Open Access
Add to BibSonomy
Abstract
A silica-based LP11 mode rotator, which is one of the basic and indispensable optical components for space division multiplexing, with multiple tapered trenches is proposed. Compared with the conventional interference-based LP11 mode rotator with a simple L-shape waveguide, the proposed LP11 mode rotator has many advantages in a mode conversion efficiency, an insertion loss, and a fabrication tolerance because the operation principle is based on the adiabatic mode conversion. By using an approach of the shortcut to adiabaticity, the proposed device is effectively miniaturized rather than the standard tapered structures. Among the LP11 mode rotators in the silica-based mode multi/demultiplexers, the proposed type will be a considerably promising candidate.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Space-division multiplexing (SDM) is a key technology to deal with exponentially increasing Internet traffic [1]. As a kind of SDM transmission, a lot of attention has been paid to mode-division multiplexing (MDM) using few-mode fibers (FMFs), in which each spatial mode (e.g., linearly-polarized (LP) modes in the fiber) can be used as a channel. To excite fiber modes, a mode multi/demultiplexer (MUX/DEMUX) is indispensable. So far, MUX/DEMUXs based on spatial light modulators (SLMs) [2,3] and photonic lanterns [4,5] have been reported. There is another promising approach: designated modes are multiplexed in silica planar lightwave circuit (silica-PLC) waveguides, and then these modes are coupled to LP modes in a FMF [6–8]. Such silica-PLC MUX/DEMUXs have many advantages including a small device size, a low fabrication cost, a high conversion efficiency, and a low connection loss to a FMF.
Traditionally, in silica-PLC MUX/DEMUXs, a higher order mode is multiplexed by asymmetric directional couplers (ADC) or by Y-branch waveguides [7,8]. It is easy to convert from the Emn mode to the Em′n mode (m, m′, n ∈ {1, 2, …}, m ≠ m′), where subscriptions of Emn mode indicate the order of the electric field distribution for the horizontal (m) and vertical (n) directions, respectively. However, in the standard silica PLC, since the waveguide height is fixed and the waveguide is vertically symmetric (cladding is formed by buried SiO2), the coupling coefficient between the Emn and the Emn′ modes becomes 0 (n ≠ n′), which makes it difficult to excite the Emn′ mode from the Emn mode. It is known that, if |m – n| = 2, the Emn mode can be converted to the Enm mode by the simple tapered waveguide [7]. Nevertheless, e.g., the E12 mode cannot be excited by the Em1 mode as long as the waveguide is vertically symmetric. For the MDM transmission, it is inconvenient that some modes cannot be excited. To overcome this problem, an E21→E12 mode converters (so-called LP11 mode rotator) using a waveguide with a trench have been reported [6–9]. Figure 1(a) shows the schematic of a conventional E21→E12 mode converter, in which the L-shape waveguide is inserted between rectangle waveguides [8,9]. Note that the mode rotator here we call does not rotate the polarization. It can be assumed that the polarization coupling does not occur due to a small refractive index difference. The L-shape waveguide has two guided modes as shown in the left side of Fig. 1(a) because the optical axis tilts. By appropriately designing the trench so that the inclination angle is almost 45 degrees, the E21 mode input from the rectangle waveguide can excite equally two tilted modes at begin of the L-shape waveguide. If the phase difference between these modes becomes π, E12 mode is converted to E21 mode. The fabrication of such a trench to excite E12 mode requires the two-step etching process, in which an alignment accuracy of two etching patterns (namely core and trench patterns) significantly affects the mode conversion efficiency. Therefore, the high-tolerant design of the LP11 mode rotator is strongly desired. Although, as another type of converter, a top-grating E11→E12 converter based on the long period grating (LPG) has also been proposed [10], it does not only have a relatively large scattering loss due to waveguide discontinuities, but it has also a large wavelength dependency in general.
Fig. 1. Schematics of (a) conventional [8] and (b) newly proposed E21→E12 mode converters (LP11 mode rotators). Blue and red filled areas denote core and trench (partially etched) regions, respectively. E21 (LP11a-like) mode input from upper side propagates along z-direction, and is converted to E12 (LP11b-like) mode. Field distributions and refractive index distributions at various z positions are depicted at left and right sides, respectively.
The principle of the mode conversion in the L-shape waveguide as shown in Fig. 1(a) can be categorized as the interference type (also called resonant type), in which the LPG-type mode converter is included [11]. Whereas, the adiabatic mode transition is also one of the feasible techniques, in which the guided modes are converted by gradually and appropriately modulating the waveguide structure [12]. In this study, we newly proposed a silica-PLC E21→E12 mode converter with multiple tapered trenches as shown in Fig. 1(b), which is based on the adiabatic mode conversion. As described in the following sections, the proposed mode converter has a high mode conversion efficiency, broadband characteristics, and high tolerant characteristics to the fabrication errors compared with the interference types. Although the adiabatic conversion generally requires a large device size, by applying the fast quasi-adiabatic (FAQUAD) approach [13] to the proposed structure as shown in Fig. 1(b), it enables miniaturizing the device size while maintaining the advantages of adiabatic mode conversion.
This paper is organized as follows. In Section 2, we explain the operation principle of the proposed E21→E12 mode converter. In Section 3, the numerical results of the E21→E12 mode converter are demonstrated. Subsection 3.1 describes the proposed mode converter with straight tapers. In Subsection 3.2, the FAQUAD approach and its application to the proposed mode converter are described. In Subsection 3.3, we compared the device characteristics of the conventional and proposed E21→E12 mode converters, where the tolerance to fabrication errors are also described. And finally, Section 4 is dedicated to the conclusions.
2. Device design and its operation principle
To explain the mode conversion in Fig. 1(b), the guided modes in the inverse T-shape (InvT-shape) and L-shape waveguides as shown in Fig. 2(a) are investigated, where wt1 and wt2 denote the widths of left and right trenches that are secondary etched with a height of ht. The total amount of etched width is defined as wt = wt1 + wt2. Setting to 0 < wt1 = wt2 < w/2 leads to the InvT-shape waveguide. Whereas, setting to wt1 = 0 and 0 < wt2 < w leads to the L-shape waveguide. The core and cladding are assumed to be Ge-doped SiO2 and pure SiO2, respectively. The refractive index difference is defined as Δ = (n12 – n02)/n02, where n1 and n0 are the refractive indices of core and cladding, respectively. To compare with the conventional mode converter as shown in Fig. 1(a), we designed the mode converter as to enable it to be fabricated with the same fabrication process as [14], where h = 10 µm, ht = 2.6 µm, and Δ = 1%. If we set to w < 10 µm, the cross section becomes horizontally long rectangle waveguide (h > w). If the trench is fully etched (wt = w), the cross section becomes the vertically long waveguide (w > h) for w > 7.4 µm. Such a structural parameter setting is one of important points for the operation in our proposed design. Here, to match the aspect ratios between these two cross sections (h : w ≈ w : h − ht), we set to w = 8.6 µm.
Fig. 2. Schematics of silica-PLC waveguide with trench and structural dependence of effective indices of the guided modes at wavelength of 1550 nm. (a) Cross-sectional view, where wt1 = wt2 = wt/2 leads to inverse T-shape (InvT-shape) waveguide, whereas wt1 = 0 and wt2 = wt leads to L-shape waveguide. (b) Effective index in InvT-shape waveguide as a function of wt. (c) Effective index in L-shape waveguide as a function of wt. In (b) and (c), structural parameters are w = 8.6 µm, h = 10 µm, ht = 2.6 µm, and Δ = 1%.
Figures 2(b) and (c) show the effective index (neff) in the InvT-shape and L-shape waveguides as a function of wt. The numerical results are obtained by the scaler finite element method (FEM) [15]. For both of Figs. 2(b) and (c), if wt = 0, the neff of the E12 mode is larger than that of the E21 mode. As increasing wt, neff of the E12 mode decreases, and finally, the neff of the E12 mode becomes smaller than that of the E21 mode.
We would like to note that the InvT-shape waveguide in Fig. 2(b) has a symmetric cross section for the x axis, and hence, the E21 mode (red solid line) and the E12 mode (blue dashed line) do not couple to each other. In the vicinity of wt = 6 µm in Fig. 2(b), E12 and E21 modes are completely orthogonal. By tapering with increasing wt from 0 to w, neff changes along with the red solid (blue dashed) line, keeping the optical axis.
On the other hand, as shown in Fig. 2(c), the L-shape waveguide has an asymmetric cross section for the x axis, which enables the coupling between E12 and E21 modes, leading to the mode rotation by graduate changing wt. By tapering with decreasing wt from w to 0, along with the blue dashed line, the E21 mode can be converted to the E12 mode, and vice versa for the red solid line. By using such a nature, along with the blue dashed line in Figs. 2(b) and (c) corresponding to Fig. 1(b), the E21 mode at the input waveguide can be converted to the E12 mode at the output waveguide.
If merely the LP11 mode rotation (E12→E21 and E21→E12 mode conversions) is required, only the L-shape waveguide with a tapered trench seems to be sufficient, corresponding to red or blue lines in Fig. 2(c). Considering the connection of the mode rotator to other components on the PLC platform, it is preferable to match the cross-sectional geometry of the input and output ports. By using the InvT-shape waveguide with a tapered trench, as shown in the right side of Fig. 2(b), we can obtain the low-loss mode transition without the mode rotation from the input port (cross section of w × h) to the fully-etched point (cross section of w × (h − ht)).
3. Numerical results and discussion
3.1 Proposed mode rotator with standard trench taper
Since the mode conversion in the proposed structure as shown in Fig. 1(b) depends on the adiabatic conversion, a sufficiently graduate change of wt is needed for a high mode conversion efficiency, especially in the L-shape waveguide with a tapered trench. Figures 3(a) and (b) show the mode conversion efficiencies in the L-shape waveguide with a tapered trench as a function of the taper length, Ltp‐L, where E21 and E12 modes are launched. The numerical simulations are done by the scaler beam propagation method (BPM) [16] and the coupled local-mode theory (CLMT) [17], which are plotted by filled circles and lines, respectively. In the CLMT, the coupling coefficient is obtained by scaler FEM [15] and a first-order differential equation with a 4 × 4 matrix corresponding to lowest four modes is solved. As we can see, both results by BPM and CLMT agree well and the mode conversion efficiency saturates for roughly Ltp‐L > 3 mm. The small differences is seen for Ltp‐L < 0.5 mm because the CLMT cannot treat a rapid structural change (total transmission power is basically preserved). However, Figs. 3(a) and (b) are almost similar, which means that the mode coupling except for E12 and E21 modes is negligible.
Fig. 3. Mode conversion efficiency in the L-shape waveguide with a tapered trench as a function of taper length Ltp‐L, where (a) E21 and (b) E12 modes are launched, respectively. The structural parameters are the same as Fig. 2. At the input side, the trench is fully etched (w > h).
Figures 4(a) and (b) show the mode conversion efficiencies in the InvT-shape waveguide with a tapered trench as a function of the taper length, Ltp‐InvT, where E21 and E12 modes are launched. We can see that high mode conversion efficiencies are obtained when Ltp‐InvT > 0.5 mm. The InvT-shape waveguide required smaller taper length rather than the L-shape waveguide because the mode coupling between E21 and E12 modes does not occur due to the x-axis symmetry. However, care should be taken not to couple from Emn mode to Emn′ mode. As shown in Fig. 4(a), the launched E21 mode couples to the E22 mode when Ltp‐InvT < 0.5 mm. Compared with it, when launching the E12 mode, we can see the tendency that the insertion loss and undesired mode coupling is larger because the electric field are largely affected by refractive index modulation. This is also proved from that the change of effective index corresponding to the red solid line in Fig. 2(b) is large. Therefore, in the proposed structure as shown in Fig. 1(b), the conversion from E21 (LP11a-like) mode to E12 (LP11b-like) mode seems to be preferable, corresponding to blue dashed line in Figs. 2(b) and (c). Anyway, the proposed operation of the LP11 mode rotation is numerically confirmed.
Fig. 4. Mode conversion efficiency in the InvT-shape waveguide with a tapered trench as a function of taper length Ltp‐InvT, where (a) E21 and (b) E12 modes are launched, respectively. The structural parameters are the same as Fig. 2. At the output side, the trench is fully etched (w > h).
3.2 Proposed mode rotator with trench taper optimized by FAQUAD
As described above, to obtain a sufficient mode conversion efficiency, the total length of 3.5 mm should be required at least. Here we utilize the FAQUAD approach to shorten our proposed mode rotator, which is a kind of techniques called shortcuts to adiabaticity [18]. Just as it is proved that the FAQUAD approach has been effective for Y-junction mode sorters [19,20], polarization splitter rotator [21], 3-dB power divider [22], and a connection between strip and slot waveguides [23], it is expected to be also effective for our proposed mode rotator.
For the tapered InvT- and L-shape waveguides, the adiabaticity parameter ηpq between p and q modes can be defined as
Figures 5(a) and (b) show the adiabaticity parameter ηpq and the corresponding geometry z(wt)/Ltp‐L for the L-shape waveguide, where p and q modes correspond to 2nd and 3rd modes (E12 and E21 modes or these mixed modes). Since ηpq coincides with ηqp, only ηpq is plotted. Around wt = 6 µm, ηpq reaches a maximum value, which means that a much graduate waveguide change is required. On the other hand, ηpq becomes a minimum value around wt = 8.6 µm, permitting the large change of waveguide width per the propagation distance. Figure 6 shows the mode conversion efficiency as a function of Ltp‐L for the L-shape waveguides with a straight taper trench (∂wt/∂z is constant) and a FAQUAD-based taper trench (∂wt/∂z is set according to Fig. 5(b)), where the E12 mode is launched from the horizontally long rectangle side (h > w). It is calculated by the CLMT, in which only two modes are considered. As seen from Fig. 6, the mode conversion efficiency (E12→E21 mode) reached 100% (> −0.001 dB) at Ltp‐L = 1.2 mm for the FAQUAD-based taper. At this point, the mode remaining ratio (E12→E12 mode) becomes less than −30 dB. Even if combined with InvT-shape waveguide with Ltp‐InvT = 0.8 mm (enough longer than 0.5 mm), the total length becomes 2.0 mm, which is shorter than the conventional LP11 mode rotator (e.g., 2.1 mm in [14]). As we can see from Fig. 6, a high mode conversion efficiency is also obtained at Ltp‐L = 2.7 mm. Compared with Ltp‐L = 1.2 mm, it is expected that the L-shape waveguide with Ltp‐L = 2.7 mm tends to have a high tolerant and broadband operation. But as described in the following subsection, even the L-shape waveguide with Ltp‐L = 1.2 mm has an enough good characteristics. Figure 7 shows the mode evolution in the L-shape waveguide corresponding to Ltp‐L = 1.2 mm for FAQUAD taper in Fig. 6, where the scalar BPM analysis is performed. In the scalar BPM analysis, all modes including radiated modes are automatically treated unlike the CLMT. As expected from the results by the CLMT, the designated mode conversion can be also seen by the BPM. From BPM results, the transmission of E12→E21 mode is −0.01 dB and the remaining mode ratio of E12→E12 mode is −30.4 dB.
Fig. 5. (a) Adiabaticity parameter ηpq and (b) the corresponding geometry z(wt)/Ltp‐L for the L-shape waveguide, where p and q modes correspond to 2nd and 3rd modes (E12 and E21 modes or these mixed modes).
Fig. 6. Mode conversion efficiency as a function of taper length Ltp‐L for the L-shape waveguides with a straight taper trench (∂wt/∂z is constant) and a FAQUAD-based taper trench (∂wt/∂z is set according to Fig. 5(b)), where the E12 mode is launched from the horizontally long rectangle side (h > w).
Fig. 7. Mode evolution in the L-shape waveguide with the FAQUAD taper of Ltp‐L = 1.2 mm, where the E12 mode is launched from the horizontally long rectangle side (h > w).
For the InvT-shape waveguide, according to Fig. 4(a), we focus on the mode coupling between E21 and E22 modes. Although it is better to treat the other mode coupling corresponding to Fig. 4(b) (and the other possible mode coupling) by using another approach that can optimize multiple mode coupling, such as proposed in [24], we here demonstrate one pair of mode coupling for simplicity. Figures 8(a) and (b) show the adiabaticity parameter ηpq and the corresponding geometry z(wt)/ Ltp‐InvT for the InvT-shape waveguide, where p and q modes correspond to 3rd and 4th modes (E21 and E22 modes or these mixed modes). ηpq in Fig. 8(a) is smaller than that in Fig. 5(a) because the mode rotation does not arise and the deformation of electric field is small. Figure 9 shows the mode conversion efficiency as a function of Ltp‐InvT for the InvT-shape waveguides with a straight and a FAQUAD-based taper trench, where the E21 mode is launched from the horizontally long rectangle side (h > w). It is also calculated by the CLMT with only two modes. At Ltp‐InvT = 0.4 mm and Ltp‐InvT = 0.75 mm, the FAQUAD-based taper trench has high transmissions of almost 100%. Figure 10 shows the mode evolution in the InvT-shape waveguide calculated by the scalar BPM, corresponding to Ltp‐InvT = 0.4 mm for the FAQUAD taper in Fig. 9. From BPM results, it is confirmed that the transmission of E21→E21 mode is −0.01 dB and the undesired mode coupling of E21→E22 mode is −29.4 dB.
Fig. 8. (a) Adiabaticity parameter ηpq and (b) the corresponding geometry z(wt)/Ltp‐InvT for the InvT-shape waveguide, where p and q modes correspond to 3rd and 4th modes (E21 and E22 modes or these mixed modes).
Fig. 9. Mode conversion efficiency as a function of taper length Ltp‐InvT for the InvT-shape waveguides with a straight taper trench (∂wt/∂z is constant) and a FAQUAD-based taper trench (∂wt/∂z is set according to Fig. 8(b)), where the E21 mode is launched from the horizontally long rectangle side (h > w).
Fig. 10. Mode evolution in the InvT-shape waveguide with the FAQUAD taper of Ltp‐InvT = 0.4 mm, where the E21 mode is launched from the horizontally long rectangle side (h > w).
3.3 Comparison with conventional and proposed LP11 mode rotator
In this subsection, we investigate the wavelength dependence and the fabrication tolerance of LP11 mode rotators, including the conventional interference-based mode rotator as shown in Fig. 1(a) and the proposed mode rotator based on adiabatic mode conversion with L-shape and InvT-shape waveguides as shown in Fig. 1(b). Here, all numerical analysis is done by scalar BPM instead of the CLMT.
3.3.1 Wavelength dependence
Figures 11(a)-(f) show the wavelength dependence of the mode conversion efficiencies in the three types of LP11 mode rotators. The illustrations of the structural geometry are depicted in the insets. The interference-based mode rotator, corresponding to Figs. 11(a) and (b), has the L-shape waveguide with a trench length of 2.1 mm and the cross-sectional structure of w = 10.1 µm, h = 10 µm, wt = 1.5 µm, ht =2.6 µm, and Δ = 1%, which is one of the optimized structural parameters [14]. The structure is symmetric for the propagation axis, and therefore, the E12→E21 mode rotation agrees with E21→E12 mode rotation. An insertion loss of 0.1 dB for the mode rotation operation is seen due to the discontinuities at the start and end of trench regions. The E11 mode also attenuates by 0.04 dB. The crosstalk of E12→E11 mode is suppressed at the level of −25 dB.
Fig. 11. Wavelength dependence of the mode conversion efficiencies in three types of mode rotators. (a), (b) the conventional mode rotator with an L-shape waveguide. The trench length of 2.1 mm and the cross-sectional structure of w = 10.1 µm, h = 10 µm, wt = 1.5 µm, ht =2.6 µm, and Δ = 1%. (c), (d) One of our proposed mode rotators, which has the L-shape waveguide with a FAQUAD taper of Ltp‐L = 1.2 mm and the InvT-shape waveguide with a straight taper of Ltp‐InvT = 0.8 mm. (e), (f) Another one of our proposed mode rotators, which has the L-shape waveguide with a FAQUAD taper of Ltp‐L = 1.2 mm and the InvT-shape waveguide with a FAQUAD taper of Ltp‐InvT = 0.4 mm.
Figures 11(c) and (d) correspond to the one of our proposed mode rotator, which has the L-shape waveguide with a FAQUAD taper of Ltp‐L = 1.2 mm and the InvT-shape waveguide with a straight taper of Ltp‐InvT = 0.8 mm. Since the mode conversion basically relies on the adiabatic mode conversion, the insertion loss is considerably improved. Although we worried about the degradation of transmission of E21→E12 mode due to the InvT-shape waveguide, and also the degradation of the broadband operation due to the use of the peak of ηpq as shown Fig. 6, a high mode conversion efficiency can be obtained in the wide waveband. The transmission of E21→E12 mode is higher than −0.026 dB in the range from 1500 to 1600 nm. The remaining modes (E12→E12 and E21→E21) are less than −27 dB at the wavelength of 1500 nm. In addition, the device length in this configuration is 2.0 mm, which is shorter than the conventional mode rotator. We also would like to emphasize that the insertion loss of E11→E11 mode is suppressed less than 0.003 dB, which was difficult to achieve by the conventional interference-type mode rotator.
Another one of the proposed mode rotator is examined as shown in Figs. 11(e) and (f), in which, as shown in the inset in Fig. 11(e), the straight taper in the structure of Fig. 11(c) is replaced into the FAQUAD taper of Ltp‐InvT = 0.4 mm designed by Figs. 8–10. The device length becomes 1.6 mm. Since the InvT-shape waveguide is optimized for E21 mode, the transmissions of E21→E12 mode and E11→E11 mode are degraded about to −0.9 dB and −0.15 dB, respectively. But the transmission of E12→E21 mode reaches the highest value of −0.0015 dB, and thus, there may be cases that this configuration is preferred.
3.3.2 Fabrication tolerance
Finally, we show the fabrication tolerances of the conventional mode rotator and the proposed one, corresponding to Figs. 11(a) and (c), respectively. Here, we consider two fabrication errors; trench depth and the alignment shift in the two-step etching.
Figure 12(a) depicts the situation when the trench depth changes from ht to ht + Δht. Δht > 0 means the over etching in the trench etching process. Inversely, Δht < 0 means the insufficient etching. The numerical results of mode conversion (rotation) efficiency for such a situation are shown in Figs. 12(b) and (c), where Δht is set to 0 and ±0.2 µm. Each structure has the degradation about 0.1 dB due to the change of the trench depth. In the proposed structure, the degradation of Δht > 0 is smaller than that of Δht < 0, which implies that higher tolerances can be obtained by preliminary designing with such a fabrication error.
Fig. 12. Comparison of the conventional and proposed mode rotator, where the fabrication errors of the trench depth arise with ht ± Δht. (a) Illustration of the change in the trench depth. (b) Spectra of the conventional mode rotator corresponding to Fig. 11(a). (c) Spectra of the proposed mode rotator corresponding to Fig. 11(c).
Figures 13(a) and (b) depict the situations when the alignment error arises with Δx for the x axis. In the conventional mode rotator (L-shape waveguide), as shown in Fig. 13(a), the amount of alignment shift agrees with the change of the trench width wt. However, in the proposed structure, as shown in Fig. 13(b), a whole trench etching layer is shifted. Generally, at the outer area of the originally designed etching area, the extra etched region is prepared. Note that, the x-symmetry in the InvT-shape waveguide is lost due to the alignment error, arising a concern about the undesired mode rotation in the InvT-shape waveguide. In the following simulation, such a situation for the alignment error is supposed. The numerical results of mode conversion (rotation) efficiency for such a situation are shown in Figs. 13(c) and (d), where Δx is set to 0 and ±0.2 µm. The conventional structure has a degradation larger than 0.2 dB. Whereas in the proposed structure, the degradation is suppressed to less than 0.2 dB. Especially in Δx = −0.2 µm, the degradation is about 0.1 dB and a higher transmission of E21→E12 mode can be obtained. In this simulation of Δx > 0, there is the discontinuity point at the bottom and left side of the extra etched area. This may be the reason that the degradation of Δx > 0 is larger than that of Δx < 0. By appropriately designing the extra etched area, further improvement of the tolerance will be expected.
Fig. 13. Comparison of the conventional and proposed mode rotator, where the alignment error between the waveguide and trench with Δx. (a), (b) Illustrations of the alignment error. (b) Spectra of the conventional mode rotator corresponding to Fig. 11(a). (c) Spectra of the proposed mode rotator corresponding to Fig. 11(c).
4. Conclusion
We proposed a silica-PLC E21→E12 (E12→E21) mode converter (so-called LP11 mode rotator) with multiple tapered trenches. By appropriately designing the tapered trench structure in the InvT-shape and L-shape waveguides, the high mode conversion and broadband characteristics can be obtained with the device length of 2 mm. Due to the continuous change of the cross section, the insertion loss of E11 (LP01-like) mode is drastically reduced. It has also the high tolerant characteristics to the fabrication errors compared with the conventional device. Furthermore, the effectiveness of the FAQUAD design for the silica-based mode rotator is confirmed through the numerical investigations.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]
2. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012). [CrossRef]
3. G. Labroille, B. Denolle, P. Jian, P. Genevaux, N. Treps, and J.-F. Morizur, “Efficient and mode selective spatial mode multiplexer based on multi-plane light conversion,” Opt. Express 22(13), 15599–15607 (2014). [CrossRef]
4. S. G. Leon-Saval, N. K. Fontaine, J. R. Salazar-Gil, B. Ercan, R. Ryf, and J. Bland-Hawthorn, “Mode-selective photonic lanterns for space-division multiplexing,” Opt. Express 22(1), 1036–1044 (2014). [CrossRef]
5. A. M. Velázquez-Benítez, J. E. Antonio-López, J. C. Alvarado-Zacarías, N. K. Fontaine, R. Ryf, H. Chen, J. Hernández-Cordero, P. Sillard, C. Okonkwo, S. G. Leon-Saval, and R. Amezcua-Correa, “Scaling photonic lanterns for space-division multiplexing,” Sci. Rep. 8(1), 8897 (2018). [CrossRef]
6. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, K. Tsujikawa, T. Uematsu, and F. Yamamoto, “PLC-based four-mode multi/demultiplexer with LP 11 mode rotator on one chip,” J. Lightwave Technol. 33(6), 1161–1165 (2015). [CrossRef]
7. K. Saitoh, N. Hanzawa, T. Sakamoto, T. Fujisawa, Y. Yamashita, T. Matsui, K. Tsujikawa, and K. Nakajima, “PLC-based mode multi/demultiplexers for mode division multiplexing,” Opt. Fiber Technol. 35, 80–92 (2017). [CrossRef]
8. T. Fujisawa, Y. Yamashita, T. Sakamoto, T. Matsui, K. Tsujikawa, K. Nakajima, and K. Saitoh, “Scrambling-type three-mode PLC multiplexer based on cascaded Y-branch waveguide with integrated mode rotator,” J. Lightwave Technol. 36(10), 1985–1992 (2018). [CrossRef]
9. Y. Yamashita, S. Makino, T. Fujisawa, N. Hanzawa, T. Sakamoto, T. Matsui, K. Tsujikawa, F. Yamamoto, K. Nakajima, and K. Saitoh, “PLC-based LP11 mode rotator with curved trench structure devised from wavefront matching method,” IEEE Photonics Technol. Lett. 29(13), 1063–1066 (2017). [CrossRef]
10. Y. Asama, T. Fujisawa, T. Sato, T. Mori, T. Sakamoto, R. Imada, Y. Yamashita, K. Nakajima, and K. Saitoh, “Cascaded wavefront-matching-method designed mode-exchangers for MDL management in MDM transmission,” in Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2022), pp. CWP10B-05.
11. T. Sato, K. Homma, T. Fujisawa, Y. Sagae, T. Sakamoto, T. Matsui, K. Nakajima, and K. Saitoh, “Mode converter using bent and twisted coupled-multicore fibers for group delay spread reduction,” Opt. Fiber Technol. 77, 103286 (2023). [CrossRef]
12. J. D. Love, R. W. C. Vance, and A. Joblin, “Asymmetric, adiabatic multipronged planar splitters,” Opt. Quantum Electron. 28(4), 353–369 (1996). [CrossRef]
13. S. Martínez-Garaot, A. Ruschhaupt, J. Gillet, T. Busch, and J. G. Muga, “Fast quasiadiabatic dynamics,” Phys. Rev. A 92(4), 043406 (2015). [CrossRef]
14. M. Shirata, T. Fujisawa, T. Sakamoto, T. Matsui, K. Nakajima, and K. Saitoh, “Design of small mode-dependent-loss scrambling-type mode (de)multiplexer based on PLC,” Opt. Express 28(7), 9653–9665 (2020). [CrossRef]
15. M. Koshiba, Optical Waveguide Theory by the Finite Element Method (Springer, 1993).
16. M. Koshiba and Y. Tsuji, “A wide-angle finite-element beam propagation method,” IEEE Photonics Technol. Lett. 8(9), 1208–1210 (1996). [CrossRef]
17. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic Publishers, 2000).
18. D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: concepts, methods, and applications,” Rev. Mod. Phys. 91(4), 045001 (2019). [CrossRef]
19. S. Martínez-Garaot, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides using fast quasiadiabatic dynamics,” Opt. Express 25(1), 159–167 (2017). [CrossRef]
20. H.-C. Chung, K.-S. Lee, and S.-Y. Tseng, “Short and broadband silicon asymmetric Y-junction two-mode (de)multiplexer using fast quasiadiabatic dynamics,” Opt. Express 25(12), 13626–13634 (2017). [CrossRef]
21. H.-C. Chung and S.-Y. Tseng, “Ultrashort and broadband silicon polarization splitter-rotator using fast quasiadiabatic dynamics,” Opt. Express 26(8), 9655–9665 (2018). [CrossRef]
22. Y.-J. Hung, Z.-Y. Li, H.-C. Chung, F.-C. Liang, M.-Y. Jung, T.-H. Yen, and S.-Y. Tseng, “Mode-evolution-based silicon-on-insulator 3 dB coupler using fast quasiadiabatic dynamics,” Opt. Lett. 44(4), 815–818 (2019). [CrossRef]
23. N. Dhingra, G. J. Saxena, K. Kishor, and E. K. Sharma, “Efficient strip to slot waveguide mode converter using fast quasi-adiabatic approach,” Eng. Res. Express 2(3), 035014 (2020). [CrossRef]
24. Y.-L. Wu, F.-C. Liang, H.-C. Chung, and S.-Y. Tseng, “Adiabaticity engineering in optical waveguides,” Opt. Express 28(20), 30117–30129 (2020). [CrossRef]
