Based on the evanescent-field coupling between the cladding modes of two adjacent and parallel all-fiber acousto-optic tunable filters, tunable broadband light coupling with relatively uniform insertion loss of trapping spectrum was achieved. In the experiments, a wide spectral tuning range from 1490 nm to 1610 nm, covering the whole C- and L-band and parts of S-bands, was demonstrated with a wavelength tunability slope of −0.72 nm/kHz. The insertion loss of the trapping spectrum was uniform (around −5.0 dB, which can be improved with a longer evanescent-field coupling length) within the whole tuning spectral range. Such a light coupling structure would be useful in tunable broadband light coupler and broadband optical fiber add/drop multiplexer for applications in coarse wavelength division multiplexing systems.
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All-fiber acousto-optic tunable filter (AOTF) has attracted much attention since the first report on the all-fiber acousto-optic frequency shifter by Kim et al.  in 1986. Because it has the properties of tunable passband isolation [2, 3], wide tunability of resonant wavelength [4, 5], relatively fast tuning speed [6,7] and low insertion loss , it can be used as the band-rejection filter [9, 10], the band-pass filter [11, 12], the gain flatting of erbium-doped fiber amplifier (EDFA) [13, 14], and to control slow and fast light in optical fiber [15, 16], and so on.
Besides the applications mentioned above, we reported a tunable add/drop channel coupler based on an AOTF and a tapered fiber . This light coupler is of relatively fast tunability, but the insertion loss is inherently not uniform at different operating wavelengths, and the transmission and the trapping spectra are in general not complementary with respect to each other when the operating wavelength deviates from the specially designed one. This is because the structural parameters of the AOTF and the tapered fiber are not the same, therefore, the propagation constants of the cladding modes in the AOTF and the tapered fiber are mismatched at wavelengths other than the specially designed one . We noticed that light coupling can also be realized by a pair of identical long period fiber gratings (LPFGs), in which light is transferred from the transmission fiber to the trapping fiber through the evanescent-field coupling between their cladding modes [19–22]. With the same diameter of the transmission and trapping fibers, the propagation constants of two cladding modes could be the same at any wavelength, and the above problem of propagation constant mismatch can be solved [18, 23]. The most recent tunable broadband light coupler based on such structure modified the central wavelength by two divided voltage-controllable coil heaters to provide the appropriate temperature distribution along the two parallel LPFGs . The insertion loss of the trapping spectrum was almost the same within the tuning spectral range, but the wavelength tuning is a relatively slow process. Since a pair of AOTFs could offer similar function as two parallel LPFGs and is of relatively fast tunability, it is possible to realize reasonably fast responding tunable broadband add/drop channel coupler with a relatively uniform insertion loss of trapping spectrum.
In this paper, a tunable broadband light coupler consisting of two adjacent and parallel all-fiber AOTFs was fabricated, and its central wavelength and passband isolations could be controlled respectively by tuning the frequency and power of the radio frequency (RF) driving signals. With complementary transmission and trapping spectra, the central wavelength tunability slope was measured to be −0.72 nm/kHz with a tuning spectral range from 1490 nm to 1610 nm, covering the whole C-band and L-band and parts of S-bands. More over, a relatively uniform insertion loss of the trapping spectrum was achieved within the whole tuning spectral range. This light coupling structure can be employed as a tunable broadband light coupler or optical fiber add/drop multiplexer (ADM) in coarse wavelength division multiplexing (CWDM) systems, which is one of the most important components to enhance the efficiency and flexibility of the optical fiber communication network.
2. Structure configuration and operating principle
It is known that the all-fiber AOTF is composed of an acoustic wave generation system and an unjacketed single mode fiber (SMF). When the acoustic wave propagates along the unjacketed SMF, a periodic modulation of the refractive index is produced with a period of hundreds of micrometers in the core of the unjacketed SMF. Such a refractive index modulation would induce a mode-coupling between the core fundamental mode (LP01) and the co-propagation cladding modes (LP1u) when the phase matching condition 
The configurational light coupler composed of two parallel AOTFs (AOTF1 and AOTF2) is shown in Fig. 1. The two ends of the AOTF1 are named as Port1 and Port2, while Port3 and Port4 are the two ends of AOTF2. When light from an unpolarized broadband light source is launched into the Port1 of AOTF1 in the transmission fiber, the AOTF1 couples the light from the core fundamental mode (LP01) to the co-propagation cladding mode (LP1u) of the transmission fiber, which will excite the cladding mode of the trapping fiber through the evanescent-field coupling between the two optical fibers. The excited cladding mode in AOTF2 will be coupled to the core fundamental mode of the tapping fiber and lead out from Port3. Therefore, the non-resonant and resonant lights can be separated and lead to the outputs of the transmission fiber (Port2) and the trapping fiber (Port3), respectively.
The transmission spectrum (Port2) and the trapping spectrum (Port3) can be expressed as 8], n0 is the core refractive index of SMF, λ is the central wavelength of the two AOTFs, Δn(x,y) = n0(1 + χ)(2π/Λ)A0y is the refractive index modulation caused by the acoustic wave with χ = −0.22 being the photoelastic coefficient of the fiber and A0 being the acoustic wave amplitude , ψ1(x, y) and ψ2(x, y) are the field distribution of the LP01 mode and the LP1μ mode, respectively. δ is the phase mismatching given by δ = 2π(1/LB − 1/Λ) with LB being the beat length between the two modes and Λ being the acoustic wavelength in the two AOTFs, LAO = LAO1 = LAO2 is the acousto-optic interaction length of the two AOTFs, C and LC are the evanescent-field coupling coefficient and coupling length, respectively, between the two cladding modes (LP1μ) of the two AOTFs. It is seen that the output spectrum of the transmission fiber (Port2) would show the band-rejection characteristics and that of the trapping fiber (Port3) would show the band-pass characteristics. Furthermore, the output spectra of the two fibers are complementary with respect to each other when the two AOTFs (AOTF1 and AOTF2) have the same spectral property.
One also notes that such an AOTF pair can work as an add/drop channel coupler with relatively uniform insertion loss within a broad tunable trapping spectral range. With a fixed evanescent-field coupling length LC and coupling coefficient C, the insertion loss of the trapping spectrum TPort3 is mainly determined by the coupling coefficient κ, which is dependent on not only the spatial overlap between the LP01 mode and the LP1μ mode but also the core refractive modulation Δn. Since Δn is proportional to the amplitude A0 of the acoustic wave, this parameter is dynamically adjustable according to the requirement in the AOTF pairs. Thus, it is possible to realize a relatively fast responding tunable light coupler of uniform insertion loss within the trapping spectrum with a pair of AOTFs. At the same time, the grating period Λ of the two AOTFs can be adjusted by tuning the frequency f of the driving RF signal, so the resonant wavelength λ of the light coupler can be conveniently adjusted.
3. Experimental results and discussions
In the experiments, the structure of each AOTF in Fig. 1 was the same as that in . An axial mode piezoelectric transducer (PZT) with a resonant frequency f = 1.0 MHz was attached to a cone acoustic transducer and its other side was attached to a steel plate as a mount. The unjacketed SMF, with a core radius ρco = 4.5 μm and a cladding radius ρcl = 62.5 μm, had a step-index of Δ = 0.32%. The outer diameter of the SMF was etched down to 45 μm by the hydrofluoric acid to adjust the central wavelength based on the phase matching condition and to enhance the overlap between the acoustic and the optical waves, and therefore, to increase the acousto-optic coupling efficiency of the AOTF. The length of the etched region was 100 mm. Two AOTFs (AOTF1 and AOTF2) were placed in parallel and appressed to each other in such a way that an evanescent-field coupling region of a length LC = 50 mm was formed, as shown in Fig. 1. The structure was supported by a piece of MgF2 substrate with a lower refractive index of n = 1.37. To increase the evanescent-field coupling efficiency between the cladding modes of two adjacent optical fibers, the evanescent-field coupling region was dipped into a refractive-index-matched liquid (n = 1.452) , where the acoustic waves of the two AOTFs were absorbed and therefore the acousto-optic interaction lengths LAO1 and LAO2 were limited to LAO1 = LAO2 = 50 mm.
To realize the light coupling between the two parallel all-fiber AOTFs, controlling the structure parameters of the two AOTFs is one of the key issues. The passband isolation, the central wavelength and the 3-dB bandwidth should be identical or at least very close to each other. The AOTF1 and AOTF2 were driven by two independent RF signals with the same driving frequency f = 0.9795 MHz but different driving powers P = 8 dBm and 9 dBm, respectively. This is because the two AOTFs are of slightly different acousto-optic coupling efficiency in the case with the same RF driving frequency. Based on the relationship between the acoustic wavelength Λ in fiber and the RF driving frequency f[9, 26], the grating period induced by the acoustic wave in the two AOTFs was calculated to be Λ = 644.6 μm. Figure 2 shows the transmission spectra of the AOTF1 (black curve) and AOTF2 (red dash-dotted curve). The passband isolation, the central wavelength and the 3-dB bandwidth were about T = −11.5 dB (93%), λ = 1550 nm and Δλ = 16 nm, respectively. One sees that the transmission spectra of the two AOTFs are nearly the same, which provides a good base for efficient light coupling.
In the further light coupling experiments with the configuration shown in Fig. 1, the two AOTFs were also driven by two independent RF driving signals with the same driving frequency f = 0.9795 MHz but different driving powers P = 8 dBm and 9 dBm, respectively. When light from an unpolarized broadband light source was coupled into Port1 of the transmission fiber, the output spectra from Port2 and Port3 were measured by an optical spectrum analyzer (OSA). Figure 3(a) shows the corresponding output spectra when the RF signals are of a driving frequency f = 0.9795 MHz. The black curve denotes the transmission spectrum from Port2, and it shows a band-rejection characteristics with a passband isolation of about TPort2 = −11.5 dB (93%) at the central wavelength λ = 1550 nm due to the mode-coupling between the LP01 mode and the LP11 mode. The red curve denotes the trapping spectrum output from Port3, showing a band-pass characteristics with an insertion loss of about TPort3 = −5.0 dB (32%). The two measured spectra are complementary with respect to each other. Meanwhile, by coupling light into Port3, the output spectra from Port4 and Port1 were also measured and depicted as the blue and green curves in Fig. 3(b), respectively. One sees that the red curve in Fig. 3(a) coincides with the green one in Fig. 3(b), which means that the signal adding and dropping are of the same insertion loss.
The insertion loss of trapping spectrum shown in Fig. 3 is too large for practical applications. From the measurement results shown in Fig. 2, one knows that the acousto-optic coupling ef-ficiencies of two AOTFs are 93%. This means that the evanescent-field coupling efficiency between the cladding modes of two parallel fibers is only 37%. Theoretically, the overall insertion loss of trapping spectrum can be improved by optimizing the interaction lengthes so that both κLAO = π/2 and CLC = π/2 are satisfied. There are also other facts that may lead to a large insertion loss, such as the roughness of the fiber surface and the fluctuations of fiber diameters, and the distance between two parallel fibers in the configuration.
Based on the phase matching condition  expressed by Eq. (1), the central wavelength of the transmission and trapping spectra from Port2 and Port3 can be controlled through the frequency of the RF driving signals applied to the two AOTFs. As a proof of principle, Fig. 4 depicts the experimental results showing the central wavelength tunability of the light coupling configuration, where the central wavelength of the transmission and trapping spectra from Port2 and Port3 was selectively set at λ = 1490 nm, 1510 nm, 1530 nm, 1550 nm, 1570 nm, 1590 nm and 1610 nm when the RF driving frequency applied to the two AOTFs was set to be f = 1.066 MHz, 1.036 MHz, 1.008 MHz, 0.9795 MHz, 0.9535 MHz, 0.9270 MHz and 0.9001 MHz, respectively. The corresponding grating period induced by the acoustic wave was calculated to be about Λ = 617.9 μm, 626.7 μm, 635.4 μm, 644.6 μm, 653.3 μm, 662.6 μm and 672.4 μm, respectively. One sees that a broad central wavelength tuning range from 1490 nm to 1610 nm, which covers the whole C- and L-band and parts of S-bands, is obtained. With increasing frequency of the RF driving signal, the central wavelength shifts toward short wavelength with a spectral tunability slope of −0.72 nm/kHz, as shown in Fig. 4(b). Moreover, the transmission and trapping spectra are complementary with respect to each other and the insertion loss of the trapping spectra was measured to be around −5.0 dB within the whole tunable spectral range, as shown in Fig. 4(a).
The response time of the light coupler is mainly determined by the transit time of the acoustic wave traveling through the acousto-optic interaction region of the AOTF. In order to measure the response time of the light coupler, we coupled a laser beam at λ = 1550 nm into Port1 and monitoring the intensity variation output from Port2 when one switched on and off the driving RF signal. The result is shown in Fig. 5, from which the response time of the light coupler was measured to be τ = 83 μs, which is close to the calculated response time of τ = 79 μs.
In conclusion, a tunable broadband light coupler consisting of two parallel all-fiber AOTFs was fabricated, in which the cladding modes of the two parallel AOTFs are coupled through the evanescent field. The light coupler offers a wide spectral tuning range from 1490 nm to 1610 nm covering the whole C- and L-band and parts of the S-bands, a nearly uniform insertion loss within the whole tuning spectral range of the trapping spectrum, a complementary transmission and trapping spectra, and no back reflection. It can be used as a tunable broadband light coupler or an optical fiber ADM for applications in CWDM systems.
This work is financially supported by the 973 Programs ( 2013CB328702, 2013CB632703 and 2010CB934101), the CNKBRSF ( 2011CB922003), the NSFC ( 11174153), the 111 Project ( B07013), the Natural Science Foundation of Tianjin ( 12JCQNJC00900) and the International S&T Cooperation Program of China ( 2011DFA52870).
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