Acousto-optic modulation of a 1 cm fiber Bragg grating at 10.9 MHz frequency and 1065 nm wavelength is demonstrated for the first time. A special modulator design is employed to acoustically induce a dynamic radial long period grating which couples power of the fundamental mode to the higher-order modes supported by the Bragg grating. A modulated reflection band with a depth of 16 dB and 320 pm bandwidth has been achieved. The results indicate a higher modulation frequency compared to previous studies using flexural acoustic waves. In addition, the reduction of the grating length and the modulator size points to compact and faster acousto-optic modulators.
© 2015 Optical Society of America
All-fiber acousto-optic modulators (AOMs) have been successfully employed in tunable filters, gain equalizers for erbium-doped fiber amplifiers (EDFAs), Q-switched and mode-locked fiber lasers [1–8]. AOMs based on optical fibers provide lower insertion loss, higher beam quality and easier integration with fiber-optic devices if compared to the traditional bulk devices based on crystals. The first approach of a coaxial acousto-optic modulator is based on the interaction of flexural acoustic waves and optical modes in an optical fiber. The AOM is composed of an optical fiber passing through a drilled piezoelectric transducer (PZT) and a cone-shaped capillary silica horn axially aligned . The PZT generates flexural acoustic waves which are amplified by the horn and propagate along the fiber. The acoustic wave creates bends along the fiber inducing a periodic refractive-index perturbation which couples power of the fundamental mode to higher-order modes. Such devices work as dynamic long period gratings (LPGs) being usually employed as notch filters with high rejection efficiencies and relative fast switching times (~40 µs). However, the AOMs in general require long fiber lengths or high powers to achieve the acousto-optic modulation .
In contrast, the acousto-optic modulation of fiber Bragg gratings (FBGs) is suitable to reduce the size, the switching time (~17 µs) and power consumed by the acousto-optic devices, since the interaction length between the acoustic wave and the optical modes is reduced to the grating length [8–14]. In particular, the interaction of flexural acoustic waves and FBGs enables the switching of the Bragg wavelength by coupling power of the fundamental mode to higher-order modes at shorter wavelengths [9,10]. However, the modulation of standard fibers with flexural acoustic waves is limited for frequencies f < 10 MHz because the acoustic wave tends to propagate by the fiber surface with the increasing frequency, reducing the interaction with the optical modes in the core [15,16].
On the other hand, longitudinal acoustic waves interacting with FBGs compress and extend the grating period inducing lobes on both sides of the Bragg wavelength [11,12,17]. In general, modulators based on longitudinal waves operate with higher frequencies and velocities compared to the devices employing flexural waves. AOMs employing standing longitudinal acoustic waves are suitable to mode-lock all-fiber lasers inducing amplitude modulated side lobes at twice the acoustic frequency [5–8]. An increase of the acoustic velocity v reduces the switching time of the acousto-optic devices, since the acoustic wave takes shorter time to propagate along the grating. In particular, an increase of the acoustic frequency f and bandwidth is an efficient way to shorten the pulse width τ of mode-locked fiber lasers according to ,6]. However, the narrowband wavelength modulated by the acoustic wave imposes a strong filtering in the broad ytterbium bandwidth (FWHM > 40 nm ), resulting in a small wavelength range (axial modes) of the gain band for mode-locking. Since the modulated bandwidth increases by reducing the interaction length between the acoustic wave and the grating, the use of short Bragg gratings in the modulator is favorable to shorten the pulse width τ.
In standard optical fibers, the acoustic wave is mostly distributed over the fiber cross section reducing the interaction with the grating in the core with the increasing frequency. Consequently, several approaches of AOMs using combinations of gratings with long lengths L and high modulation index ∆nac (strong gratings), high acoustic powers Pac, cladding-etched and tapered fibers and, suspended core fibers (SCFs), have been employed to increase the acousto-optic interaction. For example, AOMs operating at f = 4.55 MHz frequency are employed to modulate a L = 12 cm grating for mode-locking an erbium-doped fiber laser achieving a pulse width of 780 ps . Devices operating at f = 5.58 MHz modulate a L = 10 cm grating to produce 740 ps pulses in a mode-locked ytterbium-doped fiber laser . Modulation of 1 cm grating in a SCF at 5.1 MHz has been demonstrated to mode-lock an ytterbium-doped fiber laser with pulses shorter than ~550 ps . Nevertheless, the reduction of the fiber diameter by means of etching or tapering techniques makes the device fragile and degrades the fiber mechanical stability. In addition, the inscription of gratings in SCFs and their fusion-splicing with standard fibers are a challenge and may require more elaborate techniques . Moreover, the inscription of long gratings requires the use of long phase masks or additional equipment to shift the fiber and the phase mask with respect to the beam . The use of long fiber or grating lengths increases the switching time of acousto-optic devices because the acoustic wave takes more time to travel along the fiber.
In this study, we report on the fabrication and demonstration of an all-fiber acousto-optic device modulating a 1 cm long FBG at 1065 nm wavelength and f = 10.9 MHz. A new acousto-optic interaction based on an acoustically induced radial long period grating (RLPG) and a FBG is shown. The RLPG couples power of the forward-propagating fundamental mode to backward-propagating higher-order modes supported by the FBG. A considerable reduction of the device size points to compact and faster all-fiber photonic devices. For the best of our knowledge, this is first all-fiber acousto-optic modulator operating with these properties. The device can be used as output coupler and exhibits a higher modulation frequency compared to previous studies using flexural acoustic waves, which might be suitable to shorten the pulse width of mode-locked ytterbium-doped fiber lasers at the repetition rates higher than 20 MHz.
2. Operation principle
Figure 1(a) illustrates a fiber Bragg grating (FBG) without acoustic modulation. The forward propagating mode with the effective index n01, interacts with a grating of period Λ, resulting in a reflected band at the Bragg wavelength λB = 2n01Λ. Figure 1(b) illustrates an acoustically induced radial long period grating (RLPG) composed by the superposition of radial and longitudinal strains along an optical fiber. The distribution of the radial and longitudinal strains changes over the fiber cross section with the radius r (r changes from the fiber axial center (zero) to the maximum value a). Previous theoretical studies show that for acoustic excitation at frequencies in general higher than f > 10 MHz in an optical fiber with diameter 2a = 125 µm, the distribution of the longitudinal strain is gradually reduced over the fiber cross section with the ratio r/a, giving place to a radial strain increasing with the same ratio r/a . The longitudinal strain is most concentrated in the fiber core compressing and stretching the grating. The overlap of the longitudinal and radial strains causes an asymmetric perturbation along the fiber with a period λRLPG. It is expected that the RLPG induces a very slight radial variation in the fiber cross section caused by the maximums and minimums of the resultant superposition of the strains. Figure 1(b) is a simple sketch based on information in . The real superposition of the radial/longitudinal strains might result in a complex strain pattern, since radial/longitudinal strains are intrinsically overlapped over the fiber cross section (it is illustrated in Fig. 1(b) as red arrows in the cladding). Figure 1(c) illustrates the power coupling interactions between the fundamental mode LP01 and the higher-order mode LP11 induced by the FBG and the RLPG. Under ideal conditions the coupling between the symmetric LP01 mode and the spatially anti-symmetric LP11 mode would be expected to be negligible for a symmetric index modulation in the fiber core. However, in experimental grating structures asymmetries and modal field deformations have been observed, which provide such coupling effects between LP01 and LP11 modes [22,23]. The coupling between the forward-propagating mode LP01 and the backward-propagating mode LP11 at the coupling wavelength λm induced by the FBG satisfies the phase-matching condition as ,Fig. 1(c). On the other hand, the phase-matching condition for the coupling between the backward-propagating modes LP01-LP11 (c3) at the coupling wavelength λm induced by the RLPG, is given as [9,10],Equation (3) also satisfies the condition for the coupling between the forward (c4) and backward (c5) propagating modes LP01-LP11 at the Bragg wavelength λB induced by the RLPG. These couplings are illustrated as red dashed arrows in Fig. 1(c). Note in Fig. 1(c), if both phase-matching conditions in Eqs. (2) and (3) are simultaneously satisfied at the wavelength λm, the energy of the higher-order mode LP11 reflected by the FBG (c2) is coupled to the mode LP01 by the RLPG (c3) resulting in a reflected side lobe centered at λm. Here, we considered only the coupling between LP01-LP11 modes; however, the principle is similar to the coupling with other higher-order modes.
3. Experimental results and discussion
3.1 Acousto-optic modulator assembly and experimental setup
The acousto-optic modulator is composed of a piezoelectric transducer (PZT) disc, a capillary acoustic horn and two pieces of distinct optical fibers. The acoustic horn is obtained by tapering a silica capillary with the commercial machine Vytran GPX-3200. The capillary outer/inner diameters are reduced from 1.06 / 0.81 mm to 0.18 / 0.13 mm along ~12 mm length. Later, a multimode double clad optical fiber (DCF) (fabricated at the IPHT with 125 µm cladding diameter) is inserted into the tapered capillary and fused together at the capillary tip along ~0.8 mm. The capillary and fiber are carefully aligned during the fusion process to avoid microbends. The fusion is made by means of the commercial Vytran GPX-3400, which has additional alignment functions compared to the GPX-3200 model. Figure 2(a) shows the scanned profile of the horn diameter indicating the fused region (dashed red circle). Figure 2(b) shows a detail of the fused region between the capillary and the fiber. The capillary and DCF are doped with fluorine to decrease the refractive index in the cladding. It prevents the leaking and absorption of power from the core to the cladding caused by fiber bends into the capillary or along the fused region. Figure 2(c) illustrates the PZT disc (0.2 mm thickness and 3 mm diameter) in xyz planes, which has a longitudinal acoustic resonance of ~10 MHz according to the manufacturer. The PZT is drilled in its center region by means of a metal driller resulting in a hole of ~0.5 mm in diameter, as illustrated in Fig. 2(c). Figure 2(d) shows the DCF passing through the PZT and the horn and being spliced to a commercial single-mode optical fiber (Nufern SM-GDF-10/125). We inscribed a 1 cm long FBG in the SMF by means of a femtosecond laser and two-beam interference, using the phase mask interferometer arrangement according to the methodology described in . Figure 2(e) illustrates the experimental setup used to characterize the reflectivity spectrum of the FBG. The PZT basis is fixed on a metallic support connected to an arbitrary signal generator (SG).
The electrical connection between the PZT and the metallic support is made by using conductive glue. An electrode is also glued to the opposite PZT surface to connect the signal generator. By using this technique, the use of conventional soldering methods which cause undesired loads on the PZT is avoided. The fiber tip and PZT basis are fixed and the modulator works as a resonant acoustic cavity exciting standing acoustic waves. The PZT is excited by a 9 V - 16 V sinusoidal signal at the f = 10.9 MHz resonance. The grating is characterized by using a broadband light source (SLED), and the reflection spectrum is recorded by means of a circulator and an optical spectrum analyzer (OSA Yokogawa AQ6370C) with a 20 pm wavelength resolution. The SMF of the modulator is spliced to another DCF segment. The whole modulator is 7.5 cm long.
3.2. Reflectivity modulation of the Bragg grating by the RLPG
Figure 3(a) shows the FBG spectrum without acoustic modulation (thick curve) and with acoustic modulation (thin curves) for a 9 V – 16 V voltage range applied to the PZT at the resonance of f = 10.9 MHz. The non-modulated grating has the Bragg wavelength at λB ~1065.3 nm, a 3-dB bandwidth of 0.6 nm and a maximum reflectivity of ~99.9%. The RLPG induces a side lobe with a strong peak at λm = 1064.76 nm, as indicated with the arrow in Fig. 3(a) and previously illustrated in Fig. 1(c). Figure 3(b) shows the variation of the side lobe reflectivity at λm for the considered voltage range. For voltages lower than 9 V, no relevant modulation is observed. The spectra in Fig. 3(a) also show a non-modulated reflection band which is caused by the high grating reflectivity and the influence of higher-order modes. Although the SMF is specified as being single-mode in the wavelength range of interest, the increase of the averaged reflective index to achieve the high reflectivity may induce multimode behavior along the grating length.
The effective indices of the fundamental mode LP01 (n01 ~1.451) and the higher-order mode LP11 (n11 ~1.45) are estimated from the Bragg wavelength λB and side lobe peak λm, considering the period used in the grating inscription Λ ~367 nm and the equation λ = 2neffΛ. Here, we considered only the coupling between the modes LP01-LP11, however, the RLPG might couple power to other higher-order modes with effective index close to n11 ~1.45 at adjacent wavelengths of λm. This effect is seen in Fig. 3(a) as a band of low reflectivity lobes overlapping on the shorter wavelength range. No modulated lobe is noticed on the right side of the grating spectrum indicating the longitudinal strain in the core is too weak compared to the radial strain composing the RLPG. The frequency dependence f of the induced side lobe λm is not investigated because of the discrete behavior of the PZT resonances used in this study.
The coupling wavelength λm = 1064.67 nm is calculated by means of Eq. (2) with the modal indices n01, n11 and the grating period Λ, which agrees well with the measured value at λm = 1064.76 nm. The period of the RLPG λLPG ~1065 µm is calculated by means of Eq. (3) considering the modal indices n01, n11, and the coupling wavelength λm. The RLPG period corresponds to the beat length of the modes LP01-LP11 satisfying the phase-matching conditions in Eqs. (2) and (3) for a difference of effective indices (n01 - n11 ~1x10−3). For the resonance of f = 10.9 MHz and the acoustic velocity in silica of vext = λL f = 5740 m/s, the period of the longitudinal acoustic strain in the fiber core is estimated as λL~527 µm, which is almost the half of the period of the RLPG (λLPG/2 ~532 µm). For the frequency of f = 10.9 MHz achieved in this experiment, the RLPG modulates a FBG at a frequency 10 times higher compared to a modulator based on flexural acoustic waves (f ~1 MHz) (the frequency is calculated considering the same parameters and equation λLPG = [πavext /f ] ). The results show the long period of the RLPG can couple power between modes with a very low difference of effective indices at higher frequencies. Oppositely, the increasing frequency of flexural acoustic waves considerably reduces the acoustic period, requiring a larger difference of the effective indices between the coupled modes.
The RLPG modulates a bandwidth of λmFWHM = 320 pm, indicating a broader bandwidth compared to previous studies with longitudinal acoustic waves (λmFWHM = 200 pm) . Considering λmFWHM = 320 pm equivalent in frequency to 85 GHz and, an application of this modulator to mode-lock a fiber laser with the cavity modes spaced 21.8 MHz apart, the modulator could lock a large number of axial modes (85 GHz / 21.8 MHz ~3900 modes). For a transformed limited laser pulse with an almost Gaussian shape in the time domain, the theoretical lower limit for the pulse width is around 0.315 / 85 GHz = 4 ps . We noticed during the experiments, that the measured reflectivity of the higher–order modes supported by the grating is quite sensitive to bends and environmental noise along the DCF and of the splices connecting to the SMF. Consequently, this effect also changes the modulated side lobe reflectivity and bandwidth. However, it can be reduced by implementing high quality splices or by employing bend insensitive fibers. A maximum side lobe reflectivity of 16 dB is achieved at the voltage of 16 V compared to the grating spectrum without modulation. The absolute side lobe reflectivity is ~1%. An increase of the side lobe reflectivity could be obtained by the application of higher voltages to the PZT (in this study, the voltage is limited to the maximum of 16 V provided by the signal generator) or improvement of the modulator design, acoustic horn and PZT, e.g., reducing the diameter of the hole in the PZT. Moreover, the side lobe reflectivity may also be increased by the use of techniques discussed in Sec. 1 (e.g. cladding etched or tapered fibers, long FBGs or the used suspended-core fibers with large air holes).
In conclusion, acousto-optic modulation of a 1 cm FBG at 10.9 MHz by means of an acoustically induced radial long period grating is investigated, and its application to couple power between optical modes is demonstrated at the 1060 nm range. The modulated side lobe has a reflectivity depth of 16 dB and a 3-dB bandwidth of 320 pm. The reduction of the grating length and the modulator size indicates possibilities for compact and faster acousto-optic devices. In addition, the use of standard fibers provides better mechanical stability compared to fiber taper and etching techniques. The acousto-optic modulator could be used as an output coupler with a higher modulation frequency compared to previous studies using flexural acoustic waves, which is useful to shorten the pulse width of mode-locked all-fiber lasers at the repetition rates higher than 20 MHz.
Funding by the Thuringian Ministry of Education, Science and Culture (EFRE program), (Grant number: B715-11005), Germany, is gratefully acknowledged. This work was also supported by the Cordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil (Grant number: 12645-12-5).
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