REPORTS
◥
ULTRAFAST OPTICS
Ultrafast optical control by few
photons in engineered fiber
R. Nissim,* A. Pejkic,* E. Myslivets, B. P. Kuo, N. Alic, S. Radic†
Fast control of a strong optical beam by a few photons is an outstanding challenge that
limits the performance of quantum sensors and optical processing devices. We report that
a fast and efficient optical gate can be realized in an optical fiber that has been engineered
with molecular-scale accuracy. Highly efficient, distributed phase-matched photon-photon
interaction was achieved in the fiber with locally controlled, nanometer-scale core
variations. A three-photon input was used to manipulate a Watt-scale beam at a speed
exceeding 500 gigahertz. In addition to very fast beam control, the results provide a path
to developing a new class of sensitive receivers capable of operating at very high rates.
The prospect of light-wave digital processors has motivated a decades-long pursuit of the optical transistor (1–4). The optical gate should control an intense beam with only a few photons (3) and be fast. Intuitively, by
replacing electron carriers with massless photons, faster switching can be expected (3). Although desirable, the original transistor analogy
also faces fundamental differences between light-wave and electronic carriers. Where electrons are
easily manipulated in submicrometer structures
(5), the interaction between photons is extremely
weak (6). This weakness is countered by strong-field (7) or highly nonlinear material (8) serving as
a photon-photon mediator. In practice, spatial (7)
or spectral (2, 4, 8) resonances are necessary to
efficiently manipulate photons. Recent experiments
(1, 2, 4, 7, 8) have shown that direct, few-photon
control is viable and can lead to transistor-like
behavior. Unfortunately, the operating frequencies remain orders of magnitude below the
terahertz rate relevant to light-wave communication. Resonant engineering, used to increase
interaction efficiency, also induces spectral inhibition: Although very efficient, resonant devices
are inherently slow (3).
However, an efficient optical gate can, at least
in principle, also be fast if the nonlinear mech-
anism mediating photon-photon interaction re-
mains spectrally uninhibited. Four-photon mixing
(FPM) in a Kerr material (9, 10) is an example of
such interaction: It is both fast (11) and efficient
in waveguides with a large product of non-
linearity g and length L (11). In this regard,
silica fiber represents a nearly ideal physical
platform: With optical loss a below 0.0003 dB/m,
its exceptional transparency (12) means that
kilometer-scale interaction lengths can be used
to offset the weak glass nonlinearity (12, 13) and
guarantee a gL product in excess of 100 W−1. This
advantage (14) can be fully realized only if phase
matching is controlled by local dispersion (15).
Unfortunately, local fiber dispersion, defined by
its transverse geometry, varies a lot with small
core fluctuations (16) (Fig. 1). Until recently, control
of such small variations was not considered feasible (15), particularly over long scales.
We show that silica fiber core can be controlled
with subnanometer precision and be used for fast,
few-photon control. We find that the strongest
interaction between few- and many-photon beams
does not occur in ideal, constant core fibers.
Instead, the optimal photon control requires a
small but finite and specific core variation com-
parable to the size of a silicon-oxygen molecular
ring (16). To demonstrate the feasibility of such
distributed, microscopically controlled photon-
photon interaction, we switched a 1.49-W beam
by using a classically attenuated, 520-GHz band-
width pulse containing an average of three pho-
tons. These measurements reveal that FPM in a
fiber with a unique core profile is a nonreciprocal
process, contrary to the well-established no-
tion of directional invariance in passive wave-
guides (17).
In the simplified notion of few-photon control
of a strong beam (Fig. 2A), weak input signal
induces depletion of the many-photon pump via
phase-matched FPM. Parametric mixing annihi-
lates pump photons and recreates them at new
(signal/idler) frequencies. In ideal fiber with
constant core radius r, the instantaneous pump
power P(z) defines the local gain peak as sep-
aration between the pump (wP) and signal (ws)
frequencies W ¼ wS − wP ~
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pðz Þ=r
p
(12). With
signal amplification, the pump is depleted and
the maximum-gain frequency W is shifted away
from the signal. In contrast, when phase matching is controlled locally, the maximum-gain frequency W can be maintained even when the
pump is depleted (Fig. 2B). To adjust the phase
matching, the fiber core can be adjusted to
Department of Electrical and Computer Engineering,
University of California, San Diego, La Jolla, CA 92093, USA.
*These authors contributed equally to this work. †Corresponding
author. E-mail: sradic@ucsd.edu
Fig. 1. Four-photon mixing in ideal (A) and physical (B) fiber waveguides. (A) An ideal fiber has a
constant transverse geometry, and the phase matching imposed on pump kP, signal kI, and idler kS wave
vectors 2kP −kS −kI ¼ Dk results in spatially invariant dispersion Dk(w) (inset). With weak signal and
strong pump inputs, sufficiently long phase-matched nonlinear fiber leads to complete pump depletion
POUT ∼ 0. (B) In a physical fiber, the core size fluctuates, with the fundamental limit set by the diameter
of the Si-O molecular ring. This variation leads to a Dk(w, z) that randomly fluctuates along the fiber
(inset). Stochastic phase matching results in random, suboptimal pump depletion.
