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Abstract
An acousto-optic reconfigurable filter (AORF) is proposed and demonstrated based on vector mode fusion in dispersion-compensating fiber (DCF). With multiple acoustic driving frequencies, the resonance peaks of different vector modes in the same scalar mode group can be effectively fused into a single peak, which is utilized to obtain arbitrary reconfiguration of the proposed filter. In the experiment, the bandwidth of the AORF can be electrically tuned from 5 nm to 18 nm with superposition of different driving frequencies. The multi-wavelength filtering is further demonstrated by increasing the interval of the multiple driving frequencies. The bandpass/band-rejection can also be electrically reconfigured by setting the combination of driving frequencies. The proposed AORF gains the feature of reconfigurable filtering types, fast and wide tunability, and zero frequency shift, which is advantageous for high-speed optical communication networks, tunable lasers, fast optical spectrum analyzing and microwave photonics signal processing.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Reconfigurable optical filters have been widely applied in optoelectronic technology fields such as optical communication [1], microwave photonics signal processing [2], laser wavelength tuning [3], optical spectrum analyzing [4], and hyperspectral imaging [5], due to the flexibility of selecting optical spectrum. The rapid development of high-speed optical communication and optoelectronic signal processing has put forward more requirements for the reconfiguration ability of optical filters. In terms of bandwidth reconfiguration of optical filters, wavelength division multiplexing (WDM) optical communication requires wide tuning of the filter bandwidth to achieve flexible channel switching. At present, WDM systems are divided into three categories: wide wavelength division multiplexing (WWDM), coarse wavelength division multiplexing (CWDM), and dense wavelength division multiplexing (DWDM). The typical single channel bandwidth of WWDM is 50 nm, while the typical single channel bandwidth of CWDM is 20 nm. The typical single channel bandwidth of DWDM includes 12.5 GHz, 25 GHz, 50 GHz, and 100 GHz. In order to achieve compatibility and device sharing among different communication systems, as well as flexible selection of multiple channels within the same communication system, the optical filter in the WDM system is required to achieve bandwidth reconfiguration. In terms of filtering reconfiguration for single/multiple wavelengths, WDM optical communication systems require tunable filters with reconfigurable number of filtering peaks to achieve flexible selection of single/multiple channels. The gain equalization and dispersion compensation should also be ensured among multiple channels to reduce the bit error rate (BER) [6,7]. At the same time, the number of laser wavelengths for WDM communication also needs to match the number of WDM channels. By utilizing a multi-wavelength reconfigurable filter as the wavelength selector in the laser cavity, an arbitrary tunable multi-wavelength laser is promising [8], which can further improve the flexibility of the WDM communication system. In terms of band-rejection and bandpass feature reconfiguration, microwave photonics requires selective transmission or removal of specific frequency bands of microwave signals through bandpass or band-rejection filtering of optical signals [9]. Therefore, reconfiguration of the optical filter bandwidth, wavelength number and bandpass/band-rejection will help improve the flexibility of signal transmission and processing in optical communication, microwave photonics and other fields.
The in-fiber acousto-optic tunable filter (AOTF) utilizes the acoustic wave to generate dynamic gratings in optical fiber. By tuning the acoustic frequency, the resonant wavelength of the AOTF can be fast and widely tuned [10–12], which can be further utilized to construct the acousto-optic reconfigurable filter (AORF) by superposition of the acoustic frequency. The existing in-fiber AOTF mainly concerns the wavelength tuning within the theoretical framework of scalar mode coupling in fiber. In terms of reconfiguration of filtering types, the main methods include mode extraction, acoustic frequency multiplexing, and dispersion control, to achieve the reconfiguration of bandpass/band-rejection, wavelength number, and bandwidth of the in-fiber AOTF [13–17]. The reconfiguration of bandpass/band-rejection based on scalar mode theory requires the separation of the high-order mode and fundamental mode in the AOTF, and the separation structure mainly includes two types: the fiber core mode blocker and high-order mode extractor. Although the high-order mode extractor can obtain the bandpass and band-rejection output ports simultaneously, the bandpass port typically has an optical frequency shift, which will limit its application in optical communication, microwave photonics signal processing and other fields. Furthermore, the in-fiber AOTF based on scalar mode coupling cannot achieve resonance peak fusion of the same scalar mode by acoustic frequency superposition [18], resulting that it is difficult to achieve dynamic reconfiguration of the filter bandwidth, and the filtering type also cannot be fast switched between band-rejection and bandpass by acoustic tuning.
In 2018, we proposed an acousto-optic tunable bandpass filter (AOTBF) based on the vector mode coupling theory [19]. This scheme utilizes the refractive index non-degeneracy of vector modes to split the single resonance peak of the scalar mode into multiple resonance peaks of vector modes. Based on the polarization dependence of vector mode coupling, the polarization state of the fundamental mode in the AOTBF can be rotated. Due to the feature of none frequency shift of the fundamental mode, combination of the polarizer and analyzer can achieve the frequency shift free AOTBF. It is convenient to switch between band-rejection filtering and bandpass filtering, by rotating the polarization orientation of the analyzer. In 2019, we further applied this scheme to dispersion compensating fiber to form a dual-wavelength AOTBF with a filtering bandwidth of less than 1 nm [20].
In this work, an acousto-optic reconfigurable filter (AORF) is proposed based on vector mode fusion in dispersion-compensating fiber. It is proposed and demonstrated that the resonance peaks of different vector modes in the same scalar mode group can be effectively fused into a single peak, by superposition of multiple acoustic frequencies. In the experiment, the 3-dB bandwidth of the AORF can be electrically tuned from 5 nm to 18 nm with superposition of 4 different driving frequencies. The multi-wavelength filtering is demonstrated by increasing the interval of the multiple driving frequencies. The band-rejection filtering can be electrically tuned in the superimposed bandpass spectrum by removing the specific driving frequency. In principle, the resonance wavelength and transmission, bandwidth, resonance peak number and bandpass/band-rejection feature can be fast tuned and programmed, by electrically controlling the frequency and amplitude of each radio frequency (RF) driving signal. The tuning speed is mainly determined by the acoustic wave propagation time along the acousto-optic interaction (AOI) region, which is faster than 100 µs in the experimental configuration. The proposed AORF gains the feature of reconfigurable filtering types, fast and wide tunability, and zero frequency shift, which is beneficial for reconfigurable optical communication networks, fast tunable lasers, microwave photonic signal processing and fast optical spectrum analyzing.
2. Principle of operation
The schematic diagram of the proposed in-fiber acousto-optic reconfigurable filter is shown in Fig. 1(a). Its core component is the acoustically induced fiber grating (AIFG), which consists of the piezoelectric transducer (PZT) and cladding etched dispersion compensating fiber (DCF). The PZT is utilized to generate and converge the acoustic wave to the DCF, and the acoustic frequency can be electrically tuned by tuning the RF driving frequency. In the AIFG structure, the acoustic flexural wave (AFW) vibrating in the y direction propagates along the DCF in the z direction, and induces dynamic micro-bending gratings with refractive index perturbation of $\Delta n = {n_0}(1 + \chi ){K^2}{u_0}y$, where n0 is the refractive index of silica, χ=−0.22 is the elasto-optic coefficient of silica, K is the wave vector of the AFW, u0 is the amplitude of the AFW, y is the coordinate of the fiber cross-section, and y = 0 represents the cross-section center [21]. The AIFG can induce coupling between the fundamental mode (LP01) and the high-order mode (LP11) in the circularly symmetric step-index fiber. The LP01 scalar mode is composed of two degenerated vector modes ($\textrm{HE}_{11}^x$ and $\textrm{HE}_{11}^y$), and the LP11 scalar mode is composed of four vector modes, including TE01, TM01 and two degenerated HE21 modes ($\textrm{HE}_{21}^{\textrm{even}}$ and $\textrm{HE}_{21}^{\textrm{odd}}$) [22].
Fig. 1. (a) Sketch map of the AORF based on the acoustically induced fiber grating. DCF: dispersion compensating fiber. RF: radio frequency signal. PZT: piezoelectric transducer. OSA: optical spectrum analyzer. (b) Polarization rotation induced by the polarization dependent vector mode coupling. Pin: input polarization state through the input polarizer. Pout: output polarization state after the acousto-optic interaction region.
The coupling coefficient between the fundamental vector mode f (f=$\textrm{HE}_{11}^x$, $\textrm{HE}_{11}^y$) and high-order vector mode h (h = TE01, $\textrm{HE}_{21}^{\textrm{even/odd}}$, TM01) could be written as [23]
The phase-matching condition of AIFG satisfy λ=ΛΔn, where λ is the resonant wavelength, Δn is the effective refractive index difference between the fundamental mode and high-order mode [21]. $\Lambda = \sqrt {\mathrm{\pi }RC/f} $ is the period of the AFW propagating along the cladding-etched DCF, where R is the fiber cladding radius, C = 5760 m/s is the speed of the phase velocity of the extensional acoustic wave in silica, and f is the acoustic frequency. Therefore, one can dynamically control the resonance wavelength of the AIFG by tuning the acoustic frequency. As the effective refractive indexes of the TE01, HE21, and TM01 modes are slightly different, their resonant wavelengths are separated based on the phase-matching condition. Thus, the coupling to vector modes of the LP11 group could be controlled independently by controlling the polarization state and wavelength of the input fundamental mode.
When only the fundamental mode is poured into the AIFG, the relationships between the input and output fundamental mode polarization states, at the resonant wavelengths of the TE01, TM01 and HE21 modes, respectively, could be expressed in the Jones matrix forms as
Assuming that the input fundamental mode of the AIFG is linearly polarized with the polarization angle of φin to the x axis, we utilize an output polarization analyzer with the orthogonal polarization direction of the input polarizer, as shown in Fig. 1(b). In such a configuration, the fundamental mode intensity transmissions through the analyzer at the resonant wavelength of the AIFG are denoted by T⊥. For the TE01/TM01/HE21 vector mode coupling, the resonance intensity transmissions could be expressed as
In the meantime, the fundamental mode at the non-resonant wavelength can not pass through the analyzer, so the output port shows bandpass characteristics at the resonance wavelengths of TE01/TM01 vector modes with the peak transmissions described by Eqs. (5) and (6), respectively. It is worth noting that the resonance wavelength of the HE21 vector mode cannot show the band-pass peak in the output port, as the resonance transmission equals 0, because the coupling to the HE21 mode cannot induce the polarization rotation. In principle, the bandpass resonance transmission of the output port for the TE01/TM01 vector mode could be tuned to 100% (${T_{ \bot ,\textrm{TE}}} = {T_{ \bot ,\textrm{TM}}}\textrm{ = }1$), under the conditions of φin=π/4 and κfhLAO=π.
To obtain reconfiguration of the proposed acousto-optic tunable bandpass filter, multiple acoustic waves with different frequencies need to be superposed in the acousto-optic interaction. In particular, multiple resonance peaks need to be fused to a single peak, in order to electrically tune the filter bandwidth by multiple acoustic frequencies. Figure 2 shows the peak fusion in two different situations. When the fused peak comes from two different vector modes, i.e. TM01 and TE01 modes in the proposed AORF, the acoustic frequencies are denoted by f1 and f2, respectively, as shown in Fig. 2(a). The optical frequency of the AORF input light is denoted by f0. In the acousto-optic interaction region, when the input light is coupled to the TM01 mode, the light will be down frequency shifted to f0-f1, as shown in Fig. 2(b). The light in the converted TM01 mode can be further coupled back to the HE11 fundamental mode with up frequency shift of f1, such as in the over-coupling state. Thus, the coupled-back light in the HE11 mode recovers its original frequency of f0, which means that the coupling between the HE11 mode and the TM01 mode will not shift the optical frequency of the HE11 mode. Similarly, the coupling between the HE11 mode and the TE01 mode will not shift the optical frequency of the HE11 mode. Thus, when the resonance wavelength of the TE01 mode is tuned close to that of the TM01 mode, the two resonance peaks can be effectively fused.
Fig. 2. Spectral fusion of the resonance peaks of vector modes. (a) Spectral fusion and (b) frequency shift for resonance peak fusion of different vector modes. (c) Spectral fusion and (d) frequency shift for resonance peak fusion of the same vector mode.
When the fused peak comes from the same vector mode, such as the TM01 mode, one can utilize two different acoustic frequencies, which are denoted by f1 and f2 respectively, to form two different resonance peaks, as shown in Fig. 2(c). In the acousto-optic interaction region, when the input light is coupled to the TM01 mode by the AIFG with the acoustic frequency of f1, the light will be down frequency shifted to f0-f1, as denoted by the solid red curve in Fig. 2(d). However, the light in the converted TM01 mode can be further coupled back to the HE11 fundamental mode with two different routes. The light frequency will be upshifted back to f0, with over coupling of the AIFG with the original acoustic frequency of f1. In the meantime, the light frequency can also be upshifted to another value of f0-(f1-f2) by the AIFG with the acoustic frequency of f2. Similarly, the input light can also be firstly coupled to the TM01 mode by the AIFG with the acoustic frequency of f2, as denoted by the solid green curve in Fig. 2(d). Then the coupled-back light in the HE11 mode can either recover the frequency of f0, or have up frequency shift to f0 + (f1-f2). In the further crossing coupling process between the two AIFGs with acoustic frequencies of f1 and f2, the HE11 mode can obtain a series of frequencies of f0, f0 ± (f1-f2), f0 ± 2(f1-f2) … f0 ± n(f1-f2), where n is an integer, which will break the peak fusion condition. Therefore, the resonance peak fusion with zero frequency shift can only be obtained by coupling the fundamental mode to two different high-order vector modes.
As the effective refractive indexes of the TE01 and TM01 modes are slightly different, their resonant wavelengths are commonly separated in the nm order, when the AIFG is driven by a single acoustic frequency in the ordinary DCF. To obtain the single wavelength filtering based on the vector mode coupling, one can utilize the spectral fusion of the resonance peaks of TE01/TM01 vector modes, with the 3 dB bandwidth of each peak tuned to approach the resonance peak interval, as shown in Fig. 3(a). The filtering 3-dB bandwidth Δλ of each vector mode is related to the AOI length and the mode dispersion of the utilized fiber, which could be expressed as [17]
Fig. 3. Bandwidth tuning strategy of the AORF based on vector mode fusion. (a) Single wavelength filtering based on the vector mode fusion with a single acoustic frequency. (b) Broadband vector mode fusion with multiple acoustic frequencies.
3. Experimental results and discussions
In the experiment to demonstrate the proposed AORF, the diameter of the DCF with the dispersion parameter of −160 ps/nm/km @1550 nm, is etched to 35 µm to improve the acousto-optic coupling efficiency. By immersing the end of the etched fiber into the refractive index matching liquid (n = 1.456) as the acoustic absorber, the AOI length is controlled to be 5 cm, which is suitable for peak fusion between the TE01 and TM01 vector modes. To satisfy the condition of maximal coupling efficiency, the direction of the input polarizer should be set to 45 degrees, and the output analyzer should be set to 135 degrees. In the experiment, two fiber polarization controllers (PCs) are inserted between the polarizer, AIFG and analyzer. When the PC is rotated, the rotation of the light polarization is equivalent to rotate the input polarizer or output analyzer, because we essentially just need to adjust the relative polarization relationship between the polarizer, AIFG and analyzer. Although it is not convenient to exactly tune the polarization state to a specific polarization angle, the directions of the two PCs can be changed continuously until the resonance-wavelength coupling efficiency of the output port reaches the maximal peak. This tuning process can be utilized to realize the optimization of the polarizer and analyzer directions.
The wavelength tunability of the constructed AORF can be realized by tuning the RF driving frequency, as shown in Fig. 4. The single-wavelength filtering is obtained by fusing the resonance peaks of the TE01 and TM01 vector modes. When the RF driving frequency is tuned from 874 kHz to 390 kHz, the center wavelength of the AORF can be tuned from 1520.1 nm to 1579.1 nm, with a tuning slope of –0.122 nm/kHz. The bandpass spectrum maintains a stable filtering shape with 3-dB bandwidth of about 5 nm in the tuning process, as shown in Fig. 4(a). In order to ensure the tuning accuracy of the filter, the resonant wavelength of the AORF is fine-tuned with a step of about 1 nm by fine-tuning the RF driving frequency with a step of about 8 kHz, as shown in Figs. 4(b) and 4(d). The wide and fine wavelength tunability established the basis for reconfiguring the bandwidth and filtering type of the AORF in a large wavelength range.
Fig. 4. Wavelength tunability of the constructed AORF. (a) Widely-tuned spectra by tuning RF driving frequencies. (b) Spectrum fine tuning. (c) and (d) Relationship between the resonance wavelength and the RF driving frequency.
The bandwidth reconfiguration of the AORF is obtained by superposition of the RF driving frequencies, as shown in Fig. 5. As a typical demonstration, four different driving frequencies of 600 kHz (f1), 562 kHz (f2), 528 kHz (f3), and 488 kHz (f4) are utilized, and the individual bandpass spectrum is firstly measured before superposition, as shown in Fig. 5(a). The resonance wavelength interval is about 5.5 nm, which is close to the 3-dB bandwidth of each resonance peak. The frequency superposition is then conducted, as shown in Fig. 5(b). Multiple driving frequencies in the experiment are generated by an arbitrary waveform generator, and the amplitude of each frequency can be tuned independently, to ensure nearly equal efficiencies of different resonance peaks. The green, blue, red and black curves denote the fused spectra by single, two, three and four RF frequencies, respectively, and the corresponding 3-dB bandwidth can be electrically reconfigured as 5 nm, 8 nm, 13 nm and 18 nm, respectively. Figure 5(c) shows another combination of reconfiguring the AORF with 3-dB bandwidth of 5 nm, 10 nm, 14 nm and 18 nm, respectively. It is worth noting that there exists a transmission fluctuation of about 1 dB in the reconfigured band. To decrease the fluctuation, one can choose to tune the resonance wavelength interval smaller. However, the reconfigured bandwidth will be smaller, accordingly. Under the condition of a limited quantity of the superposed driving frequencies, one needs to balance the performance of transmission fluctuation and bandwidth reconfiguration range. In the bandwidth reconfiguration process, the driving voltage of each RF frequency needs to be increased when the superposition number of the RF frequency is increased, because the amplitude response of the PZT will be decreased for each RF frequency. In order to increase the number of frequency superposition, it is necessary to further improve the acoustic conversion efficiency of the PZT. Using multiple PZTs to simultaneously drive the AIFG is also a candidate solution.
Fig. 5. Bandwidth reconfiguration of the constructed AORF. (a) The individual bandpass spectrum before superposition. (b) and (c) Bandwidth reconfiguration based on superposition of multiple RF driving frequencies.
Reconfiguration of filtering types is further explored. The comb filter type can be obtained by increasing the interval of the multiple driving frequencies, as shown in Fig. 6(a). With RF driving frequencies of 792 kHz (f1), 669 kHz (f2), 584 kHz (f3), and 497 kHz (f4), each resonance wavelength of the comb filter is 1528.3 nm, 1541.5 nm, 1551.7 nm and 1563.7 nm, respectively, with an average wavelength interval of 11.8 nm. Within the bandpass filtering span, band-rejection filter type can be obtained by removing specific driving frequency. With simultaneous frequency superposition of 600 kHz (f1), 562 kHz (f2), 528 kHz (f3), and 488 kHz (f4), the AORF shows characteristic of broadband bandpass filtering covering wavelength from 1548 nm to 1566 nm. With the driving frequency f3 removed, the filter can be reconfigured to show band-rejection filtering characteristic at the resonance wavelength of 1558 nm, as shown in Fig. 6(b). Similarly, the band-rejection filtering wavelength can be reconfigured to 1555 nm, when the removed frequency is electrically switched to f2, as shown in Fig. 6(c). In principle, the reconfiguration response time is mainly determined by the acoustic wave propagation time along the AOI region, which can be expressed as $\tau = {L_{\textrm{AO}}}/(2\sqrt {\mathrm{\pi }RCf} )$ [24]. With experimental parameters of LAO = 5 cm, R = 17.5 µm, C = 5760 m/s, and f = 600 kHz (typical value), the response time can be calculated as 57 µs.
Fig. 6. Filtering type reconfiguration of the constructed AORF. (a) The spectrum of the reconfigured comb filter. (b) and (c) The spectra of the reconfigured band-rejection filter within the bandpass span.
The narrowest bandwidth of the constructed AORF is mainly limited by the separation interval of the vector mode resonant wavelengths. In this work, the DCF is mainly used to realize narrow bandwidth of each vector mode under the condition of shorter fiber than traditional SMF. The vector mode resonance wavelength interval (about 4 nm) of the dispersion-compensating fiber (DCF) used in this work is also smaller than that of the single-mode fiber (SMF) used previously (about 18 nm) [19]. In order to make the fused peak bandwidth smaller, it is necessary to use specially designed fiber with smaller interval of vector mode resonance wavelengths. In the future, the optical fiber with large dispersion and small interval between vector mode resonant peaks will be explored to satisfy the requirements of narrower fused bandwidth. Currently, the quantity of reconstructed wavelengths is limited by the acoustic conversion efficiency of the PZT. To further enhance the acoustic-optic coupling efficiency, one can utilize thinner fiber to enlarge the refractive index modulation with the same RF driving power.
4. Conclusion
In conclusion, we propose and demonstrate an acousto-optic reconfigurable filter (AORF) based on vector mode fusion of the acoustically induced fiber grating (AIFG) in dispersion compensating fiber (DCF). The resonance peaks of different vector modes in the same scalar mode group can be effectively fused into a single peak with zero frequency shift. Based on superposition of multiple RF driving frequencies, the 3-dB bandwidth of the AORF can be electrically tuned from 5 nm to 18 nm. The AORF can be further reconfigured to a comb filter type by increasing the interval of the multiple driving frequencies. The AORF can also be reconfigured to a band-rejection type within the bandpass span, by removing specific driving frequency. The response time of reconfiguration can be faster than 100 µs in the experimental configuration. The proposed AORF gains the feature of reconfigurable filtering types, fast and wide tunability, and zero frequency shift, which is beneficial for the practical applications in WDM optical communication, tunable lasers, microwave photonics and spectroscopy.
Funding
National Natural Science Foundation of China (61935007, 61927818, 62075020, 61975022); Chongqing Natural Science Foundation of Innovative Research Groups (cstc2020jcyj-cxttX0005); National Science Fund for Distinguished Young Scholars (61825501).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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