005). [CrossRef]
21. M. I. Zibaii, H. Latifi, M. G. M Karami, S. M. Hosseini, and M. H. Ghezelayagh, “Non-adiabatic tapered optical fiber sensor for measuring the interaction between alpha-amino acids in aqueous carbohydrate solution,” Meas. Sci. Technol. 21(10), 105801 (2010). [CrossRef]
22. Z. Cai, F. Liu, T. Guo, B.-O. Guan, G.-D. Peng, and J. Albert, “Evanescently coupled optical fiber refractometer based a tilted fiber bragg grating and a d-shaped fiber,” Opt. Express 23(16), 20971–20976 (2015). [CrossRef]
23. D. Liu, A. K. Mallik, J. Yuan, C. Yu, G. Farrell, Y. Semenova, and Q. Wu, “High sensitivity refractive index sensor based on a tapered small core single-mode fiber structure,” Opt. Lett. 40(17), 4166–4169 (2015). [CrossRef]
24. M. Śmietana, M. Koba, P. Mikulic, and W. J. Bock, “Towards refractive index sensitivity of long-period gratings at level of tens of micrometers per refractive index unit: fiber cladding etching and nano-coating deposition,” Opt. Express 24(11), 11897–11904 (2016). [CrossRef]
25. Z. Wang, J. R. Heflin, R. H. Stolen, and S. Ramachandran, “Analysis of optical response of long period fiber gratings to nm-thick thin-film coatings,” Opt. Express 13(8), 2808–2813 (2005). [CrossRef]
26. I. D. Villar, I. R. Matías, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Express 13(1), 56–69 (2005). [CrossRef]
27. J.-M. Renoirt, C. Zhang, M. Debliquy, M.-G. Olivier, P. Mégret, and C. Caucheteur, “High-refractive-index transparent coatings enhance the optical fiber cladding modes refractometric sensitivity,” Opt. Express 21(23), 29073–29082 (2013). [CrossRef]
28. M. Hernaez, C. Zamarreño, J. Goicoechea, I. Matias, and F. Arregui, “Nanostructured materials in optical fiber sensing,” Open Opt. J. 7(1), 84–94 (2013). [CrossRef]
29. D. Feng, W. Zhou, X. Qiao, and J. Albert, “High resolution fiber optic surface plasmon resonance sensors with single-sided gold coatings,” Opt. Express 24(15), 16456–16464 (2016). [CrossRef]
30. Z. Li, Z. Yu, Y. Shen, X. Ruan, and Y. Dai, “Graphene enhanced leaky mode resonance in tilted fiber bragg grating: A new opportunity for highly sensitive fiber optic sensor,” IEEE Access 7, 26641–26651 (2019). [CrossRef]
31. S. D. Dyer, P. A. Williams, R. J. Espejo, J. D. Kofler, and S. M. Etzel, “Fundamental limits in fiber bragg grating peak wavelength measurements,” in 17th International Conference on Optical Fibre Sensors, vol. 5855 of Proceedings of SPIEM. Voet, R. Willsch, W. Ecke, J. Jones, and B. Culshaw, eds. (SPIE, 2005), pp. 88–93.
32. D. Tosi, “Review and analysis of peak tracking techniques for fiber bragg grating sensors,” Sensors 17(10), 2368 (2017). [CrossRef]
33. M. Shaimerdenova, A. Bekmurzayeva, M. Sypabekova, and D. Tosi, “Interrogation of coarsely sampled tilted fiber bragg grating (tfbg) sensors with klt,” Opt. Express 25(26), 33487–33496 (2017). [CrossRef]
34. S. Cieszczyk, P. Kisała, and J. Mroczka, “New parameters extracted from tilted fiber bragg grating spectra for the determination of the refractive index and cut-off wavelength,” Sensors 19(9), 1964 (2019). [CrossRef]
35. F. Ouellette, “Apparatus for measuring optical signals from multiple optical fiber sensors,” US Patent 9810556 (2017).
36. F. Ouellette and J. Li, “Dual-wavelength differential detection of fiber bragg grating sensors with a single dfb laser diode,” in Asia Communications and Photonics Conference (ACPC) 2019, (Optical Society of America, 2019), p. M4A.180.
37. R. Cheng and L. Xia, “Interrogation of weak bragg grating sensors based on dual-wavelength differential detection,” Opt. Lett. 41(22), 5254–5257 (2016). [CrossRef]
38. Z. Li, Y. Tong, X. Fu, J. Wang, Q. Guo, H. Yu, and X. Bao, “Simultaneous distributed static and dynamic sensing based on ultra-short fiber bragg gratings,” Opt. Express 26(13), 17437–17446 (2018). [CrossRef]
39. J. Rohollahnejad, L. Xia, R. Cheng, Y. Ran, U. Rahubadde, J. Zhou, and L. Zhu, “Tdm interrogation of intensity-modulated usfbgs network based on multichannel lasers,” Opt. Express 25(2), 670–680 (2017). [CrossRef]
40. A. Wilson, S. W. James, and R. P. Tatam, “Time-division-multiplexed interrogation of fibre bragg grating sensors using laser diodes,” Meas. Sci. Technol. 12(2), 181–187 (2001). [CrossRef]
41. H. Shalom, A. Zadok, M. Tur, P. Legg, W. Cornwell, and I. Andonovic, “On the various time constants of wavelength changes of a dfb laser under direct modulation,” IEEE J. Quantum Electron. 34(10), 1816–1822 (1998). [CrossRef]
42. G. W. Yoffe, P. A. Krug, F. Ouellette, and D. A. Thorncraft, “Passive temperature-compensating package for optical fiber gratings,” Appl. Opt. 34(30), 6859–6861 (1995). [CrossRef]
43. T. Guo, H.-Y. Tam, P. A. Krug, and J. Albert, “Reflective tilted fiber bragg grating refractometer based on strong cladding to core recoupling,” Opt. Express 17(7), 5736–5742 (2009). [CrossRef]
44. J. E. Saunders, C. Sanders, H. Chen, and H.-P. Loock, “Refractive indices of common solvents and solutions at 1550 nm,” Appl. Opt. 55(4), 947–953 (2016). [CrossRef]
