A mathematical model describing the sum frequency generation of passively synchronized Q-switched pulses simultaneously emitted from two separate Nd^{3+}:YVO_4 lasers has been demonstrated. This model describes the temporal behavior of the output pulses, and studies the impact of the pumping energy variation on the characteristics of these pulses (output power, pulse separation, pulse widths, delay time). V^{3+}:YAG and Cr^{4+}:YAG saturable absorbers and a periodically poled KTP crystal are used to achieve and improve the synchronization of the emitted 1342 nm and 1064 nm wavelengths. The synchronization process generates pulsed yellow light with 593.5 nm wavelength, and it can be realized through adjusting the pumping energy of the gain media.
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