A LCD device element of frequency modulation mode enables high speed on and off control of an electro-optical response by switching the frequency of applied electric field. The LCD device element is capable of changing a frequency modulation range freely. The LCD device element has conductive layers between two parallel substrates; liquid crystal (LC) alignment layers with pre-tilt angle on these conductive layers; and a LC layer between the two liquid crystal alignment layers. LC soluble particles (nanoparticles composing a core and a liquid crystal molecules or like molecules on its periphery), are in the LC layer. A control circuit applies voltage while modulating frequency on the conductive layer for varying light transmittance of the LC layer. Under a constant voltage, an electro-optical response is turned on by switching the frequency from low to high frequency and is turned off by switching the frequency from high to low frequency. The electro-optical response is varied also by varying voltage.