J. Eur. Opt. Society-Rapid Publ. 22, 16( 2026) 155
Table 1. The thickness of various materials in multi-layer structures.
Material |
Geometric parameters [ lm ] |
Material properties |
LN |
Width = 12, thickness = 0.3 |
Refractive Index = 2.13902 Relative permittivity = 27.9,44.3 Relative permeability = 1 Electrical conductivity = 0 S / m Electro-optic coefficient r 33 = 30.8 [ pm / V ] |
SiO 2 |
Width = 12, thickness = 4.7 |
Refractive Index = 1.4446 Relative permittivity = 2.08689 Relative permeability = 1 Electrical conductivity = 0 S / m |
Si 3 N 4 |
Width = 1, thickness = 0.3 |
Refractive Index = 1.99768 Relative permittivity = 3.99072 Relative permeability = 1 Electrical conductivity = 0 S / m |
Al |
Width = 1, thickness = 1 |
Refractive Index = 1.44 + 16 j |
Air |
|
|
|
Width = 12, thickness = 5 |
Refractive Index = 1.0006 Relative permittivity = 1 Relative permeability = 1 Electrical conductivity = 0 S / m |
Si 3 N 4-LN |
Thickness = 0.05 |
Heterostructure layer, with optimized interface properties |
Note: The thickness of Si 3 N 4( 0.3 lm) and TFLN( 0.3 lm) refers to the functional layer thickness of the heterogeneous |
integration structure. The Si 3 N 4-LN layer with a thickness of 0.05 lm is the interface transition layer. |
Fig. 6. Layout of multifunctional on-chip devices.
2w
k cutoffðTE00 Þ ¼ q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi < k: ð22Þ n 2 � n2 LN sio 2
By controlling the relationship between the waveguide dimensions and the operating wavelength, the generation of higher-order modes can be avoided, the inter-mode interference can be reduced, and the stability and efficiency of optical signal propagation can be improved.
First, fix the waveguide height h, solve for the effective refractive index n eff in the width w direction, and then substitute it into the equation in the height direction.
n 2 eff ¼ n2 � p
2 2 k
� p
2 2 k: ð23Þ
LN h 2p w 2p
For the multifunctional on-chip device designed in this paper, n LN = 2.139 and n SiO2 ¼ 1:4446, with a target effective refractive index of 1.82. Substituting these data gives w = 12 lm, h = 4.7lm.
3.2.2 Length of the modulation arm
The length of the modulation arm of the DD-MZM is a key parameter affecting the device performance. Its design needs to comprehensively consider factors such as electrooptic effect efficiency, phase modulation requirements, and high-frequency response characteristics [ 35 ]. Equation( 24) is the calculation formula of the modulation arm based on the half-wave voltage V p. k V p ¼
2r 33 n 3 eff C L: ð24Þ
In equation( 24), k is the operating wavelength, r is the electro-optic coefficient, and n eff is the effective refractive index. C is the electro-optic overlap integral factor, which reflects the degree of overlap between the electric field and the optical field. w is the width of the waveguide, and L is the length of the modulation arm. At the 1550 nm optical communication wavelength, the C value of the LN waveguide is approximately 0.85. The electro-optic coefficient of LN r 33 30 pm / V, and the effective refractive index is n eff = 2.139.
In high-frequency applications, the length of the modulation arm is limited by the microwave loss of the electrode and the optical and microwave velocity matching. Based on the RC delay model of microwave transmission lines, formulas( 25) and( 26) are derived by combining the frequency response of RC circuits and the definition of 3dB bandwidth.