It is quite common to confuse (aerosol) optical depth as transmittance which can have values only between 0 to 1 and fact that typical AOD values are less than one.  However, there is no theoretical upper limit on AOD. As correctly pointed out by @Alexander Solntsev, AOD is negative of natural log of transmittance of aerosol in atmospheric column in nadir direction.

Yes, optical depth is defined as the negative natural logarithm of the fraction of radiation (e.g., light) that is not scattered or absorbed on a path. If this fraction is less than about 36.7%, then optical depth is above unity, otherwise it's below unity.

How that 36.7% came ?

http://www.wolframalpha.com/input/?i=-ln%280.367%29

Thank You sir

36.7% = exp-1

It is quite common to confuse (aerosol) optical depth as transmittance which can have values only between 0 to 1 and fact that typical AOD values are less than one.  However, there is no theoretical upper limit on AOD. As correctly pointed out by @Alexander Solntsev, AOD is negative of natural log of transmittance of aerosol in atmospheric column in nadir direction.

thank you sir

AOD can indeed be >1, and it is frequently measured to be so over areas impacted by dust storms, smoke plumes or heavy pollution.  There is no maximum value (as Harish mentioned), although at some point (above a value of approx. 2) measurements become inaccurate and useless because it is virtually impossible to distinguish between a dense aerosol cloud and a thin cirrus cloud, for instance, at least when using ground-based instrumentation.