Resonances and signal to noise ratio of electromagnetic sensors

We illustrate the concept of the resonance for noise by considering the example of the current induced by an external electromagnetic field and the noise current in the well studied split ring resonantors in the thin wire limit, which is analytically tractable. We found that both the signal and the noise exhibit resonances at the same frequencies. However, their ratio exhibits interesting frequency dependences which also is a function of the nature of the external driving field. This previously unanticipated result suggests the signal to noise ratio does not just depend on the resonance frequency; further study is required of the fundamental physics for different structures and help improve the design of devices.