Ultrawideband (UWB) and optical waveforms with arbitrary and wideband modulation can be generated by sculpting the spectrum of a broadband optical pulse and subjecting it to linear dispersion. The technique can be visualized as a two-step process. First, the optical spectrum is shaped according to the desired temporal waveform. The spectrum is then mapped into time by passing the waveform through a linearly dispersive element, such as an optical fiber. Adaptive computer control is necessary to mitigate the nonideal features inherent in the optical source and in the spectrum sculpting process.

The ability to generate high frequency and complex waveforms is central to many commercial and military applications. In communication receiver testing, for example, an arbitrary waveform generator (AWG) is used to emulate a channel-impaired received signal. The military relies on sophisticated and agile RF waveforms in applications such as low-probability-of-intercept (LPI) radar.¹ Hybrid LIDAR-RADAR systems require a wide-band amplitude-modulated optical carrier in order to attain high-range resolution.²

The development of electronic AWGs is hindered by the limited speed and dynamic range of digital-to-analog (DAC) technology. Currently, state-of-the-art commercial systems are limited to less than 2 GHz analog bandwidth and sampling rates of approximately 4 GSamples/s.³ The all-optical approach to generating UWB RF waveforms introduced here does not rely on electronic switching and so is free of the limitations of DAC technology. Implemented using presently available commercial off-the-shelf components, the system would have a bandwidth of 60 GHz.⁴

Photonic methods in generating microwave and millimeter-wave signals have largely been limited to coherent techniques. In one approach, two modes of an optical frequency comb generator are filtered and mixed at a photodetector to generate a 60-GHz signal that is equal to the difference frequency between the two optical signal components.⁵ Multiple 60-GHz signals have also been reported by mixing pairs of coherent light waves.⁶ In a multiple-source approach, a 36-GHz carrier was demonstrated by optical heterodyning using an optical injection phase-locked loop.⁷ When the beating technique is combined with a programmable amplitude/phase filter, arbitrarily shaped optical pulse trains can be generated by Fourier spectrum synthesis.⁸ Unfortunately, waveforms generated by means of coherent optical techniques lack phase stability and, thus, signal fidelity.

An alternative approach to coherent optical techniques is shown in Fig. 1.⁹ The spectrum of a wideband optical pulse is sculpted by an optical filter and then passed through an optically dispersive medium such as an optical fiber. The dispersive medium exhibits a group velocity that is linearly dependent on the optical wavelength. Hence, dispersion performs wavelength-to-time mapping converting the spectral modulation to a temporal modulation. In other words, the intensity of the (broadened) optical pulse will acquire a temporal modulation waveform that is identical to the waveform imposed on the optical spectrum. Any arbitrary temporal waveform can be generated by properly shaping the spectrum of the broadband optical source. For a given spectral waveform, the frequency of the temporal waveform is determined by the amount of dispersion.

To quantify the wavelength-to-time mapping, consider a simple example. Assume that the total optical bandwidth is Δλ = 100 nm and the period of spectrum modulation is δt = 0.1 nm (Fig. 1). If 10 km of standard single-mode fiber (SMF) is used as the dispersive medium, then the total dispersion is D = 170 ps/nm. After propagation through this fiber, the resulting pulse-modulated RF waveform will be 17 ns long (DΔλ) and will have a modulation frequency of 59 GHz [(DΔλ)^-1]. Implemented when using presently available commercial components, the system's bandwidth will be limited by the photodetector. As previously mentioned, this limit is currently 60 GHz.⁴ A useful figure of merit for the dispersive element would be its dispersion-to-loss ratio. From this point of view, a dispersion compensating fiber (DCF) is preferred over SMF as the dispersive medium since it offers a two times higher dispersion ratio.

Modulation of the optical spectrum can be achieved using a variety of optical filtering approaches, including the two approaches shown in Fig. 2. In Fig. 2a, the different spectral components of the optical pulse are separated and imaged onto a liquid-crystal spatial light modulator (SLM). Since the transmission of each SLM pixel depends on the applied pixel voltage, the spectrum can be shaped to any desired waveform. After the SLM, the spatially dispersed beam is combined and focused into the output optical fiber. The setups in Figs. 2b and 2c make use of a particular optical filter called an arrayed waveguide grating (WG). This is an integrated optics device commonly used as a wavelength multiplexer/demultiplexer in telecommunication networks.¹⁰ It can be thought of as a frequency-scanned phased array with the distinction that, here, the array has a curved geometry resulting in the focusing of the transmitted beam. In Fig. 2b, the first WG separates the individual wavelength components that are subsequently shaped (by optical attenuators) and delayed before being combined in the second WG. In Fig. 2b, the same function is performed with a single WG, by recognizing its symmetry properties.^11,12