Foundry-compatible Hybrid Silicon / Lithium Niobate Electro-Optic Modulator

High-Performance Mach–Zehnder Modulator Based on Thin-Film Lithium Niobate with Low Voltage-Length Product

“…Based on electromagnetic theory, , the refractive index variation in the x-cut TFLN is given by eq : normalΔ n normale normalf normalf = 1 2 n normale 4 r 33 n normale normalf normalf V g normalΓ normalm normalo where λ is the free-space wavelength, n e is the material index of extraordinary rays, V is the modulation voltage, and Γ mo is the normalized overlap between the optical and electric fields in the x – z plane, which can be expressed as eq : normalΓ normalm normalo = g V ∬ ln false| E normalo ( x z ) false| 2 E normalR normalF ( x , z ) .25em normald x .25em normald z ∬ ∝ false| E normalo ( x , z ) false| 2 d x d z ≤ 1 …”

“…However, n eff plays a dominating role, especially when the Γ mo is a constant. In principle, there are three key factors to guarantee high-performance operation of an EOM . First of all, the EOM must be impedance matched, i.e., the characteristic impedance of the electrodes ( Z 0 ) should be 50 Ω.…”

“…Then, Z 0 = 49 Ω and n RF = 2.24 were obtained. Since in the case where the velocities of the optical wave and the microwave are matched, the 3-dB E-O bandwidth can be estimated by the 6.34-dB electrical loss. ,, Therefore, the theoretical E-O response of the designed EOM is evaluated by the loss of transmission line electrodes; according to the simulated curve of the microwave transmission S 21 and reflection S 11, it is found that the EO response is much larger than 70 GHz, and the RF return loss is lower than −17 dB.…”

“…Based on electromagnetic theory, , the refractive index variation in the x-cut TFLN is given by eq : where λ is the free-space wavelength, n e is the material index of extraordinary rays, V is the modulation voltage, and Γ mo is the normalized overlap between the optical and electric fields in the x – z plane, which can be expressed as eq : Here, E o and E RF are the optical and RF fields along the z direction, respectively. When the optical field is perturbed by an applied electric filed, the optical phase variation Δϕ is calculated by eq : If we set Δϕ = π, the V π ·L for the TFLN-based EOM in the push–pull conditions can be calculated using eq : …”

“…Based on electromagnetic theory, 35,36 the refractive index variation in the x-cut TFLN is given by eq 1:…”