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Abstract
A long-period fiber grating (LPFG) mode converter based on a two-mode polarization-maintaining photonic crystal fiber (PM-PCF) is proposed and demonstrated. The mode converters realize conversions between the LP01 modes and LP11a modes with parallel polarization directions. Different from typical conventional mode converters, the PM-PCF-LPFG mode converters most notably can separate out two linearly polarized LP11a modes at different wavelengths. The highest mode-conversion efficiency is more than 99%. In addition, the bandwidth of the mode converter is adjustable by changing the grating number of the LPFG.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As a crucial component in the technology of mode-division multiplexing (MDM) optical communications and laser, the mode converter performs conversions between guided modes in a few-mode fiber (FMF) [1]. To date, mode converters of diverse configurations have been demonstrated; they may be classified into three categories: bulk-optic, integrated-optics, and fiber mode converters [2, 3]. The drawback of bulk-optic mode converters is their bulkiness, lossy-ness, and difficulty in fabrication [4, 5], whereas integrated-optics mode converters require complicated and expensive fabrication techniques [6, 7]. Low insert loss, compactness, and excellent compatibility with optical fiber systems make fiber mode converters very attractive [8]. Currently, there are four major configurations used in all-fiber mode converters: mode selective couplers [9], fiber photonic lanterns [10], fiber Bragg gratings (FBGs) [11], and long-period fiber gratings (LPFGs) [12]. LPFG mode converters of high efficiency may be fabricated using one of a variety of technologies such as the ultra-violet technique [13], electric arc discharge [14] and CO2 laser technology [15]. In Zhao et al. reported an all-fiber LPFG mode converter that converts the LP01 mode into other high-order modes (LP11, LP21, and LP02 modes) with the highest conversion efficiency of ~99.5% [1, 16]. Dong et al. proposed a temperature-insensitive LP01–LP11 mode converter with a maximum conversion efficiency >99% [2]. Wang et al. demonstrated LP01–LP11 (LP21) mode conversion that is applicable to high-order optical vortex pulsed lasers [17]. However, all these mode converters are based on few-mode optical fibers with symmetric structures. Specifically, the vector modes of the same-order linearly polarized (LP) modes in symmetric structure fibers have approximately the same propagation constant. As a result, the vector modes of the output LPmn modes via mode converters are hard identify from just their propagation constant and wavelength. In addition, mode converters based on photonic crystal fibers have been widely reported. Employing holey fiber technology, Bellanca et al. demonstrated the first realization of a mode converter for LP01 and LP11 mode multiplexing [18]. Lai and colleagues proposed LP01 to LP11 and LP01 to LP02 fiber mode converters using two different photonic crystal fiber (PCF) techniques [19]. Zhang et al. reported a novel polarization converter based on a PCF with an anisotropic square-lattice core whose polarization conversion efficiency is over 99% [20]. Similarly, the abovementioned PCF-mode converters cannot separate out the vector modes of the LPmn modes just from propagation constant and wavelength.
In this paper, we propose and demonstrate an LPFG mode converter based on a two-mode polarization-maintaining photonic crystal fiber (PM-PCF) using a CO2 laser-inscribing technology. First, we investigate the mode characteristics of the PM-PCF from theory, to confirm that the PM-PCF supports non-degenerate LP01 modes and LP11 modes, respectively. In the experiment, LPFGs with different grating periods and grating numbers were fabricated. The mode converters convert LP01 modes to LP11 modes and separate the linearly polarized LP11 output modes at different wavelengths, featuring two resonance dips in the transmission spectra of LPFG. The bandwidth of the LPFG mode converters may broaden by decreasing the grating number of LPFG, although contrast is sacrificed in the resonance dip. The highest mode efficiency of the LPFG mode converters is over 99%. Moreover, we confirmed that the LPFG mode converters are low temperature sensitive.
2. Principle and simulation
A pure silica PM-PCF supporting two modes was chosen in the fabrication of the LPFG. The PM-PCF was designed and produced by Tongsheng New Material Limited using the stack-and-draw technique. Figure 1 presents an image obtained in scanning electron microscopy (SEM) of the cross-section of an 80.800-µm-diameter PM-PCF. The highest measurement precision of the scanning electron microscope is 0.001 µm. Five rings of air holes with diameter 3.352 µm are arranged along the radial direction spaced at equal intervals of 6.000 µm. Two larger air holes of diameter 5.536 µm are situated diametrically opposed in the fiber core resulting in a non-circular core. As a result, the refractive index of the fiber core differs along the two orthogonal directions. In Fig. 1(a), we indicate the slow and fast axes (with nco, slow > nco, fast). The PM-PCF supports LP01 and LP11 modes consisting of six vector modes [see insets of Fig. 1(b)], which were calculated from theory using commercial software (COMSOL) based on the finite-element method (FEM). Different from a fiber with symmetric structure, the vector modes of the LP01 and LP11 modes in the PM-PCF are non-degenerate, respectively. In addition, the polarization state of the LP11 modes remains linear in the vertical polarization direction as LPy11a and LPy11b corresponding to the slow axis and in the horizontal polarization direction as LPx11a and LPx11b corresponding to the fast axis [21]. In the experiment, we initiated mode conversion using the LPFG based on the two-mode PM-PCF and excited by a beam from a CO2 laser. The phase -matching condition of the LPFG mode converter is expressed as
where λres represents the resonance wavelength, Λ is the grating period, neff,01 and neff,11 are the effective refractive indices of the LP01 modes and LP11 modes, respectively. Figure 1(b) presents the phase-matching curves of four kinds of mode conversions. From the theory of coupled modes, the LP01 mode couples to the LP11 mode of the same polarization state when there is no perturbation. This will be further validated in the next experimental part.
Fig. 1 (a) SEM image and schematic of the cross-section of the PM-PCF, (b) Calculated grating periods for the LP01 and LP11 mode coupling at resonance wavelengths; the insets are the calculated electric field distributions of the six vector modes.
3. Fabrication and characteristics of PM-PCF-LPFG mode converters
In the experiment, we use an 80-cm PM-PCF to fabricate the LPFG using CO2 laser engraving (Fig. 2). A segment of the PM-PCF is sandwiched between two sections of a single mode fiber (SMF). Note the large mismatch in cross-section size between the PM-PCF and SMF. We align the two fibers axially in a commercial fusion splicer without fusion splicing to reduce splice loss. Light from a broadband source (BBS) (1250–1640 nm) passes through a polarizer, a polarization controller (PC), the sandwich structure in sequence, and is finally received by an optical spectrum analyzer (OSA) set at its highest resolution of 0.02 nm. The polarizer turns the input light to linearly polarized light and the PC working at 1550 ± 50 nm modulates the polarization state of the linearly polarized light. After setting up the optical circuit, we employed the CO2 laser system (Han’s laser) to notch the different scanning circles in a periodic arrangement into the PM-PCF.
Fig. 2 Experimental setup to fabricate LPFG in PM-PCF. PC: polarization controller, BBS: broadband source, OSA: optical spectrum analyzer, DC: data cable, SMF: single mode fiber, PM-PCF: polarization-maintaining photonic crystal fiber.
In view of simulation data and experimental experiences, we set the grating period to 253 µm and the period number to 40. Figure 3(a) depicts transmission spectra of the LPFG with different scanning circles. At the 3rd scanning circle, we modulated the polarization state of the linearly polarized input light by changing the state of the PC to three different directions: along the slow axis, at 45° to the slow and fast axes, and along the fast axis. The spectra are shown in Fig. 3(b). Along the slow axis (black curve), the resonance dip of the LPFG has a grating contrast of ~16 dB at 1452.7 nm. The mode-conversion efficiency is ~97%. By modulating the polarization state of input light, a resonance dip at the longer wavelength of 1531.7 nm appears and the grating contrast of the resonance dip at the shorter wavelength diminishes. Along the fast axis (red curve), the grating contrast of the longer resonance dip at 1531.7 nm reaches ~10.5 dB whereas the resonance dip at 1452.7 nm disappears. The result indicates that the coupling efficiency is modulated by the scanning circles and by the polarization input light.
Fig. 3 Transmission spectra of the CO2-laser-notched LPFG with the grating period of 253 µm and number of 40 (a) with the increasing scanning circles; (b) at the 3rd scanning circle with three different states of polarization of input light.
To confirm the experiment is repeatable and study the polarization properties of the PM-PCF-based LPFG, we fabricated LPFGs with a grating pitch of 245 µm and with different grating numbers of 30 and 15. Moreover, we obtained the polarization-dependence-loss (PDL) spectra of the LPFGs for the two grating numbers using a tunable laser (1454–1640 nm, KEYSIGHT, 8164B, N7786B). With the polarization state of the input light parallel either to the slow axis or fast axis [Figs. 4(a) and 4(b)], the transmission spectra of the LPFG features two resonance dips with a wavelength separation of 84.5 nm and 86.5 nm, respectively. In addition, the wavelengths of the two peaks in the spectral PDL match well with those of the two resonance dips, thereby confirming the polarization characteristics of the LPFG. Note that the maximum PDL of PM-PCF-LPFG is ~30 dB, which is much higher than in previous work where the authors used a two-mode fiber LPFG made by CO2 laser engraving technology (~6 dB) [16]. The higher PDL is mainly attributed to the polarization sensitivity of the LP11 modes in the PM-PCF arising from its asymmetric structure. The mode-conversion efficiency [Fig. 4(a)] at shorter wavelengths is higher at ~99%. Notably, it is clear that from Eq. (1) the resonance wavelength λres changes as a function of grating period Λ which is verified from Figs. 3(b) and 4(a). Therefore, the mode converters can work at a wide range of wavelength in principle. In the experiment, we also found that the LPFG bandwidth can be tailored by changing the grating period. With the two grating numbers of 15 and 30, the 3 dB-bandwidth of the resonance dips are 20.5 nm and 11.1 nm, respectively. By decreasing the period number of LPFG, we can appropriately broaden the bandwidth. However, the higher broad bandwidth sacrifices grating contrast in the resonance dip.
Fig. 4 Transmission spectra of the CO2-laser-notched LPFG for two orthogonal polarization states of input light and the corresponding PDL spectra for a grating pitch of 245 µm and grating number of (a) 30 (7.35-mm long), (b) 15 (3.68-mm long).
The simulations indicated that there are four mode conversions, specifically, four resonance dips appear in the LPFG transmission spectra. However, we only observed two resonance dips. To explain these coupling patterns, we set up an experiment (Fig. 5) to characterize the polarization states of the LP01 modes and LP11 modes. Here, the grating pitch of the LPFG mode converter is 253 µm. A tunable laser is used to input single-wavelength light into the LPFG-based mode converter. A PC is inserted between the tunable laser and the mode converter to transform the input light into linearly polarized light and adjust the polarization state of the input light to within 360°. Thereafter, the mode converter transforms the LP01 mode into LP11 mode. A lens with a focal length of 40 mm focuses the output light of the LPFG into the CCD camera; the mode patterns are finally displayed on the computer. A polarizer before the CCD camera is used to determine the polarization state of the output light from the mode converter. In a series of experiments, we set the wavelength of the tunable laser to 1454 nm, 1532 nm, and 1560 nm; the first two are the resonance wavelengths of the grating, whereas the third is beyond the resonance wavelength. At the resonance wavelengths, we first used the PC to modulate the polarization state of the input light to attain the most obvious LP11 mode patterns [Figs. 6(a) and 6(b)]. At this point, the polarization state of the input light is parallel with either the fast axis or the slow axis of the PM-PCF. Next, we adjusted the state of the polarizer (black arrows) to get the strongest intensity distributions of the LP11 mode patterns while simultaneously indicating the polarization state of the converted modes. Note well that, in the process of rotating the polarizer, the intensity of the beam profile of LP11 mode changes alternately every 90°. This behavior indicates that the LP11 mode is linearly polarized. In the experiment, the polarization direction of the input light changes by 90° from the shorter resonance wavelength (1454 nm) to the longer resonance wavelength (1532 nm). This implies that for the LP01 modes participating in mode conversion at two resonance dips, the polarization states are orthogonal. We next fixed the polarization state of the input light at 1532 nm and set the wavelength of the tunable laser to 1560 nm. By adjusting the polarization axis of the polarizer, we found that the weakest intensity distribution of the LP01 mode is at 98°. At this point, the polarization state of the LP01 mode participating mode conversion should be orthogonal with the axis of the polarizer. Furthermore, at wavelength 1532 nm, the axis of the polarizer is approximately orthogonal to that at 1560 nm, indicating that the polarization directions of the LP01 and LP11 modes participating in mode conversion are parallel.
Fig. 5 Experimental setup to characterize the polarization state of the LP01 and LP11 modes. TL: tunable laser, PC: polarization controller.
Fig. 6 Intensity distributions at the output PM-PCF and patterns rotated with the polarizer (a) at 1454 nm; (b) at 1532 nm; (c) at 1560 nm. The black arrows indicate the polarizer axis.
The foregoing results indicate that, at the two resonance dips, the two linearly polarized orthogonal LP01 modes couple with the LP11 modes via their parallel polarization states. However, determining the exact high-order converted modes among the four vector LP11 modes requires consideration. In Fig. 6(c), the initial beam profile of the mode before the polarizer is ellipse-like. Compared with the calculated electric field distribution of the LP11 modes [Fig. 1(b)], we confirmed the relative direction of the two large air holes and the beam profile and further ensured the identification of the LP11a modes. This verifies that the LPFG converts the LP01 modes to LP11a modes. However, in Fig. 1(b), the grating pitch for the LP01 and LP11a modes coupling at 1532 nm is ~126 µm, which is approximately half the actual grating pitch. Hence, we deduce that there is a 2nd order coupling between the LP01 and LP11a modes through LPFG, for which the phase-matching condition is expressed as
Hence the diffraction order is two, which is in good agreement with the experimental results for the LPFG. A 2nd order coupling implies that if the grating period of A is twice as large as the grating period of B, the 1st order diffraction resonances generated from B will be consistent with 2nd order diffraction resonances from A at the same wavelength. As early as 2002, Shu et al. proposed the fabrication and characterization of LPFGs with different diffraction orders [22]. In 2012, Guo et al. reported compact LPFGs with resonances at 2nd order diffraction [23].Figure 7 shows plots of the calculated grating pitches in 2nd-order coupling for the LP01 and LP11a modes at resonance wavelengths. When we set the period at 253 µm, the resonance wavelengths are in theory 1529 nm and 1578 nm, whereas from the experiment the resonance wavelengths are 1452.7 nm and 1531.7 nm. Thus the discrepancy between the shorter and longer resonance wavelengths are 76.3 nm and 46.3 nm whereas the deviation in wavelength separation is 30 nm. We deduce that there are two main reasons causing these deviations. One is the asymmetric index distribution induced by the CO2 laser exposure [16] and the applied strain along the fiber [1]. The other is deviations in parameter values between the actual PM-PCF and numerical fiber models. During fiber fabrication, perfect and uniform PM-PCF with ideal design parameters are hard to produce. Moreover, two-dimensional models may cause differences in simulations [24]. Therefore, the resonance wavelengths in the experiment are taken to be within the margin of error.
Fig. 7 The calculated grating pitches for LP01 and LP11a mode 2nd order coupling at resonance wavelength.
Finally, we studied the temperature characteristics of the PM-PCF-LPFG. Based on the experimental setup [Fig. 2], we placed the LPFG part in a temperature control box to modulate the temperature. By adjusting the PC state, we obtained the transmission spectra at both shorter and longer resonance wavelengths [Fig. 3(b); black and red curves]. Moreover, by changing the temperature in 10-°C increments, we obtained the temperature dependence of the resonance wavelengths and the LPFG contrasts [Fig. 8]; the curves are non-linear, fluctuating within narrow ranges of ~0.11 nm and ~0.44 dB, respectively. This fluctuation originates with changes in conditions and measurement error. Therefore, the PM-PCF-LPFG is low temperature sensitive, which is mainly attributed to the air-hole structure of the pure silica PM-PCF [25].
Fig. 8 Temperature variations of the resonance wavelengths and LPFG contrasts (a) at the shorter resonance wavelength and (b) at the longer resonance wavelength (grating period is 253 µm and grating number is 40).
4. Conclusion
A mode converter based on a two-mode PM-PCF-LPFG inscribed by CO2 laser was proposed and demonstrated. The converters achieve mode conversion between LP01 and LP11a modes having the same polarization direction. The highest conversion efficiency is ~99% with a grating length of 7.35 mm, making the converter a candidate for the high efficiency and compact mode-converting device. We also demonstrated that the bandwidth of the LPFG mode converter is controllable by modulating the period number of the LPFG. In addition, because of the birefringence characteristics of the PM-PCF, the LPFG mode converter separates the two linearly polarized LP11a modes outputted at different wavelengths with polarizations in orthogonal directions. Compared with conventional LPFG mode converters, the PM-PCF-LPFG mode converter has a low temperature sensitivity, eliminating the requirement for temperature compensation. We believe that such compact, temperature-insensitive, and mode separable PM-PCF-LPFG mode converters have potential applications in all-fiber based MDM systems and all-fiber mode-locked fiber laser.
Funding
National Natural Science Foundation of China (NSFC) (11674177, 61775107); Tianjin Natural Science Foundation, China (16JCZDJC31000).
Acknowledgments
The authors thank Tongsheng New Material Limited for providing PCFs. We thank Richard Haase, Ph.D, from Liwen Bianji, Edanz Group China (www.liwenbianji.cn/ac), for editing the English text of a draft of this manuscript.
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