The dispersive effects of optical fibers can be used to optically shape ultra-wideband waveforms that exhibit high stability without the limitations of electronic arbitrary waveform generators.
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 -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
In the experiments described below, an SLM array was used to shape the spectrum of the broadband pulse. SLMs have been used by Weiner et al. for femtosecond optical pulse shaping via spectral phase control.13 Their approach employed a coherent Fourier transform process where a temporal waveform was synthesized through manual control of optical phase. The approach described here is incoherent. Instead of performing a Fourier transform, the desired temporal waveform is created by direct wavelength-to-time mapping.
A broadband optical source is produced by amplifying the output of a mode-locked laser and passing it through a specialty fiber called a super-continuum (SC) fiber.14 Optical nonlinearities in the SC fiber cause broadening of the optical spectrum to over 100 nm. Next, a spatial light modulator filters and shapes the spectra according to the desired optical waveform. In the current experiments, a 4-f grating and lens apparatus were used such that each wavelength will be focused and incident normal onto the SLM plane. The grating has 1000 lines/mm while the lens focal length is 20 cm. The distances between gratings and lenses are set for zero net temporal dispersion. Two high-extinction-rate polarizers are placed in parallel before and after the liquid crystal to achieve amplitude modulation (AM). The pixels are independently controlled by a computer-operated electronic driver, which manipulates the voltage (and thus the attenuation) to gray-scale accuracy. A maximum optical dynamic range of 30 dB optical (60 dB electrical) can be achieved for AM. This can be doubled by cascading two SLMs in series, with a small increase in optical loss and system complexity. Finally, the beam is coupled back into single-mode fiber through an identical optical path.
The experiment constructed at UCLA has an optical insertion loss of 6.2 dB and a 3-dB spectral passband of 9.5 nm and 15-dB spectral passband of 20 nm. The system uses 20 nm of optical bandwidth, which corresponds to 110 SLM pixels available for waveform generation. A length of Corning SMF-28 fiber having a dispersion parameter D = 17 ps/nm-km is used for wavelength-to-time mapping. The system generates arbitrary waveforms at the repetition rate of the optical source (20 MHz in this case). The time aperture (T) of the waveform is related directly to the length (L) of optical fiber by T = DΔλL, with Δλ the optical bandwidth (20 nm).
The maximum frequency that can be generated for a given fiber length L is determined by the Nyquist requirement of fmax = 1/(2DδλL), with δλ = 0.625 nm = the filter spectral resolution. The spectral resolution is the ratio of the spot size at the pixel plane to the spatial dispersion of the grating lens.
In practice, the process of wavelength-to-time mapping is not ideal because of the following two issues. First, the finite focal size spanning multiple pixels removes the 1:1 correspondence between wavelength and pixel. Second, the broadband spectrum is not uniform resulting in the distortion of the desired waveform. Because of these issues, the control voltage for the SLM array cannot be a simple replica of the desired waveform. To create a practical and robust system, an adaptive algorithm was developed to ensure correct wavelength-to-time mapping. The desired waveform serves as the input to an adaptive algorithm running on a laptop computer. Before photodetection, a portion of the optical signal is coupled out and into an optical spectrum analyzer (OSA) as illustrated in Fig. 3. A feedback loop is made such that a least-squares (LS) algorithm iteratively adjusts the pixel voltages until the input waveform matches the measured spectrum. The error is reduced until a user-specified tolerance is reached. This solution is implemented using the LabVIEW data acquisition and programming tool from National Instruments (Austin, TX). Once a desired waveform is generated, the pixel voltage information can be saved and used to generate the same waveform at a later time. The algorithm plays an important role since complex waveforms cannot be generated trivially by manual manipulation of the pixel voltages.
Figure 4 shows UWB frequency-hopped waveforms using 5 km of fiber. The frequency hops between 2 and 8 GHz in increments of 2 GHz. The system generates finite-length replicas of arbitrary waveforms at the repetition rate of the super-continuum source. The repetition rate can be easily increased by using a laser with higher repetition rate, for example, a harmonically mode-locked fiber laser or a semiconductor mode-locked laser. The use of actively mode-locked lasers will afford much higher pulse-to-pulse stability.15
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