Based on an optically injected semiconductor laser (OISL) operating at period-one (P1) nonlinear dynamical state, high-purity millimeter-wave generation at 60 GHz band is experimentally demonstrated via 1/4 and 1/9 subharmonic microwave modulation (the order of subharmonic is with respect to the frequency f(c) of the acquired 60 GHz band millimeter-wave but not the fundamental frequency f(0) of P1 oscillation). Optical injection is firstly used to drive a semiconductor laser into P1 state. For the OISL operates at P1 state with a fundamental frequency f(0) = 49.43 GHz, by introducing 1/4 subharmonic modulation with a modulation frequency of f(m) = 15.32 GHz, a 60 GHz band millimeter-wave with central frequency f(c) = 61.28 GHz (= 4f(m)) is experimentally generated, whose line width is below 1.6 kHz and SSB phase noise at offset frequency 10 kHz is about -96 dBc/Hz. For f(m) is varied between 13.58 GHz and 16.49 GHz, f(c) can be tuned from 54.32 GHz to 65.96 GHz under matched modulation power P-m. Moreover, for the OISL operates at P1 state with f(0) = 45.02 GHz, a higher order subharmonic modulation (1/9) is introduced into the OISL for obtaining high-purity 60 GHz band microwave signal. With (f(m), P-m) = (7.23 GHz, 13.00 dBm), a microwave signal at 65.07 GHz (= 9f(m)) with a linewidth below 1.6 kHz and a SSB phase noise less than -98 dBc/Hz is experimentally generated. Also, the central frequency f(c) can be tuned in a certain range through adjusting f(m) and selecting matched P-m. (C) 2016 Optical Society of America