Fig. 1: Joint time-frequency filtering concept.
From: Agile manipulation of the time-frequency distribution of high-speed electromagnetic waves
a–c We target to eliminate a single frequency tone around a prescribed time \({t}_{1}\) of an electromagnetic (EM) wave, which is composed of two different single-frequency components (\({f}_{1}\) and \({f}_{2}\), respectively). This operation cannot be implemented using temporal modulation (a) or frequency filtering (b). c We show how the target manipulation requires modulating (or filtering) the joint time-frequency (TF) energy distribution of the wave. d Principle of the proposed concept for user-defined joint TF filtering of an EM wave. An input nonstationary microwave signal consists of three different frequency components. We consider that only two components are present in the first temporal segment of the signal to illustrate the case of an input non-stationary waveform. We show here how the proposed TF filtering scheme can be designed to preserve/eliminate a prescribed set of frequency components in different signal temporal segments. For this purpose, the input microwave signal is first modulated on an optical carrier (electro-optic, E-O, conversion). The optical wave then undergoes two suitable phase transformations, implemented through temporal phase modulation with a discretized quadratic phase pattern followed by a quadratic spectral phase filtering with a group-velocity dispersive medium (e.g., a reflective chirped fibre Bragg grating). These phase transformations induce a continuous mapping of the time-varying frequency spectrum of the signal, or its two-dimensional (2D) joint TF distribution, along the time domain. This distribution can then be easily manipulated at will using temporal modulation techniques (temporal filtering pattern indicated by the red-dashed traces). For the considered microwave photonics filtering scheme, recovering the processed wave simply involves compensating the input group-velocity dispersion and a photodetection step to transfer the optical processed wave back into the electrical domain. E-O: Electrical to Optical conversion, O-E: Optical to Electrical conversion, PM: electro-optic Phase Modulator.
