Polymer Clad Silica Fibers for Tailoring Modal Area and Dispersion

Abstract

We demonstrate higher-order-mode (A_eff up to ~2000 μm²) propagation in a 100 μm outer diameter pure-silica fiber with a low-index polymer jacket commonly used for fiber-laser pump-guidance. This simple structure obviates the need for complex designs deemed necessary for realizing large-mode-area fibers. Modes ranging from HE_1,12 to HE_1,22 were found to propagate stably over 15 m in this fiber. The index step is approximately 4 times larger than that obtained with fluorine down doping, thus the fiber supports even higher order modes, which may have implications for building rare earth doped fiber lasers or achieving enhanced dispersion tunability for high-energy fiber nonlinear phenomena.

Higher order modes (HOMs) are known to be scalably stable in step-index multimode fibers [1,2], and have been used for rare earth doped high power fiber amplifiers [3]. The high confinement of these modes, in spite of being large in mode area, is also useful for tailoring dispersion [4,5] for high-power nonlinear applications [6]. The guidance region for HOMs in fibers has typically been defined by either a fluorine doped outer cladding or an air-clad microstructured cladding [2]. For fluorine doped fibers, the dispersion tunabilty is limited by the number of guided modes, which depends on manufacturing constraints in achievable refractive index step contrasts. On the other hand, air-clad microstructured fibers may not have the azimuthal symmetry required for stably guiding very high order modes. Given recent advances in efficient free-space excitation of vortices and HOMs [7,8], it is worth considering whether a very simple fiber structure for HOM guidance could be realized, using low-index polymer jackets, conventionally used for multimode pump propagation in high power fiber lasers [9].

Here, we demonstrate, for the first time to the best of our knowledge, stable HOM (HE_1,m modes; LP_0,m modes in the scalar approximation) propagation in a simple fiber structure. The guiding region is defined by a silica core surrounded by a low-index polymer cladding (Efiron PC373). Modes ranging from HE_1,12 to HE_1,22 were found to be stable (>10.9-dB mode purity compared to other mode groups) over 15.6 m of this fiber. The effective areas of these modes are as high as 2000 μm².

The fabricated fiber has a pure silica core with a diameter of 100 μm, surrounded by a low index polymer jacket of 62 μm thickness (total outer diameter ~224 μm). The simulated dispersion for a selection of HE_1,m modes in this fiber are shown in Fig 1(a). The refractive index profile of the fiber is shown (blue trace) in Fig. 1(b). For reference, a fictitious fiber of identical dimensions, but with a down doped fluorine region instead of low index polymer is also shown (red dashed trace). The simulated dispersion at 1064 nm for different modes of the two fibers is shown in Fig. 1(c). The index step for the polymer fiber is approximately 4 times larger than that possible with a fluorine down doped region, thus the modal cut-off occurs at a much higher mode order (HE_1,41 instead of HE_1,20). This leads to anomalous dispersion at 1064 nm as large as 7× that possible in the all-glass HOM fiber. The effective area of the modes between HE_1,10 and HE_1,40 range from 1600 μm² to 2000 μm². Additionally anomalous dispersion is attainable at even shorter wavelength (down to 425 nm, past that possible with PCF [10]). Both these properties are of great interest in nonlinear applications.

Fig. 1.

a) Simulated dispersion for a selection of HE_1,m modes in the fabricated fiber. b) Refractive index profile for the fiber, along with an equivalent fiber of same dimensions, but with a down doped fluorine region instead of low index polymer. c) Simulated dispersion at 1064 nm as a function of mode order for the two fibers.

The experimental setup is shown in Fig. 2(a). The source used for mode imaging is a fiber Bragg grating stabilized laser diode at 1048 nm with a FWHM bandwidth of 0.08 nm. Quantitative mode purity measurements are performed by frequency-domain cross correlation imaging (fC²) using a 10xx nm tunable external cavity diode laser (ECL) [11], or time-domain cross correlation imaging (C²) using a 1064-nm LED with 2.8-nm full-width at half maximum (FWHM) [12,13]. Modes are excited using a spatial light modulator (SLM) that encodes the desired spatial phase on the linearly polarized incident Gaussian beam before the light is coupled into the fiber under test (FUT). This mode conversion technique is versatile, and has also been shown to yield high purity mode excitation in glass-glass HOM fibers [8].

Fig. 2.

a) Experimental setup for higher order mode excitation. The source is at 1048 nm (FWHM = 0.08 nm) for images, a 10xx nm tunable ECL for fC², or a FWHM = 2.8 nm filtered LED centered at 1064 nm for C², single mode fiber (SMF), spatial light modulator (SLM), fiber under test (FUT), polarizing beam displacing prism (PBDP). b–g) Imaged modes after 15.6 m of propagation.

All guided HE_1,m modes were selectively excited and imaged in a 15.6 m long FUT with a coiling radius of 13 cm [output images in Fig. 2(b)–(g)]. Modes below HE_1,11 [Fig. 2(b)–(c)] exhibit distributed mode coupling, as apparent from the mode images. This was further confirmed by performing cut-back experiments, and observing that the mode images more closely resembled simulated modes as the propagation length decreased. In this class of large-mode-area (LMA), step-index multi-mode fibers, mode stability is largely determined by the effective index (n_eff) separation between a given HE_1,m mode and its nearest neighbor anti-symmetric mode – as these modes are preferentially coupled by bends in the fiber [1]. Separation in n_eff increases with radial mode order (m), thus we expect that higher modes orders propagate more stably – in keeping with the “pure” mode images measured for HE_1,14 and HE_1,17 [Fig. 2(d)–(e)]. However, above HE_1,24 [Fig. 2(f)–(g)] the mode images start to degrade even though the n_eff separation is expected to be beneficially large. In order to better understand the origin of this modal degradation for very high mode orders, and explain why even the “pure” modes have a non-circular first ring, cross correlation measurements were performed [11–13]. Before discussing the cross correlation measurements, we will first consider modes in high index waveguides.

Mode classification within the scalar approximation leads to azimuthally symmetric LP_0,m modes, also called HE_1,m modes in the full vectorial description. This uniformly (e.g., linearly) polarized approximation gradually breaks down as the field strength at a large refractive index step increases, in any waveguide [14–16], because the radial and azimuthal components of the electric field must satisfy different boundary conditions. Consequently, the electric fields of the HE_1,m modes become quasi-radially polarized, while another set of vector modes, the EH_1,m modes (part of the LP_2,m mode in the scalar picture), become quasi-azimuthally polarized. The HE_1,m and EH_1,m-1 modes are nearly degenerate in most fibers, and consequently have similar locations for ring peaks and nulls. Since the polymer-clad fibers discussed herein have especially high index contrast (by design, to tailor dispersion), we expect the modes of these fibers to also show significant polarization non-uniformities Figure 3(a)–(d) shows the simulated intensity distribution overlaid with polarization projections, for a lower and higher order mode pairs comprising the almost degenerate HE_1,m and EH_1,m-1 modes for our fiber, simulated using a full-vectorial mode solver described in [17]. For lower mode orders, the LP approximation holds well, but for higher mode orders, the polarization, and even the intensity distribution along the azimuth, becomes non-uniform (these high order modes have been named “bow-tie” modes [15,16]). Stated differently, as mode order increases (and the mode field increasingly encounters the high-index step boundary), the HE_1,m modes’ polarization extinction ratio (PER), the power ratio between the maximum and minimum linear polarization projection of the mode, decreases dramatically [Fig. 3(e)]. Likewise, even assuming the most perfect phase structured free-space coupling setup, for example, with a well-aligned spatial light modulator (SLM) and coupling setup (as in [8] that can achieve > 18 dB mode excitation purity for scalar modes), as much as 3 dB of power would be coupled into the undesired EH_1,16 mode with respect to the intended HE_1,17 mode, for example. Figure 3(f) summarizes this calculation using overlap integrals, and shows that, even with perfect scalar mode excitation, other parasitic modes are increasingly excited as mode order increases in a step index guide comprising silica and air (note that, while our fibers have an index boundary defined by silica and polymer, our simulations in Fig. 3 assume an air-silica guide because mode excitation and imaging is performed on a cleaved fiber input/output, where the guidance structure is effectively silica-air). These calculations qualitatively match the observations illustrated in Fig. 2(d)–(e), which show progressively more distorted output mode images as mode order is increased, in spite of the fact that n_eff separations increase with mode order, which would have predicted more stable guidance for higher mode orders. Thus, while high index contrasts easily enabled by glass-polymer clad structures provide expansive dispersion tailoring opportunities, the number of modes actually available for such tailoring may depend on the aforementioned vector effects, and quantitative mode purity analysis is needed to understand the subset of modes available.

Fig. 3.

Simulated intensity distribution of four modes (Γ=0.6), orange arrows indicate local polarization: a) HE_1,3. b) HE_1,17. c) EH_1,2. d) EH_1,16. e) Simulated polarization extinction ratio (PER) as a function of mode order. f) Simulation of most parasitic modal content excited in the fiber relative to the targeted HE_1,m mode.

For quantitative measurements, we employ a polarization-resolved variant of the fC² technique presented in [11] (see setup in Fig. 2a). An fC² trace shows the power of excitation at different temporal delays, and since temporal delays map directly to mode order, mode purity is simply deduced by comparing the highest peak (where the desired dominant mode is excited) with the parasitic peaks at other temporal delays. Moreover, temporal signatures along with digital mode reconstructions also help identify the mode order causing the parasitic peaks in the trace. Three example traces are shown in Fig. 4(a)–(c). In Fig. 4(a), where we attempt to excite the HE_1,5 mode, peaks after 200 ps are spurious and are caused by reflections in the system. The desired mode appears at a delay of about 95 ps, as expected, however the temporal response around this peak is significantly wider than the expected delay to the neighboring HE_1,m modes, which is about 16 ps. This indicates that the mode is not pure and that distributed coupling has occurred to other modes, as suggested by the mode images in Fig. 2(b)–(c). In Fig. 4(b), the peak at a delay of 92 ps is the mode group containing the targeted HE_1,17 mode, and the most parasitic mode is suppressed by 17 dB. The peak is narrow compared to the resolution of the fC² system, and also significantly narrower than the peak for the HE_1,5 mode, which is evidence of negligible distributed mode coupling between mode groups. Figure 4(c) shows the fC² measurement when exciting the HE_1,30 mode (appears at delay of 214 ps), and in this case, the nearest parasitic mode group has 8.2 dB lower power. This lower purity [compared to that for the HE_1,17 mode of Fig. 4(b)] is consistent with observation that the images of modes of very high order were degraded [Fig. 2(f)–(g)]. Since their fC² peaks are narrow, mode propagation appears to be stable, and hence we speculate that the cause for the lower measured purity is impure excitation with our SLMs (due to vector effects discussed in context of Fig. 3). Similar measurements were performed thrice for each of the modes from HE_1,5 to HE_1,33, and are summarized in Fig. 4(d). The red crosses are individual measurements and the blue line denotes the average result. The modes are divided into three groups. The green region represents “pure” modes, the blue region illustrates modes suffering from distributed mode coupling, and the red region are the modes that we suspect to be free from distributed coupling but not purely excited.

Fig. 4.

a) Three examples of fC² traces: a) HE_1,5. b) HE_1,17. c) HE_1,30. d) Modal purity as a function of targeted mode order. Each red cross represents mode purity to most parasitic mode found from a fC² trace. The blue line is the average over three measurements for each mode. Representative mode images in the three regimes are shown in Fig. 2.

The fC² measurements, however, do not reveal some subtleties related to mode purity in these fibers. For instance, when the HE_1,17 mode is excited, fC² measurements reveal parasitic modes to be below −17 dB. This is normally a very high purity mode that would not have a distorted first high-intensity ring, as the mode intensity image in Fig. 2e shows. This apparent discrepancy is addressed by considering that HOMs in a step-index fiber are divided into mode groups that are (almost) degenerate in group-index. That is, the HE_1,m and EH_1,m-1 (LP_0,m and LP_2,m-1 in the scalar approximation) modes of given radial order m, form a mode group. The delay between modes within a group is typically less than the temporal resolution of the fC² system, meaning that fC² measurements probe the purity between mode groups rather than individual modes. To analyze the modal content within a mode group higher resolution (time-domain) C² measurements are needed.

The setup for performing higher resolution time-domain C² measurements is shown in Fig. 2(a). Similar to fC², the time domain version also time-gates the envelopes of the interferometric traces, but with much finer resolution enabled by a mirror scanned with a translation stage, resulting in image acquisition at much finer temporal delays. Due to the computationally intensive nature of C² data acquisition, only the center portion of the HE_1,m mode images (center spot and first ring) were included in the analysis. In post processing, the envelope of each pixel and polarization was found separately, and the envelopes for all pixels for a given polarization were then added together and normalized by the peak. Figure 5(a) illustrates C² traces for the HE_1,12 mode, which, based on excitation purity predictions [Fig. 3(e)], is substantially uniformly polarized like an LP_0,12 mode, and hence is expected to be excited with high purity. In either polarization bins there is only a single Gaussian envelope at the same delay, confirming the aforementioned theoretically expected behavior. The HE_1,17 mode [Fig. 5(b)], on the other hand, becomes harder to excite with a uniform polarization setup, and the excitation purity is expected to be only ~3 dB [see Fig. 3(f)]. In this case each mode within the mode group (HE_1,17 and EH_1,16) projects into orthogonal polarization bins, and the measured (1.45 ps) and simulated (1.58 ps) delays between the individual modes of this group match well. The excitation of these two modes is also predicted in Fig. 3(f). The two modes being distinct and narrow also confirms that these modes remain pure and stable while propagating. Note that modes in this class may not necessarily separate into orthogonal polarization bins – even so, observing their shape provides insight into mode purity. For even higher mode orders the envelopes always have several peaks in each polarization projection [Fig. 5(c); target mode: HE_1,26 mode]. The envelopes are broader than the theoretically deduced 2.7 ps group-delay difference between the target mode and the closest mode within the group (EH_1,25). This indicates that higher azimuthal order modes, e.g. HE_3,m-1, HE_5,m-2, EH_3,m-2, etc (each of these modes have a simulated delay of a few picoseconds relative to EH_1,25) may have been additionally excited since the need for encoding higher spatial frequencies on the SLM may cause under-sampling. The dispersion of the modes in the FUT can be calculated from the width of the envelopes and the dispersion in the reference arm. This was performed for each pixel, and the results are shown for different mode orders in Fig. 5(d). For the lower order modes, where a single mode was excited, the agreement is good. This validates the assertion that distributed mode coupling did not take place along the fiber. However, the error bars increase with increasing mode order, and for modes larger than HE_1,24 the dispersion is over estimated. This likely is due to the difficulty in accurately fitting the C² envelope in the presence of numerous peaks as seen in Fig. 5(c).

Fig. 5.

a) Three examples of C² traces target mode is: a) HE_1,12. b) HE_1,17. c) HE_1,26. d) Dispersion at 1064 nm for different mode orders. Black circles are average over all pixels, error bars denote a single standard deviation, and blue crosses are simulated results.

Thus, we believe that, given our current excitation method there is an amount of EH_1,m-1 content being excited when targeting a HE_1,m mode in the bowtie-regime. This is in agreement with the C² measurements shown in Fig. 5(b), which showed the presence of two modes that both propagated stably in the fiber. Furthermore, this is also evident from the non-circular first ring observed in the mode images of Fig. 2(b)–(g), caused by interference between these two modes. Therefore, excitation of pure modes in high index contrast fibers such as the silica fiber simply jacketed with a low-index polymer would require an excitation scheme that offers spatial polarization tailoring in addition to phase tailoring. Given the existence of devices such as q-plates [18] and continual developments in the field of micro-optics that can achieve many SLM functionalities in a compact, manufacturable, high-power tolerant platform, we believe that such field-profile tailoring can be practically realized. Another concern with such fibers is related to the fact that the guiding region and the physical edge of the glass fiber are the same – hence care may be needed when cleaving or polishing the fiber. Nevertheless, quantitative interferometric measurement techniques allow us to confirm, independent of our ability to excite the modes cleanly, that HOM propagation is stable in these fibers, and dispersion design is enhanced by the presence of many more modes than is available in all-glass waveguiding structures.

In summary, we demonstrate stable LMA propagation in a simple fiber comprising of only silica drawn with a low-index polymer jacket Modes ranging from HE_1,12 to HE_1,22, with mode areas ranging 1700–2000 μm², and dispersion-zeroes ranging from 1037 to 835 nm, were found to be stable (≳11 dB pure compared to other mode groups) over 15.6 m of propagation in this fiber. The simplicity of this fiber design, which could potentially be scaled to even larger A_eff, may be beneficial for building doped fiber lasers or achieving enhanced dispersion tunability for high-energy fiber nonlinear phenomena. Although such structures are the only way, to the best of our knowledge, to achieve large dispersion tunability in large mode area fiber, future work would clarify if the inherent simplicity offered by this design is, however, offset by the need for a more complicated (polarization-diverse) excitation setup.