Phase-shifted Brillouin dynamic gratings using single pump phase-modulation: proof of concept

Yongkang Dong; Dengwang Zhou; Lei Teng; Pengbai Xu; Taofei Jiang; Hongying Zhang; Zhiwei Lu; Liang Chen; Xiaoyi Bao

doi:10.1364/OE.24.011218

1. Introduction

During the past several decades, many highly efficient and flexible applications of Brillouin scattering (BS), an important nonlinear phenomenon in optical fibers, have been developed in a variety of directions, such as optical amplification [1], Brillouin lasers [2, 3], distributed optical fiber sensors [4–10], stored light [11], slow [12] and fast light [13], optical polarization control [14], as well as microwave photonics [15–17].

In particular, the characterization of the so-called Brillouin dynamic gratings (BDGs) based on stimulated Brillouin scattering (SBS) process is theoretically analyzed and experimentally demonstrated in polarization-maintaining fibers (PMFs) in Ref [18–27]. Generally, the operation principle of BDG is that the refractive index in one polarization axis is periodically modulated by the interaction of two counter-propagating pump waves, whose frequency difference is equal to the Brillouin frequency shift (BFS) of PMF, through the electrostriction effect as a writing process, while a probe wave under the phase-matching condition is launched into the orthogonal polarization axis to explore the properties of BDG resulting in a reflection wave with a Doppler frequency shift as a reading process. Furthermore, several BDGs generated in single-mode optical fiber [28], elliptical-core two-mode fiber [29], few-mode optical fiber [30], and photonic chip [31], are also reported.

With its high versatilities such as easy to generate, reconfigurable, tunable, moving, more new potential applications and novel BDGs have been drawing increasing interest. The central frequency shift of reflection spectrum of BDG depends on the PMF birefringence which is related to the strain or temperature, therefore BDGs can be applied on the distributed birefringence measurement with a long range and high spatial resolution [32, 33] and dynamic strain sensing [34]. A long length BDG with a high reflectivity in a single-mode fiber (SMF) is used for an optical spectrometry with an ultra-high resolution of 4fm covering S + C + L communication bands [35]. In Ref [36], BDG is selected to achieve various all-optical signal processing functions such as all-optical time differentiation, time integration and true time reversal, because the acoustic wave can store the information of two pump waves for a phonon lifetime. In Ref [37], a novel type of photonic delay line is demonstrated using movable BDG reflectors, which can provide continuously tunable signal delaying for high capacity optical data streams and wide bandwidth microwave signals. Additionally, sampled Brillouin dynamic gratings (SBDGs) are created by one pulse and a series of pulses in the opposite direction along one polarization axis and are used to generate a multichannel optical filter with a 3-dB bandwidth tuned from 12.5MHz to 1GHz [38].

Conventional fiber Bragg gratings (FBGs) are permanently fabricated by ultraviolet light [39, 40] or femtosecond laser [41] giving rise to the periodic variation in the core refractive index of an optical fiber and can reflect particular wavelengths of input optical wave while transmits all others. The phase-shifted fiber Bragg grating (PS-FBG), one of the widely used FBG, is usually generated by means of inducing a certain phase shift into conventional FBG in a particular point, producing two cascaded but out-of-phase FBGs. It has a wide range of potential applications including optical temporal integrator [42, 43] and optical differentiator [44, 45], all-optical switching [46, 47], single longitudinal mode fiber laser [48], optical fiber sensing [49, 50], microwave generation [51] and microwave photonic filter [52, 53]. Because their parameters cannot be easily changed the conventional FBG’s applications would be limited while this shortcoming can be complemented by the BDGs in many areas. The difficulty of generating the controllable phase-shifted Brillouin dynamic grating (PS-BDG) is that: 1) if two continuous waves are used to create a BDG in the whole fiber, it is difficult to induce a phase-shifted point at a fixed location; 2) if two long pulses are used to create a BDG, it is hard to make two uniform but out of phase acoustic wave field because of the exponential decay of acoustic wave associated with the phonon lifetime.

In this paper, we focus on the generation of the controllable PS-BDG. To build uniform but with different phase-shifted acoustic wave fields, the pump1 pulses with width of 2ns is phase-modulated into two equal-length segments corresponding to different phases. Then the pump1 and a counter-propagating pump2 pulse with a width of 100ps are launched into one polarization axis of PMF to create two adjacent BDGs with different phase shifts, and a continuous probe wave is responsible for obtaining the reflection spectrum. From the standard five-wave BDG coupled equations, we simulate two novel PS-BDGs. Using two segments with the phase shift of π for pump1 pulse, a transient PS-BDG is written by the pump1 pulse and the narrow-width optical pump2 pulse. With a high repetition rate for two pump waves, an enhanced PS-BDG with a deep notch depth is obtained. Finally, a proof-of-concept experiment is assembled to generate a transient PS-BDG and show the changing of its notch frequency through tuning the phase shift $Δ φ$ .

2. Principle and simulation model for PS-BDG

In our scheme, a coherent anti-Stokes Brillouin scattering condition as discussed in Ref [54] is shown in Fig. 1. For a PMF depicted in Fig. 1(a), a pump1 pulse that makes main contribution to the shape of the generated PS-BDG and a counter-propagating narrow-width pump2 pulse are injected into the slow polarization axis. Note that the pump1 pulse is phase-modulated into two or more segments corresponding to the phase $φ_{j} (j = 1, 2, 3 \dots)$ , and this method is named as single pump phase-modulation (SPPM). When the frequency difference between the pump1 and pump2 is equal to the BFS, the SBS process is accurately excited and accompanied by the generation of an acoustic wave. As a result, a periodically modulated and moving refractive index i.e. Brillouin dynamic grating is written in PMF thanks to the electrostriction effect. Hence, a reflection wave with a frequency up-conversion by the Doppler shift can be obtained after a continuous probe wave is employed to read the PS-BDG in the fast polarization axis. From Fig. 1(b), it's worth noting that the frequency difference between two optical waves along the same principle axis is equal to the BFS $ν_{B}$ while the frequency difference between the two optical waves in the same direction is equal to the birefringence-induced frequency shift $ν_{B i r e}$ .

Fig. 1 Principle to generate PS-BDG in the PMF, (a) two pump pulses meet in the middle of PMF to write two pieces of BDGs and a continuous probe wave can read BDGs obtaining a reflection wave; (b) The frequency relationship of four optical waves, two waves along the same principle axis has a BFS $ν_{B}$ , and two waves at the same direction has a birefringence-induced frequency shift $ν_{B i r e}$ ; (c) The refractive index distribution diagram of the PS-BDG, $Δ n (z)$ contains two BDG segments with a phase shift point at the junction.

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As an important operation of PS-BDG, in the simplest case, we assume that the pump1 pulse is divided into two equal-width segments corresponding to the phase $φ_{1} and φ_{2}$ , so that two equal-length BDGs (BDG₁ and BDG₂) cascaded through a phase-shifted point can be created, which is schematically described in Fig. 1(c). The normalized index change is represented:

Δ n (z) = {\begin{matrix} \bar{n} + Δ n^{'} (z) \cos (2 π ν_{B} t - \frac{2 π}{Λ} z + φ_{1}) (L_{BDGs} / 2 < z < L_{BDGs}, B D G_{1}) \\ \bar{n} + Δ n^{'} (z) \cos (2 π ν_{B} t - \frac{2 π}{Λ} z + φ_{2}) (0 < z < L_{BDGs} / 2, B D G_{2}) \end{matrix}

where

\bar{n}

is the “dc” refractive index change,

Δ n^{'} (z)

is the “ac” refractive index modulation,

ν_{B}

is the Brillouin frequency shift,

Λ

is the grating period,

L_{BDGs} = (t_{p 1} + t_{p 2}) c / 2 n_{x}

is the interaction length of the two pumps, where

t_{p 1}

and

t_{p 2}

are the pulse widths of pump1 and pump2 respectively.

Compared with BDG₁ (green line), a phase shift $Δ φ = π$ is induced into BDG₂ (red line). Thus a PS-BDG is composed of these two adjacent BDGs and the notch frequency of the reflection spectrum can be tuned by changing the phase shift $Δ φ$ . Moreover, with a high repetition rate for two pump pulses, the acoustic wave can be maintained over time resulting in an enhanced PS-BDG, because the residual acoustic wave field of the former period can be enhanced by the newborn acoustic wave field of the latter period. In order to produce only one PS-BDG in the PMF, the repetition rate is limited as followed:

f < \frac{1}{n_{x} L / c + t_{\max}}

where

n_{x}

is the refractive index at the slow polarization axis in PMF,

L

is the PMF length,

c

is the light velocity in vacuum, and

t_{\max} = \max {t_{p 1}, t_{p 2}}

.

To simulate the PS-BDG, considering the slowly varying amplitude approximation, the coupled-wave equations of the coherent anti-Stokes Brillouin scattering condition are given by [54]:

(\frac{\partial}{\partial z} + \frac{n_{x}}{c} \frac{\partial}{\partial t}) E_{1} = i g_{o} ρ E_{2} - \frac{α}{2} E_{1}

(- \frac{\partial}{\partial z} + \frac{n_{x}}{c} \frac{\partial}{\partial t}) E_{2} = i g_{o} ρ^{*} E_{1} - \frac{α}{2} E_{2}

(- \frac{\partial}{\partial z} + \frac{n_{y}}{c} \frac{\partial}{\partial t}) E_{3} = i g_{o} ρ^{*} E_{4} e^{i Δ k z} - \frac{α}{2} E_{3}

(\frac{\partial}{\partial z} + \frac{n_{y}}{c} \frac{\partial}{\partial t}) E_{4} = i g_{o} ρ E_{3} e^{- i Δ k z} - \frac{α}{2} E_{4}

(\frac{\partial}{\partial t} + \frac{Γ_{B}}{2}) ρ = i g_{a} (E_{1} E_{2}^{*} + E_{3}^{*} E_{4} e^{i Δ k z})

where

E_{j} (j = 1, 2, 3, 4)

represent pump1, pump2, probe, and reflection waves, respectively;

ρ

is the amplitude of the acoustic field;

n_{x}

and

n_{y}

are respectively the refractive index of the slow and fast axes in PMF;

g_{o}

and

g_{a}

are respectively the coupling coefficients of optical wave and acoustic wave;

α

is the attenuation coefficient of the PMF;

Δ k

is phase mismatch value;

Γ_{B} =1/ τ_{p}

is the Brillouin gain width and

τ_{p}

is the phonon lifetime. Obviously, the above Eqs. (3) can be used to describe the interaction between four optical waves and one acoustic wave.

3. Simulation results and discussions

Based on the operation principle mentioned above and the coupled-wave equations, we now focus on two numerical simulation examples that demonstrate the different reflection spectra of PS-BDGs. The main simulation steps are as follows. 1) The temporal evolution of acoustic wave and reflection signal of the transient PS-BDG are calculated in case of the two phase-shifted segments of pump1 pulse in one period. 2) The notch frequency tunability of an enhanced PS-BDG is calculated by changing the phase shift $Δ φ$ with a high repetitive rate for two pumps. For these simulations, some basic parameters about the pump pulses and PMF are listed in Table 1.

Table 1. Simulation parameters.

View Table

3.1 Transient PS-BDG

First of all, we demonstrate a transient PS-BDG. Table 1 and Fig. 2(a) show the boundary conditions: the pump1 pulse has a fixed width of 2ns and is phase-modulated into two equal-length adjacent segments with the phase shift $Δ φ =π$ , respectively; compared to pump1 pulse, pump2 pulse with the width of 100ps has a delay of 1.0 ns; a continuous probe wave is set at a small power of 10mW in order to decrease the influence on PS-BDG. Additionally, the length of PMF is 40cm and simulation time is 24ns, so that the attenuation coefficient of the PMF can be neglected ( $α = 0$ ).

Fig. 2 (a) Input waveforms of pump1 with a fixed width of 2ns and pump2 with a narrow width of 100ps. (b) Temporal evolution of acoustic waves. (c) Intensity of acoustic wave filed along the PMF at point A. (d) Intensity of acoustic wave filed over the time at point A. (e) The temporal evolution of reflection signal. (f) Time integral reflection spectrum of PS-BDG and transient spectrum at 4ns.

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Although the SBS process induce an energy transfer from the high-frequency component i.e. pump1 pulse to the low-frequency component i.e. pump2 pulse, the increment rate of pump2 can be still ignored thanks to its high peak power of 30W compared to the lower one of pump1 which is equal to 0.4W. As shown in Fig. 2(b), a relatively uniform PS-BDG made up of two cascaded BDGs (BDG₁ and BDG₂) is obtained, and its spatial and temporal intensity distributions of PS-BDG at point A are, respectively, illustrated in Figs. 2(c) and 2(d). It is clearly shown in Fig. 2(c) that a π-phase-shifted point is located in the middle of the PS-BDG. The valley region is determined by the overlapping between BDG₁ and π-phase-shifted BDG₂, and the slit width has relation to the width of pump2 pulse, so that a longer pump2 pulse will cause a wider slit in the middle of the PS-BDG. The intensity of the later generated BDG₂ is slightly larger than that of the first generated BDG₁, since the intensity of PS-BDG follows exponential decay over time which is illustrated in Fig. 2(d). For a pair of pump pulses, the acoustic wave would vanish after tens of ns and it can be regard as transient PS-BDG. The location of PS-BDG can be easily moved by changing the delay time between the two pump pulses.

A temporal evolution of reflection signal is shown in Fig. 2(e) and its notch integral reflection spectrum (blue line) with the 3-dB bandwidth of 354MHz is obtained in Fig. 2(f). The notch depth in Fig. 2(f) has been influenced by the reflection signal in Fig. 2(e) at time of 2.0~3.8ns when the transition process from the reflection signal of conventional BDG₁ to that of PS-BDG occurs. After 3.8ns, two symmetric high-power reflection peaks are stood on both sides of the notch and two side-lobes are settled in the frequency of ± 1480MHz. The generation of an instantaneous high-depth notch spectrum (red line) at 4ns can be interpreted as the destructive interference between two reflection signals that are reflected from BDG₁ and π-phase-shifted BDG₂ respectively. If the length of the BDG₁ is unequal to that of the π-phase shifted BDG₂, two unequal-amplitude reflection signals will be generated. As a result, the destructive interference is broken and the notch depth of the integral reflection spectrum is reduced. Then, if we increase the repetitive rate of two pump pulses to enhance the SBS process and to decrease the loss of two peaks, a much deeper notch of PS-BDG will be achieved.

3.2. Enhanced PS-BDG

We now increase the repetition rate of two pump pulses from just one-time as shown in the section 3.1 to 250MHz corresponding to the periodic time of 4ns, and an enhanced PS-BDG will be generated. Figure 3(a) shows the input waveforms of pump1 pulse and pump2 pulse remain invariant for repeat times of 20 and the simulation time has increased up to 84ns.

Fig. 3 (a) Input waveforms of pump1 and pump2 at the repetition rate of 250MHz. (b) Temporal evolution of acoustic waves in PMF. (c) Intensity of acoustic wave filed along the PMF at point A and B. (d) Intensity of acoustic wave over the time at point A. (e) The temporal evolution of reflection spectrum. (f) Integral reflection spectra of PS-BDG at the case of phase shift $Δ φ = 0.8 π, 1 .0 π, 1.2 π$ .

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The residual acoustic wave of the former SBS process is enhanced by the latter SBS process shown in Fig. 3(b). Although the normalized spatial intensity distributions of PS-BDG at point A (blue line) and B (red dash line) are consistent as shown in Fig. 3(c), the intensity of the enhanced acoustic wave field at the point B in Fig. 3(d) is ten times higher than that of the initial acoustic wave field at the point A. The intensity of acoustic wave has a saw-tooth waveform over time, which has influence on the uniformity of PS-BDGs and can be weakened by shortening the length of PS-BDG and increasing the repetition rate. Finally, the temporal intensity distribution of PS-BDG tends to be stable after 50ns.

As a result, an enhanced PS-BDG with a notch channel between two symmetric high-power reflection peaks in Fig. 3(e) and a high-depth notch (red line) shown in Fig. 3(f) is clearly achieved. Moreover, the notch frequency of PS-BDG is easily tuned from −100MHz (green line) to 100MHz (blue line) by the adjustment of phase shift $Δ φ = 0.8 π ~ 1.2 π$ as illustrated in Fig. 3(f). However, the notch frequency tunability of the PS-BDG is coming true at the expense of the symmetry of the two high-power reflection peaks.

4. Experimental setup

Considering the equipment performance limitation in our laboratory that can’t satisfy the demand about the narrow-width and high peak power for two pump pulses, a simplified proof-of-concept experiment is performed for the characterization of transient PS-BDG using SPPM as illustrated in Fig. 4.

Fig. 4 Experimental setup for the generation and characterization of transient PS-BDG. OS: optical switch; PG: pulse generator; EDFA: erbium doped fiber amplifier; PD: photodetector; MG: microwave generator; OSA: optical spectrum analyzer; PBS: polarization beam splitter; TFBG: tunable fiber Bragg grating.

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A narrow linewidth (~10 kHz) optical fiber laser operating at 1550.030nm/120mW is used to provide two pump waves and its output light is divided into two optical branches through a 90:10 optical coupler 1 (OC1). In the upper branch, the optical wave with 90% component is firstly phase-modulated by an electro-optic phase modulator (PM, THORLABS, 40GHz), which is driven by the electrical signal from the channel 1(CH1) of a pulse generator (PG). When the output peak-to-peak voltage, demonstrated in Fig. 5(a), of the CH1 is adjusted to match the half-wave voltage ( $V_{π} ~ 7.07 V$ ) of the PM, the phase shift between the optical segments corresponding to low-level voltage and the high-level voltage will be equal to $π$ . After amplified by an Erbium-doped fiber amplifier 1 (EDFA1), the phase-modulated light wave is then intensity modulated into an optical pulse with the width of 5.4ns (the red dotted area in Fig. 5(a)) by an electro-optic modulator 1 (EOM1), which is driven by an electric pulse signal from CH2. Note that the position of phase-shifted point in this optical pulse can be tuned by changing the delay between CH1 and CH2. Afterwards the phase-modulated optical pulse from a 50% port of OC2 is amplified by EDFA2 to ~2.1W and injected into the slow principle axis of a 4.3m-length PMF through a polarization beam splitter1 (PBS1).

Fig. 5 (a) Input driven voltage of PM and (b) the interference signals at phase-shift of $π$ measured by the M-Z configuration, black line: the former part and the latter part in case 1 are in the maximum condition and the minimum condition respectively in case 1, blue line: the former part and the latter part are in the minimum condition and the maximum condition respectively in case 2. Red line: the phase-modulated optical pulse at the output of EOM1.

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On one hand, in order to monitor the phase shift value between the two parts of the phase-modulated optical pulse, a Mach-Zehnder configuration [55–59] is assembled through OC3 when an optical switch (OS) is switched to port 1 in the lower branch. Then the interference signals between the light from another 50% port of OC2 and the light in lower branch are detected by a photodetector 1(PD1, New Focus, 26GHz) with the high speed and wide bandwidth. Due to the extra-phase in two arms of MZ configuration induced by the change of surrounding environment (e.g. temperature or vibration) in a slowly-varying random state, the intensities of the two interference signals with a $π$ -phase shift are two orthogonal functions of time. As shown in Fig. 5(b), a phase-modulated optical pulse (red line) with the width of 5.4ns which has a $π$ -phase shift between the first 2.7ns and the second 2.7ns is directly detected at the output of EOM1, because the intensities of the two interference signals (black line) at the first 2.7ns and the second 2.7ns in case 1 are in the maximum and minimum conditions respectively while the opposite conditions for the intensities of interference signals (blue line) in case 2, revealing an orthogonal state, when OS is switched to port1.

On the other hand, when the OS is switched from port 1 to port 2, the light wave in lower branch is modulated by a single sideband modulator (SSBM), which is driven in the suppressed carrier and upper sideband regime with a sinusoidal microwave from a microwave generator (MG) setting the frequency of $10.696 GHz$ equivalent to the slow axis BFS of the PMF. Subsequently, an optical spectrum analyzer (OSA, YOKOGAWA, AQ6370D) with the wavelength resolution of 0.02nm is applied to monitor the sidebands and with appropriate parameters the measured rejection ratio between the −1th sideband and others can reach 20dB as shown in Fig. 6. The single sideband signal is amplified by EDFA3 to compensate the insertion loss of SSBM and then is intensity modulated into a narrow-width 2.0ns optical pulse by EOM2 which is driven by an electric pulse from CH3. After being amplified by EDFA4 to 3.1W, the optical pulse regard as pump2 is counter-propagated with pump1 into the slow principle axis of PMF through PBS2.

Fig. 6 Optical spectrum of the single sideband modulated light.

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A tunable laser with a resolution of 0.1 pm is used as the probe wave. The output is intensity modulated into an optical pulse of 50ns by EOM3 which is driven by an electric pulse from CH3 and amplified by EDFA5 to 0.39W. The probe pulse is launched into fast axis of PMF through an optical circulator (C1) and PBS2 to detect the PS-BDG. Finally, a tunable fiber Bragg grating with a bandwidth of 0.12nm is used to filter off the reflection signal that is detected by PD2.

5. Experimental results

In the experiment, the distributed BDG reflection spectra of PMF in Fig. 7(a) are firstly measured by setting pump1, pump2 and probe pulse to 200ns, 2ns and 4ns respectively. Based on Ref [18, 60], the central frequency of BDG reflection spectrum is named birefringence-induced frequency shift and can be expressed as:

Δ ν_{B ire} = \frac{Δ n ν}{n_{g}}

where

Δ n

is the birefringence of the PMF,

n_{g}

is the group refractive index of PMF and

ν

is the frequency of probe wave. It can be seen that the birefringence-induced frequency shift, which is calculated from Fig. 7(a) by Gaussian function fitting method, is proportional to the local birefringence of the PMF under test. As a result, the relationship between the birefringence-induced frequency shift and the local birefringence is shown in Fig. 7(b). It is worth mentioning that the non-uniform birefringence may cause the BDG spectrum broadening or multiple-peak spectra [21, 22]. Therefore, to avoid the spectrum distortion, a section fiber in the red line area in Fig. 7(b) with the relatively uniform birefringence of

Δ n ~ 5.854 \times 10^{- 4}

, is selected to create the PS-BDG.

Fig. 7 (a) Measured distributed BDG reflection spectra and (b) the distributed Birefringence-induced frequency shift and local birefringence of PMF.

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When setting the phase shift $Δ φ =0$ , the temporal evolution of the BDG reflection signal is shown in Fig. 8(a). Because of the existence of the acoustic phonons lifetime, the intensity of this BDG is decay over time as well as its reflection signal. When setting the phase shift $Δ φ =1 .0π$ , the temporal evolution of the reflection signal is depicted in Fig. 8(b), which has the feature of one-peak spectra at 42~45ns and a notch between two reflection peaks after 45ns. It can be clearly seen that these evolution are consistent with the character of the transient PS-BDG spectra, which are simulated in section 3.1. Note that the slightly asymmetry of two reflection peaks and the shallow notch shown in Fig. 8(b) in case of $Δ φ =1 .0π$ may be induced by the following reasons: 1) the inequality-intensity between BDG₁ and BDG₂; 2) the phase fluctuation; 3) the off-center position of the phase-shifted point. Figure 8(c) is corresponding to the phase shift $Δ φ =0 .93π$ , and it shows that the intensity of low-frequency side is higher than that of high-frequency side, while opposite result appears in Fig. 8(d) corresponding to the phase shift $Δ φ =1 .13π$ . Figure 8(e) shows the time integral reflection spectra of the above-mentioned PS-BDGs. The time integral BDG spectrum without phase shift (black line) is like a one-peak Gaussian profile, while the PS-BDG spectra show a two-peak profile with a notch frequency. The notch frequency of PS-BDG can also be tuned by changing the phase shift $Δ φ$ , where for $Δ φ =0 .93π$ (red line) the notch frequency is higher than that of $Δ φ =1 .0π$ (blue line) and for $Δ φ =1 .13π$ (green line) the notch frequency is lower than that of $Δ φ =1 .0π$ . The transient reflection spectra of different phase shifts at time of 47ns in Fig. 8(f) show more deeper notches compared with the integral reflection spectra, which is consistent with the simulation results in section 3.1.

Fig. 8 Measured temporal evolution BDG reflection signal in the uniform birefringence section of PMF with the phase-shift (a) $Δ φ =0$ , (b) $Δ φ =π$ , (c) $Δ φ =0 .93π$ , (d) $Δ φ =1 .13π$ . (e) Time integral reflection spectra and (f) the reflection spectra at time of 47ns.

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6. Conclusions and discussions

In this work, we have proposed two types of PS-BDGs: transient PS-BDG and enhanced PS-BDG. A novel transient PS-BDG was created when an optical pump1 pulse with two phase-modulated segments interfere with a narrow-width optical pump2 pulse based on a SBS process in slow axis of PMF, where the notch integral reflection spectrum with the 3-dB bandwidth of 354MHz is detected through a continuous probe wave in another orthogonal polarization axis. With the repetition rate of 250MHz, an enhanced PS-BDG with a deep notch depth was demonstrated. Finally, a proof-of-concept experiment is performed to verify the transient PS-BDG and it is obviously shown that the notch-type reflection spectra are appeared after time 4.7ns and the notch frequency can be tuned by changing the phase shift. The proposed PS-BDGs have many intriguing potential applications in the microwave photonics, all-optical signal processing and radio-over-fiber networks.

To reduce the pump power of PS-BDG, several kinds of functional optical fiber can be used. Due to its larger refractive index contrast, photonic crystal fibers (PCFs) [61, 62] with a small core area can have strong confinement of both optical and acoustic modes, which will enhance the interaction between photons and acoustic phonons, equivalently increasing the pumps power density of SBS. Since chalcogenide glasses have high third-order nonlinearity, for example, As₂S₃-based [63] or As₂Se₃-based [63–66] chalcogenide photonic crystal fiber with small effective mode areas, their Brillouin gains can reach two orders of magnitude larger than that of standard silica single-mode fiber [67]. Furthermore, by using these highly nonlinear materials to reduce the length of SBS medium, on-chip SBS [68–71] have been built on As₂S₃ platform which indicates that the fabrication of the low-power on-chip PS-BDG can be predicted.

Acknowledgments

The authors would like to acknowledge the financial support from the 863 Program of China (2014AA110401); National Key Technology Research and Development Program of the Ministry of Science and Technology of China (2014BAG05B07); National Key Scientific Instrument and Equipment Development Project of China (2013YQ040815), NSF of China (61575052 and 61308004); Foundation for Talents Returning from Overseas of Harbin of China (2013RFLXJ013); Scientific Research Fund of Heilongjiang Provincial Education Department of China (2531093).

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Pump1 power	P₁	0.4W
Pump2 power	P₂	30W
Probe power(CW)	P₃	10mW
Pump1 width (total)	t₁	2ns
Pump2 width	t₂	100ps
PMF length	L	40cm
Brillouin gain line-width	Γ_B/2π	30MHz
Brillouin gain factor	g_B	2.5 × 10⁻¹¹m/W
Phonon lifetime	τ _p	5.3ns
Effective Area	A_eff	50μm²
Refractive index of slow (x) axis	n_x	1.4686
Refractive index of fast (y) axis	n_y	1.4683

Phase-shifted Brillouin dynamic gratings using single pump phase-modulation: proof of concept

Abstract

1. Introduction

2. Principle and simulation model for PS-BDG

3. Simulation results and discussions

3.1 Transient PS-BDG

3.2. Enhanced PS-BDG

4. Experimental setup

5. Experimental results

6. Conclusions and discussions

Acknowledgments

References and links

Cited By

Figures (8)

Tables (1)

Equations (8)

Optics Express