1. Introduction

Chirped pulses, known as frequency-swept pulses have been widely used in radar technologies [1], spread-spectrum communication system [2], chirped pulse microwave computed tomography [3] and also other applications covering military and civilian systems such as communications, surveillance, countermeasures, navigation and imaging equipment [4]. Most radar applications make use of long chirped pulses with wide bandwidth, or pulses with a high time-bandwidth product (TBWP), allowing the detection of targets at long distances with improved range resolution. High TBWP chirped pulses could be generated by many photonic approaches, including space-to-time mapping (STM) [5], frequency-to-time mapping (FTM) [6] and Self-Heterodyne Technique [4,7,8]. FTM methods attract more attention thanks to its simplicity and low cost. Such technique is enabled by sending a short optical pulse with large frequency bandwidth from mode-locked laser with fixed repetition rate through a dispersive element (e.g. chirped fiber Bragg grating), so that the accumulated quadratic spectral phase impresses a large linear chirp on the resulting time-domain waveform.

For distributed optical fiber sensing, optical chirped pulses have increasingly gained the attention of researchers, as they can be used as interrogation signal for quantitatively detecting the environmental disturbance along the sensing fiber, without requiring the frequency sweep process. As a novel technique for distributed sensing, it has been widely used for temperature [9], dynamic strain [10] and seismic [11] sensing, based on chirped pulse $\phi$-OTDR (CP-$\phi$-OTDR) or chirped pulse BOTDA (CP-BOTDA) [12]. Although long duration chirped microwave pulses are required for radar applications, short duration chirped optical pulses are key for fiber-sensing applications. In most chirped pulse based systems, the spatial resolution is limited by the pulse width. An exception is the combination of chirped pulse with non-matched filter [13], but it requires an ultra-high coherent laser source, such that conventional techniques with narrow optical pulses are still of great interest. Therefore, optical chirped pulses with large bandwidth and small pulse width, i.e. with large FCR, are required to achieve large static measurement range with high spatial resolution. Due to limitations of electrical devices, the optical chirped pulses generated by arbitrary waveform generator (AWG) combined with frequency shifter (FS) usually have small chirping range and wide pulse width, resulting in limited chirping rates up to several tens of MHz per nanosecond. An alternative method to generate optical chirped pulses is by direct modulation of the DFB laser current, since the emitted optical frequency of a DFB laser varies with the injected current [9,14]. However, the limited modulation speed and linear variation range increase the complexity to arbitrarily enhance the chirping rate [8]. FTM method, which is usually used for chirped microwave generation, is a good candidate for optical chirped generation by using one dispersive device to stretch the ultra-short pulses. However, the ultra-short pulses usually have a fixed repetition rate and because dispersive devices are passive elements, the FTM method is not suitable for the generation of optical chirped pulses with tunable parameters, such as repetition rate, chirping rate, and center frequency.

In this paper, we propose a novel scheme to generate optical chirped pulses with tunable frequency chirping rate (up to 0.8 GHz/ns), central frequency and repetition rate based on Kerr effect in nonlinear optical fiber. In our approach, high order Kerr pulses were generated from single laser chirp, showing a lower frequency drifting noise and higher frequency chirping range. As a demonstration for the application of our proposed approach, dynamic strain measurement with enhanced static measurement range is achieved in CP-$\phi$-OTDR system. Experimental results show low strain measurement uncertainty and larger static measurement range by using the generated high order Kerr pulse with large chirping rate. Beyond that, the proposed method is also a promising alternative for other applications, such as radar [1], ultra-wideband sensing [15], bio-medical imaging [3], and non-contact healthcare monitoring [16].

2. Theory

When optical waves propagate in dielectric media with molecular inversion symmetry such as optical fibers, changes in the effective refractive index are induced and governed by the third-order susceptibility, $\chi ^{(3)}$. The higher is the intensity of the optical waves, the greater are the changes in the refractive index, a phenomenon known as Kerr effect. Media with high $\chi ^{(3)}$, or high nonlinear parameter, exhibit higher index changes even for low powers, and will be henceforth referred to as Kerr media. As a result of optical Kerr effect, two laser lights with different frequencies undergo self-phase modulation (SPM) and cross-phase modulation (XPM) along a Kerr medium [17]. Assuming that the angular frequencies of two light waves entering a Kerr medium are $\omega _p$ and $\omega _c$, with optical electric fields $E_p$ and $E_c$, respectively, and $\omega _p<\omega _c$, then the total input electric field is $E_{in}=E_p + E_c$, introducing a slowly varying envelope modulation in the intensity profile with modulation frequency $\omega _d = \omega _c - \omega _p$. Therefore the amplitude of the slowly varying electrical field and its optical power at the input end of the Kerr medium are given by:

Equation (5) shows that the $m^{\text {th}}$ order sideband generated by the Kerr effect is $m$ times $\omega _d$ apart from $\omega _p$. Also, since sidebands are generated at both sides of $\omega _p$ but $J$ only assume non-negative orders, we will hereafter refer to lower frequency sidebands as negative orders, but the positive value should be used for the Bessel function calculation, i.e. $J_{|m|}$. By modulating one of the laser lights with chirped pulses, say $\omega _c$, after propagation through the Kerr medium the chirping range of the $m^{\text {th}}$ sideband would also be enhanced $m$ times after propagation through the Kerr medium as predicted by Eq. (5). Fig. 1(a) shows a schematic spectral diagram of the fixed-frequency and chirped pulse configuration, where chirped pulses with spectral content $\Delta \nu$ and pulse width $(T_1 - T_0)$ are injected into a highly nonlinear fiber (Kerr medium). Considering the output spectrum at the end of the fiber, the starting frequency component of chirped pulses signal at time $T_{0}$ (solid line) will interact with pump signal yielding numerous sidebands that will be $\omega _m = m\omega _d=m(\omega _c -\omega _p)$ away from $\omega _p$, while the ending frequency component at time $T_{1}$ (dashed line) of chirped pulses will generate sidebands that will be $\omega _m = m(\omega _d+\Delta v)=m(\omega _c+\Delta v -\omega _p)$ away from $\omega _p$. Note that $m=0$ corresponds to the output sideband located at the frequency of the input pump, $\omega _p$, while $m=1$ corresponds to the output sideband located at the same frequency as the input chirped pulses. In addition, the input pulse intensity profile is square-shaped, higher order sidebands does not alter the intensity profile or duration of the output pulse. Therefore, for the $m^{\text {th}}$ order sideband Kerr pluses, the frequency chirping range is improved from $\Delta v$ to $m\Delta v$, but with same pulse duration $W$ that equals to $(T_{1}-T_{0})$. It is noted that the generated Kerr chirped pulses in the left side experience a decreased in optical frequency (red shift), while the right side Kerr chirped pulses undergo an increased in optical frequency (blue shift).

 

Fig. 1. Schematic diagram of normalized spectrum for generated sidebands from Kerr effect for (a) fixed-frequency pump and (b) chirped pump.

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In order to further improve the frequency chirping rate ($\Delta v/W$) without changing the pulse width $W$, an anti-chirped pump signal from the same laser source, i.e. with chirping content $-\Delta \nu$, is utilized to extend the frequency chirping range. This new optimized method is shown in Fig. 1(b). Since the chirped pump and original chirped pulses are synchronized in time domain, the interaction between starting frequency components (at time $T_{0}$) of chirped pulse (blue solid line) and chirped pump (red solid pump) generates sidebands with frequency $\omega _m = m\omega _d=m(\omega _c -\omega _p)$ apart from $\omega _p$. On the other hand, the two ending frequency components (at time $T_{1}$) from chirped pump and chirped pulse will interact with each other and yield negative sidebands that will be $\omega _m = m(\omega _d+2\Delta v)=m(\omega _c+2\Delta v -\omega _p)$ apart from $\omega _p-\Delta v$. Note that the ending frequency of negative order Kerr pulse at time $T_{1}$ is generated from the chirped pump signal at frequency of $\omega _p-\Delta v$ since the blue shifts occurs within the pulse duration from $T_{0}$ to $T_{1}$, resulting an additional frequency chirping extension of $\Delta v$. The frequency chirping range for negative sidebands is extended from $\Delta v$ to $(2m+1)\Delta v$ with same pulse duration. Thus, the chirping rate enhancement factor is (2$m$+1) for the negative $-m^\text {th}$ order sideband Kerr pulses. Similarly, the positive sidebands will experience a chirping rate enhancement factor of (2$m$-1), since the first positive sideband is considered as the original chirped pulse, shown in Fig. 1(b).

In the chirped pulse $\varphi$-OTDR, to avoid the trace-to-trace distortion and decorrelation, the largest measurable time delays between two consecutive traces is usually limited to 10$\%$ of pulse width [20]. The relationship between external disturbance-induced optical path length change, $\Delta L$, and time delay, $\Delta t$, is given by [14]:

3. Experimental setup

To verify the principle mentioned in section 2 and investigate the noise performance of high order Kerr pulses, a chirped pulse $\varphi$-OTDR system with Kerr pulses is implemented for dynamic strain sensing. The experimental setup is depicted in Fig.2. A DFB laser with 1 MHz linewidth is periodically modulated by triangular-shaped current pulses with equal rising and falling edges of 20 ns and at a 1 ${\mathrm {\mu }}$ s repetition period from a signal generator (8130A, Hewlett Packard). Thus, the output optical frequency of the DFB experiences a periodic modulation including blue and red shift, as shown in Fig. 2(a). The output modulated signal is divided into two branches, and the optical wave in the upper branch is then chopped by the SOA with 6 ns pulses, acting as a gate device, only allowing the transmission of the blue-shifted portion of the modulated signal. Note that, despite the application of a linearly varied input current, the output frequency change of the DFB laser is not linear across 20 ns. However, within a carefully selected interval of 6 ns, the frequency chirp exhibits high linearity. In the bottom branch, a single-sideband suppressed-carrier (SSB-SC) modulator shifts the optical frequency of the input signal by $\omega _d = 25$ GHz, which is used as the pump signal $\omega _p$. Another way to obtain such frequency difference from the upper branch is to use a second laser as the pump, although this can only be used as a fixed pump as shown in Fig. 1(a). These two methods have different noise performance and will be discussed in next section. Before being combined by the 50/50 coupler and sent to the Kerr medium, the chirped pulse and chirped pump signals are amplified by two EDFAs to enhance the efficiency of Kerr effect. A delay line is employed to align the original chirped pulse signal and the chirped pump signal to make sure they have the same frequency chirping range but with opposite chirp [22]. As shown in Fig. 2(b) and (c), the two optical signals have the same frequency content of 545 MHz and the same chirping period of 6 ns. After propagating along the Kerr medium, numerous Kerr chirped pulses with extended frequency chirping range but same pulse width are generated, as shown in Fig. 2(d). After that, a single high order Kerr pulse can be selected through an optical tunable filter for high performance sensing application. Note that, by filtering one high order Kerr pulse, the intensity beating between pairs of high order pulses is removed, such that the output pulse has the same shape of the original chirped pulse, as shown in Fig. 2(e).

 

Fig. 2. Experimental setup of chirped pulse $\varphi$-OTDR based on Kerr pulses.DFB, distributed feedback laser; SOA, semiconductor optical amplifier; EDFA, Erbium doped fiber amplifier; PC, polarization controller; NLL, narrow linewidth laser; PG, pulse generator; PD photo-detector; OSC, oscilloscope; EM, electrical modulation; CIR, circulator; RFGA, random fiber grating array.

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After being amplified by the EDFA, the high order Kerr chirped pulse is sent through an optical circulator to a random fiber grating array (RFGA) that acts as a strain sensor with enhanced Rayleigh scattering. Before detecting the reflected Rayleigh signal by a photodiode (PDB435C, Thorlabs), the amplified spontaneous emission (ASE) noise is removed by another tunable filter. Finally, the Rayleigh signals are collected by an oscilloscope (infiniium DSO81204B, Agilent) with sampling rate of 40 GSa/s, which corresponds to a sampling period of 25 ps.

4. Experimental results

The measured optical spectra of Kerr chirped pulses are shown in Fig. 3(a) for the two schemes discussed in section 2 – using an opposite chirping pump and a fixed-frequency pump from a second laser with 100 kHz-linewidth. The maximum order of the Kerr chirped pulses is limited by the optical powers of the pump ($0^\text {th}$) and the original chirped pulse ($1^\text {st}$ order). This can be confirmed by analysing Eq. (5), in which the amplitude of the $J_m$ term decays with $m$, so that higher input powers are required to generate high order sidebands. However, too high powers give rise to other nonlinear effects in the fiber, such as stimulated Brillouin scattering, which could significantly deplete the pump power and prevent the generation of high order Kerr pulses. To optimize the generation of high order Kerr pulses while preventing undesired non-linear effects, the peak power of the chirped pulse signal was tuned to about 13 dBm and that of the pump signal to $\sim$20-23 dBm. Another important aspect that has a significant impact on the number of Kerr chirped pulses is the relative SOP between pump and original chirped pulses, described by the parameter $\eta$ in Eqs. (1) and (2). The physical reason is that the peak power of the optical beating signal from two optical waves in Eq. (2) is SOP dependent, directly affecting the phase modulation depth. After optimizing the optical power and the SOP of two injection signals, more than 8 order Kerr chirped pulses were well generated. In order to verify the frequency chirping range of high order Kerr pulses, the frequency content of the $-1^\text {st}$ and $-4^\text {th}$ orders is measured at 5 dB linewidth, as shown in Figs. 3(b) and (c). In Fig. 3(b), the frequency chirping range of the $-1^\text {st}$ order by using fixed-frequency pump remains of 545 MHz, which is the same as the original chirped pulse signal, while that of the $-1^\text {st}$ order by using chirped pump signal is about 1.61 GHz, a 3 times improvement. For the frequency chirping range of the $-4^\text {th}$ order Kerr pulses from fixed-frequency and chirped pumps, as shown in Fig. 3(c), the former is enhanced by 4 times to about 2.18 GHz, while the latter is increased to 4.84 GHz, which is almost a 9 times enhancement. The frequency chirping range is linearly proportional to the order $m$, which is consistent with the theoretical analysis in section 2. As predicted, the frequency chirping range of negative $-m^\text {th}$ order is improved by 2$m$+1 times when using chirped pump, while the enhancement factor is $m$ times when using a fixed-frequency pump.

 

Fig. 3. Spectrum of generated high order Kerr pulses at the output end of the Kerr medium by using fixed-frequency or chirped pump. (a) overview spectrum, and close-up view of the (a) $-1^{st}$ order and (c) $-4^{\text {th}}$ order from fixed-frequency and chirped pump, respectively.

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Compared with fixed-frequency scheme by employing two lasers source, the proposed method with chirped pump not only have higher efficiency in term of frequency chirping range extension, but also have a lower noise performance benefits from the usage of single laser source. Given the fact that low frequency fluctuation of laser central optical frequency is one of the main noise sources that limits the accuracy in distributed sensing systems, we analyzed the optical frequency stability for both pumping schemes. In the experiments, different order of Kerr pulses from the two schemes are used as interrogation pulses in the chirped pulse $\varphi$-OTDR. Based on Eq. (6), any central optical frequency drifting of the interrogation pulses will introduce overall time delays in the reflected Rayleigh traces, and this time delay is calculated by the frequency drifting divided by pulse chirping rate, i.e., $t_\text {delay} = \frac {f_\text {drift}}{\Delta \nu /W}$. By measuring the trace-to-trace time delays, the equivalent frequency jitters of high order Kerr pulses can be obtained. Figures 4(a) and (c) present the equivalent frequency jitters of different orders Kerr pulses for chirped and fixed-frequency pump configurations, respectively. It clearly shows that the unwanted frequency jitters are increasing from lower order to higher order Kerr pulses in both pumping schemes. The reason is that two consecutive Kerr pulses do not share the same central frequency due to laser frequency fluctuation, and this central frequency difference is greater for higher order Kerr pulses. For instance, for the positive $m^\text {th}$ order Kerr pulses, the instantaneous central frequency is $m (\omega _d + \Delta \omega _\text {drift}(t))$, indicating an increase in the frequency drift by a factor $m$. However, if we compare the frequency jitters from the same $-4^\text {th}$ order between the fixed-frequency case and chirped pump case, the latter has lower frequency jitter noise, as shown in Fig. 4(b) and (d). Since the central frequency fluctuation of chirped pulses and chirped pump signals come from the same laser, nearly the same central frequency drift is expected in chirped pulses, $\omega _c$, and chirped pump, $\omega _c$, thus resulting in a low central frequency drifting noise. The standard deviations of the frequency jitter for all measured Kerr pulses are shown in Fig. 4(e), revealing that the noise performance of Kerr pulses in the chirped pump scheme using a single 1 MHz-linewidth laser is comparable to the fixed-frequency scheme with 5 kHz-linewidth laser, and much smaller than the fixed-frequency scheme with 100 kHz-linewidth laser.

 

Fig. 4. Frequency jitter noise of different high order Kerr pulses with chirped (a) or fixed-frequency (c) pump, and their respective histograms (b) and (d). (e) shows the comparison of frequency jitter noise from different order Kerr pulses with fixed-frequency (5 kHz/100 kHz linewidth laser source) or chirped pump (1 MHz linewidth laser source).

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To verify the capability of frequency chirping range extension, dynamic and static strain measurement experiments are conducted. In the principle-proof experiments, a Rayleigh back-scattering enhanced sensor, RFGA, is used to acquire Rayleigh traces with a high signal-to-noise ratio. The RFGA has an average reflection of about -30 dB and a length of 0.8 m. It consists of 8 alternating sub-gratings of lengths 10 mm and 5 mm. The periods of the sub-gratings are randomly distributed between 0.5180 ${\mathrm {\mu m}}$ and 0.5464 ${\mathrm {\mu m}}$. More details about the fabrication of this sensor can be found in our previous publication [23]. The setup for applying strain variation is shown in Fig. 2, in which one end of the RFGA is glued on the fixed translation stage and another end is fixed on a Piezo Transducer (PZT). The displacement of the PZT could be precisely controlled so that the desired strain variation could be applied on the RFGA accurately. Firstly, a triangle-shaped strain variation with an amplitude of 50 $\mu \epsilon$ and a period of 2 s is applied on the RFGA, and the reflected Rayleigh signal from the RFGA is continuously collected in the oscilloscope over 4 s, resulting in 4000 traces with a duration of 10 ns each. The differential strain was then calculated for each pair of consecutive traces through cross-correlation operation, and by integrating the differential strain over the measurement time we obtained the overall strain variation as shown in Fig. 5(a). It clearly shows that higher-order Kerr pulses with the same pulse width but larger frequency chirping range introduce smaller time delays. This is consistent with Eq. (6), which shows an inverse proportional relationship between strain-time delays coefficient and frequency chirping rate ($\Delta \omega /W$). Figure 5(b) depicts the relationship between time delays and applied strain variations when different order of Kerr pulse are utilized. According to the ratio between coefficients of the different order of the Kerr pulses, the frequency chirping range enhancement factor could be calculated as shown in Fig. 5 (c). The enhancement factor of Kerr pulses in chirped pump scheme is close to the theoretical values. As a comparison, the enhancement factor of different order Kerr pulses in the fixed-frequency pump scheme is also calculated, and results are consistent with the predictions in section 2.

 

Fig. 5. (a) Dynamic strain measurement of using different order Kerr chirped pulses in chirped pump scheme (10 times averaging); (b) The relationship between applied strain and time delays in chirped pump scheme; (c) Frequency chirping range enhancement factor of fixed-frequency and chirped pump scheme.

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In chirped pulse $\varphi$-OTDR, similarly to other Rayleigh scattering-based dynamic strain measurements, the strain variation is measured by the differential strain measurement from two adjacent Rayleigh traces, and then the whole strain variation is calculated by integration over time. Hence, the maximum measurable strain variation over certain time period is limited by the system acquisition rate (based on pulse repetition rate) and the measurable strain variation between two single-shot measurements, as known as static strain measurement range, which is limited by frequency chirping range of the interrogation pulse based on the analysis in section 2. The maximum pulse repetition rate is limited by the length of the sensor, so the only way to increase the dynamic strain measurement range is to increase the frequency chirping range. Note that, when the applied strain variation between two Rayleigh traces exceeds the static measurement range, then the two traces become decorrelated, which translates into large uncertainty in the measured strain variation. For this reason, the generated Kerr pulses with extended chirping range could give a larger static strain measurement range and a lower uncertainty. In order to demonstrate the static measurement range of each order of Kerr pulses, different static strain variations are applied on the RFGA and the demodulated strain variation results are shown in Fig. 6(a). Each measurement has been repeated 20 times, and the average value of 20 tests used as the final measured strain variation result. For each order sideband, the measured results start to experience a larger uncertainty after a certain value of applied strain variation, which in fact could be potentially used to determine the static measurement range. So a measurement error, $\beta$, is introduced, and it is expressed by:

 

Fig. 6. Static measurement range assessment of Kerr pulses. (a) Static strain measurement and its measurement error (b).

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Ultimately, the strain uncertainty was verified for Kerr pulses of different orders in the absence of strain variations. 8000 Rayleigh traces were collected within 8 seconds, and the relative time delays between consecutive pulses were calculated. In order to compare the strain uncertainty of Kerr pulses with the same chirping range for fixed-frequency and chirped pump schemes, we define an enhancement factor $\alpha$, which represents the chirping range of Kerr pulses over the chirping range of the original chirp pulse, $\alpha =\Delta \nu _{out}/\Delta \nu _{in}$. Note that the fixed-frequency case requires higher order Kerr pulses to obtain the same enhancement factor achieved from the chirped pump configuration, as clearly shown in Fig. 5(c). Figures 7(a) and (b) show the demodulated strain of high order Kerr pulses with enhancement factors 3 and 5, respectively (all results were obtained from negative order sidebands). Based on Figs. 7(a) and (b), the strain measurement uncertainty from chirped pump scheme is always lower than that from the fixed-frequency scheme, which agrees with results from Figs. 4 and 5, as lower order Kerr pulses can always achieve higher enhancement factor in chirped pump scheme, and with a reduced laser drifting noise. The summarized results are shown in Fig. 7(c), in which four negative order Kerr pulses are evaluated. It shows that the measurement uncertainties for Kerr pulses with the same chirping range are lower in the chirped pump scheme. Furthermore, since wider chirping ranges are obtained in the chirped pump scheme for lower order Kerr pulses, the chirped pump case exhibits a significant benefit in terms of SNR, which can be seen in Fig. 3(a). Experimentally, utilization of sidebands beyond m = 6 is limited by their rapidly decreased power due to high order Bessel function. The constant electrical noise from detector and amplifier and lower signal power leads to higher power fluctuations, which will reduce accurately calculation of time delays for the CP-$\phi$-OTDR application. There is a trade off in increasing chirp range by higher order Kerr pulses for large strain range at the cost of reducing strain measurement accuracy.

 

Fig. 7. Comparison of strain measurement uncertainty from fixed-frequency and chirped pump schemes when frequency chirping range enhancement factor is (a) 3 and (b) 5; (c) The strain measurement uncertainty achieved from different enhancement factors $\alpha$ for chirped and fixed-frequency schemes.

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5. Discussion and conclusion

It is interesting to note that, although the SOA simply acts as a gating device by chopping a linear frequency chirping region, the abrupt intensity change in the rising and falling edges of the SOA pulse induce an additional SPM to the system. Hence, across the pulse width, the chirp is not purely linear. However, since in the current experiment the pulse edges have a duration of 500 ps, much smaller than pulse width of 6 ns, this edge effect can be neglected since it contributes minimally to the resulting Rayleigh traces. Furthermore, based on the results in Fig. 5(b), the relationship between relative strain variation and time delays has good linearity for all sideband orders despite non-linear chirp near the pulse edges.

Another relevant point to mention is the trade-off between static strain measurement range and measurement sensitivity. By enhancing the chirping range we showed that the static measurement range can be highly enhanced. However, as shown in Fig. 5, higher chirping ranges result in lower strain sensitivities, such that the minimum detectable strain is higher for high order Kerr pulses. Although most applications for strain measurement are more interested in high static strain measurement range than in high strain sensitivity, the proposed scheme offers a way to combine both features: with the addition of a few extra components, high and low order Kerr pulses could be sent alternately to the fiber sensor, thus generating two different measurement results, one with high static strain measurement range, and another with high sensitivity. Thus, the proposed method is general enough to cover multiple demands in strain measurement applications.

In our cross-correlation calculation based sensing system, a section of Rayleigh trace (time window) is selected for local time delays demodulation. And the fiber section covered by each time window is determined by the duration of time window and pulse width. Therefore, the spatial resolution is the convolution between pulse width and time window duration. In our experiments, the selected time window and pulse width are both 6ns, hence the spatial resolution of our proposed system is 1.2m. In fact, time window can be adjusted to increase or decrease the spatial resolution depending on positioning resolution of events and sampling rate of OSC depending on signal to noise ratio.

In conclusion, we generated high order chirped Kerr pulses with enhanced optical frequency chirping range from a single DFB laser to improve the performance of distributed strain sensing. By combining an up-chirped pulsed signal with a down-chirped pump in a novel configuration, we showed that the frequency chirping range of the $m^\text {th}$ order Kerr chirped pulse is enhanced by a factor of 2$m$+1, which is more efficient than the fixed-frequency pump scheme, which only enhances by a factor $m$. To experimentally validate the effect of high order chirped Kerr pulses in a strain sensing application, we used the $-4^\text {th}$ order Kerr pulse from the proposed scheme to interrogate a strain sensor (RFGA) under strain variation induced by a PZT. With the chirped-pump configuration we achieved about 8 times larger static strain measurement range, much higher than that obtained with a fixed-frequency pump. Moreover, the chirped-pump configuration have also shown better performance in terms of measurement uncertainty. This novel scheme with anti-chirped pump exhibits better chirping enhancement factor, lower strain measurement uncertainty and higher SNR than the fixed-frequency configuration. Our proposed all-optic method opens new avenues to generate chirped pulse with higher chirping rate over nano-second pulse widths, without using complicate cascaded scheme and expensive electronic devices.