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We propose a horizontally symmetrical three-layer dielectric structure composed of a high-index central (core) layer surrounded by two identical low-index cladding layers, which acts as an optical differentiator in reflection. If the refractive index of the surrounding medium is greater that the refractive index of the cladding layers, the spectra of the considered structure may exhibit resonant features associated with the excitation of a leaky mode localized at the central layer. At resonant conditions, the reflection coefficient will vanish at certain values of frequency and angle of incidence, which enables the differentiation of the incident optical pulse. We theoretically justify that this three-layer structure can perform temporal differentiation (differentiation of an incident optical pulse envelope), spatial differentiation (differentiation of an optical beam profile) and the so-called “spatiotemporal differentiation” (differentiation of an optical signal envelope along a certain direction in the (x,t)-plane). Rigorous numerical simulation results demonstrate high quality of differentiation. It is shown that the resonance quality factor increases with the increase in the thickness of the cladding layers, which makes it possible to achieve a required linearity interval of the differentiating filter. The proposed differentiator is more compact than Fourier correlators containing graded-index lenses and substantially easier to fabricate than metasurface-based devices incorporating periodically arranged nanoresonators and may find application in ultrafast analogue computing and signal processing systems.
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