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 c
ompanion 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.
