Traveling wave optical pumping and laser amplifier are studied. In the case of rhodamine 6G (ethyl alcohol solution, $τ=5×10^{-9}sec$), the usual approximation of ignoring the spontaneous emission gives only crude picture of output photon flux, particularly when $N_2$-laser with pulse width comparable to the transition time constant of the molecule is used for excitation.
For the square top pulse (pulse width $t_d=5×10^{-9}sec$) of the pumping beam, a set of non-linear differential equations are derived and solved numerically by using a computer. As rhodamine 6G molecule has such a large absorption cross section, the calculation is made along the direction of incident pumping flux for x=0~x=0.1 cm. From this calculation the time dependent inversion ratios are obtained for x=0, 0.05 and 0.1 cm. The logarithmic photon flux for the leading edge of the absorbed pulse is linear as expected. These calculations provide the data useful in designing dye laser cell, laser resonator and laser amplifier using rhodamine 6G as active material.
