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We analyze all-optical switching in chlorophyll-A (Chl-A) molecules for different combinations of pump-probe wavelengths, based on nonlinear intensity-induced excited-state absorption. It is shown that for a pulsed pump beam at 672 nm with peak pump intensity of 5 kW/cm2 and Chl-A concentration of 1.5 mM, the transmission of a continuous-wave probe beam at 476 nm can be completely switched off (100% modulation) with switch on-off time of 0.58 and 0.18 mus, respectively. It is also shown that the switching characteristics can be inverted by changing the probe beam wavelength. The effect of various parameters, such as concentration, pump beam intensity, pump pulsewidth, absorption cross section of the ground state, and lifetimes of different states, on the switching characteristics has been analyzed in detail. It is shown that there exists an optimum value of concentration of Chl-A for maximum switching contrast, for the case when the ground state also absorbs the probe beam. The switching characteristics of Chl-A have also been compared with Chl-B and Bchl. Experimental results for all-optical switching in Chl-A with a train of pulses are in good agreement with theoretical results. It is shown that higher contrast and faster switching can be achieved as opposed to what was reported recently in other biomolecules such as archael rhodopsin and phototropin proteins. The results have also been used to design switches and logic gates.