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Abstract
In this paper, a universal LP01 to any LPlm mode converter structure is proposed based on a circular waveguide. As examples, nine mode converters from LP01 to LP02, LP03, LP04, LP05, LP06, LP07, LP11, LP21 and LP31 are designed. It is shown that an insertion loss of less than 3 dB is achieved over the entire C-band for all the mode converters. Furthermore, two mode (de)multiplexers based on directional couplers are demonstrated, showing an insertion loss less than 2.5 dB and a crosstalk less than −10 dB over the C-band.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Space/mode division multiplexing (SDM/MDM) has been proposed to overcome the capacity limitations of optical transmission networks based on standard single mode fibers (SMF). The MDM uses the orthogonal guided optical modes of the few mode fibers to carry different optical signals, i.e. one mode corresponding to one optical channel. However, for the MDM, mode converters/(de)multiplexers are usually required at optical transmitters and receivers. In other words, mode conversion from fundamental to higher order modes is required at optical transmitters, while mode conversion from higher-order modes to the fundamental modes is usually required at optical receivers [1].
Mode conversion can be achieved using either free-space or waveguide-based optics. Free-space mode conversion is based on matching the spatial mode profile from an input mode to a desired output mode using phase mask or spatial light modulator such as liquid crystal on silicon (LCOS) [2]. This type of conversion includes optical phase plates, optical beam splitters, optical mirrors and lenses, therefore, it results in bulky structures with high insertion loss. Free-space based mode converters could be achieved in almost any wavelength bands since they are wavelength insensitive.
Mode converter structures based on either fibers or waveguides could be realized through a variety of techniques, such as optical grating, optical couplers, optical tapers, optical lanterns, and photonic crystal fibers, etc. [2–9]. The principle of these mode converters is as follows: The propagation constant of the input mode is matched to a desired output mode by altering the physical characteristics of the fiber or the waveguide such as its cross-section area or its refractive index.
In [10], a mode converter was proposed that is used to convert LP01 to LP11 based on long period fiber grating (LPFG). The mode converter was designed for the C-band, and an insertion loss of 1.5 dB and an extinction ratio of 22 dB at 1550 nm were achieved. However, the mode converter can operate in a narrow bandwidth (13 nm centered at 1551 nm). The work presented in [11] describes an LP01 to LP02 mode converter based on multimode interference (MMI) in a fiber, which was realized by interconnecting a single mode fiber (SMF) with a few mode fiber (FMF) using a multimode fiber (MMF). The extinction ratio and insertion loss of the mode converter were 55 dB and 1.8 dB at 1550 nm, respectively.
Directional and tapered velocity mode-selective couplers can also be used to convert and multiplex different spatial modes [12–15]. Moreover, optical couplers can be cascaded to convert and multiplex more modes such as the one illustrated in [16] for converting and multiplexing LP01, LP11, LP21 and LP02 with low insertion loss. Optical couplers can also be designed using Silica based planar lightwave circuits (PLC) [6,17]. In principle, mode conversion using optical couplers is achieved through matching effective index of one mode in one waveguide to the desired output mode in the other waveguide.
Optical Y-junctions and optical lanterns are another waveguide structures to realize mode converters [17,18]. Waveguides-based mode converters and multiplexers have features of high mode conversion efficiency [19] and compactness in footprint. However, they may in general be wavelength dependent, i.e. broadband is not inherent but may be obtained through optimization of the structures and related parameters.
In this work, we propose a universal mode converter structure that can be used for any mode conversion from LP01 to LPlm. Furthermore, the modes can be multiplexed and demultiplexed using proposed mode converter structures combined with directional couplers.
2. Mode converter structure
shows the block diagram of the proposed mode converter as well as some cross-sectional views, which consists of an outer tapered circular waveguide section of length L1 followed by a non-tapered circular section of length L2, both sections have a refractive index nco.The tapered section starts with a radius r0 and ends with a radius r1. The radius r0 is chosen to allow better optical coupling with a single mode fiber used to input the signal from the LP01 mode. Inside these two sections, a matrix of small elements is inserted. Each element that is denoted by a row i and a column j, i.e. element (i, j), consists of three sections: a tapered section followed by a circular non-tapered section, and then followed by another tapered section. The beginning section of the elements starts with zero radius and tapers to rij with a length L1ij. The middle section is circular with a radius rij and a length L2ij. The last section is circular with a radius rij that is tapered to zero over a length L3ij. The refractive index of element (i, j) is nij. Elements (i, j) and (i, j + 1) (in the same column) are spaced by a gap gij. Elements (i, j) and (i + 1, j) (in the same row) are spaced by a gap dij. Table 1
Table 1. List of Symbol Definitions Used in Fig. 1
The principle of the mode conversion is to introduce some perturbations in the physical characteristics of the structure. For design of LP01 to any LPlm mode converter, a large set of structural and material parameters are used to obtain perturbation, and thus the input LP01 mode to the desired output LPlm mode is matched in effective index. The structure perturbations are caused mainly by changing the radii of the different elements through tapering and by changing the core-cladding refractive index difference by inserting (i, j) elements inside the core.
Two classes of modes are grouped here, i.e. LP0m and LPlm (l≠0). The strategy for grouping these two classes of modes is motivated by the fact that LP0m modes are non-degenerate, circularly symmetric and share a common concentric intensity profile similar to LP01 mode. Figure 2
shows the 2D intensity profile of the first four LP0m modes (m = 1, 2, 3 and 4). It is seen that all LP0m modes present a peak intensity in the center (red spot in the color figures) surrounded by (m-1) circular rings. To convert from an LP01 to any LP0m mode, the structure shown in Fig. 1 can be simplified by keeping only one single element (i, j). However, LPlm (l≠0) modes are different from LP0m, and they are degenerate, symmetrical but not circular. Figure 3 shows the 2D intensity profiles of some LPlm (l and m = 1, 2) modes.2.1. LP01 to LP0m converters
The simple circular symmetry of the intensity profiles of LP0m modes results in simple mode converter structures. Indeed, one single element in the inner section is sufficient to convert LP01 to any desired LP0m mode. The proposed LP01 to LP0m mode converter is shown in Fig. 4
. Based on our knowledge, these structures can be easily fabricated by taking nco = 1.4907, and ncl = n1_1 = 1.4877 [17], which are used for this work. Table 2Table 2. Optimal Parameters for the LP01 to LP0m Mode Converters (μm)
To evaluate the performance of the mode converter, two performance parameters are used, which are the insertion loss (IL) of LP0m mode and the mode extinction ratio (ER), defined as [9]:
where, and are the optical input power of LP01 mode at point and the optical output power of mode LP0m, (m = 1, 2, …) at the output of the mode converter, respectively.
Fig. 5 (a) Insertion Loss of the proposed LP01 to LP0m mode converters over a broadband. (b) Insertion Loss of the proposed LP01 to LP0m mode converters over the C-band.
Fig. 6 (a) Extinction ratio of the proposed LP01 to LP0m mode converters over a broadband. (b) Extinction ratio of the proposed LP01 to LP0m mode converters over the C-band.
2.2. LP01 to LPlm converters
To convert LP01 to LPlm mode (l ≠ 0), the structure shown in Fig. 1 is used, where a single inner element is not sufficient. The number of the inner elements depends on the desired output LPlm modes. As an example, we consider three modes only here, i.e. LP11, LP21 and LP31. Five inner elements are required to obtain LP11 and LP31, and six inner elements are required for LP21, shown in Fig. 7
.All three structures start with an initial radius r0 of 5 µm for better coupling to a SMF. The LP01-LP11 mode converter has a final radius r1 of 30 µm, whereas the LP01-LP21 and LP01-LP21 mode converters both have r1 = 26 µm. The inner elements have different radii ranging from 2 µm (element (2,2) in LP01-LP11 MC) to 26 µm (element (2,1) in LP01-LP31 MC) and different segment lengths ranging from 50 µm (end segment of element (1,2) in LP01-LP21 MC) to 1500 µm (start segment of element (2,2) in LP01-LP31 MC). All inner elements have the same refractive index as the cladding (1.4877).
Fig. 8 (a) Insertion loss of LP01 to LP11, LP21 and LP31 mode converter over a broadband. (b) Insertion loss of LP01 to LP11, LP21 and LP31 mode converter over the C-band.
Fig. 9 (a) Extinction ratio of LP01 to LP11, LP21 and LP31 mode converter over a broadband. (b) Extinction ratio of LP01 to LP11, LP21 and LP31 mode converter over the C-band.
2.3. Discussion
In fact, all simulation results presented in this paper are obtained by Rsoft CAD software [20], a vector mode solver based on Eigen Mode Expansion (EME) [19] method to find the modes inside the waveguide. These results can still be enhanced further with more optimizations of the structure parameters.
It is worth mentioning that mode converters for any other similar modes can be achieved using the structure in Fig. 1. Even though not presented here, LPlm modes can be multiplexed/demultiplexed with a coupling structure. In Appendix, a multiplexer and demultiplexer for LP0m modes (m = 1, 2, 3, 4, 5) are given as an example.
Usually, these kind of mode converters can be fabricated by using direct 3D femtosecond laser inscription on a bulk of glass. In the above designs, the fabrication limits of the structural parameters of the mode converters were already considered in optimizing the designs. In our previous work [21], an LP01 to LP02 mode converter structure was fabricated, validating the working concept and fabrication of the proposed structure.
3. Conclusion
In this paper, we have proposed a universal LP01 to LPlm mode converter structure. The converter structure is based on tapered waveguides. The converter structure can be simplified when converting to LP0m modes. By converting LP01 mode to LP02, LP03, LP04, LP05, LP06, LP07, LP11, LP21 and LP31, an insertion loss (IL) is ranged from 0.1 dB to 3 dB and the extinction ratio is larger than 8 dB over the entire C-band.
Appendix
In this Appendix, an example of two mode (de)multiplexers is given. One (de)multiplexer is for the LP0m modes and the other is for the LPlm modes. We have chosen to use directional couplers (DCs) for multiplexing and demultiplexing. The first DC-based mode multiplexer is shown in Fig. 10
Fig. 10 LP0m (m = 1…5) mode multiplexer from left to right, and opposite direction for demultiplexer.
Fig. 11 (a) Insertion loss of LP0m (m = 1, 2, 3, 4, 5) modes at the output of the multiplexer. (b) Insertion loss of LP0m (m = 1, 2, 3, 4, 5) modes at the output of the demultiplexer.
Fig. 12 (a) Crosstalk of LP0m (m = 1, 2, 3, 4, 5) modes at the output of the multiplexer. (b) Crosstalk of LP0m (m = 1, 2, 3, 4, 5) modes at the output of the demultiplexer.
In a systematic design, one can optimize the two structures (mode converter and mode multiplexer) to balance the insertion losses from both structures for all the modes.
shows the LPlm (de)multiplex for the three obtained modes (LP11, LP21 and LP31). To simplify the structure design, all waveguides have the same radius (30 μm). This choice of using the same radius was motivated by the three radii (r1) of the converters (LP01~LP11, LP01~LP21 and LP01~LP31) which are 30 μm, 26 μm and 26 μm respectively. Furthermore, the same structure can be used at the transmitter side (for multiplexing) as well as at the receiver side (for demultiplexing) with similar performances.Fig. 14 (a): Insertion Loss over the C-Band for the LP11, LP21 and LP31 Multiplexer. (b) Insertion Loss over the C-Band for the LP11, LP21 and LP31 Demultiplexer.
In Fig. 15
Fig. 15 (a) Cross Talk over the C-Band for the LP11, LP21 and LP31 Multiplexer. (b) Cross Talk over the C-Band for the LP11, LP21 and LP31 Demultiplexer.
Funding
Discovery Grants of the Natural Sciences and Engineering Research Council of Canada (NSERC).
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