1. Introduction

The transverse microstructure of air-silica photonic crystal fibers (PCFs) provides great flexibility in terms of dispersion and mode profile, as well as offering opportunities for the fabrication of a wide range of different in-fiber devices. The structures discussed here are formed from a strand of pure silica glass with a regular arrangement of hollow channels extending along its entire length. The central air hole is omitted, creating a solid glass core or “lattice defect” for trapping light [1]. In the case of a hexagonal lattice of holes, such a core supports only the fundamental guided mode at all wavelengths provided the hole diameter to spacing ratio is less than ~0.4. The result is a fiber that is endlessly single-mode (ESM) and usable at all wavelengths where the glass is transparent [2].

Over the past several years, methods for further enhancing the versatility of PCF have been proposed and explored. For example, fiber post-processing can be used to create longitudinal changes in core size and air filling fraction [3, 4], and the hollow channels filled with materials such as polymers [5], liquid crystals [6] or metals [7, 8]. High pressure chemical vapor deposition has been used to deposit Ge wires of diameter 5 µm in PCF [9]. We recently reported that arrays of high quality metallic nanowires can be formed by pumping molten gold and silver into the hollow channels [10, 11]. Coupling into guided plasmon modes on these metallic nanowires was shown to occur at wavelengths where the modes of both glass core and nanowire are phase-matched. In this Letter we report on the material and optical properties of PCFs filled with germanium, a material that can provide electrical conductance together with low-loss guidance in the mid-IR, at the same time potentially allowing construction of different kinds of in-fiber detector and sensor. The fabrication procedure involved selective hole closure followed by pumping in molten Ge at high pressure [12]. As we shall show, the resulting wires are of high purity and excellent optical quality.

The paper is organized as follows. In the next section we describe the process of wire preparation and the conductivity and micro-Raman measurements. In section 3 we introduce the optical set-up, and in section 4 we discuss the results and compare them with numerical simulations. In section 5 a toy model based on a multilayer structure is used to help interpret the results. In section 6 the temperature dependence of the optical transmission is investigated and conclusions are drawn in section 7.

 

Fig. 1. (a) Scanning electron micrograph (SEM) of a PCF in which two channels 600 nm in diameter (at each end of the rectangular core) have been filled with Ge. (b) SEM of an ESM-PCF with a single Ge-wire adjacent to its glass core (hole spacing 2.90 µm, hole diameter 1.7 µm).

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2. Sample preparation and material characterization

Before filling with Ge, the PCFs were thermally processed so as to close all holes except selected ones on the fiber end-face. The procedure involved a combination of hole-blockage (using polymeric glue) and in-hole pressure at the softening temperature of the glass. Pure Ge was then pumped into the remaining open holes at a pressure of ~60 bar and a temperature of ~1000°C. To avoid oxidation of Ge at these temperatures, the pressure cell was continuously flushed with argon. Filled lengths of a few cm were routinely achieved. Fig. 1 shows scanning electron micrographs (SEMs) of the cross-sectional microstructure of two such filled PCFs, one with a pair of wires 600 nm in diameter, and the other with a single wire of diameter 1.7 µm, adjacent to the core.

2.1 Conductivity

To check the quality of the wires, the electrical conductivity was measured by placing the end-faces of a 2.2 cm long sample of the two-wire PCF into liquid Ga and measuring its resistance with a Hewlett-Packard 4339A meter. These measurements yielded a resistivity of 49 Ω.cm, compared to 47 Ω.cm for pure undoped crystalline Ge [13]. The slightly lower conductivity we attribute to polycrystallinity, which causes trapping of charge carriers in surface states at grain boundaries, forming energy barriers against subsequent carrier motion [14].

2.2 Raman spectrum

Next, a micro-Raman spectrometer (Jobin Yvon LabRAM HR 800) was used to probe a Ge wire (diameter 1.9 µm) at a sequence of different positions along the fiber. Light from a HeNe laser (wavelength 632.8 nm) was focused through the cladding with a 100× objective and the back-scattered light was coupled into the spectrometer. A representative spectrum is depicted in Fig. 2. At all measured positions, the spectra showed a highly symmetric peak at around 298 cm^-1, which corresponds to the transverse optical (TO) Raman-active mode of the Ge crystal. The position of the peak is shifted to lower frequency by ~2 cm^-1 compared to bulk single-crystal Ge, which has a Raman shift of 300 cm^-1 [15, 16]. Since the TO peak in amorphous Ge is located at a yet lower frequency (~270 cm^-1), and displays a characteristic shoulder on its low-frequency side [17, 18], it seems likely that the Ge in our samples has a high degree of crystallinity. In addition, the measured TO-peak has a width (~3.6 cm^-1) only slightly wider than that of single crystal Ge (2.4 cm^-1), and much narrower than for amorphous Ge (>50 cm^-1) [16], which further supports this conclusion.

 

Fig. 2. Micro-Raman spectrum taken through the side of a capillary containing a Ge wire of diameter 1.9 µm.

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3. Optical set-up

The set-up used to measure the transmission spectrum of light guided in the glass core of Ge-filled PCF is shown in Fig. 3. Since the transmission losses were extremely high when all holes were filled, only a single hole adjacent to the glass-core was filled with Ge. This was sufficient to produce strong spectral and polarization-dependent changes in the transmitted signal. Fig. 1(b) shows an SEM of the sample used in the experiments. Optical measurements were performed after cleaving away the thermally-processed section close to the end-face of the fiber, resulting in a few cm of PCF filled with a single Ge wire.

Light from a PCF-based supercontinuum source (400-1600 nm) was launched into the unfilled end of the Ge-PCF using an achromatic 40× microscope objective. Since the unfilled section of ESM-PCF supports only one guided core-mode at all wavelengths, the launching conditions into the Ge-filled section are well-defined and reproducible, although there is the possibility that higher order modes might be excited by imperfections at the filled/unfilled transition. At the output end of the Ge-PCF, light was collected using a second achromatic objective and passed through a broad-band polarizer to allow selection of specific output polarization states. We define x-polarization as the state when light is polarized along the axis joining the center of the PCF with the center of the wire (Fig. 1(b)). Light of a desired polarization can be selected by rotating the output polarizer. Finally, the output was coupled into an optical spectrum analyzer. Polarization-dependent measurements of the transmission were performed by rotating the output polarizer to different angles and recording the respective spectrum. Each individual spectrum was normalized to that of an unfilled ESM-PCF measured at the same angle.

 

Fig. 3. Schematic diagram of optical measurement setup (L: Nd-YAG microchip laser; SCF: 20 cm long endlessly-single mode fiber for supercontinuum generation; MO: 40× microscope objective; MO1: 20× microscope objective; PL: broad-band polarizer; M: mirrors; OSA: optical spectrum analyzer; MS: microscope slide with index-matching oil to strip off cladding modes).

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4. Results

The experimental results were compared to numerical solutions obtained using a commercially available finite-element solver (JCMWave). The simulations were for an ideal structure with identical equally-spaced circular holes. Data for the complex-valued dielectric constant of Ge was taken from the literature [19] and the Sellmeier expansion was used for the refractive index of silica [20]. The finite-element simulations produce a large number of modes, only one of which has a field distribution in the glass-core that corresponds to a fundamental mode. This mode was selected and used in the comparisons with experiment.

4.1 Transmission in the range 500 to 1050 nm

Experimental transmission spectra and corresponding numerical results for x- and y-polarization are shown in Fig. 4 for a wire length of 0.8 mm. Theory and experiment show reasonable agreement at all wavelengths, allowing us to infer that the polarization state is preserved when the light crosses into the Ge-filled section. Simulations show that the overall drop in transmission at longer wavelengths is caused by increasing field overlap between the glass-core mode of the PCF and the wire, which dominates over the falling absorption of Ge. Experiment and theory follow the same trend with an offset of roughly 3 dB. This we attribute to two main effects: First, excitation of higher order modes at the interface between filled and unfilled sections increases the measured loss (the normalization procedure does not permit removal of this effect). Second, the Ge dielectric function used in the simulations applies to crystalline material, whereas the Ge wires are polycrystalline, leading to enhanced scattering. In both spectra distinct (though weak) dips can be seen in the range 900 to 1000 nm. These are result of coupling from the glass-core mode to resonances on the Ge wire (this effect is much stronger for λ ₀ > 1000 nm, as will be discussed in the next section). Near-field images at the end-face of the Ge-filled section confirm that only the fundamental mode of the glass core is present in all cases (see inset in Fig. 4(a)).

In Fig. 5, T_x/T_y (expressed in dB) is plotted as a function of wavelength for a sample length of 1.7 mm. The transmission at fixed wavelength (950 nm) is plotted as a function of analyzer angle in the inset of Fig. 5. It drops rapidly to a minimum at as the pure x-polarized state is approached.

 

Fig. 4. Experimental (a) and modeled (b) transmission spectra for x- and y-polarization (T_x and T_y) in a PCF with a single Ge wire (diameter 1.7 µm; length 0.8 mm) positioned adjacent to the glass core. The inset in (a) is a CCD image of the transmitted mode pattern for y-polarization. In the simulations, the fundamental mode of the glass core was selected from the numerical solutions. A calculated example of this mode at wavelength 550 nm is depicted in the inset of (b), showing the axial component of the Poynting vector (y-polarization).

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The transmission ratio also increases at longer wavelengths, reaching a maximum of 28 dB at around 850 nm. This high value can be explained by the fact that the power absorbed at the surface of a conductor is proportional to the tangential magnetic field inside the conductor (H parallel to surface) [21]. For x-polarization, the tangential magnetic field in the wire is much stronger than in the orthogonal case. Since Ge has finite conductivity at optical frequencies, higher losses are expected for x-polarized light. Apart from some weak features, the transmission in this wavelength range is quite flat without any pronounced dips, suggesting that the structure could be used as an in-fiber polarizer.

4.2 Transmission in the range 1050 to 1500 nm

Measured and simulated loss spectra for x- and y- polarization in the wavelength range 1050 to 1500 nm are shown in Fig. 6, normalized to those of an unfilled fiber. The spectra display multiple pronounced peaks, caused by coupling of the glass-core mode to successive resonances on the Ge wire. These peaks occur at wavelengths where the dispersion curves for the wire-resonances and PCF core-mode anti-cross, causing light to couple strongly to the Ge wire and enhancing the loss. The modes guided in the glass-core have effective phase indices that lie below that of silica and above that of the fundamental space-filling mode (FSM) in the PCF cladding, which means that the anti-crossings occur at Mie resonances on the wire. By comparing the axial Poynting vector distributions inside the wire at each anti-crossing wavelength (calculated using the finite-element code) with those at resonances in an isolated Ge-wire embedded in silica, the resonance order could be identified. Three such examples are shown in Fig. 7. At longer wavelengths, when coupling to the Mie resonances is stronger, the mode patterns differ more noticeably, although it is still possible to identify the mode order accurately.

 

Fig. 5. Ratio (in dB) between minimum (x-pol.) and maximum (y-pol.) transmission as a function of wavelength. The inset depicts the transmission versus analyzer angle at a fixed wavelength (λ ₀=950 nm). Sample length 1.7 mm.

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The experimental positions of the transmission dips agree with finite-element simulations to within 1%, despite the idealized structure used in the simulations and uncertainties in the value of the Ge dielectric function in the IR (especially Im(ε_Ge)). The dips for orthogonal polarizations are not always located at the same position, indicating that the mode coupling is somewhat polarization-dependent. This is especially clear for the loss peaks marked TM₀₅ and TE₀₅ in Fig. 6; for x-polarization, this peak appears at around 1206 nm whereas for y-polarization it is at 1182 nm.

 

Fig. 6. Loss of a PCF with a single Ge wire (length 0.8 mm) adjacent to the core. The red curves are simulations (fundamental glass-core mode) and the black are experiments. The labels on the loss peaks refer to the resonances on the Ge wire that phase-match to the glass-core mode. (a) x-polarization. (b) y-polarization. The three encircled points correspond to the modes whose Poynting vector distributions are shown in Fig. 7.

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For y-polarization, the simulations predict the magnitude of the loss at the peaks quite well. For x-polarization, the loss at the peaks was very high and could not be measured accurately for λ ₀>1200 nm, resulting in a significant disparity between experiment and theory, particularly for HE15. The simulations also revealed that the Ge-filled section supports two higher order glass-core modes which might be excited experimentally at the filled-unfilled transition. Especially for x-polarization, the first such higher-order glass-core mode shows much lower loss than the fundamental one due to a node in the electric field distribution along the central mirror-plane of the structure. Such higher-order glass-core modes, if excited even slightly, can significantly increase the transmission, reducing the measured loss at the peaks. Despite this, the relative magnitude between the loss peaks, and the tendency for higher resonant losses at longer wavelengths, are predicted correctly. Between the peaks the slightly higher experimental loss can be again ascribed to modal mismatch at the filled-unfilled interface – an effect that cannot be removed from the experimental data.

It is noticeable that for y-polarization the loss peak near 1450 nm is not clearly resolved in the experiments (Fig. 6(b)). As discussed earlier, we believe this is because light guided in higher-order glass-core modes contributes significantly to the overall measured transmission at longer wavelengths, masking the loss peak for the fundamental mode. The calculated TE₀₄ and TM₀₄ modes show a spectral splitting that is weakly present only in the experimental x-polarized spectrum.

 

Fig. 7. Axial Poynting vector distributions in vicinity of Ge-wire (a-c) in PCF, calculated using finite-element modelling and (d-f) for Ge wire embedded in silica, calculated by directly solving Maxwell’s equations for Mie resonances on the wire. The wire radius in both cases is R=0.85 µm. The calculations refer to the three points marked by small blue circles in Fig. 6: (a) and (d) are at wavelength 1110 nm for y-polarization, resonance order EH₁₆; (b) and (e) are at wavelength 1201 nm for x-polarization, resonance order TM₀₅; (c) and (f) are at wavelength 1397 nm for x-polarization, resonance order HE₂₄. In (d-f), the fields outside the wire (since the resonance is unbound, these grow in amplitude) have been removed from the plot so as to highlight the internal field patterns.

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5. Discussion and toy model

As pointed out in the previous section, the modes guided in the glass core have an effective index that lies below that of silica, meaning that the Ge wire, which sits inside the silica guiding core of the PCF, cannot support proper bound modes, but rather will exhibit Mie-like resonances for certain combinations of wavelength and axial phase index. When the glasscore mode passes through a wavelength region where it phase-matches to a resonance on the wire, its attenuation rises and its phase index undergoes a local distortion as a result of the Kramers-Kronig relations. To understand the physics of this interaction more clearly, we present here the results of a simple analysis of the modes guided in a thin-film waveguide consisting of a layer of silica (4 µm wide) and a layer of Ge (1 µm wide), sandwiched between cladding material of refractive index 1.35. The full dispersion of Ge and silica is included, and the cladding material is assumed dispersionless.

The results confirm that the TM mode (closely related to the x-polarized mode in the PCF) experiences much larger loss, that the loss peaks occur when a resonance is strongly excited in the Ge layer, and that they fade away at wavelengths below 900 nm (Fig. 8(a)). The distributions of electric field (Fig. 8(b)) illustrate how the loss is highest when a resonance exists in the Ge layer (B and D), while being much lower at anti-resonances (A and C).

 

Fig. 8. (a) Loss in dB/mm of the fundamental TE and TM guided modes in a silica layer 4 µm thick, placed adjacent to a Ge layer 1 µm thick, sandwiched between transparent cladding regions of index 1.35. The full dispersion of Ge and silica is included. The main features are qualitatively very similar to those seen for Ge-filled PCF: loss peaks at wavelengths beyond 900 nm, much higher loss for the TM mode, and a gradual reduction in average loss at shorter wavelengths. (b) Modulus squared of the electric field for the four modes marked A, B, C and D in (a). The presence of a resonance in the Ge layer causes the loss to peak strongly (B and D). In between resonances, the loss falls below its average value. At wavelengths below 900 nm, the loss in the Ge is so high that resonances cannot form, resulting in an absence of strong loss peaks.

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6. Temperature dependence of loss peaks

Over a broad spectral range, the real and imaginary parts of the dielectric function of Ge are functions of temperature [22], so as a next step we investigated the temperature dependence of the loss peaks in the optical transmission measurements for the 0.8 mm long device (Fig. 6). A Peltier element, attached to the fiber holder, was used to set temperatures in the range 295 to 343 K and the transmission spectrum measured. The investigations focused on the TE₀₅ (1180 nm), EH₁₅ (1300 nm) and EH₂₄ (1390 nm) peaks in y-polarization, since they have lower loss and consequently good spectral visibility (Fig. 6(b)). Figure 9 shows the measured percentage shift 100(λ _T-λ ₂₉₅)/λ ₂₉₅ of each peak relative to its spectral position at ambient temperature. As the temperature rises, the peaks shift to longer wavelength at rates of 0.13 nm/K (TE₀₅), 0.15 nm/K (EH₁₅) and 0.18 nm/K (EH₂₄). The physical origin of this shift lies in the decrease in width of the indirect electronic band gap of Ge with increasing temperature, which shifts the absorption band to longer wavelength [22]. This leads to an increase in the real part of the dielectric function in the IR region [21].

Next, finite-element calculations, including the temperature dependence of the dielectric functions for both Ge and silica, were used to evaluate the slope dλ/dT for the resonances. The simulations yielded slopes of 0.36 nm/K, 0.30 nm/K and 0.37 nm/K for the TE₀₅, EH₁₅ and EH₂₄ modes respectively, and show that the shift is almost entirely due to the temperature dependence of Ge (i.e., the contribution from silica is negligible). That these values are higher than the experimental ones (see the plot in Fig. 9), we attribute to temperature-dependent changes in stress in the composite Ge:silica structure. This is quite likely to be the case, since Ge expands when it solidifies from the liquid state [23].

Although a thorough assessment of Ge-filled PCF as a fiber-based thermometer belongs in a separate paper, it is perhaps worthwhile to compare its measured sensitivity with that obtained in other fiber-based devices. Bragg grating sensors provide ~0.01 nm/K [24], and long-period gratings are somewhat more sensitive, yielding ~0.1 nm/K [25, 26]. The use of hybrid structures can enhance the sensitivity considerably in each case, up to 19 nm/K (over a <2 K range) in the case of long-period gratings in standard fiber [27] and ~10 nm/K in hollow-core PCF filled with fluids or liquid crystals [28, 29], although the temperature range over which such hybrid devices operate is often quite restricted. Device length is also an important consideration, and here the 0.8 mm long Ge-silica device leads the field. For comparable sensitivities, it is between 10 and 100 times shorter than the Bragg grating and long-period grating devices reported in the literature, which are typically between 1 and 10 cm long.

 

Fig. 9. Measured relative spectral shift of the position of three of the resonance peaks in Fig. 6(b), plotted versus temperature, for y-polarization. The slopes of the fitted linear curves are shown in units of nm/K.

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7. Conclusions

Ge wires of high material and optical quality can be produced by pumping molten Ge into the hollow channels of silica-air PCF. In ESM-PCF, the presence of a single Ge wire placed adjacent to the core renders the waveguide birefringent, causing strongly polarization-dependent transmission losses (~30 dB at 850 nm). In the IR (900 to 1500 nm), anti-crossings between the glass-core mode and Mie resonances on the Ge wire are seen at a series of different wavelengths, resulting in clear dips in the signal transmitted through the fiber. In the range 500 to 900 nm the high absorption in Ge prevents the formation of resonances. In both cases, the transmission loss is much higher for electric field polarized along the x-axis (joining the glass core and the Ge wire), and the device operates as an effective broad-band polarizer for wavelengths <900 nm. The loss peaks in the IR move to longer wavelength at a rate of ~0.2 nm/K, suggesting that the structure could form the basis for a new kind of in-fiber thermometer. Numerical simulations based on finite-element modeling show excellent agreement with the experimental results in all cases.