Origin of high propagation loss in electrospun polymer nanofibers Open Access

Nanofibers, which are fibers with diameters less than 1 μm, are attracting considerable attention owing to unique optical interactions that arise from their subwavelength size including guiding,^1–7 confinement,⁸ and amplification.^9,10 These properties make them promising candidates for applications in small optical devices such as waveguides,^1–7 light sources,^11,12 sensors,¹³ resonators,¹⁴ gratings,¹⁵ and switches,¹⁶ and the fibers are also applicable to the field of plasmonics¹⁷ and optomechanics.^18,19 Electrospun polymer fibers have nanometer diameters and high aspect ratios, making them well-suited for use in such optical devices. Additionally, the fibers can be directly deposited in fine patterns using near-field electrospinning^20,21 or controlling electrical fields²² on two- and even three-dimensional substrates. Recently, several groups have demonstrated using poly(methyl methacrylate) (PMMA) as a core material optical waveguiding in electrospun polymer nanofibers and reported the propagation loss to be higher than orders of 10 dB cm⁻¹.^10,23 Although this value is more than 10⁴ times higher than that of a well-studied graded-index PMMA-based optical fiber with a diameter of 0.5 mm,²⁴ the origin of such high loss has been unclear. In this paper, we evaluate propagation loss in electrospun PMMA nanofibers at different wavelengths and determine the origin of the high propagation loss.

PMMA was chosen as a core material because it shows high transparency in the visible range and is well-studied as a core material in the field of thick polymer optical fibers.²⁵ The amorphous fluoropolymer CYTOP^® (CTX-109AE, Asahi Glass Co., Ltd.) was chosen as cladding material because it has lower refraction index than does PMMA and shows high transparency in the visible range.²⁶ PMMA (Mw ∼ 350 000, Sigma-Aldrich) was dissolved in N,N-dimethylformamide (DMF) at a concentration of 12 wt.%. Next, rhodamine 6G (R6G, Sigma-Aldrich) was added to the solution to evaluate propagation loss in produced fibers. The concentration of R6G was 4.9 × 10⁻³ wt.% relative to the solution, which was 1 × 10⁻³ mol L⁻¹ relative to the volume of dissolved PMMA. The PMMA/R6G solution was dispensed from a needle tip (0.3 mm in diameter) of syringe at a constant rate of 0.20 mL h⁻¹ and electrospun with a voltage of 2.2 kV. Two collectors were placed 15 cm below the tip of the needle, and one of the two collectors was biased with a negative voltage (−800 V) while the other collector was grounded. Then, a single aligned fiber was formed bridging the two collectors after switching the biased collector once.²⁷ All experiments were performed in air at room temperature with a humidity of 58 ± 5%. We prepared seven single-fiber samples (labeled Fiber A–G) to assess the variability of propagation loss among them. The single fibers were individually cladded in CYTOP. After cutting the ends of the fibers, each was irradiated with a laser beam (wavelength λ = 532 nm) from a laser module (LCM-T-111, Laser-Export Co. Ltd.) incident perpendicularly to the fiber axis²³ (see Fig. 1). The radius and power of the laser beam were 388 ± 5 μm and 5 mW, respectively, and the direction of polarization of the beam was set parallel to the fiber axis. Photoluminescence (PL) from the R6G molecules within each fiber was guided and its spectrum measured at one end with a spectrometer (USB4000, Ocean Optics, Inc.), which was connected to a fluorescence microscope (BX-51, Olympus) with a sharp-cut filter which transmitted light with λ longer than 590 nm. The circular detection area had a diameter of 8 μm, and the PL spectra were measured at 0.21-nm increments. The shape of each single fiber was seamlessly characterized along a 1200-μm length by means of a field-emission scanning electron microscope (FESEM, SU8000, Hitachi). The average diameter for each fiber was calculated from diameters measured at 4-μm intervals from the FESEM images; 300 readings for each fiber were recorded. For the transmittance spectrum measurements, R6G was dissolved in DMF at a concentration of 1 × 10⁻³ mol L⁻¹. Transmittance spectra of the R6G solution were measured using an UV-Vis spectrophotometer (U-4100, Hitachi) at various solution thicknesses (t), controlled using different sizes of quartz cells.

We measured spectra of PL guided in each cladded fiber at one end for various heights (h) between the fiber end and the point of irradiation [Fig. 1]. The PL intensity decreased with increasing h at each wavelength (λ) as shown in Fig. 2(a) because increased propagation length enhanced attenuation of the intensity. The origin of the attenuation is discussed later. To suppress noise [solid lines in Fig. 2(a)], we averaged PL intensities for each spectrum over 30 neighboring data points for each λ. The averaged PL intensities were logarithmically plotted as a function of h for different λ as shown in Fig. 2(b). The PL intensity for each curve (fixed λ) decreased with increasing h, and the plots were well-fitted with function A × 10^−a′h [solid lines in Fig. 2(b)], where A is an arbitrary constant and a′ the loss coefficient. From the fitting function, propagation loss (α) was evaluated using α = −10Log(A10^−a′·h|_{h = 1 cm}/A10^−a′·h|_{h = 0 cm}) = 10a′ [dB cm⁻¹], which is plotted in Fig. 3 as a function of λ⁻⁴, to be discussed later in regard to the origin of α. α was less than 63 dB cm⁻¹ at λ from 590 nm to 680 nm and decreased with increasing λ. Among the seven fibers, α ranged, for example, from 29 dB cm⁻¹ to 46 dB cm⁻¹ at a wavelength of 650 nm, indicating variability in propagation loss among the fibers. We also estimated the number of possible guiding modes in the fiber samples. The normalized frequency (V) is expressed by the following equation,

where n₁ and n₂ are the refractive indices of PMMA and CYTOP, respectively, k is the wave propagation constant in a vacuum, and D is the diameter of the fibers. If we assume n₁ = 1.49, n₂ = 1.34, λ = 590–680 nm, and D = 585–661 nm (average fiber diameters will be discussed below), V yields 1.76–2.29. Consequently, the fiber samples allow only a single mode (HE₁₁ mode) to propagate because the calculated V is less than 2.405, which is a cut off value of V for the LP₁₁ mode.²⁸ 

The evaluated α was more than 10⁴ times higher than the reported value of 1.3 × 10⁻³ dB cm⁻¹ which was measured for a grated-index PMMA-based optical fiber with a diameter of 0.5 mm at λ of 650 nm.²⁴ The high α of the nanofiber waveguides appears to originate from the following phenomena: (i) re-absorption of guided light by R6G molecules,^23,29 (ii) excess light scattering in the fibers resulting from density inhomogeneity of PMMA,^30,31 and (iii) loss at the interface between fiber-core and cladding because of non-uniformity with the fibers.²⁸ We note that absorption via the vibration modes of PMMA is negligible because it is less than 5.0 × 10⁻³ dB cm⁻¹ within the wavelength range 590−680 nm.²⁵ First, to investigate the loss through re-absorption of guided PL by R6G molecules (α_ab), phenomena (i), we measured transmittance spectra of the 1 × 10⁻³ mol L⁻¹ R6G solution at different thickness t [Fig. 4(a)] and evaluated α_ab at different λ. The concentration of R6G in the solution was the same as that of R6G according to the volume of PMMA in the electrospun PMMA/R6G fibers. As seen in Fig. 4(a), transmittance decreases with increasing t, especially at λs shorter than 630 nm, due to absorption by R6G molecules. We plotted the transmittance as a function of t for different λs [see inset in Fig. 4(b)], and fitted it with function 10^−b′t; here b′ is a loss coefficient. From the fitting function, α_ab was evaluated using expression α_ab′ = −10Log(10^−b′·t|_{t = 1 cm}/10^−b′·t|_{t = 0 cm}) = 10b′ [dB cm⁻¹]. The evaluated α_ab is logarithmically plotted in Fig. 4(b) as a function of λ. α_ab is less than 1.3 dB cm⁻¹ at λs longer than 590 nm, and decreases with increasing λ. Furthermore, α_ab is saturated at λs longer than 630 nm as these λs are longer than the absorption edge of R6G at room temperature. The value of α_ab is less than 3% of α even at λ of 590 nm, thus the loss through re-absorption of guided PL by R6G molecules is very small and negligible.

Loss owing to excess light scattering in the fibers resulting from density inhomogeneity of PMMA (α_sc), phenomena (ii), is a possible reason for high α as scattering is present in thick polymer optical fibers.^30,31 Moreover, loss at the interface between the fiber-core and cladding owing to non-uniformity of fiber (α_un), phenomena (iii), is also a possible reason as the non-uniformity is considerable, especially for small-diameter fibers, as reported, for example, for silica nanofibers.²⁸ To determine the ratio of α_sc and α_un for α, we plotted α as a function of λ⁻⁴ (Fig. 3). α linearly increased with increasing λ⁻⁴, and the plots were well-fitted to B + Cλ⁻⁴, where C is an arbitrary constant; B, a wavelength-independent constant, represents a wavelength-independent loss. As α_un is independent of λ for the α evaluated in this study, B directly represents α_un. Conversely, Cλ⁻⁴ represents a wavelength-dependent loss proportional to λ⁻⁴. From Debye theory, α_sc is known as a loss depending on λ⁻⁴,^32,33 hence Cλ⁻⁴ here represents α_sc. The calculated α_un (= B) and C are summarized in Table I. We have determined α_un to be in the range 6.9–22 dB cm⁻¹ for the seven fibers. As these values are 19%–50% of α at λ of 650 nm, we concluded that high α in these fibers originates from both their density inhomogeneity and poor uniformity. Note that α for conventional thick PMMA-based optical fibers exhibits low values at λ of approximately 570 nm and 650 nm because of lower absorption via the vibration modes of PMMA, although using guiding light with longer λ suppresses α_sc. To investigate uniformity within each fiber, we measured fiber diameters along a 1200-μm length of each fiber at 4-μm intervals using FESEM images (Fig. 5). The same fibers were investigated as those used for propagation loss measurement, separating the individual fibers before cladding. We calculated an average diameter and root-mean-square roughness (R_RMS) for each fiber; see listing in Table I. The R_RMS, ⟨ΔD/2⟩, was calculated using an approximation of

where D_ave is the average diameter of each fiber, and l the position where the diameter was measured. The range for R_RMS was 5.5–9.0 nm for the seven fibers, which was more than 14 times higher than that of a silica microfiber, 0.37 nm,³⁴ with α of 5.0 × 10⁻² dB cm⁻¹. This high degree of non-uniformity of the fibers supports the results of high α_un. We also estimated α_un for the fibers analytically, based on perturbation theory, using^34,35

where β and γ are the respective longitudinal and transverse propagation constants of the fibers, and L the characteristic variation length. For the fiber samples, β and γ were found to be 13–14 μm⁻¹ and 3.6–4.0 μm⁻¹, respectively, considering the HE₁₁ mode operation at λ of 650 nm and D of 584–661 nm. From the evaluated R_RMS and average diameter, ⟨ΔD/2⟩/(D/2) was approximately determined to be 2 × 10⁻². Assuming L to be 1 μm for silica nanofibers,²⁸ we obtained α_un ∼ 1 dB cm⁻¹, which yields reasonable agreement with our experimental data. Using Eq. (3), α_un is suppressed below 10⁻² dB cm⁻¹ if we reduce R_RMS to the silica fiber level, ⟨ΔD/2⟩/(D/2) ∼ 10⁻³. Note that the surface morphology of the individual fibers must remain unchanged after CYTOP cladding because we have confirmed insolubility of PMMA nanofibers after the cladding.³⁶ Besides, cross-linking between CYTOP and PMMA molecules at the core-cladding interface, which could locally affect density and refractive indices, is hard to occur because the repeat unit of CYTOP is quite difficult to cross-link and the cladding was performed at room temperature and under near-neutral condition without catalysts.

In summary, we evaluated propagation loss of single electrospun nanofibers of PMMA at various wavelengths and determined the origin of propagation loss to be both density inhomogeneities in PMMA and poor uniformity in the fibers. A quantitative investigation of the latter revealed that R_RMS ranged over 5.5−9.0 nm and the theoretical value of α_un was ∼1 dB cm⁻¹ showing reasonable agreement with experimental data. These findings hold for low-loss polymer nanofiber waveguides, which have high aspect ratio and fine patterning even in three dimensions. The low-loss waveguides should be promising candidates for applications in small optical devices such as waveguides, light sources, sensors, resonators, gratings, and switches, and the waveguides are also applicable to the field of plasmonics and optomechanics.

This work was partially supported by the Japan Society for the Promotion of Science KAKENHI Grant No. 24810013 and Research Grants from the Research Foundation for Opto-Science and Technology.