lithium niobate / 06 Devices / 6.3
6.3 The Vπ L, bandwidth, footprint trade
L1 Phenomenon
Low voltage, wide bandwidth, small size: each dot below is one measured device from the literature, placed by its voltage-length product and its bandwidth; arrows mark bandwidths that ran past the instrument.
VπL vs 3 dB EO bandwidth, MZM and IQ device rows 71 points, 30 bandwidth lower bounds
SiPh: no push-pull VπL rows under the default filter
Default: device rows, telecom band (O, C, L, CL), push-pull convention; VπL = reported DC value, else Vπ·L, else reported RF value reported. Arrow: bandwidth stated as a lower bound, drawn at the stated value. No frontier is fitted.atlas eb97f96 · 2026-10-20 · fetched 2026-10-25
Include
Each mark is one published device; arrows mark bandwidths that ran past the instrument (67 and 110 GHz), drawn at the stated value. Drag the year to replay 2017 to 2026. Default: device rows, telecom band (O, C, L, CL), push-pull convention; VπL = reported DC value, else Vπ·L, else reported RF value reported. No frontier is fitted.atlas eb97f96 · 2026-10-20 · fetched 2026-10-25
L2 What the atlas sample shows
What the atlas sample shows
Statistics over eo-modulator-atlas rows at commit eb97f96: telecom band (O, C, L, CL), MZM and IQ device rows; VπL only for the push-pull convention derived.
| Platform | Papers / rows | VπL n / median / min (V cm) | BW n / median / max (GHz) | Share of BW values that are bounds | Median electrode length (mm) |
|---|---|---|---|---|---|
| TFLN | 46 / 88 | 66 / 2.44 / 0.21 | 67 / ≥ 70 / 170 | 0.42 | 6.4 |
| TFLT | 15 / 21 | 17 / 2.43 / 1.36 | 10 / ≥ 85 / 110 | 0.40 | 7.5 |
| SiPh (carrier depletion) | 14 / 25 | no push-pull rows | 21 / ≥ 66 / 110 | 0.29 | 0.9 |
| InP | 6 / 12 | 3 / 0.70 / 0.60 | 9 / ≥ 67 / 100 | 0.44 | 4.0 |
| BTO | 7 / 9 | 2 / 0.72 / 0.72 | 5 / ≥ 70 / 110 | 0.20 | 1.38 |
| Polymer (incl. SOH/POH) | 12 / 36 | 9 / 0.09 / 0.04 | 8 / ≥ 80.3 / 110 | 0.12 | 0.28 |
Atlas-sample statistics (not field-wide):
- Median telecom TFLN VπL stayed between 1.23 and 2.92 V cm per year from 2018 to 2026, while the highest symbol rate per year rose from 100 GBd (2018) to 225 GBd (2026) derived.
- The 170 GHz maximum is one row (Zhang 2022 (a), sideband method, Vπ convention unspecified) whose bandwidth comes from an experimentally verified model with measurements to 325 GHz reported.
- The 0.21 V cm minimum is one 1 mm slow-light device (Shen 2024 (a)).
- Footprint is the TFLN cost: median electrode length 6.4 mm vs 0.9 mm for SiPh, 1.38 mm for BTO, 0.28 mm for polymer derived.
Footprint: device rows, MZM/IQ, telecom, push-pull, Vπ (DC) and length; dashed: constant VπL = 0.1, 0.3, 1, 3, 10 V cm. Wavelength: TFLN/TFLT push-pull rows, all classes; dashed: VπL = λg/(2ne3r33Γ) with Zelmon ne and r33 30.8 pm/V derived; shaded: O, E, S, C, L bands. reportedatlas eb97f96 · 2026-10-20 · fetched 2026-10-25
Footprint: drive voltage against electrode length; the dashed diagonals are constant VπL. Wavelength: shorter wavelengths need less voltage-length (VπL scales with λ/n3 and the gap shrinks with the mode); gold dashed curve = VπL = λg/(2ne3r33Γ) with template gap and overlap template, Zelmon ne and r33 30.8 pm/V derived. Footprint: device rows, MZM/IQ, telecom, push-pull, Vπ (DC) and length; dashed: VπL = 0.1, 0.3, 1, 3, 10 V cm. Wavelength: TFLN/TFLT push-pull rows, all classes; shaded: O, E, S, C, L bands. reportedatlas eb97f96 · 2026-10-20 · fetched 2026-10-25
| Visible / near-IR device | VπL | Wavelength | Source |
|---|---|---|---|
| TFLN MZM | 0.17 V cm (Vπ 0.21 V, 8 mm) | 450 nm | reported |
| TFLN MZM | 0.55 V cm, bandwidth > 35 GHz | 738 nm | reported |
| TFLT MZM | 0.085 V cm (Vπ 4.2 V, 0.2 mm, lumped) | 375 nm | reported |
L3 Sample and conventions
- Sample, not census: 233 papers from web search, author-group follow-up, landmark papers and OFC 2026 proceedings; 95 are from 2026, 54 from OFC 2026.
- Paper year is the year of the earliest version (arXiv v1); the Shen slow-light MZM carries 2024.
- Bounds: arrows start at the stated value; medians include bounds at their stated values and are printed as "median ≥ x" when any input is a lower bound.
Sources
| Ref | Title | Link |
|---|---|---|
| Renaud et al. 2023 | Sub-1 Volt and high-bandwidth visible to near-infrared electro-optic modulators | doi:10.1038/s41467-023-36870-w |
| Xue et al. 2023 | Full-spectrum visible electro-optic modulator | doi:10.1364/optica.482667 |
| Zhang et al. 2022 | Systematic investigation of millimeter-wave optic modulation performance in thin-film lithium niobate | doi:10.1364/prj.468518 |