Using the expression of output spectrum derived from the ray trace method, the spectral characteristics of the external cavity semiconductor laser (ECLD) have been analysed. Based on this, the analytical expression of the threshold carrier density applicable to any selected wavelength for the ECLD has been deduced. Combining the spectrum and the carrier rate equation, the carrier deficit from the threshold can be obtained self consistently and the output can be determined without resorting to the photon rate equation.