A mode-(de)multiplexer with low loss and large spectral bandwidth is proposed. The device is designed by utilizing a structure with cascaded asymmetric Y-junctions. By carefully controlling the widths of the wide and narrow arms of the Y-junctions, the fundamental mode of a narrow arm excites the higher-order mode of its stem in the multiplexing case, and a high-order mode of the stem separated from other lower-order modes evolves into the fundamental mode of the narrow arm in the demultiplexing case. As an example, a 1 × 4 mode-(de)multiplexer is analyzed by using the beam propagation method. Simulation results show the demultiplexed crosstalk is lower than –21.8 dB, under a common spectral bandwidth of 140 nm. The insertion loss is negligible.
© 2013 Optical Society of America
As the rapid growth of Internet traffic, to expand the capacity of optical links is required. There are many means to increase bandwidth, such as spatial-division multiplexing (SDM), wavelength-division multiplexing (WDM), polarization division multiplexing (PDM) and mode-division multiplexing (MDM). Among these technologies, MDM transmission in which each optical mode is used as a separate data channel provides an attractive option to enhance the capacity of a single link of optical interconnects, due to its convenience of handling the eigen modes [1,2].
As a key component in MDM transmission, mode (de)multiplexers have attracted significant attention in recent years. Previously, several mode (de)multiplexers have been reported based on Y-splitter, multimode interference (MMI), asymmetrical directional couplers (ADCs) and grating-assisted contra-directional couplers (GACCs). The mode (de)multiplexers based on Y-splitter and MMI only handle two optical modes with the same polarization [3–5]. The mode (de)multiplexers based on ADCs and GACCs can achieve more than four channels. However, the mode (de)multiplexer based on ADCs requires accurate control of the coupling length and coupling strength , and the one based on GACCs has a limited bandwidth .
Y-junctions are commonly used as broadband power dividers . Asymmetric Y- junctions where each arm has a different effective index can be designed to act as polarization splitters, mode combiners, mode splitters, wavelength multiplexers and mode sorters [9–17]. For the case of a two-mode mode-sorting asymmetric Y-junction, an arm can adiabatically excite the first odd (even) mode of the Y-junction stem [4,16]. When the theory of mode-sorting is applied to multi-arm asymmetric Y-junctions with multiple modes in the stem, the separation of more than three or four modes is practically limited because of the restriction on insertion loss and the length of the Y-junction, which is approximately proportional to the fourth power of the number of modes [17,18].
In this paper, a 1 × N (N≥4) mode-(de)multiplexer based on cascaded asymmetric Y-junctions (CAYJs) is proposed and designed. By taking advantage of CAYJs in which the fundamental mode in the narrow arm is coupled to the higher-order mode in the stem with a negligible loss of modal power, the proposed mode-(de)multiplexer can realize broadband and low-loss operation. We numerically study the behavior of a 1 × 4 CAYJs mode-(de)multiplexer using the beam propagation method (BPM). In the simulation, a pure silicon dioxide (SiO2) cladding and small index contrast (0.01) are considered. Numerical simulations show the 1 × 4 mode-(de)multiplexer has a demultiplexer crosstalk lower than −21.8 dB under a common spectral bandwidth of 140 nm and a maximum insertion loss of 0.03 dB.
2. Operation principle
The schematic of a CAYJs mode (de)multiplexer is shown in Fig. 1(a). The branching angles of all Y-junctions are sufficiently small to ensure the modes can approximately adiabatically propagate through the device. Each narrow arm supports just the fundamental mode and the stems support multiple eigen modes. When the higher-order optical mode appears in the stem, it exits as the fundamental mode of the narrow arm where its effective index better matches the effective index of the higher-order optical mode in the stem, as illustrated in Figs. 1(c), 1(e) and 1(g). The remaining modes in the stem are keeping forward modal propagation, as depicted in Figs. 1(b), 1(d) and 1(f). On the contrary, when one mode of an arm propagates through the junction, it will be transformed into another mode in the stem, which has the closest effective index.
That is to say, whether the k-th (k = 1,2,3…) mode in the stem propagates forward or backward through the asymmetric Y-junction, once the effective index of the fundamental mode in the narrow arm is between the effective index of the k-th mode and the one of the (k + 1)-th mode in the wide arm, the mutual conversion between the k-th mode in the stem and the fundamental mode in the narrow arm will be achieved. Meanwhile, in order to obtain a branching angle as large as possible in the case of approximate adiabatic propagation of modes, the effective index difference between the adjacent modes should be as large as possible to reduce the mode coupling. This indicates that the narrow arm is expected to support the fundamental mode rather than the higher-order mode. In addition, take mode-demultiplexing for example. When the k-th mode in the stem is going to be adiabatically separated from other lower-order modes and transformed into the fundamental mode in the narrow arm, the width of the wide arm should be chosen rationally to ensure the effective index difference between the k-th and (k + 1)-th modes in the wide arm is as large as possible and the effective index of the fundamental mode in the narrow arm is almost midway between the effective index of the k-th mode and the one of the (k + 1)-th mode in the wide arm. The principle of modal effective index matching also works in the multiplexing case and the parameters involved are optimized to reduce the mode coupling and improve the multiplexing efficiency in the simulation.
3. Structure description and analysis
As an example, a 1 × 4 CAYJs mode-(de)multiplexer is shown in Fig. 2(a). In the proposed mode-(de)multiplexer, there are three-stage asymmetric Y-junctions. Between the stem of an asymmetric Y-junction and the wide arm of the next one, there is an adiabatic taper to link them. The i-th (i = 1, 2, 3) asymmetric Y-junction is formed by adding a narrow input access waveguide to excite the higher-order mode of its stem.
In this work, a SiO2 channel waveguide with a height of 7 μm is considered. The refractive index of SiO2 is 1.45 and the refractive index difference is 0.01. As shown in Fig. 2(b), the calculated effective indices of the guide modes are changing as a function of the core width. The dashed and solid curves represent TE and TM polarizations respectively. All the narrow input access waveguides are designed to support just the fundamental mode. The width W0 of the narrow input access waveguide is 5 μm while the width of the wide input access waveguide is equal to W1-W0. Wi -W0 is the width of the wide arm of the i-th asymmetric Y-junction. Lj (j = 0, 1, 2) associated with the branching angle is the length of the wide arm of the i-th asymmetric Y-junction. Both the width Wi and the length Lj are optimized according to the principle of modal effective index matching.
The width W1 and the length L0 dependence of the optical transmission of the first-stage asymmetric Y-junction for the cases of inputting the fundamental mode into ports Input1 and Input2 are shown in Fig. 3. Note that in Figs. 3(a) and 3(b), as the width W1 increases, the output power of the second mode excited by putting the fundamental mode into port Input2 is significantly increased. In addition, the output power of the non-target excited modes can be well suppressed with increasing length L0. When the width W1 and the length L0 are chosen to be 13 μm and 5000 μm, the output power of the second modes are effectively suppressed and the fundamental and first modes have good extinction ratios. Therefore, the width W1 and the length L0 are set to be 13 μm and 5000 μm in our simulation with an extinction ratio of 41.0 dB for the fundamental mode and an extinction ratio of 41.2 dB for the first mode at the wavelength of 1550 nm.
Figure 4 shows the width W2 and the length L1 dependence of the optical transmission of the second-stage asymmetric Y-junction, for the cases of inputting the fundamental mode into ports Input1, Input2, and Input3. From Fig. 4(a), the output power of the third mode excited by putting the fundamental mode into the Input3 port increases rapidly with increasing width W2. In Fig. 4(b), as the length L1 increases, the extinction ratio of the second mode excited by putting the fundamental mode into the Input3 port is getting larger until the advent of the inflection point. Therefore, in order to reduce the mode coupling and improve the extinction ratio, the width W2 and the length L1 are respectively set to be 22 μm and 5000 μm with an extinction ratio of 33.2 dB for the second mode at the wavelength of 1550 nm.
Figure 5 shows the optical transmission of the third-stage asymmetric Y-junction as a function of the width W3 and the length L2, for the case of inputting the fundamental mode into ports Input1, Input2, Input3 and Input4. As depicted in Figs. 5(a) and 5(b), on one hand, when the width W3 ranges from 29.5 μm to 31.5 μm, the modal conversion is achieved with no loss of power. On the other hand, a marked increase in the output power of the fourth mode excited by putting the fundamental mode into port Input4 comes along with the increase of the width W3. Furthermore, when the length L2 increases from 5000 μm to 10000 μm, the extinction ratio of the third mode excited by putting the fundamental mode into the Input4 port is improved, but the mode coupling is not reduced too much. Therefore, the width W3 and the length L2 are chosen as: W3 = 30 μm, and L2 = 5000 μm with an extinction ratio of 18.9 dB for the third mode at the wavelength of 1550 nm.
From Fig. 6, one can see that the higher-order modes are excited when the fundamental mode is launched into the ports Input1, input2, input3 and input4 at the wavelength of 1550 nm. A three-dimensional BPM is used in the simulation. Figure 7 shows the spectral responses of the designed 1 × 4 CAYJs mode-(de) multiplexer by putting fundamental modes into the access waveguides. The calculated dominant optical power at the Output1, Output2, Output3, and Output4 ports of the demultiplexer are denoted with rectangle, circle, diamond and triangle traces respectively. Figures 7(a)-7(d) represent the transmission spectra from ports Input1, Input2, Input3, and Input4. It can be found within a bandwidth from 1520 nm to 1660 nm, the best demultiplexed crosstalk of different modes is up to −57.0 dB, while in the worst case it is −21.8 dB. Simulation results show that the insertion loss of the designed mode-(de)multiplexer varies from 0.01 dB to 0.03 dB at a wavelength of 1550 nm, depending on I/O port.
In conclusion, we have proposed a CAYJs mode (de)multiplexer with low loss and large bandwidth. It provides another optional approach for increasing the capacity in mode-division multiplexing system. According to the principle of modal effective index matching, the fundamental mode of a narrow arm can adiabatically excite the higher-order mode of its stem in the multiplexing case, and a high-order mode in the stem can be adiabatically separated from other lower-order modes and exit as the fundamental mode of the narrow arm in the demultiplexing case. By using BPM simulations, the crosstalk level for the designed 1 × 4 CAYJs mode-(de) multiplexer is found to be between −21.8 dB and −57.0 dB for channels (de)multiplexed different modes under a common optical bandwidth of 140 nm. The maximum insertion loss is about 0.03 dB. These properties make the proposed CAYJs mode-(de)multiplexer suitable for application in high-capacity data transmission.
This work is sponsored by the Natural Science Foundation of China under Grants 61228501, 61274132, 61307071, the 863 project under Grant 2012AA012203, the Doctoral Discipline Foundation of Ministry of Education under Grant 20120101110054, 20133305120004, the Science and Technology fund of Zhejiang Province under Grant 2013C31083, the Natural Science Foundation of Ningbo under Grant 2013A610005, and the K. C. Wong Magna Fund in Ningbo University.
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