156 J. Eur. Opt. Society-Rapid Publ. 22, 16( 2026) f 3dB 1: 4 ps RC
;
s RC ¼ R elec C elec: ð25Þ
ð26Þ
C elec is proportional to the electrode length L. Toimprove the bandwidth, it is necessary to either shorten L or adopt a T-type electrode. Through multi-physics simulations, the phase modulation performance under different L values is verified, and the value of L is optimized to balance V p and bandwidth. Finally, L is set to 5000 lm, i. e., 5 mm. At this point, V p L is 2.8 V cm, and the applicable frequency band of the phase modulator is greater than 70 GHz.
3.2.3 Parameter calculation of T-shaped track electrode
There are many geometric shapes of electrodes. The T-shaped electrode has a simple structure and can take into account both the uniformity of the electric field and the compatibility of the leads. The width and height of the electrode need to satisfy the microwave transmission line theory to reduce the skin effect loss. The formula for calculating the characteristic impedance of the microwave transmission line theory is as follows:
Z 0 ¼ 1 rffiffiffiffi L pffiffiffiffiffiffi: ð27Þ
C v p
Herein, v p represents the phase velocity and e eff denotes the effective dielectric constant, while L and C stand for the inductance and capacitance per unit length, respectively. The electrode dimensions are adjusted to set the characteristic impedance Z 0 50 X, thereby reducing microwave reflection. The electrode thickness must be greater than the skin depth, typically taking a value 2 – 3 times the skin depth d. The electrode designed in this paper, the skin depth d of the Al electrode is 0.321 lm for a 70 GHz microwave signal. Therefore, the thickness of the electrode designed is 1 lm.
Table 2 lists various parameters of the electrode. The metal isolation dH is 0.2 lm. An excessively small metal isolation distance may lead to poor insulation and large crosstalk, while an excessively large value will increase the device size. The electrode spacing is 4 lm because a smaller electrode spacing contributes to higher modulation efficiency and lower half-wave voltage( V p), provided that the spacing does not cause excessive electric field crosstalk.
e eff
3.3 Design parameters of the MRR
In the implementation of the frequency-doubling function, an external signal source is used to apply an RF signal to the electro-optic modulator, generating sidebands on both sides of the optical carrier. A thermally tuned micro-ring is utilized to achieve secondary suppression of the optical carrier through its resonant peak. The processed signal is then input into a broadband photodetector, where the beating of the two first-order sidebands generates an RF signal
Table 2. Parameters of electrode.
Variable |
Value [ lm ] |
Description |
dH |
0.2 |
Metal isolation |
thickness |
1 |
Thickness of metal electrode |
G _ width |
6 |
Width of ground electrode |
S _ width |
6 |
Width of signal electrode |
gap |
4 |
Electrode spacing |
with twice the input frequency, ultimately realizing the signal frequency doubling process.
3.3.1 Radius of the micro-ring resonator
The micro-ring structure designed in this paper is composed of a straight waveguide segment and a semicircular bending segment. Figure 7 depicts the structural design of the racetrack MRR with a semicircular radius of 80 lm anda straight segment of 280 lm, and this optimized structure achieves the optimal balance between large FSR and low bending loss. Compared with the circular MRR, the racetrack structure not only improves the coupling efficiency with the straight waveguide( mode field overlap efficiency > 95 %), but also realizes an FSR of 120 GHz, which is greater than twice the modulation bandwidth(> 70 GHz) of the device, effectively avoiding the overlapping interference of sideband components in the MRR cavity. Meanwhile, the 80 lm radius avoids the sharp increase of bending loss caused by a smaller radius( 65 lm), ensuring the MRR Q-factor is as high as 3.210 5, which is the core structural guarantee for efficient frequency doubling.
3.3.2 Waveguide dimensions
To avoid interference from higher-order modes, the MRR waveguide adheres to the same cut-off wavelength condition( Eq.( 22)) as the DD-MZM waveguide. Considering the material properties of Si 3 N 4( refractive index 1.99768) and the requirement of high optical confinement for resonance enhancement, the waveguide width is determined as 1.2 lm by extending the single-mode transmission condition derived in Section 3.2.1. This parameter is consistent with the theoretical framework of equation( 22) and ensures no higher-order mode excitation within the operating wavelength range( 1550 nm).
Substituting Si 3 N 4 refractive index( n = 1.99768), operating wavelength k = 1550 nm, and waveguide height h = 0.3lmintoequation( 22), the cut-off wavelength of the TE 01 mode is calculated as 1320 nm < 1550 nm, confirming single-mode transmission. This result is consistent with the width design of 1.2 lm, ensuring parameter consistency across the device.
3.4 Design of coupling structure
3.4.1 Coupling spacing between straight waveguide and ring waveguide
The coupling efficiency should enable the first order sideband to be efficiently coupled into the micro-ring while