We have experimentally studied the multiple side-band generation for two-frequency components injected into a tapered amplifier and demonstrated its effects on atomic laser cooling. A heterodyne frequency-beat measurement and a Fabry Perot interferometer have been applied to analyze the side-band generation with different experimental parameters, such as frequency difference, injection laser power and tapered amplifier current. In laser cooling potassium40 and potassium41 with hyperfine splitting of 1.3GHz and 254MHz, respectively, the side-band generation with a small frequency difference has a significant effect on the number of trapped atoms.c 2018 Optical Society of America OCIS codes: 140.3520, 140.4480, 190.4223, 020.3320 Multiple side bands with an equal frequency spacing have various applications in quantum optics and laser cooling. Zhu et. al. observed the multiple-mode sideband fluorescence around the resonant transition with a strong dichromatic field coupling two energy levels [1]. Multiple electromagnetic induced transparencies [2] and four-wave mixing have been observed with two coupling components and one probing component in a three-level system [3]. And an arbitrary side-band with squeezing has been demonstrated in the experiment [4]. In laser cooling of alkali atoms, two frequency components are required, one for optical pumping and the other for cooling. The semiconductor laser has become a standard tool in laser cooling due to its easy operation and low price. But its low output power (generally less than 100mW) puts a limit on the number of trapped atoms. The output power of a tapered amplifier can be very high (generally more than 500mW), which enables us to improve the parameters of trapped atoms. Different spectra have been achieved on the base of a tapered amplifier. For example, two-frequency components can be simultaneously injected into a tapered amplifier [5]. A high power output around 670nm has been obtained with an external coupling cavity [6,7]. And a tapered amplifier has been injection seeded with a femtosecond comb [8].To get a high-power multi-mode output, multiple frequency components can be simultaneously amplified in a tapered amplifier to simplify the experimental setup. But at the same time, the wave-mixing process can result in a multiple side-band generation, which may have nonnegligible effects on atomic behaviors. Here, we will use a heterodyne frequency-beat measurement with a high resolution (<500kHz) and a FPI (Fabry Perot interferometer) to analyze the side-band generation when twofrequency components are injected into a tapered amplifier. Laser cooling potassium40 and potassium41 with different hyperfine splitting can demonstrate the effect of the side-band generation on the interaction between atoms and light.Our experimental setup is shown in Fig.1. Each half wave plate (from HWP1 to HWP8) is used to rotate the laser polarization direction for adjusting the relative powers in the two outputs of its following PBS (polarization beam splitter). The output of ...