1. Introduction

Photonic crystal fibers (PCFs) are optical fibers for which the refractive index profile of the cladding is periodic in one or two dimensions, typically with a silica/air hole microstructure. These fibers have attracted great interest during the past decade because of their unique properties such as endless single-modedness, large mode area, high nonlinearity, or bandgap guidance [1]. The dispersion and field distribution of PCF modes can be accurately controlled over a very wide range through adjustment of the geometric arrangement and size of the airholes. The refractive index of the air holes in the PCF cladding can be altered by filling them with other materials, such as UV-curable polymers [2, 3] isotropic fluids [4–7], anisotropic liquid crystals [8] or even semiconductors [9], thus providing an additional degree of freedom in the PCF design.

When the air holes of a solid core index guiding PCF are filled with a material having a refractive index larger than that of the background material, [8, 10] one can realize a solid-core Photonic BandGap Fiber (PBGF). In this case, total internal reflection is forbidden, and the core modes are instead confined by anti-resonant scattering from the high index inclusions, manifesting in discrete frequency transmission bands; this type of guidance is referred to as Anti Resonant Reflection Optical Waveguiding (ARROW) [11, 12]. These fibers offer unique properties, particularly useful for studying nonlinear propagation effects, active device applications and novel fiber components. For example, the wavelength dependent loss of these fibers has been exploited to suppress unwanted gain in Nd-doped fiber, allowing for more efficient fiber lasers [13]. In a different context, the engineered waveguide dispersion, combined with the strong optical nonlinearity, offers a unique geometry for nonlinear pulse propagation effects and soliton dynamics [14].

One may expect that the higher-order core and cladding modes of solid-core PBGFs also have interesting or beneficial properties, for example in the context of long-period grating devices, which rely on coupling to higher order modes. Stress- or arc-induced long period fiber gratings (LPFGs) have been recently demonstrated in order to characterize the dispersive properties of the higher-order modes of PBGF [15, 16]. In the same context, tunable optical filters have been demonstrated by thermally tuning PBGF-based LPFGs [17]. Although useful results were obtained in these previous experiments, the stress- and arc-induced grating results revealed some unwanted geometric distortions of the microstructure and small axial variations in the grating strength, which lead to deterioration of their spectral response. In addition, thermally tuning the PBGF significantly changes other waveguide properties such as the spectral position of the transmission bands and the modal dispersion, which may not be desirable for the realization of tunable devices.

In this paper we present a demonstration of tunable long period grating based on acousto-optic (AO) interactions in a solid-core PBGF. AO interactions represent a very elegant and simple approach for realizing electrically tunable grating resonances in optical fibers [18]. We obtain several resonances produced by AO interaction in each of the transmission bands and fully characterize the dispersive property of coupling in PBGF. In particular, the measured beat length dispersion shows strong wavelength-dependent behavior because of the resonant nature of guidance in PBGFs, which enables very narrow band filtering. We simulate the dispersion of the PBGF modes using the multipole method [19] and obtain good agreement with experiment.

 

Fig. 1. (a). Cross-sectional image of the fiber used in the experiment, (b) measured transmission spectrum of the PBGF, and (c) a schematic diagram of the acoustic device embodiment.

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2. Experiment and analysis

The schematic of the fiber used in the experiment, a commercially available silica PCF (ESM 12-01, Crystal fiber A/S) is shown in Fig 1(a). The fiber has four rings of air holes surrounding the core formed by single missing hole defect, where the average hole diameter (d) is 3.5μm and the average hole spacing (Λ) is 7.7 μm. We filled the cladding air holes with a high index fluid (Cargille Laboratories, n_D=1.64) using a vacuum pump. The solid line in Fig. 1(b) shows the linear transmission spectrum through a 30 cm length of solid-core PBGF measured on an optical spectrum analyzer (OSA) using a PCF-based supercontinuum broadband source [20]. The measured transmission bands correspond to the 4^th, 5^th, 6^th and 7^th transmission bands of the PBGF according to the designation in Ref. 15. The background loss of the transmission is ~5dB, which mainly originates from input and output coupling loss. The sharp peaks in 4^th transmission band appear at wavelengths where we expect avoiding crossings with LP₄₁-derived supermodes of the cladding cylinders [21], though the strength, width, and number of these peaks are not in complete agreement with theory and they are not well understood at present.

We then fabricated the AO device using this fiber. Figure 1(c) shows a schematic diagram of the experimental embodiment, where the AO interaction length is 15-cm long. The basic configuration of the AO device is similar to that described in Ref. [18], where the acoustic transducer includes a piezoelectric material poled to the shear direction and the metal horn amplifies the acoustic wave and efficiently generates a flexural acoustic wave along the fiber. We launched the broadband supercontinuum source into the solid-core PBGF through a microscope objective and collected the output with a butt-coupled length of standard single mode fiber which transmitted the light to an OSA. The output fiber was bent in order to strip out the coupled higher-order guided modes in the solid-core PBGF, thus allowing direct measurement of the coupling efficiency and bandwidth.

 

Fig. 2. Measured transmission spectrum of the AO resonance coupled to the LP₁₁-like mode in 6^th band using polarized light. The simulated intensity profiles of the fundamental mode and LP₁₁-like mode are also shown.

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In our analysis, we focus primarily on the 6^th transmission band centered on 850 nm where the most efficient AO interaction is observed. Figure 2 shows the spectrum of the resonance in this band with the applied electrical frequency of 1.72 MHz and peak-to-peak amplitude of 15 V; the spectrum is measured using polarized light, and normalized with respect to transmission through the fiber with no applied acoustic wave. This resonance corresponds to the coupling to the leaky LP₁₁-like mode of the cladding microstructure [15]. The figure also shows the simulated intensity profile of the fundamental mode and coupled LP₁₁-like mode. The 3dB optical bandwidth and notch depth of the measured resonance are ∼1.1 nm and -21 dB respectively. The polarization-dependent wavelength splitting of the resonance is about 0.7 nm ∼ 1 nm over the range from 840 nm to 880 nm. Based on our multipole simulations, we calculated the effective index difference between nearly degenerated LP₁₁-like modes to be ∼5×10^-6 over this range (840 nm ∼ 880 nm). The resultant splitting of the LP₁₁-like modes in the ideal structure should monotonically increase from 0.6 to ∼ 1.9 nm over this bandwidth where we ignore stress-induced birefringence [22] because thermal stress will be not developed in pure silica fiber. Although the increase of splitting with wavelength is not clearly observed in our experiment, the magnitude of the splitting in the measured spectra reasonably agrees with our modeling within a factor of two.

The tuning property of the acoustic grating in spectrum is shown in Fig. 3(a). We obtain a notch depth >10dB over the range from 1.4 MHz ∼2 MHz despite the frequency-dependent response of the acoustic transducer. A small notch at slightly longer wavelength than the main peak was observed, which exhibits different strength and spacing relative to the main peak as the applied frequency changes. The wavelength splitting between the main peak and small notch varies from 1.5 to 4 nm as the center wavelength decreases from 880 nm to 840 nm. We expect these notches originate from the acoustic birefringence arising from transverse and longitudinal geometric imperfections of the PCF [23]. Further investigation into the acoustic birefringence and polarization properties of the device will be needed to reconcile our measured spectra and numerical modeling.

 

Fig. 3. (a). Tuning properties of the AO resonance in 6^th transmission band. The spectra are vertically offset by -20 dB in each frequency step for clear visualization. (b) The tuning slope of the center wavelength of the resonance as a function of the applied frequency.

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Figure 3(b) shows the relationship between the measured resonance wavelength and applied electric frequency. The tuning slope is 0.079 nm/kHz, which is 2.5-6 times smaller than the value in conventional single-mode fiber (-0.199∼-0.223 nm/kHz) [18] or air/silica PCF (0.32 ∼ 0.52 nm/kHz) [23, 24]. Such a small wavelength-tuning slope implies the small optical bandwidth for a given grating pitch, as we describe below. Previous studies of acoustic interactions in PCFs have shown that the presence of the air holes in the fiber cross-section only weakly modifies the fiber’s acoustic properties [23]. The fluid we use in our experiments has sufficiently low viscosity that it does not support flexural acoustic waves, and so we expect that the fluid-filled fiber should have almost the same acoustic properties as the unfilled fiber. This was confirmed experimentally through acoustic dispersion measurements of filled and unfilled fiber samples using a laser probing technique [25]. The gentleness of the wavelength-tuning slope in our PBGF is thus not a product of acoustic dispersion; rather, it is due to the strong waveguide dispersion of the PBGF modes. The slope may be written as ∂λ/∂f = (∂f/∂L_B)^-1(∂L_B/∂λ)^-1, where f is the acoustic frequency, L_B is the intermodal beat length, and λ is the optical wavelength, and it is the last term which is unusually small (or conversely, ∂L_B/∂λ is unusually large) in PBGFs [15–17].

Figure 4 shows the estimated optical beat length as a function of the wavelength; the left y-axis is derived from the measured acoustic dispersion of the fiber. These measurements agree very well with the multipole method simulation results. One or two resonances appear in each transmission band, and each resonance corresponds to excitation of an anti-symmetric mode of the core or cladding, depending on whether the band is even or odd [15]. The beat length of the coupled modes increases as it approaches to the transmission band edges, where the propagating light resonantly couples to the modes of the high-index cladding cylinders. The slope of the beat length is related to the 3-dB optical bandwidth of the resonance by [26]

where L and ∆n_g are the grating length and group index difference between two coupled modes, respectively. The 3-dB bandwidth is inversely proportional to the slope of the beat length with respect to the wavelength, and the steepness of this slope in solid-core PBGF, particularly near the transmission band edges, should enable very narrow LPFG resonances.

The measured beat length slope for the LP₁₁-like resonances in the 6^th transmission band is 3.58 μm/nm (simulated value=3.67 μm/nm), so from Eq. (1) we expect an optical bandwidth of 1.06 nm for a 15-cm-long interaction length, which reasonably agrees with the experimental value of 1.1 nm. The 3-dB bandwidth is also proportional to the square of the optical beat length, which is actually quite large in our device (>700μm in the 6^th transmission band), but the optical bandwidth still maintains similar value with that of previously reported narrowband AO filters using specially designed fiber [22, 27]. We expect that much narrower filters can be realized by designing a fiber with the appropriate hole size, hole spacing, and index contrast so as to reduce the magnitude of the beat length while maintaining its steep slope. While these parameters are generally optimized for a high index contrast, small core fiber, it may be that narrow band resonances by AO interaction are also possible in low index contrast all-solid PBGFs [28], which would be preferable for more temperature-stable devices.

 

Fig. 4. Left axis: Measured (scatter plots) and simulated (solid lines) optical beat length between the fundamental and anti-symmetric higher order PBGF modes. The scatter plot data are obtained from combining the measured resonance wavelengths as a function of acoustic frequency and the measured acoustic dispersion. Right axis: Simulated PBGF transmission spectrum (loss/m).

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3. Conclusion

In conclusion, we demonstrated resonant narrow-band rejection in solid-core PBGF based on an AO interaction. The resonances are electrically wavelength-tunable, and their tuning properties agree very well with simulations. We showed that the highly dispersive inter-modal properties of this fiber result in very narrow-band rejection in the spectrum for a given grating pitch. The results of this investigation will be useful information for the realization of photonic devices based on the PBGF.