1. Introduction

Chalcogenide materials hold promise both in all-optical processing, because of their high Kerr non-linearity compared to Silica, and also in mid-IR linear processing because of the material’s intrinsic transparency at those wavelengths [1,2]. Chalcogenide fiber was originally developed for transmission of light at mid-IR wavelengths but has recently found application as a compact non-linear medium allowing, Raman amplification [3] and lasing [4], efficient pulse compression [5], optical regeneration [6], wavelength conversion [7] as well as generation of slow light using Stimulated Brillouin Scattering [8]. To create fully integrated components, it is desirable to include periodic structures in the Chalcogenide to create resonances, which may then be used to alter the local dispersive properties and to provide simple filters or intensity tuned blocking filters for non-linear switching. We may even imagine such a broad, tunable, adjustable depth resonance finding application in Raman lasers [4], providing dynamic power control and reconfigurability.

Long period gratings (LPGs) have long been observed in Silica [9] and may be generated quite easily in Chalcogenide fiber. Pudo and co-workers [10], recently demonstrated deep resonances (>-20dB) in Chalcogenide fiber by pressing the teeth of a threaded ~40 mm long rod against the outside of the coated fiber to induce periodic microbends of period ~0.7 mm. Whilst pressure induced LPGs are relatively easy to generate, they cannot be easily tuned and may experience both pressure induced birefringence and damage.

Typically, long period gratings have resonant widths ~100 times wider than Bragg gratings of equivalent length, depending on the exact details of the fiber modes and propagation constants. In contrast, it is difficult to create Bragg gratings in Chalcogenide fiber because, unlike Germanium doped Silica fiber, the cladding absorbs light in the same way as the core. Yet, by using a wavelength of light not strongly absorbed by the Chalcogenide material Asobe et al. have written Bragg gratings in As₂S₃ fiber, but with only 90% reflectivity and evidence of self chirping [11]

In this work, we generate a long period grating structure in a Chalcogenide fiber by generating a periodic microbend structure via a flexural acoustic wave traveling along the fiber. The results demonstrate optical resonances with FWHM 17 nm, which are adjustable in depth to -9 dB and tunable over 235 nm. While such acousto-optic long period gratings have been demonstrated and extensively investigated in Silica fibers [12–16], including photonic crystal fibers [17], to our knowledge nothing has yet been reported in non-Silica fibers. This is, therefore, the first report of an acousto-optic resonance in a soft glass fiber. As expected, the material properties of Chalcogenide fiber, as compared to Silica, change the propagation of the acoustic wave in a predictable way. The resonant structure presented here will form a cornerstone on which to build future experiments exploiting the unique characteristics of Chalcogenide material.

The paper is structured in the following way. First, we introduce briefly the theory of long period gratings generated by traveling acoustic waves. Then we introduce the experimental realization and present the results obtained. We conclude with a discussion of the results.

2. Theory

2.1 Long Period Gratings

A fiber may guide modes in both the core as well as in the cladding, with the fiber dimensions and index profile imbuing each mode with a characteristic propagation constant. The coupling of these modes via periodic perturbations has been described in detail previously [18]. Briefly, by applying a periodic perturbation to the core mode one may couple light from the core into a cladding mode as depicted in Fig. 1i), providing the phase matching condition is satisfied. The phase matching condition is illustrated in Fig. 1ii) for the core mode and a given cladding mode, with the effective indices for core and cladding mode denoted by n_core and n^(l,m)_clad, respectively. The vector subtraction of the propagation vectors for the two modes yields the magnitude of the perturbation momentum vector and hence the LPG period. The equation linking the period of the perturbation to resonant optical wavelength is, therefore, given by

where Λ is the period of the acoustic wave, or beat length of the pair of modes, and λ_LPG is the wavelength of the optical resonance.

 

Fig. 1. (i) Periodically stressed fiber, with microbends of period matching the intermodal beat length, to couple light from the core mode LP₀₁ into the first cladding mode LP₁₁. (ii) Vectorial representation of the phase matching condition showing the propagation vectors for each mode and the requirements for the long period grating to allow coupling.

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The detailed fine structure of each LPG resonance will depend also on the polarization of both the exciting acoustic wave and the light propagating in the core [19].

2.2 Acoustic Wave Propagation

The propagation of acoustic waves in fibers has been already described in detail [14] and will not be reproduced here. The propagation of acoustic waves in a fiber is quite different from in the bulk given the boundary conditions, and some vibrational modes can be very dispersive for acoustic wavelengths long compared to fiber dimensions. Solving the acoustic wave equation in a fiber generates three modes of vibration, including longitudinal motion, torsional motion and transverse flexural motion. Generally, only the lowest order modes propagate in the fiber when the acoustic wavelength is long compared to the fiber dimensions. It is the lowest order mode of flexural motion which is of interest, since it is the one which easily propagates and can couple light from the symmetric core mode into the asymmetric cladding modes.

To ascertain the frequency of operation for a given optical resonance one needs to know the dispersion relation for the particular fiber geometry. This is quite involved [14] but we may estimate the value required by comparing the material properties of Silica to As₂Se₃. The speed of sound in a bulk material depends on the density as well as the restoring force of the material coupled with Poisson’s ratio. The simplest formula for longitudinal sound speed relating restoring force and density is that for propagation in a thin rod (eq. 2), where M_Y is Young’s modulus, ρ is the density and C_E is the velocity of the longitudinal compression wave in the rod.

For propagation in bulk extensive material, the appropriate formulae also depend on Poison’s ratio but roughly retain the square root dependence on the respective moduli and density. We will use this generalized square root dependence to obtain an approximate number for the acoustic frequency required when moving from Silica fiber to As₂Se₃ fiber.

The table below compares the densities, Young’s moduli, Poisson’s ratio as well as the longitudinal (rod and bulk) and shear speeds of sound C_E , C_L and C_t for Silica and As₂Se₃ with some quantities extracted and others derived using the values and equations in references [20–22].

Table 1. Some material properties of Silica versus Chalcogenide As₂Se₃ T=300K

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Since the speed of sound in As₂Se₃ is generally lower than in Silica we expect that the acoustic excitation frequency will also be lower, assuming that the fiber dimensions and characteristics are roughly equivalent.

The characteristic frequency for transverse acoustic wave propagation in a fiber of given diameter is given by f_char =C_t /a, where C_t is the transverse propagation speed in bulk material and a the fiber radius [14]. This corresponds to an acoustic wave with a wavelength of similar dimensions to the fiber. Above this frequency, the acoustic wave travels only on the surface of the fiber, with the characteristic constant velocity of a transverse surface wave. Below this frequency, the transmission is highly dispersive but the interaction with the core is greater since the wave travels by displacing the entire cross-section of the fiber. For Chalcogenide fiber the radius is a = 83 μm, with C_t ~1260 m/s, yielding a characteristic frequency of 15 MHz. In our experiments, we are interested in frequencies around 1 MHz, placing the operation point squarely in the dispersive, long wavelength regime.

3. Experimental Set-up

The experimental set-up is shown in Fig. 2. A high frequency ultrasonic transducer of the kind used for pulsed, non-destructive testing is used to generate the high frequency acoustic waves. We operate this transducer c.w., driving it with a signal derived from a waveform generator (TABOR 5061) which is then amplified by an r.f amplifier to generate up to ~130 Vp-p at the transducer. To ensure appropriate loading of the amplifier, given the frequency dependence of the transducer impedance, a resistive load is placed close to the transducer.

The Chalcogenide material used is Arsenic triselenide (As₂Se₃) and is sourced as single-mode fiber from Coractive Inc. This fiber has a cladding diameter of 167 μm, numerical aperture NA=0.19 @1970 nm and core diameter of 6.3 μm. The transmission loss of the fiber was measured to be -1.0 dB/m at 1550 nm. The Chalcogenide material index of refraction is n=2.78. The section of Chalcogenide fiber used is ~100 mm long and is butt-coupled to mode matched high N.A. Silica fiber, with N.A.= 0.17 and mode field diameter 7.5 μm, then glued in place with epoxy cement. The total loss is -6 dB. The unpolarized light from a broadband E-LED source is coupled into the fiber and the transmitted light is analyzed using an OSA.

An Aluminum cone is used as a coupling horn to match the transducer dimensions ~5 mm dia. to the fiber dimensions (167 μm dia.). A second horn and transducer may be used to monitor the acoustic wave at the other end of the fiber. The amplitude of vibration is exaggerated in this diagram and is typically 10’s of nanometers [14]. The horn is fastened with cyanoacrylate glue to both the transducer and fiber. Note that, while such an excitation method may be less efficient than those previously reported [15], the experiment benefits from the ease and flexibility of set-up.

 

Fig. 2. Experimental set-up. An amplified signal generator excites a PZT at around 1 MHz and up to 130 Vp-p. An Aluminum cone matches the longitudinal mechanical vibration of the 5 mm dia. PZT into the optical fiber. The fiber is vibrated transversely leading to a flexural acoustic wave propagating out in both directions along the fiber. A broadband e-led source is coupled into the core mode of the fiber and the transmitted light is monitored on an OSA.

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In general, since the dimensions of the horn are much greater than the wavelength of the acoustic wave, the transmission response of the horn is not flat but consists of many acoustic resonances from interfering pathways. It is, therefore, necessary to adjust the drive voltage as the frequency is tuned. We have not optimized the coupling horns but if a flat response is required, then either the horn dimension must approach the dimensions of the acoustic wavelength or complex horn design must ensure an adiabatic transition from an essentially surface acoustic wave at the large end of the horn down to a vibration of the whole of the narrow tip of the horn, effecting transverse excitation of the fiber [14–16].

4. Experimental Results

To arrive at the coupling frequency required for a resonance at a desired optical wavelength, a number of assumptions were made in comparison to what one might expect for a similar fiber made from Silica. These assumptions were then coupled with information from microbend gratings [10]. Pudo et al. measured the period of the LPG, required to couple the core mode LP_0,1 to the first cladding mode LP_1,1 for a resonance around 1550 nm, to be ~0.71 mm. As this number is very comparable to the beat length of Silica LPG’s (~0.66 mm at 1550nm), we may assume that the optical properties, i.e. n_core-n^(1,1)_clad, of standard Silica fiber and the Chalcogenide fiber are similar for that wavelength, though the wavelength dependence may vary. Using a beat length of 0.71 mm yields n_core-n^(1,1)_clad = 0.0022 at 1550 nm.

We know, however, that because of the higher density and lower restoring force of the As₂Se₃ glass, the speed of sound will be ~35% that of Silica, all other things being equal for the fibers. Further, in order to couple to the lowest order cladding mode in Silica smf-28 at 1550nm, an acoustic wave of frequency ~2 MHz is required. This means that for a Chalcogenide fiber the acoustic frequency to couple to the lowest cladding mode, for a resonance at 1550 nm, needs to be in the neighborhood of 700 kHz, though the actual frequency may be slightly different when the actual cladding diameter and beat length are considered.

 

Fig. 3. Acousto-optic resonance at 1528 nm excited by an acoustic flexural wave with frequency 870 kHz. By changing the voltage applied to the PZT, the depth of the resonance may be varied from -0.6 dB through to -9.2 dB.

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In Fig. 3, the transmission resonance is shown for various peak to peak sinusoidal drive voltages on the transducer. The driving frequency is set at 870 kHz leading to a resonance at 1528 nm. For these traces the OSA resolution was 0.5 nm. At the highest drive voltage the depth is -9.2 dB. The depth in deciBells depends linearly on the drive voltage for resonances deeper than -0.6 dB. The residual noise around zero dB is the noise level from the relatively low intensity broadband source and is not a feature of the resonance. However, there is some structure associated with the peak as well as at longer wavelengths. Some of this structure may be associated with other polarization states, though initial polarization dependent measurements have been inconclusive.

 

Fig. 4. Acousto-optic resonances for different acoustic frequencies generated from a single PZT transducer. The resonance may be tuned over 235 nm by changing the frequency over 700 kHz.

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Next, the frequency of the transducer is tuned over 700 kHz either side of ~1.1 MHz in steps of 100–150 kHz. At each frequency the drive voltage is adjusted to maintain a depth of approximately -5 dB, and the optical resonance recorded with the OSA. These traces have been combined and are shown in Fig. 4, to map out the tuning range for a given transducer. The resonance is tunable from 1325 nm to 1560 nm, simply by changing the acoustic frequency.

The tuning curve derived from such measurements is shown in Fig. 5. For comparison, two of the communications bands are shown, demonstrating clearly the large wavelength range easily covered using the acousto-optic effect. The curve shows a quadratic dependence of the optical wavelength on acoustic frequency over this range. The form of the tuning curve is Λ_LPG = 8.9×10^-5 F² - 0.555 F + 1944.8, where F is the acoustic frequency in kHz and λ_LPG the wavelength in nanometers. In the C-band the slope of the tuning curve is -420 pm/kHz where as at the high frequency end it is -320 pm/kHz.

The exact form of this tuning curve depends on both the acoustic dispersion, i.e. dependence of acoustic phase velocity on acoustic wavelength Λ = Λ(F), as well as the wavelength dependence of the effective indices of the core and cladding modes n_core (λ) - $n_{\mathit{\text{clad}}}^{(l\mathit{,}m)}$ (λ). We would expect that the tuning curves from sample to sample would be slightly different due to the sensitivity of the resonance to the difference of the effective indices of the core and cladding modes, coupled with the variation between manufactured batches. Indeed, we observed a 100 nm shift when moving from one fiber draw to another

 

Fig. 5. Tuning Curve for the Chalcogenide fiber As₂Se₃ showing the optical wavelength of the acousto-optic resonance for a given acoustic frequency. The tuning range is 235 nm using a single transducer. The curve is fitted well by a 2^nd order polynomial.

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As discussed previously, because of the higher density and lower restoring force of the Chalcogenide material compared to Silica we observed an acoustic frequency ~880 kHz, which was lower than would be expected for Silica fiber ~2 MHz for resonances in the C-band. This is a ratio of 0.44, which is roughly similar to ratio of the bulk velocities (see table 1). The difference may be explained by the different core cladding index difference (see equation 1) and cladding diameter, affecting acoustic dispersion.

5. Conclusion

We have demonstrated for the first time acousto-optic coupling in a non-silica fiber. The fiber used was a soft glass Chalcogenide (As₂Se₃) and the acoustic waves were generated by transverse vibration of the fiber around 1.1 MHz to excite a flexural traveling wave along ~100 mm of the fiber. The transmission resonance could be varied from -0.6 dB to -9.2 dB by varying the driving voltage up to 130 Vp-p. At -9.2 dB the FWHM was 17 nm. The resonance could be tuned over a very wide range of 235 nm by tuning the acoustic frequency over 700 kHz. The tuning slope in the C-band was -420 pm/kHz. This capability coupled with the unique properties of Chalcogenide material, open the way for a number of novel applications in non-linear processing and for reconfigurable devices in the mid-IR.