2.1. Background
Figure 1 shows generic implementations for an incoherent finite impulse response MWP filter using taps created from (a) a single wavelength optical source or (b) a multiple wavelength optical source (we assume operation in a regime where coherent interference effects can be ignored). In the former, the output from the optical source is modulated using an electro-optic modulator (EOM), then split to create multiple taps. The amplitude and delays of each tap are adjusted before being recombined and detected. Successive taps are delayed by multiples of the delay unit
. Assuming amplitude modulation, the magnitude of the MWP filter frequency response
is proportional to [
14]
where
is the number of taps and
denotes the amplitude of the
tap. For the case of a multiple wavelength optical source, each wavelength defines a tap. The taps are modulated and then propagated through a dispersive medium characterized by a dispersion
[ps/nm]. For taps that are separated equally in wavelength by an amount
, the corresponding delay is
. The MWP filter response
can also be calculated using Equation (1).
The MWP filter response described by Equation (1) is a periodic function of
with a free spectral range (FSR) given by
If the spectral distribution of the taps from a multiple wavelength optical source follows a continuous and sinusoidal function of wavelength, then the MWP filter response features a single passband and is not periodic [
15]. This passband is located at a central frequency
.
The multiple wavelength optical source can be obtained using FBGs to spectrally slice a broadband source (BBS). The FBGs themselves can be sensors that are subjected to varying environmental conditions, such as strain, temperature, etc. If we assume a fixed dispersion
, then tuning the wavelength separation
of the taps by applying strain or temperature to the FBG sensors will cause
to shift.
Figure 2 illustrates the principle of detecting changes in the MWP filter response
by monitoring the change in RF power at a specific RF frequency. These changes can then be correlated to changes applied to the FBG sensor (e.g., strain or temperature). If
shifts to higher frequencies, then choosing a frequency along the rising (
) or falling edge (
) of
will result in a decrease or increase in detected RF power, respectively. The relationship between the change in RF power as a function of strain or temperature depends on several factors, including (1) the shape of the MWP filter response, (2) the RF frequency used for monitoring, and (3) the amount that
will shift. The relationship can be linear, but it does not need to be so.
2.2. Single Bandpass MWP Filter
First, we consider interrogating a temperature sensor based on an in-fiber FP cavity formed with two near-identical low-reflectivity FBGs, as shown in
Figure 3a. The reflection spectrum of the FBG structure is a sinusoidal-like pattern characterized by an FSR of
where
is the effective refractive index,
is the center-to-center length between the FBGs, and
is the center wavelength of the reflection response of each FBG.
Figure 3b illustrates the reflection spectrum of such an in-fiber FP cavity where the peak reflectivity of each FBG is ~17% and
= 10 mm.
When the in-fiber FP cavity is exposed to a change in temperature, both the length and the refractive index of the fiber separating the FBGs, as well as the FBGs themselves, will vary due to thermal expansion and thermo-optic effects. Thus, the FSR of the reflection response
will change, resulting in a shift in the MWP filter response
, i.e., in the value of
. For multiple sensor operations, we can wavelength multiplex multiple in-fiber FP cavity temperature sensors, each having its own FSR, and track temperature changes on the individual sensors by monitoring changes in their corresponding MWP filter passbands. Note that the use of an in-fiber FP cavity as the sensing element is more compact compared to the use of a Mach-Zehnder interferometer as demonstrated in [
10].
Figure 4a illustrates the experimental setup used to demonstrate the ability to interrogate multiple temperature sensors using the MWP filter system (two sensors were considered in our proof-of-principle demonstration) [
12]. The output from a BBS is spectrally sliced using two in-fiber-FP cavity sensors, one with
= 10 mm (Sensor 1) and the other with
= 20 mm (Sensor 2)
, that are placed at different locations and exposed to different temperature conditions. The spectrally sliced spectra are shown in
Figure 4b. Sensor 1 operates at longer wavelengths and occupies a broader optical spectrum, while Sensor 2 operates at shorter wavelengths. The corresponding FSRs for Sensor 1 and Sensor 2 are
≈ 80 pm and
≈ 40 pm, respectively.
We use an EOM for amplitude modulation and dispersion compensating fiber (DCF) with a dispersion of
= 1719 ps/nm (at 1550 nm) as the dispersive medium. The calculated frequencies of the MWP filter passbands are
7.27 GHz and
= 14.54 GHz for Sensors 1 and 2, respectively.
Figure 5 shows the measured MWP filter responses. The measured passband peaks are 7.38 GHz for Sensor 1 and 15.12 GHz for Sensor 2, in good agreement with the calculate values.
First, we characterize the response of each sensor separately.
Figure 6a shows the change in normalized RF power at frequencies
of 7.48 GHz and 7.24 GHz, which are at the falling and rising edges of the MWP filter response, respectively, as the temperature of Sensor 1 is increased from room temperature (22 °C) to 100 °C. For these two frequencies, the RF power varies linearly with temperature, and the sensitivities are 2·10
−4/°C at 7.48 GHz and −4·10
−4/°C at 7.24 GHz. Note that, for the frequency on the falling (rising) edge of
, the slope of the change in RF power with increasing temperature is positive (negative), thereby indicating that MWP filter response shifts to higher frequencies. For Sensor 2, the sensitivities at frequencies of 15.38 GHz and 15.1 GHz are 9·10
−4/°C and −3·10
−4/°C, respectively. The different sensitivities associated with the two sensors are due to the differences in their corresponding MWP filter responses. In particular, the multiple wavelength optical tap spectra associated with each sensor is different due to differences in the in-fiber FP cavities, and it is known that the shape of the multiple wavelength source will impact the shape of the MWP filter response [
15]. Additionally, we monitored the RF power at frequencies located at different points along the MWP filter responses.
When there is no overlap between the MWP filter responses corresponding to each sensor, a ratiometric measurement can be used. We can consider dividing the changes in RF power observed at a frequency located along the rising edge of the MWP filter response by those for a frequency located along the falling edge. Using this ratiometric approach for the frequencies considered previously, the sensitivities for Sensor 1 and Sensor 2 are increased to 7·10
−4/°C and 11·10
−4/°C, respectively, as highlighted in
Figure 6b.
We now consider operating the two temperature sensors simultaneously. Experiments show that, as we apply temperature changes to one sensor, the MWP filter response corresponding to the other sensor does not shift. For example, as depicted in
Figure 7, when the temperature applied to Sensor 2 is varied from 40 °C to 80 °C and Sensor 1 is maintained at a constant (room) temperature, the MWP filter response corresponding to the latter does not shift (in particular, the RF power at frequencies 7.48 GHz and 7.24 GHz does not vary).
Figure 8 depicts the shift in the two MWP filter responses when different temperature changes are applied simultaneously to the two sensors. For Sensor 1, when the temperature is increased from 25 °C to 80 °C, the normalized RF power changes from 0.84 °C to 0.8 °C at a frequency of 7.24 GHz. For Sensor 2, when the temperature is increased from 25 °C to 60 °C, the normalized RF power changes from 0.66 °C to 0.67 °C at a frequency of 15.38 GHz. These changes generally agree with the sensitivities shown in
Figure 6. However, they are not the same due to crosstalk in the MWP filter responses. In particular, as observed in
Figure 5, the MWP filter response from Sensor 1 extends slightly into the frequency range of that for Sensor 2, while the reverse is not true. As such, for simultaneous multiple sensor operation, there is a small impact in the sensitivity for Sensor 2 and negligible impact in the sensitivity for Sensor 1.
2.3. Two Tap MWP Filter Based on a Sagnac Loop Incorporating a Linearly Chirped FBG
A Sagnac interferometer incorporating a linearly chirped FBG (LCFBG) can be used to implement a tunable single wavelength, two tap MWP filter, see
Figure 9. Consider a single wavelength which is input to the Sagnac interferometer. There will be two reflected signals, one due to clockwise propagation and one due to counterclockwise propagation, in the interferometer before reflection from the LCFBG. The delay between the two reflected signals, which form the two taps of the MWP filter, depends on the input wavelength and the dispersion of the LCFBG. By tuning the input wavelength, the tap delay
can be varied, causing a change in the FSR of the MWP filter response. In Reference [
5], Fu et al. demonstrated interrogation of a single FBG sensor using this MWP filter.
We can extend this approach for simultaneous interrogation of multiple FBG temperature sensors using superimposed LCFBGs in the Sagnac interferometer. The experimental setup is shown in
Figure 9. The output from a BBS is spectrally sliced by two FBGs (again, we consider two sensors for a proof-of-principle demonstration) that define the two input wavelengths for the two MWP filters. The FBG temperature sensors have the following characteristics: The center wavelength and 3 dB bandwidth for Sensor 1 (FBG
1) are 1543.7 nm and 0.3 nm, respectively, while the corresponding values for Sensor 2 (FBG
2) are 1549.5 nm and 0.12 nm. The wavelengths are then amplitude modulated using an EOM before input into the Sagnac interferometer. The two superimposed LCFBGs have similar reflectivity of ~80%; center wavelengths of 1545.4 nm and 1551.1 nm, corresponding 3 dB bandwidths of 4.4 nm and 4.9 nm, and dispersions of 53.3 ps/nm and 47.8 ps/nm. We use an optical bandpass filter to isolate the response from one FBG sensor prior to photodetection.
First, we vary the temperature of Sensor 1 from 30 °C to 70 °C, while keeping Sensor 2 at a constant (room) temperature.
Figure 10a,c shows the MWP filter responses for Sensor 1 and Sensor 2, respectively, while
Figure 10b,d shows the normalized RF power at two different frequencies along the rising and falling edges of the filter responses. For Sensor 1, at frequencies of 3.8 GHz (rising edge) and 6.2 GHz (falling edge), we observe a linear relation between RF power and temperature with corresponding sensitivities of −11·10
−3/°C and 12.4·10
−3/°C. For Sensor 2, the RF power at frequencies of 3.8 GHz and 6.5 GHz exhibits negligible change. Next, we do the reverse and vary the temperature of Sensor 2 from 30 °C to 70 °C, while keeping Sensor 1 at a constant (room) temperature. The corresponding results are summarized in
Figure 11. The sensitivities at frequencies of 4.6 GHz (rising edge) and 6.9 GHz (falling edge) are −12.8·10
−3/°C and 19.3·10
−3/°C, respectively. The difference in sensitivities between the two sensors arises in part to the difference in the grating dispersions, which causes the amount of shift in the tap delay and hence the variation in FSR of
as a function of temperature of the MWP responses to be different. The results clearly demonstrate that the sensors can be interrogated independently with negligible crosstalk, so that varying the temperature on one sensor does not impact the MWP filter response of the other.