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Summary form only given. Ever since its first observation, optical second-harmonic generation (SHG) has been demonstrated to be a sensitive probe of electric fields in centrosymmetric media. Recent investigations have extended the capability of electric field-induced SHG (EFISH) to measure ultrafast electrical pulses and time-varying microwave electric-fields, with a time resolution limited only by the laser pulse duration. In this paper, we describe two interrelated advances in this method for probing electric fields: (1) a scheme for linearizing the relationship between the electric field and SHG intensity; and (2) an approach for determining the vector nature of the electric field. Measurements have been carried in silicon samples to demonstrate experimentally these improvements.