A focused laser beam can be used to trap and manipulate a particle in liquid, which has found applications in studying living cells. The characteristics of the interaction between the particle and the laser beam can give information of the particle. We put forward a method for determination the spring constant of an optical trap through external excitation and lock-in detection. The external sinusoidal excitations of the trapped particle can be introduced by electrostatic force through applying a sinusoidal voltage upon the transparent conductive glass substrates composing the sample cell. A sensor using the feedback effect of a laser diode with two external cavities is also proposed for monitoring the particle oscillation. This self-mixing interferometry has the capability of absolute measurement of the particle displacement, which is important to determine the interaction strength of a laser-particle trapping system.
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