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Abstract
We report on the excitation and polarization preserved propagation of a very large effective-area (Aeff ∼ 2240 μm2) higher-order-mode in an optical fiber. A laser signal operating in the 1 μm wavelength region is transported in a Bessel-like LP0,4 mode over a 10 m long section of the polarization-maintaining higher-order-mode fiber. We observe that the light propagates through the fiber with >10 dB polarization-extinction-ratio as the fiber is coiled into circular loops of 40 cm diameter.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-power fiber sources [1–4] are being rapidly adopted as an indispensable tool within many branches of natural science. Offering breakthrough capabilities, such lasers have also modernized a wide range of industries, including automotive, medicine, aerospace and military, to name a few. A further scaling of the power-level of fiber sources is a continued challenge that carries great potential rewards in terms of both the scientific capabilities and the technological development. In order to suppress the intensity dependent nonlinear-optical-effects that limit the power-scaling of the fiber-sources, a natural strategy is to develop fibers with a large-effective-area guided-mode [5–8].
Additionally, preserving the polarization-state of the propagating light is crucial for a variety of applications of the high-power fiber lasers: a few examples include polarization-multiplexing, coherent beam combination, improved material-processing, and high-harmonic-generation [9–12]. In the past, several fiber designs have been reported for the polarization-maintained (PM) propagation of light in large Aeff optical modes. Most of those fibers were designed to guide light in the lowest-order fundamental (LP0,1) mode for obtaining a single-mode operation with a deterministically controlled brightness and beam quality. In order to scale the Aeff of the LP0,1 mode while satisfying the condition (V < 2.405, where $V = (2\pi /\lambda )\cdot a\cdot \textrm{NA}$) for a single-mode operation, a typical strategy is to increase the core radius $(a )$ and to correspondingly lower the numerical aperture $({\textrm{NA}} )$ of the fiber. In practice, the lowest $\textrm{NA}$ value that can reliably be achieved with the standard methods of preform and fiber fabrication sets the upper limit on the core-size and, therefore, on the Aeff of the guided-mode. Furthermore, the lower-NA leads to a lower confinement of the fundamental mode and to a reduced index-separation ${\Delta }{n_{eff}}$ between the fundamental mode and the nearest-neighboring higher-order-mode. This can severely challenge the robustness of the fundamental-mode operation due to a reduction in the Aeff of the fundamental mode, and a distortion of the field-distribution from a detrimental mode-mixing, in the presence of fiber bends and/or physical perturbations.
On the other hand, the index-separation between the neighboring modes of an optical waveguide increases with the mode-order [13]. Moreover, the Aeff reduction of the higher-order-mode can be mitigated by a suitable fiber design where the mode is relatively well-confined within the waveguiding region. As a result, the higher-order LP0,N modes in such an optical fiber can demonstrate more robust single-mode operation with respect to the LP0,1 mode. Recognizing these advantages, higher-order-mode fibers can be designed that consist of two concentric cores of different diameters, where the smaller core is truly single-mode (V < 2.405) and facilitates low-loss fusion-splicing to the standard optical fibers, and the larger core guides the higher-order-modes. There is no strict fundamental limit on increasing the size of the larger-core in such fibers and, therefore, the higher-order-mode (HOM) fibers carry the potential for unparalleled large Aeff operation [14,15]. A PANDA-type PM-HOM fiber was demonstrated recently, and the preliminary results were reported on the propagation of an LP0,8 HOM (Aeff ∼1300 μm2) over a ∼1 m long, unbent section of the fiber [16].
In this paper, we present our studies on the polarization-maintained delivery of light in a record-large Aeff (∼ 2243 μm2, at wavelength $\lambda = $1070 nm) HOM over a 10 m long, bent section of optical fiber. Specifically, we launch light in to the fundamental LP0,1 mode of the PM-HOM fiber, perform in-fiber mode-conversion from the LP0,1 to the LP0,4 mode via a long-period grating inscribed within the smaller core, and study the polarization-preserved propagation of the HOM in the fiber. We find that the PM propagation of the HOM is robust against the fiber bends, affording the delivery of the LP0,4-mode with a polarization-extinction-ratio (PER) >10 dB as the fiber is bent into circular loops of 40 cm diameter.
2. Fiber design and analysis
Fig. 1(a) depicts the schematic of the fiber cross-section. The silica glass-based optical fiber, as shown in Fig. 1(b), consists of a small-diameter core, located concentrically within the large-diameter outer-core. The inner-core is designed to be single-mode (V∼1.897, mode field diameter (MFD) ∼ 14 μm) within the 1 μm wavelength region, thereby, allowing for a low-loss fusion-splicing to the MFD-matched OFS high-power, single-mode fiber-laser platform [18]. The inner-core region is doped with germanium to raise the refractive-index for the LP0,1-mode guidance and for facilitating the UV-inscription of long-period gratings as in-fiber mode-convertors. The outer-core, on the other hand, is ∼70 μm in diameter and has an NA ∼ 0.134, which corresponds to a V-number ∼ 29.683 at wavelength λ = 1070 nm. Using the relation derived in [19], the number of LP0,N modes of a specific polarization supported by the outer-core of the fiber is estimated as,
Fig. 1. (a) Schematic diagram of the fiber cross-section; (b) a microscope photograph of the PM-HOM fiber.
Fig. 2. (a) Numerically computed effective-refractive-index of the various guided modes as a function of the wavelength, (inset): Measured refractive-index distribution within the modes-guiding region of the fiber; (b) Effective-area of the various LP0,N fiber modes; (c) and (d) transverse intensity distribution of the LP0,1 and LP0,4 modes guided within the fiber, respectively.
We also calculate the effective-areas of the optical modes guided by the fiber [19]. As shown in Fig. 2(b), the higher-order-modes, guided within the outer-core, exhibit Aeff ranging from 1200 to 2800 μm2, which is more than an order-of-magnitude larger than that of the inner-core-guided fundamental-mode. It is known that the mode-stability in the presence of external perturbations, such as bends, increases with the mode-order [13]. As a result, we choose to operate in the LP0,4 mode (Aeff ∼ 2240 μm2) that presents a suitable combination of the increased modal stability and the large effective area. The modal analysis also reveals that all the guided-modes of the fiber exhibit normal chromatic-dispersion $({{\beta_2} > 0} )$ within the wavelength range of interest ($\lambda \sim $1070 nm), which is beneficial in suppressing such nonlinear optical effects as modulation instability [20], in addition to the Raman and Brillouin scattering that are suppressed due to the effective-area scaling. The transverse intensity distributions of the LP0,1 and LP0,4 fiber-modes are plotted in Figs. 2(c) and 2(d), respectively.
To cause PM propagation in the HOM-fiber, two circularly-shaped borosilicate-glass rods are added in the preform by drilling two longitudinally extended holes located symmetrically around the outer-core. As the preform is heated and drawn to a fiber, the difference between the thermal expansion coefficients of the (borosilicate) stress-rods and the remaining (silica) preform leads to a non-uniform stress distribution within the fiber cross-section. This asymmetric transverse stress distribution lifts the degeneracy among the orthogonally polarized optical modes i.e., $|{{n_x} - {n_y}} |> 0$, thereby lending birefringence to the fiber. The amount of stress-induced birefringence in a PANDA-type fiber is a function of the location and the diameter of the stress-rods, as well as that of the mechanical (Young’s modulus, Poisson ratio), thermal and stress-optical properties of the glass [17]. The birefringence at the center of the core of a PANDA-fiber is given as,
Fig. 3. (a) Birefringence at the center of the fiber computed for various combinations of the stress-rods location and size; (b) birefringence map across the fiber cross-section computed for the case of 125 μm diameter stress-rods with the inner-edge offset of 50 μm from the center of the fiber.
We also obtain a more precise estimate of the mode birefringence from a full computation of the various components of the stress tensor within the fiber [17]. As described in [21,22], the longitudinal stress component is negligibly small in a longitudinally extended cylindrical objects, including optical fibers. Figure 3(b) shows the transverse distribution of the birefringence, $B({x,y} )= C({{\sigma_x}({x,y} )- {\sigma_y}({x,y} )} )$, where ${\sigma _x}({x,y} )$ and ${\sigma _y}({x,y} )$ are the transverse stress components as computed from the solutions derived in [17]. We then estimate the effective birefringence that is experienced by any of the guided modes by taking in to account its transverse intensity distribution, ${B_{eff}} = \int\!\!\!\int B({x,y} )E({x,y} )\cdot {E^\ast }({x,y} )dxdy/\int\!\!\!\int E({x,y} )\cdot {E^\ast }({x,y} )dxdy$ [23]. The effective birefringence of the LP0,1 and LP0,4 modes is computed to be 2.03×10−4 and 2.01×10−4, respectively.
3. Experimental results and discussion
We characterize the PM-performance of our HOM-fiber by exciting the relevant higher-order polarized mode. We accomplish this by using a long-period-grating (LPG) inscribed directly within the PM-HOM fiber sample. As shown in Fig. 4(a), the gaussian-shaped output light from a fiberized broadband source (MFD ∼ 14 μm) is coupled into the LP0,1 fundamental mode (guided within the inner-core) of the PM-HOM fiber. Upon passing through the in-fiber LPG, a transformation of the propagating light takes place from the LP0,1 to the LP0,N mode distribution. In order to obtain mode-conversion from LP0,1 to the LP0,4 mode at λ∼1070 nm, we utilize an LPG of period $\Lambda = $797 μm. The required LPG period is computed from the standard grating equation $({{n_{0,1}} - {n_{0,4}} = \lambda /\Lambda } )$ and corresponds to the phase-mismatch that exists between the two interacting modes – the modes being LP0,1 and LP0,4 in the present case.
Fig. 4. (a) Experimental setup used for characterizing the spectrum of the LPG mode-converter inscribed within the PM-HOM fiber; (b) LPG spectra for the orthogonally polarized modes, showing the conversion of LP0,1 mode to the LP0,4 mode.
A KrF, UV-pulsed laser (repetition rate: 30 Hz, pulse energy: 6 mJ) operating at λ = 248 nm is used to photo-inscribe the 2 cm-long LPG in the germanium-doped inner-core of the fiber. After passing through a fused-silica-based amplitude mask of period $\Lambda = $797 μm, the UV-laser beam traverses across the PM-HOM fiber along its fast axis. The LPG transmission spectra for the slow and fast components of the LP0,4 HOM are shown in Fig. 4(a). In order to obtain the LPG spectra, a polarization-controlled broadband optical signal is transmitted through the PM-HOM fiber. The signal after transmission is directed to an optical spectrum analyzer via a single-mode fiber (MFD∼14 μm) that acts as a mode-filter i.e., it allows the low-loss guidance of only the fundamental mode and filters out any HOMs. Consequently, the recorded spectrum, plotted in Fig. 4(b), shows a dip in transmission within the wavelength band where mode-conversion occurs for each polarization component of the LP-mode.
The difference between the LPG resonance wavelengths for the slow and fast polarization states can be used to estimate the birefringence of the HOM. The group birefringence of the LP0,4 HOM can be expressed as, $\textrm{B}_{\textrm{L}{\textrm{P}_{0,4}}}^{group}\; \cong \; \textrm{B}_{\textrm{L}{\textrm{P}_{0,1}}}^{group} - {\Delta }{\lambda _{\; \textrm{L}{\textrm{P}_{0,4}}}}/{\Lambda }$, where $\textrm{B}_{\textrm{L}{\textrm{P}_{0,N}}}^{group}$ is the group-birefringence of the LP0,N-mode, and ${\Delta }{\lambda _{\textrm{L}{\textrm{P}_{0,4}}}}$ is the wavelength-separation between the LPG-resonances for the two orthogonal polarization components of the LP0,4-mode. Using the standard technique of spectral-beating between the two orthogonal polarization-components of a mode, we obtain $\textrm{B}_{\textrm{L}{\textrm{P}_{0,1}}}^{group}$∼ 2.4×10−4 for the fundamental mode [16]. From Fig. 4(b), we obtain ${\Delta }{\lambda _{\textrm{L}{\textrm{P}_{0,4}}}}$ ∼ 13 nm, which corresponds to the HOM-birefringence of $\textrm{B}_{\textrm{L}{\textrm{P}_{0,4}}}^{group}$∼ 2.2×10−4. The slight discrepancy between the birefringence values calculated from the numerical simulations and those estimated from the experimental results can be attributed to the group-index difference effects that are present in the phase-matching-curve of an LPG [16].
Finally, we evaluate the polarization-maintenance properties of the fiber for the higher-order-mode. We inscribe the LPG in a 10 meter long PM-HOM fiber section and measure the polarization-extinction ratio after the HOM travels through the fiber. We compare the fidelity of the polarized HOM as the fiber is coiled into circular loops of various diameters. Figure 5(a) depicts the experimental setup used in this experiment. The output of a wavelength tunable Yb-doped PM-fiber laser is collimated by a lens (L1; focal length 11mm) and is sequentially passed through a polarizer (Pol 1) and a half-wave-plate (HWP) before being launched into the LPG-containing PM-HOM fiber. After propagation through the fiber in a higher-order-mode, the light is collimated by another lens (L3) and is subsequently passed through a second polarizer (Pol 2). Before conducting the experiment, Pol 1 and Pol 2 are carefully co-aligned by rotating the Pol 1 until the output from the Pol 2 is maximized; this calibration is carried out without the HWP and the PM-HOM fiber present in the setup. The alignment is further verified by rotating the Pol 1 by 90° and observing that the transmission through the Pol 2 approaches a minimum – more than 99.8% suppression of the transmitted light is observed. Throughout the rest of the experiments, the HWP is used to align the polarization of the launched light along the slow or the fast axis of the PM-HOM fiber. At the output side, a polarization insensitive beam splitter (BS) is between L3 and Pol 2, which allows for a simultaneous observation of the near-field output-beam image and the power transmission through the Pol 2. By rotating the Pol 2 for a known polarization state of the input light, we record the maximum and minimum transmission through the Pol 2 after the LP0,4 mode has travelled through the fiber. The ratio of the maximum to the minimum power transmission (polarization-extinction-ratio) is then calculated to estimate the polarization-preserved propagation of the mode.
Fig. 5. (a) Experimental setup used for recording the mode-profile on a camera and measuring the PER for the various bend diameters of the fiber; (b)-(d) Near-field mode-images and the measured PER for the various launch conditions and bending conditions.
Figs. 5(a)−5(c) show the recorded near-field images of the LP0,4 mode while the fiber is coiled into circular loops and is placed on a flat surface. We perform measurements for the cases of 60, 40 and 20 cm coiling diameters, which correspond to the fiber being coiled in 4, 6 and 13 loops, respectively. The PER is measured under these conditions for the input light polarized along the slow and the fast axes of the PM-HOM fiber. We observe the PER values of 12.2(12.0), 10.5(9.9) and 8.2(7.1) dB for the coiling diameters of 60, 40 and 20 cm, respectively, as the light is polarized along the slow(fast) axes of the fiber. The slight degradation in the PER for the decreasing coiling diameters is attributed to the leakage of light from the LP0,4-HOM to a neighboring higher-order-mode, which is likely to be an LP1,N mode for the case of fiber bending in a well-defined two-dimensional plane without any twist. However, since the higher-order-modes are well-guided within the outer-core of the fiber, the coiling diameters of this scale do not lead to an added propagation loss in the fiber.
4. Conclusion
In conclusion, we have demonstrated the polarization-preserved propagation of light in a higher-order Bessel-like fiber mode with an effective-area exceeding 2200 μm2. To our knowledge, this is the largest effective-area linearly-polarized mode demonstrated in a fiber. We have also studied the performance of our polarization-maintaining fiber in the presence of bends and have achieved the delivery of the polarized mode (PER > 10 dB) over a 10 m long fiber section that is coiled into circular loops of 40 cm diameter.
Disclosures
The authors declare no conflicts of interest.
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