We demonstrated a frequency offset locking between two laser sources using a waveguide-type electro-optic modulator (EOM) with 10th-order sidebands for magneto-optical trapping of Fr atoms. The frequency locking error signal was successfully obtained by performing delayed self-homodyne detection of the beat signal between the repumping frequency and the 10th-order sideband component of the trapping light. Sweeping the trapping-light and repumping-light frequencies with keeping its frequency difference of 46 GHz was confirmed over 1 GHz by monitoring the Doppler absorption profile of I2. This technique enables us to search for a resonance frequency of magneto-optical trapping of Fr.
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