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A novel mode multiplexer and demultiplexer (MMUX/DEMMUX) based on 2-D photonic crystal (PC) at 1550 nm is proposed. The PC-based mode MMUX/DEMMUX including mode conversion function with a single-mode and multi-mode waveguides can be realized by quasi phase-matching TE0 & TE1 modes of two waveguides. 2D Finite-Difference-Time-Domain and beam propagation methods are used for simulation. The results show that PC-based mode MMUX/DEMMUX has the potential for high-capacity MDM optical communication systems with a low insertion loss (<0.36dB), low mode crosstalk (< −20.9 dB) and wide bandwidth (~100 nm).
© 2015 Optical Society of America
1. Introduction
Optical fiber communication system has undergone an irreversible evolution process from multi-channel, high speed to ultra-high speed, ultra-large capacity and ultra-long distance(3U). In recent years, wavelength division multiplexing system (WDM) is developing rapidly, from coarse wavelength division multiplexing (CWDM) to the dense wavelength division multiplexing (DWDM) [1–3]. However, progress in WDM transmission capacity has remarkably slowed down as experiments are approaching the fundamental Shannon limits of sing-mode optical fiber (SMF) system, limiting the development of all-optical communication systems. To break though the Shannon limits of SMF in the future, Mode-division multiplexing (MDM) is a completely new form of optical multiple-input multiple-output (MIMO) transmission and utilizes the limited stability modes as independent channels to transmit information, expanding the capacity and spectrum efficiency exponentially.
For a MDM optical-interconnect link, one of the essential key components is MMUX/DEMMUX, which can be realized by using multimode interference (MMI) couplers [4,5], PLC-based asymmetrical parallel waveguides (APW) [6–8], adiabatic couplers [9], asymmetrical Y-junction [10–12], as well as few-mode fibers [13–15]. Among them, N.Hanzawa group in Japan NTT Laboratory have successfully multi/demultiplexed two, three and four modes respectively [16–19] by quasi phase-matching (QPM) the modes of asymmetrical parallel waveguides and fabricated PLC-based MMUX/DEMMUX, but PLC-based MMUX/DEMMUX have a poor performance with a relatively high insert loss of above 1.6dB [6–8]. This is not desired because low power consumption is required in photonic networks-on-chip. On the other hand, MMUX/DEMMUX based on chip Y-splitter were designed by Jeffrey B. Driscoll in Columbia University, which can realize (de)multiplex two modes of the same polarization with a low insert loss ranging from 0.1to 0.7 dB [10]. However, these devices require complicated waveguide cross-sections with a very precise control of the angle between Y-junction arms.
In this paper, a novel TE0&TE1 mode multiplexer and demultiplexer using an APW-based on the 2-D Si square lattice PC slab is proposed. The APW consists of a single-mode waveguide(SMW) realized by removing a row of Si dielectric cylinders and a bus multi-mode waveguide(MMW) composed of two rows of size-adjustable Si dielectric cylinders which can be adjusted to satisfy the QPM condition. Based on the mode conversion features of APW, the TE0 mode of SMW in 1550nm band is converted to TE1 mode transmiting in MMW where it supports only TE1 mode with effective index that matches TE0 mode of SMW, therefore TE0&TE1 MMUX/DEMMUX can be achieved. The device designed is leading the way to have good capability to extend the application of MDM communication filed with advantages of small size, low insert loss, low mode crosstalk and easily intergrated.
2. Structural model and MDM mechanism
2.1 Structure model
2.1.1 Optimization coupling between SMW and MMW
A high-performance MMUX/DEMMUX based on 2-D PC requires highly efficient, low-loss coupling between SMW and MMW. This type of coupling needs a PC taper which is a guiding structure for transmission of electromagnetic wave that narrows/broadens towards one end [20–24]. Its width decreases/increases along its axis.
We have considered a 2D PC as shown in Fig. 1(a) as the basis for the design of MMUX/DEMMUX. The lattice consists of high index Si pillars (n = 3.4) in air (n = 1). The lattice constant a for the structure is considered to be 0.54 μm and the radius of the pillars is taken as 0.09μm. Here, we set the normalized frequency of 0.342*2πca−1 as 1.55μm. Such an arrangement of pillars is expected to provide a band gap around 1.55μm, as seen in Fig. 1(b). This PC will be used to create a SMW and MMW. SMW is formed by removing a row of Si dielectric cylinders, MMW is realized by adjusting the size of two rows of Si dielectric cylinders which supports two guided modes (TE0&TE1), and the red circles in Figs. 1(c) and 1(d) stand for the Si pillars with the adjusted radius of 0.0458μm. The step-width waveguide can be formed by the direct connection between SMW and MMW, at the port of which 1.55μm TE0 mode is incident, as shown in Fig. 1(c). Direct butt coupling results in mode mismatch that leads to high reflection loss and deteriorated collimation property, as presented in Fig. 1(e). Figure 1(g) shows that the transmittance of the light transmitting through the step-width waveguide is only 60% and the red curve becomes wider due to the dispersal light energy distribution. This insufficient light obstructs the functionality of the device. To get rid of this problem, we designed a symmetry dislocation a/2 along the vertical direction between SMW and MMW, and introduced a PC taper with width increased linearly as the connection waveguide, as shown in Fig. 1(d). The PC taper provides smooth mode profile conversion with good collimation. The fundamental mode that travels through the taper does not couple to higher order modes. Therefore, the reflection loss is reduced with a high transmittance of 97% and approaches the adiabatic regime, as shown in Figs. 1(f) and (g). The higher transmission obtained in the PC taper has a tradeoff with the fabrication difficulty as it requires very precise fabrication control and accuracy. There are, however, advanced fabrication facilities available today for PC [25,26]. Consequently, the PC taper used in mode MMUX/DEMMUX devices offers lower reflection loss, higher mode conversion and coupling efficiency.
Fig. 1 (a) Cross section of PC complete structure; (b) the TE band structure for PC complete structure; Cross section of the coupling way between SMW and MMW (c) step-width waveguide ;(d) taper waveguide.When a beam of 1.55μm TE0 light is incident at the port of SMW, (e) the steady intensity distribution in step-width waveguide; (f) the steady intensity distribution in taper waveguide; (g) the time domain steady state of transmission light in step-width and taper waveguide respectively.
2.1.2 Structure of MMUX/DEMMUX
The taper waveguide shown in Fig. 1(d) can be used in the structure of PC-based MMUX/DEMMUX. Figure 2 shows the schematic configuration of 2-D MMUX/DEMMUX. An asymmetric parallel waveguide (APW) as a mode conversion function is introduced in 2-D square lattice PC containing 43 × 17 cells. The APW is formed by putting a rectangular SMW (G1) close to the MMW (G2) so that there is an evanescent coupling Region, where G1 is formed by removing a row of Si dielectric cylinders and G2 is realized by adjusting the size of two rows of Si dielectric cylinders which supports two guided modes (TE0&TE1). The bus MMW consists of a horizontal SMW (G3) and G2 whose widths are different. In order to reduce the reflection loss caused by the mode mismatch, there is a symmetry dislocation of a/2 along z axis and a taper waveguide (G4) with width increased linearly between the APW and G3 Regions.
The width of G1 (w1) and the radius of G2 (r2) should be optimized to satisfy the phase matching condition so that the fundamental mode (TE0) of G1 could be coupled to the first-order mode (TE1) in the bus waveguide completely. Moreover, the APW gap (d = a + 2r1) and interaction length (L1) should be set to realize the maximum mode coupling efficiency between the TE0 mode and TE1 mode.
The structural parameters of the device are set as below: lattice constant is a = 0.54μm, the radius and refractive index of Si dielectric cylinders (white circles) is r1 = 0.09μm, n1 = 3.4. Table 1 shows the the APW parameters of our proposed MMUX/DEMMUX for matching the effective indices of the TE0 and TE1. The width of G1 is w1 = a = 0.54μm, the radius of the size-adjusted Si pillars (red circles) and width of G2 are set as r2 = 0.0458μm, w2 = 3a = 1.62μm. The APW gap and interaction length are L1 = 18a = 9.72μm, d = a + 2r1 = 0.72μm. The length of G4 is L2 = 5a = 2.7μm, the width increases linearly with slope equal to a/10.
Table 1. Waveguide parameters for an asymmetric parallel waveguide
2.2 MMUX/DEMMUX mechanism
An asymmetric parallel waveguide can be composed of the parallel SMW and MMW including 3 Regions, there are SMW (A), coupling Region (B) and MMW (C), as shown in Fig. 3(a). The effective refractive index of TE0 in A should be equal to that of TE1 in B according to the phasing-matching condition [18,19,27], indicating that the propagation constant of TE0 in A equals that of TE1 in B based on PC, as shown in Fig. 3(a). Here, the first-order mode dispersion curve of B intersects the fundamental mode dispersion curve at the normalized frequency of 0.342*2πca−1 where the TE0 and TE1 mode conversion can be realized. Since there is no fundamental mode dispersion intersection between A and B, the TE0 mode beams in the two waveguides are uncoupling and independent each other. In our PC-based MMUX/DMMUX designed in this paper, we set the normalized frequency of 0.342*2πca−1 as 1550nm. When a beam of TE0 mode in 1550nm is incident from the port of A, the fundamental mode (TE0) of A will be coupled to the first-order mode (TE1) of C. The light wave alternately transmit between A and C. It can be seen from the intensity distribution of B Region in Fig. 3(b). To match the effective indices of the TE0 and TE1 modes effectively, the coupling length and gap were required to be 18a = 9.72μm and a = 0.54μm respectively.
Fig. 3 (a) APW structure and the corresponding mode dispersion curve; (b) the steady field intensity distribution for mode conversion in the APW Region
Figure 4 illustrates the electrical field transition from each input port for MMUX/DEMMUX shown in Fig. 2. Since G1 and G3 are well separated to avoid interaction, the TE0 modes in 1550nm are injected into the port1 and port2 respectively. The fundamental mode of G1 will be coupled to the first-order mode of the bus MMW provided that the corresponding phase matching conditions are satisfied. On the other hand, because of the significant effective refractive index difference between the TE0 modes in the G2 and G1, a very low coupling efficiency is obtained. Thus the fundamental modes in G3 and G1 are multiplexed at port3 and vice-versa. The APW can be also used as a DEMMUX because the parallel waveguide has a symmetric property. During demultiplexing, the TE0 and TE1 modes are excited from port3, and the TE0 modes are output at port 1 and port 2 respectively.
3. Properties and analysis
3.1 The simulation of MMUX
A 2-D FDTD technique based simulation tool is used to calculate the device behavior. For the multiplexing function, CW light of TE0 mode at 1550nm was input into port 1, one power detector was placed at port 3 to probe the power transmittance multiplexed T1-3, and the other power detector was placed at port 2 to observe the power coupled to the horizontal SMW S1-3, which indicates a multiplexing crosstalk, as shown in Figs. 5(a)-5(c). Similarly, the power transmittance multiplexed T2-3 and the power coupled to the rectangular SMW S2-3 could be obtained when CW light was input into port 2, as illustrated in Figs. 5(d)-5(f). It could be seen that the two channels are multiplexed very well. The two-mode MMUX performs well with a high power transmittance multiplexed of 95% and a low power coupled to the adjacent channel reaching 10−4 order of magnitude.
Fig. 5 For TE0&TE0 MMUX (a) transmittance T1-3; (b) crosstalk intensity S1-3; (c) mode field intensity distribution. For TE0&TE1 MMUX (d) transmittance T2-3; (e) crosstalk intensity S2-3; (f) mode field intensity distribution. For TE0&TE0 DEMMUX (g) transmittance T3-1; (h) crosstalk intensity S3-1; (i) mode field intensity distribution. For TE0&TE1 DEMMUX (j) transmittance T3-2; (k) crosstalk intensity S3-2; (l) mode field intensity distribution.
3.2 The simulation of DEMMUX
During two-mode demultiplexing, CW light of TE1 mode at 1550nm was input into port 3, one power detector was placed at port 1 to detect the power transmittance demultiplexed T3-1, and the other power detector was placed at port 2 to observe the power coupled to the horizontal SMW S3-1, which implies a demultiplexing crosstalk, as shown in Figs. 5(g)-5(i). It indicates a higher crosstalk to the adjacent channel reaching 8 × 10−4 and a lower transmittance of 92%. Similarly, the power transmittance demultiplexed T3-2 and the power coupled to the rectangular SMW S3-2 could be obtained when TE0 mode was input into port 3. At the output terminal, the multiplexed multi-channel signals were demultiplexed well and output fom the two output ports separately, as presented in Figs. 5(j)-5(l). And the simulation result shows that TE1&TE0 DEMMUX performs better with a higher transmittance of 98.89% and a lower crosstalk of 10−5 order magnitude compared with TE0&TE0 DEMMUX.
3.3 Performance index Analysis of MMUX/DEMMUX
The insert loss and channel crosstalk are important indicators for evaluating the performance of MMUX/DEMMUX device. The insert loss is the loss of signal power resulting from the insertion of MMUX/DEMMUX.and represent the loss of incident TE0 mode for TE0&TE0 and TE0&TE1 MMUX respectively.Similarly,and represent the loss of incident TE0/TE1 mode for TE0&TE0 and TE1&TE0 DEMMUX respectively, expressed as:
Channel crosstalk is defined as the the degree of crosstalk caused from the transmission channel to the adjcent channel. and represent the crosstalk to port 1 and port 2 respectively for TE0&TE1 and TE0&TE0 MMUX, andand represent the crosstalk to port 1 and port 2 for TE1&TE0 and TE0&TE0 DEMMUX respectively, expressed as [17]:
Figure 6 shows the numerical simulation results for the wavelength dependence of insert loss and channel crosstalk for MMUX/DEMMUX over a wide wavelength range of 1470-1610nm. The mode insert loss is less than 0.86dB between 1510 and 1610 nm, especially when wavelength ranges from 1550 to 1610 nm the device performs better with a low insert loss achieving 0.01-0.55dB. While there is a performance deterioration with a drastic increase of 2.35dB in the insert loss between 1470 and 1510nm, meaning that TE0 mode in G1 possess the different propagation constant as TE1 carried by the bus MMW waveguide as shown in Fig. 6(a). Seen in Fig. 6(b), the TE0&TE0 DEMMUX crosstalk to G1 is higher which is consistent with the result shown in Figs. 5(h)-5(i). The crosstalk is less than −15dB between 1510 and 1610nm, in particular it is as little as −42dB in 1550nm and 1510nm. It can be seen that MMUX/DEMMUX may not operate properly when the wavelength takes the value from 1470 to 1510nm due to the large insert loss. On the contrary, the device has an optimal operation between 1510 and 1610nm. Consequently the calculated results confirmed that MMUX/DEMMUX can support a singnal transmission with the center wavelength of 1550nm over a wide C-band (100nm).
Fig. 6 (a) Wavelength dependence of mode insert loss. The black and red curves represent and for TE0&TE0 and TE0&TE1 MMUX respectively. The blue and gray curves show and for TE0&TE0 and TE1&TE0 DEMMUX respectively. (b) Wavelength dependence of mode crosstalk. The black and red curves represent and for TE0&TE0 and TE0&TE1 MMUX respectively. The blue and gray curves show and for TE0&TE0 and TE1&TE0 DEMMUX respectively.
3.4 Influence of fabrication imperfections on MMUX/DEMMUX performance
The height of Si dielectric cylinders along y direction can be considered to be infinite in 2D FDTD simulation enviroment. However, 2-D photonic crystal devices are constructed on 3-D SOI substrate platform in the actual fabrication process. Firstly, out-of-plane scattering loss can be influenced by the refractive index contrast ratio of SOI [28], limiting the usefulness of 2-D photonic crystal slabs. It is therefore important to choose a good layer structure for keeping these losses low. Moreover, the surface roughness, the cylindrical holes or pillars depth and shape are also key factors [29,30], so the fabrication process should be optimized to reduce the out-of-plane scattering loss. We discuss the effects of geometric nonuniformity in the xz plane on the performance index.
There are random irregularities existed in the practical fabrication process of PC-based devices including dimensional discrepancy, finite etch depth, shape imperfection, dislocation, and so on. These irregularities have a negative effect on the performance of PC devices [30,31]. To check the the influence of the geometric imperfections on the performance index of our proposed MMUX/DEMMUX, Fig. 7(a) shows that the coupling efficiency of taper waveguide (Region 1) and mode conversion property between SMW (Region 2) and MMW (Region 3) are major factors. Additionally, the imperfections have an effect on the mode multiplexing and demultiplexing in a similar way due to the symmetric property of the parallel waveguide.
Fig. 7 (a) The fabrication imperfections existed in taper waveguide (Region 1), SMW (Region 2) and MMW (Region 3). (b) The radius imperfections and dislocations existed in 3 regions. The blue, red and green circles respect the radius imperfections and the number n of Si pillars with a radius imperfection is 1, 2, 3 respectively. All the arrows (blue, red and green) show dislocations caused by the movement of a row of Si pillars with fixed correct size along z + and z- direction.
The actual fabrication deviations are complex problems. For instance, the dimensional discrepancy, shape imperfection and dislocation may be existed simultaneously in 3 regions, and the disordered Si pillars may have different variations between each other. Here, we simplify the research of fabrication imperfections to estimate the general influence on the MMUX/DEMMUX performance. Therefore we investigate the effect of the radius discrepancy and dislocation separately existed in 3 regions for two-mode MMUX, as shown in Fig. 7(b). For the radius discrepancy, the influence of the Si pillars with the same radius variation in Region 1 can be considered when the number n of Si pillars with a radius imperfection is 1, 2 and 3 respectively, and there are no fabrication disorders existed in Regions 2 and 3. Similarly, the radius discrepancy can be successively explored in Regions 2 and 3. For the dislocation situation, a row of fixed correct size Si pillars with the same movement create dislocation imperfections, which existed in Regions 1, 2 and 3 can be taken into account in turn. It permits us to direct the efforts in further improving the fabrication technology.
3.4.1 Influence of radius discrepancy on MMUX/DEMMUX performance
Figure 8 shows the insert loss and crosstalk as the function of the radius discrepancy of Si pillars in Region 1, 2 and 3 for two-mode MMUX. The performance changes with the number n of Si pillars with a radius imperfection. The squares, circles and stars represent the influence of size discrepancy on mode MMUX/DEMMUX performance when n = 1, 2, 3 respectively in Figs. 8(a)-8(f).
Fig. 8 The radius discrepancy dependence of (a) (black symbols) and (blue symbols) in Region 1. (b) (black symbols) and (blue symbols) in Region 1. (c) (black symbols) and (red symbols) in Region 2. (d) (black symbols) and (red symbols) in Region 2. (e) (black symbols) and (green symbols) in Region 3. (f) (black symbols)and (green symbols) in Region 3.
The caculated insert loss as the function of the radius discrepancy of Si pillars with different n = 1, 2 and 3 in Region 1 is shown in Fig. 8(a). (shown in black) is hardly influenced by the introduced radius disorder, while(shown in blue) is strongly affected and deteriorates with the increasement of n. Bothand achieve 0.5dB with the radius discrepancy between 0.07 and 0.14µm. The corresponding(shown in black) and(shown in blue) performs better, with values of −28dB and −32dB respectively according to Fig. 8(b). On the contrary, Fig. 8(c) shows that the radius discrepancy has little impact on (shown in black), but tremendous impact on (shown in red). This is because Regions 1 and 2 are well separated to avoid interaction. Similarly, bothand are less than 0.5dB only when the radius imperfection changes from 0.07 to 0.13µm. The corresponding(shown in black) and(shown in red) also performs better, with values of −30dB, as shown in Fig. 8(d). As seen from Figs. 8(e)-8(f), the inset loss and crosstalk are significantly affected by the variations of the pillar radius and aggravated with increased n. The device cannot operate properly until the radius imperfection takes the value from 0.04 to 0.05µm.It can be seen that the radius imperfection-tolerant rate in Regions 1 and 2 reaches 22% above, but the mode MMUX is sensitive to the radius imperfection of Si dielectric cylinders in Region 3. In addition, the increasement of the number n and variations of the radius disorder leads to the poor performance in all 3 regions.
3.4.2 Influence of dislocation on MMUX/DEMMUX performance
The dislocation of dielectric cylinders can be easily produced on the 2-D photonic crystal slab due to the low processing precision.We further discuss the influence of the dislocation of a row of Si pillars with fixed correct size along z axis on the MMUX, as shown in Fig. 9. Firstly, the dislocation of a row of Si pillars in Region 1 dependence on and is shown in Fig. 9(a). The dislocation has a negligible influence on, while it has a great effect on. Bothandare less than 0.5dB with the dislocation between −0.15-0.02µm. Figure 9(b) illustrates that the crosss talk exhibits better performance and reaches −30dB below. It can be seen that the influences of the radius discrepancy and dislocation of Si pillars in Region 1 have the same varying trend. Oppositely, Figs. 9(c) and 9(e) shows that the dislocation of a row of Si pillars exist in Region 2 and 3 has little impact on , but a dramatic rise ofis induced by a slight dislocation. The crosstalk (black squares) and (red circles) are −20dB below in Region 2 when the dislocation shifts from −0.1-0.05µm, as shown in Fig. 9(d). According to the results in Fig. 9(f), the crosstalk (black squares) and (green circles) are −20 dB below in Region 3 when the dislocation is in the range −0.15 −0.15µm. It can be found that the dislocation imperfection-tolerant rate in Region 1 is relatively high, reaches 7.4% above, while a slight dislocation in Regions 2 and 3 greatly deteriorates the performance. Taken into account these two cases, the radius disorders should be avoided in Region 3 due to the low radius imperfection-tolerant rate, and the dislocation imperfections should be forbided in Regions 2 and 3 because of the low dislocation imperfection-tolerant rate. Consequently, fabrication imperfections should be reduced to improve the operating characteristics.
Fig. 9 The dislocation dependence of (a) and in Region 1. (b) and in Region 1. (c) and in Region 2. (d) and in Region 2. (e) and in Region 3. (f) and in Region 3.
4. Conclusion
A novel MMUX/DEMMUX based on 2-D photonic crystal (PC) is proposed in this paper. The TE0 and TE1 modes at 1550nm can be multi/demultiplexed on the theorem of quasi-phase-matching (QPM) of an asymmetric parallel waveguide (APW) introduced in PC complete structure. The transmission characteristics of this device can be analyzed with the finite difference time domain method. The results show that the insert loss is 0.01-0.86dB and channel crosstalk reaches −20.9dB in 1550nm band. The suggested MMUX/DEMMUX is compact and overall size of the chip is about 23 × 9μm. It is feasible to fabricate this strcture nowadays by using semiconductor process technology on an SOI substrate due to its simple structure. A maximum deviation in radius/location of 0.05 microns in Region 3 is permitted, whereas much larger tolerances are acceptable in Regions 1, 2. The performance of MMUX tends to be worse as the increasement of radius disorders and dislocations, so the fabrication process should be optimized to reduce the insert loss and crosstalk. These features indicate the important application prospect in the future MDM optical transmission system.
Acknowledgments
This work was supported by National Natural Science Foundation of China(No.61571237), Natural Science Foundation of Jiangsu Province of China(No.BK20151509), Colleges and Univesities in Jiangsu Province plans to graduate research and innovation(No.CXLX13_451).
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