  Multi-wavelength observations of the black-widow binary system 2FGL
J2339.6-0532 are reported. The Fermi gamma-ray source 2FGL J2339.6-0532 was
recently categorized as a black widow in which a recycled millisecond pulsar
(MSP) is evaporating up the companion star with its powerful pulsar wind. Our
optical observations show clear sinusoidal light curves due to the asymmetric
temperature distribution of the companion star. Assuming a simple geometry, we
constrained the range of the inclination angle of the binary system to
52$^{\circ}$ < i < 59$^{\circ}$, which enables us to discuss the interaction
between the pulsar wind and the companion in detail. The X-ray spectrum
consists of two components: a soft, steady component that seems to originate
from the surface of the MSP, and a hard variable component from the
wind-termination shock near the companion star. The measured X-ray luminosity
is comparable to the bolometric luminosity of the companion, meaning that the
heating efficiency is less than 0.5. In the companion orbit, 10$^{11}$ cm from
the pulsar, the pulsar wind is already in particle dominant-stage, with a
magnetization parameter of $\sigma$ < 0.1. In addition, we precisely
investigated the time variations of the X-ray periodograms and detected a
weakening of orbital modulation. The observed phenomenon may be related to an
unstable pulsar-wind activity or a weak mass accretion, both of which can
result in the temporal extinction of radio-pulse.
