Nghiên cứu tính toán và thiết kế mạch tích hợp quang băng rộng chuyển đổi và tách ghép mode (design and simulation of wideband photonic integrated circuits for multi mode (de)multiplexing and conversion) tt tiếng anh

MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY -0 TRAN TUAN ANH DESIGN AND SIMULATION OF PHOTONIC INTEGRATED CIRCUITS FOR MULTI-MODE (DE)MULTIPLEXING AND CONVERSION Major: Telecommunications Engineering Code: 9520208 DOCTORAL ABSTRACT IN TELECOMMUNICATIONS ENGINEERING HANOI – 2020 This dissertation is completed at: Hanoi University of science and technology SUPERVISORS: PROF DR TRAN DUC HAN DR TRUONG CAO DUNG Reviewer 1: Reviewer 2: Reviewer 3: The dissertation will be defended before approval committee at Hanoi University of Science and Technology: Time…, date… month….year… The dissertation can be found at Ta Quang Buu Library Vietnam National Library INTRODUCTION Motivation Main stream in optical communication research field is to improve bandwidth for wideband applications There are some available techniques, such as WDM multilevel modulation format, polarization division multiplexing (PDM) On the other hand, (MDM) technology has been being paid attention as an emerging technology to enhance the capacity of the optical communication system besides mentioned above technology Different from applications of WDM in longdistance transmission, MDM is more suitable for transmission with short distance, ultra large capacity, like intra-chip communication Hence, MDM shows to be a promising technique applied in on-chip optical communication, along with other (de)multiplexing schemes Objectives By reviewing existing papers and research works, there are some designs with different structures and materials have been proposed However, each of them have their own pros and cons and also are suitable for different purposes Therefore, the objective of this dissertation is to proposed new Silicon on Insulator (SOI) rib/ridge waveguide mode (de)muxer designs based on some specific structures that are used as passive devices working in C band and can overcome existing disadvantages, thus resulting in better overall performances regarding number of (de)multiplexed modes, loss and footprints Research methodology All the designs’ structures are build based on theoretical foundation Then, each device optical properties are investigated and optimized by numerical simulation methods, namely BPM and EIM Then, the devices are evaluated based on performance criteria defined as follow: P    Pout I.L  10log  out  Cr T  10log    Pin    Punwanted  Where Pin is total power of input waveguides, Pout is the wanted output power of the device and  Punwanted is the total of unwanted powers to wanted output port Scientific contributions and practical applications 1) We proposed a new mode (de)muxer design based on ADC SOI waveguide, which can (de)multiplex fundamental mode and 1st-order mode The result has been published in International Conference on Advanced Technologies for Communications (ATC), 2016 2) We proposed a new mode (de)muxer design based on 3x3 MMI couplers and trident SOI waveguide, which can (de)multiplex up to three lowest modes The results have been published in Optical and Quantum Electronic Journal 3) We proposed a new mode sorting design based on branched bus SOI waveguides Our design can (de)multiplex up-to modes so far One of the results has been published in Photonics and Nanostructures-Fundamentals and Applications Our designs can operate within band C range with low insertion loss and crosstalk; have small footprint, thus can be promising candidates for high bitrate MDM on-chip photonics integrated circuits Dissertation structure The dissertation consists of chapters Chapter introduce SOI waveguide structures analysis and principles that used in this dissertation Chapter 2, and will demonstrate new specific SOI waveguide designs with MDM functionality, which are also the three main scientific contributions of this dissertation CHAPTER SOI WAVEGUIDE STRUCTURE, ANALYSIS AND FABRICATION 1.1 Shapes and functions of silicon-on-insulator waveguide In this dissertation, rib/ridge waveguide structures are used for all designs Regarding material, core layer and substrate are made from silicon and cladding layer is made from silicon dioxide (silica) Those structure and material are also used in CMOS technology, that explains the reason why SOI waveguide is suitable for low cost manufacturing PIC 1.2 Optical waveguide analysis and simulation methods 1.2.1 Effective index method Effective index method (EIM) is an appropriate analysis for calculating the propagation modes of the channel waveguides It applies the tools developed for planar waveguides to solve the problem of two-dimensional structure It consists of solving the problem in one dimension; described by the x coordinate in such a way that the other coordinates (the y coordinate) acts as a parameter In this way, we obtain a y-dependent effective index profile; this generated index profile is treated once again as a one-dimensional problem from which the effective index of the propagating mode is finally obtained 1.2.2 Finite difference method (FDM) An arbitrary electromagnetic field propagating along a waveguide can be decomposed into many elementary discrete guided modes, which can be also called eigenmodes With Finite Difference Method, the cross-section of the waveguide is made discretely with a rectangular grid of points which might be of identical or variable spacing Each grid of point is assigned to an arbitrary electric field value and adjacent electric field can be calculated correspondingly Separation by Implanted Oxygen (SIMOX) - Oxygen ions density > >1018cm - Temperature = 6000C during implantation - Implantation energy of up to 200 keV - Annealed at a temperature of 1300 Bond and Etch-back SOI (BESOI) - Two oxidized wafers are brought into contact temperature room - Wafer thinning via CMP Wafer Splitting - Implant p-type ions into wafer, hence the silicon lattice bonds are significantly weakened -Thermal processing at 600oC and 1100oC splits the implanted wafer Silicon Epitaxial Growth - Chemical vapor deposition (CVD) - (SiH2Cl2) is often used as the source gas - Temperature > 1000oC Photolithography Using Deep Ultra Violet light, photoresist layer and mask to create waveguide structure on upper layer Silicon Etching (Using Plasmas Gas) Dry etching using CF4 gas and AC power to achieve critical dimension requirements of specific waveguides Thinning Si Overlayer Fig 1.3.1 SOI waveguide fabrication process 1.2.3 Beam propagation method (BPM) FDM can solve the waveguide eigenmode, but cannot be used to solve propagation characteristic in integrated optics or fiber optics The Beam Propagation Method (BPM) is a widely used to simulate the evolution of electromagnetic fields in arbitrary inhomogeneous medium Transparent Boundary Condition (TBC) is used in FD-BPM simulation to eliminate the back reflections or incoming fluxes into the analysis window, in which radiation disappear into the boundary without any reflection when reaching the edge of simulation window 1.3 Silicon-on-insulator waveguide fabrication SOI waveguides fabrication technology is similar with CMOS ones The fabrication process is described in the diagram chart Fig 1.3.1 1.4 Silicon-on-insulator waveguide structure used for MDM functionality 1.4.1 Directional coupler Coupling can be regarded as a scattering effect The field of waveguide (which has propagation constant = 𝛽1 and amplitude a1) is scattered from waveguide (which has propagation constant = 𝛽2 and amplitude a2), creating a source of light that changes the amplitude of the field in waveguide The field of waveguide has a similar effect on waveguide Coupled equations are as below: da1 da2   j ( 1a1  12 a2 ) (1.4.1)   j (  a2   21a1 ) (1.4.2) dz dz 𝜅𝑖𝑗 can be evaluated by an overlap integral of two modes as follows:  ij    n2  n2 ( x, y) Ei* E j dxdy (1.4.3) 2 P   Differential equations system (1.4.1) and (1.4.2) above has the roots that represented as follows:   j      1 a1 ( z )   a1 ( z0 )  cos 0 z  j sin 0 z   12 a2 ( z0 ) sin 0 z  e 20   0     j      2 a2 ( z )   a2 ( z0 )  cos 0 z  j sin 0 z   21 a1 ( z0 ) sin 0 z  e   0       1   1 z (1.4.4) z (1.4.5) where 0 is a parameter that can be determined by:    2  0     12 21    12 21   (1.4.6) The power ratio between the guided modes and normal modes is obeyed by:   pr   12 21 /        12 21 /     (1.4.7) 1.4.2 Multimode interference (MMI) 1.4.2.1 Propagation constant As the core width W is quite large and the high-contrast waveguides, the propagation constant is: (m  1)2  (1.4.8) m  kneff  4neff W 𝛽0 corresponds to m=0 and 𝛽1 corresponds to m=1 By defining 𝐿𝜋 as the half-beat length of the two lowest-order modes: L   o  1  4neff W 3 (1.4.9) The different between the propagation constants of fundamental mode (m=0) and mode mth can be expressed from Eq (1.4.8) and Eq (1.4.9) m(m  2) 3L o   m  (1.4.10) 1.4.2.2 Guide-mode propagation analysis (MPA) An input field profile 𝛹(𝑥, 0) at the entrance of the multimode waveguide then can be decomposed into modal field distribution 𝜓𝑚 (𝑥) M 1  ( x, 0)   cm m ( x) (1.4.11) m0 where the field excitation coefficient 𝑐𝑚 can be calculated by using the overlap integral According to Eq (1.4.11) we have field distribution at position z is: M 1  ( x, z )   cm m ( x)e j (  m0 o  m ) z (1.4.12) Substitute Eq (1.4.10) into Eq (1.4.12), we get M 1  m0   ( x, z )   cm m ( x) exp   jz m(m  2)   3L  (1.4.13) Input field will be reproduced if the phase term satisfies the condition: exp   jz  m(m  2) / 3L   1 Those properties mentioned above illustrate the self-imaging property of MMI Based on which and where the field 𝛹(𝑥, 𝐿) is reproduced, there are general interference (GI) and restricted interference (RI) mechanism This abstract will introduce GI only as this mechanism is used in our design 1.4.2.3 General interference MMI a, Single images can be fulfilled when z = p(3𝐿𝜋 ) with p = 0,1,2 … b, Multiple images can be fulfilled when 𝐿 = 3𝑝𝐿𝜋 /𝑁 𝑤𝑖𝑡ℎ 𝑝 = 1,3,5,7 … The resulting in terms of phase and positions of reproduced imagines are expressed as follow:  ( x, L)  N 1  j  in ( x  xq )e q C q 0 (1.4.19) with W N q q  p( N  q) N C  N xq  p (2q  N ) (1.4.20) In the case of shortest devices when p=1, the optical phases of the signals in a NxN MMI couplers are given by: ij    ij   4N  4N ( j  i)(2 N  i  j )  o for i+j even (1.4.21a) ( j  i  1)(2 N  i  j  1)  o for i+j odd (1.4.21b) Where input ports i (i=1, 2…N) are numbered from bottom to top and the output ports j (j=1, 2…N) are number from top to bottom in the 𝜋 MMI coupler NxN and 𝜑0 = −𝛽0 𝐿𝑀𝑀𝐼 − is the constant phase For shortest MMI length (p=1), 𝜑0 = 1.4.3 Asymmetric Y-junction waveguide In case of two adjacent waveguides, if effective refractive index of arbitrary mode (mth) from the 1st waveguide is equal to one of arbitrary mode (nth) from the 2nd waveguide, then mode (mth) of field in 1st waveguide can be coupled into mode (nth) of field of 2nd waveguide neff m ( waveguide1)  neff n ( waveguide 2) (1.4.22) Another factor that needs to be considered is Mode Conversion Factor (MCF) The equation of MCF is expressed as below: MCF  1   12 12 (1.4.23) where β1 and β2 are propagation constants of fundamental mode at two output ports, θ12 is divergence angle between them and γ12 is: 2  12   1      2kn   1/2 2  (1.4.24) MCF is a factor indicating how well multi-modes from the main bus input can be (de)multiplexed to fundamental mode at the output arms The greater MCF is, the better mode sorting will be, otherwise it will turn out to be a power splitter device 1.5 Conclusion This chapter has introduced waveguide structure, waveguide material that used in designing all our proposed devices Then, common numerical analysis methods are mentioned SOI waveguide fabrication is also briefly introduced Finally, three different waveguide structures and their corresponding working principles are introduced Each structures have its own pros and cons when applying in MDM, which will be mentioned in the following chapters CHAPTER MODE DIVISION MULTIPLEXER BASED ON ASYMMETRIC DIRECTIONAL COUPLER (ADC) ADC is one of the structures that attracts significant amount of research due to its simplicity, straight forward operating principles ADC structure has been used by several designs but there are still some drawbacks, e.g., high measured modal loss, modal dispersion while guiding into the waveguides and complicate structure Hence in this section, we propose a new design of two-mode DeMUXer based on asymmetric directional SOI waveguide coupler with simple structure suggesting some ideas for further improvements 2.1 Two mode division (De)multiplexer based on an MZI asymmetric silicon waveguide Fig 2.1.1 shows the configuration of the TM-(de)MUXer which is based on submicron silicon strip waveguides Output port Output port g d Lc Si h1 2w g Ls d A-A’ w h2 SiO2 Ls Fundamental mode TE0 2w Input port First-order mode TE1 R w Input port Fig 2.1.1 Schematic of the ADC based SOI waveguide The device is designed for operating in electromagnetic transverse (TE) modes with the wavelength operation of 1550 nm comprising of two asymmetric directional couplers, with the gap g is chosen as g=80 nm Silicon single mode waveguide is fabricated with the width and the height to be chosen as w=500 nm and h2=500 nm, while two-mode waveguide has the width chosen as 2w=1000 nm and the height is set to h1 The two-mode waveguide is designed to satisfy two conditions: mode TE0 won’t be coupled partially to the single mode waveguide and mode TE1 will be coupled effectively to single mode waveguide In this design, d is fixed as 1.2 µm, then optimal length of sinusoidal waveguides Ls is chosen by using BPM simulation as 105 µm As seen on the Fig.2.1.2, the effective index of mode TE0 in the single mode waveguide is calculated by BPM method as 2.911 Therefore, the effective index of mode TE1 in the two-mode waveguide must also be of nm and mode conversion efficiency up to 99.74% at the designed wavelength The device has low insertion loss, crosstalk and also low sidewall roughness scattering The proposed design shows some better aspects compared to similar previous works based on asymmetric directional couplers The whole size of the device can be integrated on a footprint as 4àmì1600àm; therefore, it is potentially suitable to construct on-chip photonics integrated circuits CHAPTER MODE DIVISION MULTIPLEXER BASED ON MULTIMODE INTERFERENCE COUPLER Compare to other structures, MMI proved to be a promising candidate for a compact mode (DE)MUXer with large bandwidth tolerance and good performance Therefore, this section will introduce new MDM structures based on symmetric Y-junctions and MMI waveguides 3.1 Three-mode division (De)multiplexer based on a trident coupler and two cascaded 3×3 MMI silicon waveguides The designed structure of the three-mode division (de)muxer is presented schematically in Fig 3.1.1 The 1st MMI coupler, PS1 and PS2 are designed to split power of the fundamental mode and the firstorder mode equally to two outermost output, while combines the second-order mode to its center output Then, the 2nd MMI coupler and to the third PS is designed so that the fundamental mode and the firstorder mode are switched to different output ports and the second-order mode propagating through the central output SOI rib waveguides have the height H = 500 nm and the slab height ho = 100 nm The distance G is set as 1.1 µm and WMMI is set as 4.8 µm The stem width of the trident coupler is set is W0=1.5 µm The width w of stem waveguide is determined as 520 nm for single mode regime W1 W1 W1 WPS3 Wc W2 W1 W1 LMMI2=3Lπ /2 W 3×3 MMI W2 W1 WMMI W2 MMI1=Lπ W1 w Ls WPS2 Wc WMMI φc Port c G W 3×3 MMI L W1 W L w First-order mode TE1 +2π/3 Phase Shifter LPS PS2 Output port1 Output port2 Output port3 w PS3 LPS W W0 Second-order mode TE2 φb Ltp Port b -π/3 Phase Shifter W1 WPS1 φa Port a LPS w PS1 Input port Fundamental mode TE0 Fig 3.1.1 Proposed schematic of a three mode (de)multiplexer 12 The design of the length Ls of the sinusoidal waveguides need to satisfy conditions as express in equation (3.1.1)  i   i   e2  e2     i 4     e     2  i  i  , Y    e i , Y   e  i  e i Y0  e e      3   2   2 i  i    e  e2   2i      e 4      ( 3.1.1) Output powers of the trident (a.u) Where, θ is accumulation phase of the optical field of guided modes when propagating pass through the trident coupler The optimal length of Ls is chosen at 15 µm as marked in Fig 3.1.2 P -0th mode a 0.9 Pc-0th mode 0.8 P -1st mode a 0.7 P -1st mode 0.6 Pa-2nd moce c P -2nd mode c 0.5 0.4 0.3 0.2 0.1 LS 10 15 20 25 Length of the sinusoidal waveguides, Ls (m) Fig 3.1.2 BPM simulation for transmittance properties of the trident coupler as a function of the length of the sinusoidal The first MMI coupler was designed with the chosen length: LMMI2=Lπ The second MMI coupler was designed with the chosen length: LMMI2=3Lπ/2 As the 2nd MMI only divides 0th and 1st order mode, hence it can be considered as a 2x2 MMI The relation of the amplitudes and phases between input and output of the two MMI couplers can be obtained as follows: 13   i e  2  3i M1  e 3   e3i   2 e3 i  i e3 2 e3 i   i e3    2 i  e  M2    i    i e e          e i Phase angle over the PS,  (rad) (3.1.2) By mathematical calculation, three PS value must be ΔΦ1= ΔΦ2=2п/3 ΔΦ3=± п/2 so that each order mode can be (de)multiplexed to different output Phase shifter dimension is initially set up as Lps = 20 µm and Wps = 0.52 µm We choose Wps1=Wps2= 410 nm and Wps3= 590 nm to satisfy the corresponding phase shift value, as in Fig 3.1.3 Fig 3.1.4 shows field distributions of the mode (de)MUXer Fig 3.1.6(a) shows that I.L more than -1 dB and Cr.T smaller than -15 dB are achieved for modes as the branching angle varies within degrees to 13 degrees (Ls=15 µm equivalent to 8.4 degree) Fig 3.1.7(a) shows that variation of LMMI2 within ± µm, the I.L is more than -0.72 dB and Cr.T are smaller than -25 dB Fig 3.1.7(b) shows that variation of W0 within ± 0.2 µm, the I.L is more than -0.6 dB and Cr.T is smaller than -20 dB Fig 3.1.8 shows that the variation of etching depth within ± 50 nm I.L is more than -2 dB and Cr.T is smaller than -18 dB 2π 6.2832  (  =1550 nm) A 1.5π 4.7124 ΔΦ 2π/3 π 3.1416 C π/2 Wps Lps w 0.5π 1.5708 0.3 B Wps=W 0.4 0.5 0.6 0.7 Central width of the phase shifter, Wps ( m) 0.8 Fig 3.1.3 BPM simulation for the phase angle Φ is a function of the central width of the phase shifter 14 Crosstalk, Cr.T (dB) Insertion Loss, I.L (dB) Fig 3.1.4 Electric field patterns of the proposed three-mode (de)MUXer -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 I.L - TE0 -0.7 I.L - TE1 -0.8 I.L - TE2 -0.9 -1 1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 Wavelength,  (m) -16 -18 -20 -22 -24 -26 -28 -30 -32 Cr.T-TE0 -34 Cr.T-TE1 -36 Cr.T-TE2 -38 -40 1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 Wavelength,  (m) (a) (b) Fig 3.1.5 Performances dependence on the wavelength of the proposed three mode-(de)MUXer: (a) insertion loss and (b) crosstalk (b) (a) Fig 3.1.6 Branching angles of the trident coupler on optical performances of the proposed (de)MUXer: a) I.L, and b) Cr.T 15 0.5 0.2 0.4 0.6 0.8  Lmmi2 (m) -0.1 -0.2 -0.3 -0.4 -5 -0.5 -10 -15 -0.6 -20 I.L - TE0 -0.7 -25 I.L - TE1 -0.8 -30 -0.9 -35 I.L - TE2 -0.2 -1 -0.2 -0.15 -0.1 -0.05 Crosstalk, Cr.T (dB) Insertion Loss, I.L (dB) Crosstalk, Cr.T (dB) Insertion Loss, I.L (dB) I.L - TE -0.1 I.L - TE -0.2 I.L - TE -0.3 -0.4 -15 Cr.T- TE0 -0.5 -20 Cr.T - TE1 -0.6 Cr.T - TE2 -25 -0.7 -0.8 -30 -0.9 -35 -1 -0.5 -1 -1 -0.8 -0.6 -0.4 -0.2 Cr.T - TE0 Cr.T - TE1 Cr.T - TE2 -0.1 0 0.1 0.2 0.05 0.1 0.15 0.2 W 0, (m) (a) (b) 0Fig -15 -20 -25 -30 -35 -15 -20 -5 -25 -10 Intensity (dB) Intensity (dB) -10 Intensity (dB) -5 3.1.7 Fabrication tolerances of the proposed (de)MUXer: a) length -5 tolerance of the second MMI coupler LMMI2, and b) width tolerance of the - TE -10 input width WI.L I.L - TE -30 -35 -40 -40 -45 -0.05 I.L - TE0 Cr.T - TE I.L - TE Cr.T - TE -15 I.L - TE2 -20 Cr.T - TE -25 -30 H, -35 (m) -45 -0.05 I.L - TE2 Cr.T - TE I.L - TE0 I.L - TE Cr.T - TE2 I.L - TE2 Cr.T - TE Cr.T - TE Cr.T - TE2 Cr.T - TE2 0.05 -40 H, (m) 0.05 -45 -0.05 H, (m) 0.05 Fig 3.1.8 Insertion loss and crosstalk in the proposed structure for three mode - (de)MUXer device as functions of the etched depth tolerance 3.3 Conclusion Compared to previous proposed designs having similar structure, our proposed one has several advantages One drawback of MDM design based on MMI structure is the low fabrication tolerance of phase shifter However, designs based on MMI coupler in general have advantages such as low loss, high compact and fabrication tolerance The designs can be integrated on small footprint, that shows its huge potential compatibility with on-chip PIC CHAPTER MODE DIVISION MULTIPLEXER BASED ON TILT BRANCHED BUS STRUCTURE SOI WAVEGUIDE There have been a few designs based on multi-arm asymmetric Yjunction used for multimode sorting but there are still restrictions regarding insertion loss and the length of the device, which is proportional to the number of input modes Hence, this chapter will propose a new design which is adjusted from asymmetric Y-junction 16 structure, called branch bus structure The new design is optimized in terms of insertion loss, cross talk and minimized its footprint 4.1 Three-mode multiplexed device based on tilt branched bus structure using silicon waveguide The structure diagram of the three-mode division (de)multiplexing device is shown in Fig 4.1.1 Fig 4.1.2 shows that Wm can be chosen from 0.72µm to 1.04µm to strongly guide three lowest order modes Wm is chosen as 0.94µm Wa is chosen so that 1st order mode will be coupled to 0th order mode to O1 and 2nd order mode will be coupled to 1st order mode in the main bus and then 0th order mode to O2 Hence, Wa is chosen as 0.55µm O2 O1 a) b) Silicon core h=220 nm nSiO2 =1.445 nSi =3.465 Fig 4.1.1 The proposed design of the three-mode (de)muxer Fig 4.1.2 Dependence of effective index of the main bus waveguide on variation of the main waveguide width Wm at the height h of 220 nm Two characteristic parameters ε, δ are introduced which are called as 17 selectively uncoupled and coupled coefficients P mn  10log10  out P  in     P' mn  10log10  out  P  in (4.1.2)    (4.1.3) Pin is the input power of the waveguide normalized by power unit Pout and P’out are the power at the output port of the bus waveguide and tilted waveguide respectively, m and n denotes the order of modes and the order of tilted waveguide in the direction from the input port to the output port of the bus waveguide, respectively Fig 4.1.3 shows the characteristic curves of the dependence of δ and ε for all guided modes at the output ports regarding Wa and Wm (a) (b) Fig 4.1.3 Transmission characteristic of proposed device at the output waveguide as a function of the width Wa (nm) and Wm (nm) a) b) c) Fig 4.1.4 Simulated electric field patterns for the proposed device for: fundamental mode (a), 1st-order mode (b), 2nd-order mode (c) 18 Fig 4.1.4 shows the results of BPM simulations via field distribution of the fundamental mode, the first-order mode and the second-order mode injected into the input of the device Fig 4.1.5 shows the response of I.L and Cr.T of three injected modes to the variation of wavelength from 1.5 µm to 1.65 µm, which is more than -1.45 dB and less than -16 dB respectively Fig 4.1.6 shows transmission characteristics of the output power normalized by the input power at three output ports PO1, PO2 and PO3 for three mode TE0, TE1 and TE2 when the height and the width change in ranges from ±10 nm and ±20 nm, respectively The maximum value of I.L within that range is around – 1.41dB Fig 4.1.5 The characteristic optical performance of the device depends on the wavelength, showing the I.L and Cr.T of each three mode outputs 19 b) c) Δ a) Δ Δ f) e) Δ d) Δ Δ h) i) Δ g) Δ Δ Δ Δ Δ Fig 4.1.6 Transimissions at three output ports Po1, Po2 and Po3 within Δh (nm) and ΔW (nm) of the bus waveguide when three modes are excited: (a),(b),(c) TE0, (d),(e),(f) TE1 and (g),(h),(i) TE2 4.2 Four-mode multiplexed device based on tilt branched bus structure using silicon waveguide The structure diagram of the four-mode division (de)multiplexing device is shown in Fig 4.2.1 20 Fig 4.2.1 The proposed design of the four-mode (de)muxer Fig 4.2.2 shows that 1.38µm ≥ W0 ≥ 1.05µm strongly guides four lowest order modes Wm is chosen as 1.2µm Wa is chosen so that 3rd and 1st order mode will be coupled to 1st and 0th order mode to A1 and 2nd and 0th order mode will be coupled to 1st and 0th order mode in the Limited width for single mode Y Effective refractive index, n eff 2.5 T X TE0 (W 0) TE1(W 0) TE2(W 0) TE3(W 0) Z U TE4(W 0) TE0(W a, W b) TE1- (W a, W b) TE2- (W a, W b) V 1.5 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.5 1.6 The width of the waveguides, W and W a, W b (m) Fig 4.2.2 Dependence of effective indices by using numerical simulation for different modes on variation of the waveguide width main bus respectively Hence, Wm is chosen as 1.1µm Wb is chosen so that 3rd order mode from the main bus after being coupled to 1st order mode at A1 will then be coupled to 0th order mode at O1 Hence, Wb is chosen as 0.95µm 21 a) b) c) Fig 4.2.3 The results of transmission characteristic of proposed device for mode selective coupling coefficients a) at A1 b) at A2 and c) at A3 Fig 4.2.3 shows the characteristic curves of the dependence of δ and ε for all guided modes at the output ports regarding Wo, Wa, Wb 22 a) b) d) c) Fig 4.2.4 Simulated electric field patterns for the proposed device for: fundamental mode (a), 1st mode (b), 2nd mode (c), 3rd mode (d) a) b) Fig 4.2.5 The characteristic optical performance of the device depends on the wavelength of the four-mode a) I.L b) Cr.T Fig 4.2.4 shows the results of BPM simulations via field distribution of the all order modes injected into the input of the device 23 Fig 4.2.5 shows the response of I.L and Cr.T of four injected modes to the variation of wavelength from 1.5 µm to 1.6 µm, which is more than -1.1 dB and less than -18 dB respectively Fig 4.2.6 shows transmission characteristics of the output power normalized by the input power at four output ports PO1, PO2, PO3 and PO4 for four mode TE0, TE1, TE2 and TE3 when the height and the width change in ranges from ±10 nm and ±15 nm, respectively Fig 4.2.6 Transmissions of the proposed device at four output ports O1, O2, O3 and O4 are functions of two simultaneous variables Δh (nm) and ΔW (nm) of the bus waveguide when four modes are excited (a), (b), (c), (d) for mode TE0; (e), (f), (g), (h) for mode TE1; (i), (j), (k), (l) for mode TE2 and (m),(n),(o),(p) for mode TE3 4.3 Conclusion Compared to recent works, the proposed devices have the same performance and fabrication tolerance but structure is less complex 24 Compared to designs proposed in chapter and 3, those devices are more potential in (de)multiplexing multi-mode due to its simple structure and working principles However, one of the drawbacks of asymmetric Y-junction waveguide mode (de)MUXer is its relatively large footprint Both devices are suitable to be applied in constructing the high speed computing systems, intra-chip communication systems and DWDM-MDM communication systems DISSERTATION CONCLUSION AND FUTURE WORKS Conclusion The dissertation had proposed new mode (de)muxer designs based on silicon photonics technology Our proposed designs have significant advantages such as: stability, wide bandwidth, low insertion loss, cross talk, high fabrication tolerance, highly compatible with current CMOS technology for low cost and mass producing ability Future works An important future research field is to continue developing and optimizing performance of mode division multiplexing active devices, rather than passive ones proposed in this dissertation Plus, designs base on Photonics crystal (PhC) are good candidate for decreasing the size of integrated photonics components with reasonable performance regarding simple structures such as Y-branches, power splitters However, manufacturing cost is still a major concern in PhC and hence showing a good further research fields for a promising technology of PICs in the future 25 PUBLISHED PAPERS DURING PHD COURSES [1] T A Tran, Y V Vu, D H Tran, C D Truong, “Two mode division (De) multiplexer based on an MZI asymmetric silicon waveguide”, International Conference on Advanced Technologies for Communications (ATC), 2016 [2] T A Tran, D C Truong, H T Nguyen, Y V Vu “A new simulation design of three-mode division (de)multiplexer based on a trident coupler and two cascaded × MMI silicon waveguides”, Optical and Quantum Electronics, vol 49, pp 426, 2017 [3] H D T Nguyen, T A Tran, D H Ta, T P Bui, Q N Le, T M Nguyen, D C Truong, “A low loss mode division (de)multiplexing device based on soi waveguide in the form of a branched bus,” Journal of Science and Technology – University of Danang, vol 132, no 11, pp 25-28, 2018 [4] T A Tran, H D T Nguyen, D C Truong, H T Nguyen, Y V Vu and D H Tran, “Three-mode multiplexed device based on tilted- branch bus structure using silicon waveguide,” Photonics and Nanostructures-Fundamentals and Applications, vol 35, pp 100709, 2019 UNDER REVIEWD PAPER H D T Nguyen, D H Ta, T T T Tran, N K D Hoang, T A Tran, C D Hoang, D C Truong, “Four Mode Demultiplexer Based on Branched Silicon Waveguides For Photonics Interconnects,” Summited to Optik: International Journal for Light and Electron Optics ... results of BPM simulations via field distribution of the fundamental mode, the first-order mode and the second-order mode injected into the input of the device Fig 4.1.5 shows the response of I.L and. .. order modes Wm is chosen as 1.2µm Wa is chosen so that 3rd and 1st order mode will be coupled to 1st and 0th order mode to A1 and 2nd and 0th order mode will be coupled to 1st and 0th order mode. .. characteristic of proposed device for mode selective coupling coefficients a) at A1 b) at A2 and c) at A3 Fig 4.2.3 shows the characteristic curves of the dependence of δ and ε for all guided modes at