1. Introduction

Among various all-fiber Mach-Zehnder interferometers (MZI) [1–3 ], cascaded long period fiber gratings (LPFGs) [4–7 ] gained advantage of simple structure because all components were integrated in a single fiber, and it was applicable to multichannel isolators and multi-channel filters for multi-wavelength fiber lasers [6–8 ]. However, it was hard to rapidly optimize the spectral characteristics like the resonance wavelength and passband position. Current methods mainly highlighted applying heat or strain to LPFG, and the tuning speed of such a structure was not satisfactory [9, 10]. It was well known that acousto-optic tunable filter (AOTF) was usually used as a substitute for LPFG to introduce the feature of fast tuning [11–15 ], and it was natural to design a MZI and a fast tunable multi-wavelength (MW) laser accordingly based on cascading AOTFs. Yet, to make the cascaded AOTFs at the same driving frequency and to make the resonance wavelength overlapped, two classic acoustic optic transducers were needed, which would make the structure complicated and increase its cost [16]. When a commercial single mode fiber (SMF) was used in such structure, there were also challenges from frequency shift between two interfering beams or absorption of the cladding mode from the glue which attached the acoustic transducer and fiber. In 2013, we proposed a tunable MZI made of SMF by cascading an AOTF and a tapered fiber (TF) [17]. The TF had to be tapered with a diameter down to 12 micrometers after etching the AOTF region, which made the structure very fragile and hard to assemble. Moreover, it was difficult to make the spectrum of each part overlapped well especially in volume production, which would introduce relatively large insertion loss at the center of spectrum. When the contrast ratio at the central wavelength was around 10 dB, the insertion loss was around 7 dB.

In this paper, an in-fiber tunable MZI was constructed by driving a sandwich-structured SMF with only one acoustic transducer, based on which a tunable MW ring laser was demonstrated. Dual-wavelength laser spaced by around 3.5 nm with each other could be tuned to cover a wavelength range from 1561.6 nm to 1568.9 nm, with a tuning range of 3.6 nm which nearly equaled the free spectral range (FSR) of the MZI. Theoretically, the response time could be as small as 370 μs. Under certain polarization state, the configuration also supported four-wavelength outputs. The proposed MZI gained advantages of simple structure for volume production, no frequency-shift between output and input ports, relatively small insertion loss at the center of the spectrum and fast tuning speed, which could be useful in practical applications.

2. MZI configuration

It is well known that AOTF can be applied as a LPFG with fast tuning rate, whose refractive index modulation is induced by micro-bending in the unjacketed SMF when flexural acoustic wave propagates along it. Mode coupling between the core fundamental mode ( ${\text{LP}}_{01}^{\text{co}}$) and the co-propagating cladding mode ( ${\text{LP}}_{1u}^{\text{cl}}$) occurs when the phase matching condition [18]

However, to build a tunable MZI with cascaded AOTFs in only one piece of SMF, it will encounter challenges. The biggest challenge lies in the fact that MZIs need propagating cladding mode to generate phase delay with respect to the core mode. If the two cascaded AOTFs are driven by two independent acoustic transducers, the cladding mode will be absorbed significantly by the glue which attaches the unjacketed fiber to the second acoustic transducer. With the two acoustic transducers located at the starting point and the ending point of the unjacketed area of SMF, respectively, the problem of absorption could be avoided but the frequency shift between two interfering beams is inevitable [11], which would bring about instability when MZI acts as a band pass filter in MW laser or even ruins its function as an multichannel isolator. In our previous work, a MZI based on an AOTF and a TF was presented. Because of its fragile structure, complicated procedure in fabrication, and relatively large insertion loss, it is not suitable in volume production.

To get a better solution for above problems, we introduced an unjacketed SMF with a sandwich-like structure as shown in Fig. 1(a), which was fabricated by one-step etching. The sandwich-like structure was prepared by etching SMF with hydrofluoric acid and a protecting layer, which was of larger density and would not blend with hydrofluoric. When the RF signal was applied to the acoustic transducer, the acoustic wave would propagate along the fiber and induce dynamic gratings. In the regions of L ₁ and L ₃, which were both of 28-μm diameter and 6-cm length, it would generate cascaded identical AOTFs at the same resonance wavelength, which will be helpful to reduce the insertion loss of the MZI at the center of its spectrum. In the region of L ₂ with D ₀ = 125 μm and L ₂=13 cm, the acoustic wave would also exist but the modulation of refractive index was too small to induce effective mode coupling, because of the smaller amplitude of the acoustic wave [12] and less overlap between LP₀₁ and LP₁₁ modes [19]. Furthermore, when the frequency of RF signal was tuned to form AOTF in the regions of L ₁ and L ₃ with a resonance wavelength around 1550 nm, the resonance wavelength in the region of L ₂ did not overlap with the functional spectrum region, which could be derived from Eq. (1). The unjacketed SMF in region L ₂ would provide the phase shift between ${\text{LP}}_{01}^{\text{co}}$ and ${\text{LP}}_{11}^{\text{cl}}$ modes in the MZI. Note that in L ₁ region, when the resonant LP₀₁ mode was converted to LP₁₁ mode, which would propagate through L ₂ region, the frequency of the resonance wavelength would be down-shifted f _a; when the LP₁₁ mode with down-shifted frequency reached the L ₃ region and was converted back to the LP₀₁ mode, the frequency would be up-shifted by f _a [11], which was of the same value as before. Eventually, there was no frequency shift between the two interfering beams at the output of the MZI. The evolution of the frequency shift of LP₀₁ and LP₁₁ modes is shown in Fig. 1(b).

 

Fig. 1 Configuration of in-fiber MZI based on a sandwich-like etched single mode fiber driven by one acoustic transducer. (a) Sandwich-like fiber driven by a single acoustic transducer. L ₁ and L ₃ regions were of the same diameter, which was smaller than that of L ₂ region. Effective refractive index modulation could be generated by acoustic wave only in L ₁ and L ₃ regions. (b) Mode and its frequency evolution in the region accordingly. f: frequency of optical wave. f _a: frequency of acoustic wave.

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After constructing the cascaded AOTFs, the tuning efficiency of the structure at different RF driving power was measured, as shown in Fig. 2(a). In the experiment, at a given driving frequency, for example, 0.945 MHz with the period of acoustic grating being 518 μm at L ₁ and L ₃ regions calculated from Λ = (πRC _ext/f _a)^1/2 [12], the mode transformation efficiencies of both AOTFs were increased simultaneously by increasing the driving power of acoustic transducer from 7 dBm to 13 dBm. When the RF power was 7 dBm, 10 dBm and 13 dBm, respectively, the isolation of the MZI transmission spectrum was tuned to −3.0 dB, −6.6 dB and −13.6 dB accordingly as shown by the solid curves in Fig. 2(a). The largest insertion loss with a driving power of 13 dBm was around 3 dB when the contrast ratio at the center wavelength was around 10 dB and the free spectral range (FSR) was measured as 3.5 nm, which was suitable for the filter of multi-wavelength lasers with channel spacing of hundreds of GHz. In Fig. 2(a), the spectrum of a single AOTF was also provided as black dotted curve, which was in accordance with the MZI spectra. With shorter L ₁ and L ₃, the spectrum could be broader [20]. With longer L ₂ region, smaller FSR could be achieved [6, 16].

 

Fig. 2 The spectral tunability of the MZI based on the cascaded AOTFs. (a) The spectra of the MZI at different RF driving powers (solid curves) and the spectrum of a single AOTF of L ₁ region (dotted curve). (b) The frequency tuning spectra of the MZI.

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The wavelength tuning range of the MZI was also measured. The spectrum could be tuned continuously when we adjusted the RF frequency. When the RF frequency was set to be 0.91 MHz, 0.93 MHz, 0.95 MHz, 0.97 MHz and 0.99 MHz, the center wavelength of the MZI transmission spectrum was tuned to 1628.5 nm, 1589.9 nm, 1550.1 nm, 1515.2 nm and 1482.0 nm, respectively, and the result is presented in Fig. 2(b). The average tuning slope was calculated to be −1.83 nm /kHz. From the relationship v = Λf _a, where v was the propagation speed of the acoustic wave in the fiber, it could be easily estimated that the response time of the tunning should be around 370 μs.

3. MW laser based on the constructed MZI

With this MZI, we built a tunable MW laser as shown in Fig. 3. EDFA was erbium doped fiber amplifier, which was used as gain medium and pump. It had a spontaneous emission spectrum from 1535 nm to 1575 nm. Unidirectional laser emission was insured by an isolator (ISO) to avoid spatial or spectral hole burning. PC was polarization controller, which was used to optimize the laser output. A 10% coupler was applied to output laser beam, which was connected to optical spectrum analyzer (OSA).

 

Fig. 3 Configuration of multi-wavelength laser based on the constructed MZI. EDFA: erbium doped fiber amplifier; ISO: isolator; PC: polarization controller; MZI: Mach-Zehnder interferometer that we built; OSA: optical spectrum analyzer.

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When the RF driving frequency was set to 0.940 MHz and the pump power of EDFA was set to 5 mW, dual-wavelength laser output could be obtained with optimal polarization state. The output laser spectrum is shown in Fig. 4(a). The dual-wavelength laser had a signal-to-noise ratio (SNR) of 55 dB with an OSA resolution of 0.02 nm. The wavelength of the dual-wavelength laser was then tuned by changing the RF frequency from 0.939 MHz to 0.945 MHz. Figure 4(b) shows the spectra of the wavelength tuning dual-wavelength laser and Fig. 4(c) shows spectral tuning properties of the dual-wavelength laser at different RF driving frequencies. The red triangles and blue squares are the measured central wavelength corresponding to the peaks at the longer wavelength and shorter wavelength, respectively, and the lines are just guidance for eyes. The laser peaked at the longer wavelength could be tuned continuously from 1568.852 nm to 1565.284 nm with a tuning slope of −0.595 nm/ kHz, while that peaked at the short wavelength could be tuned from 1565.532 nm to 1561.636 nm with a tuning slope of −0.649 nm/ kHz, and the 3-dB bandwidth of the output laser varied from 0.1 nm to 0.2 nm during the tuning. The slight difference in the tuning slope was mainly from unflattened EDFA gains. The wavelength difference between two output lasers was increased from 3.320 nm to 3.648 nm during the tuning. It is also noticed that the wavelength tuning slope of the dual-wavelength laser is much smaller than that of the MZI with respect to its central wavelength. The spectral separation between the two output central wavelength was about 3.5 nm, which nearly equaled the continuously tuning range and the FSR of the MZI applied in the laser configuration.

 

Fig. 4 The spectral tunability of the fast tuning dual-wavelength laser. (a) Spectrum of dual-wavelength laser output with a RF driving frequency of 0.940 MHz and EDFA pump power of 5 mW. (b) Spectra of dual-wavelength laser at different RF driving frequency. (c) Spectral tuning properties of the constructed dual-wavelength laser.

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At certain polarization state, four-wavelength laser output could also be obtained in such setup, as shown in Fig. 5. The four-wavelength output state could not be achieved at all driving RF frequency, which might be due to unbalanced longitudinal mode competition. To achieve laser output with more wavelengths, extra filters are needed to flatten the EDFA gaining profile.

 

Fig. 5 Spectrum of four-wavelength laser output at certain polarization state.

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4. Conclusions

In summary, an in-fiber tunable MZI was constructed by driving a sandwich-structured SMF with only one acoustic transducer, based on which a tunable MW ring laser was demonstrated. Dual-wavelength laser with a spectral separation between two wavelength peaks of around 3.5 nm could be tuned to cover a spectral range from 1561.6 nm to 1568.9 nm, with a tuning range of 3.6 nm for each peak which nearly equaled the FSR of the MZI. Four-wavelength laser output could also be obtained with optimized parameters. The proposed MZI could offer similar functions as cascaded LPFGs but it is of much faster response time around 370 μs theoretically. Compared to the previous configuration composed of an AOTF and a TF, it gains advantages of robustness and easiness in volume production and relatively low insertion loss. With only one acoustic transducer and a piece of etched SMF, its low cost would also benefit its further applications.