  Electrically-tunable optical properties in materials are desirable for many
applications ranging from displays to lasing and optical communication. In most
two-dimensional thin-films and other quantum confined materials, these
constants have been measured accurately. However, the optical constants of
single wall nanotubes (SWCNT) as a function of electrostatic tuning are yet to
be measured due to lack of electronic purity and spatial homogeneity over large
areas. Here, we measure the basic optical constants of ultrathin high-purity
(>99%) semiconducting single wall carbon nanotube (s-SWCNT) films with
spectroscopic ellipsometry. We extract the gate-tunable complex refractive
index of s-SWCNT films and observe giant modulation of the real refractive
index (~11.2% or an absolute value of >0.2) and extinction coefficient (~11.6%)
in the near-infrared (IR) region (1.3-1.55 {\mu}m) induced by the applied
electric field significantly higher than all existing electro-optic
semiconductors in this wavelength range. We further design a multilayer IR
reflection phase modulator stack by combining s-SWCNT and monolayer MoS2
heterostructures that can attain >45{\deg} reflection phase modulation at 1600
nm wavelength for < 200 nm total stack thickness. Our results highlight s-SWCNT
as a promising material system for infrared photonics and electro-optics in
telecommunication applications.
