A method for determining at least one electrical property of an earth formation includes emitting an electromagnetic signal into the earth formation from an antenna and measuring an electromagnetic signal from the earth formation. The antenna is a broadband log antenna mounted on a substrate having at least a high dielectric permittivity, defined as a dielectric permittivity of about =100 to =1000 or a gigantic dielectric permittivity, defined as a dielectric permittivity of about =1000 or greater. The antenna has a radius between about 2.5 millimeters (mm) and 10 centimeters (cm). The method further includes determining at least one electrical property of one or more of a borehole, a borehole fluid, and the earth formation based on measuring the electromagnetic signal.

Measuring a sample includes providing a magnetic field at the sample using an electromagnetic field resonator. The electromagnetic field resonator includes two or more resonant structures at least partially contained within dielectric material of a substrate, at least a first resonant structure configured to provide the magnetic field at the sample positioned in proximity to the first resonant structure. The sample is characterized by an electron spin resonance frequency. A size of an inner area of the first resonant structure and a number of resonant structures included in the electromagnetic field resonator at least partially determine a range of an operating resonance frequency of the electromagnetic field resonator that includes the electron spin resonance frequency. Measuring the sample also includes receiving an output optical signal from the sample generated based at least in part on a magnetic field generated by the electromagnetic field resonator.