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Optical Engineering OPTICS IN 2008 Repetition Rate Multiplication Using All-Pass Optical Structures Miguel A. Preciado and Miguel A. Muriel (a) Input periodic pulse train a1(t) Intensity [a.u.] (b) Output periodic pulse train All-pass optical structure a2(t) Proposed structures 0.5 2x 0.25 0 0 1 2 3 4 5 6 7 8 9 10 Time [ps] (c) 0.3 Intensity [a.u.] T echniques for creating ultrahigh repetition rate pulse trains are highly sought after for future ultrahighspeed optical communication systems. Researchers have explored several strategies for generating periodic pulse trains at repetition rates beyond those achievable by mode locking or direct modulation. One alternative is pulse repetition rate multiplication (PRRM) of a lower rate source by applying phase-only spectral filtering, usually based on the temporal Talbot effect.1 We have recently proposed several all-pass structures based on optical cavities; these perform phase-only spectral filtering for the implementation of repetition-rate multipliers of a periodic pulse train with uniform output train envelopes.2,3 We found optimum solutions for 23, 33, 43, 63 and 123 multiplication factors. As can be seen in part (a) of the figure, the proposed optical structures are composed of 1-4 ring resonators (RRs). We found that a single RR structure can achieve three factors of repetition-rate multiplication (23, 33 and 43), being specially suited for 23 in terms of accuracy and robustness.2 We presented two structures that achieve accurate and robust solutions for 33 and 43 PRRM, both composed of two identical RRs in cascade or coupled configuration.3 We have also proposed several optical structures for 63 and 123 PRRM by combining filters of 23, 33 and 43 PRRM.3 Parts (b) and (c) show the results numerically for two of our studies.2,3 Part (b) shows the output pulse train intensity numerically obtained for 23 repetition rate multiplication, where an input repetition rate of 100 GHz was assumed. Part (c) shows the output pulse train intensity numerically obtained for 33, 43, 63 and 123 multiplication factors, with an input repetition rate of 0.2 0.1 0 0 10 20 30 40 50 60 70 80 90100 Time [ps] (a) Schematic of the system. The periodic pulse train is processed by the all-pass optical structure. We propose nine optical structures composed of multiple RRs. (b) Output pulse train intensity of examples for 23 multiplication with a single all-pass RR. (c) Output pulse train intensity of examples for 33 (blue), 43 (red), 63 (green) and 123 (yellow) multiplication and the respective optical structures. 10 GHz. The RR parameters obtained in these examples are readily feasible. We have also analyzed the effect of RR losses on the energetic efficiency and the output pulse train envelope uniformity and the effect of the frequency deviations on the envelope uniformity.3 In conclusion, these structures are readily feasible and present an intrinsic high energetic efficiency, ideally of 100 percent, that is only limited by internal RR losses. It is worth noting that, like other spectrally periodic filtering techniques based in optical cavities,4 the system requires the locking of the spectrum of the input signal, which is typically composed of the mode comb of the laser, to the spectral response of the optical structure. t Miguel A. Preciado ([email protected]) and Miguel A. Muriel are with the Universidad Politecnica de Madrid in Madrid, Spain. References 1. J. Azaña and M.A. Muriel. “Temporal Talbot effect in fiber gratings and its applications,” Appl. Opt. 38, 6700-4 (1999). 2. M.A. Preciado and M.A. Muriel. “Repetition rate multiplication using a single all-pass optical cavity,” Opt. Lett. 33, 962-4 (2008). 3. M.A. Preciado and M.A. Muriel. “All-pass optical structures for repetition rate multiplication,” Opt. Express 16, 11162-8 (2008). 4. J. Chen et al. “Generation of low-timing-jitter femtosecond pulse trains with 2 GHz repetition rate via external repetition rate multiplication,” Opt. Lett. 33, 959-61 (2008). OPN December 2008 | 37 Optical Engineering Electromagnetic Arbitrary Waveform Generation with Broadband Incoherent Light Sources V. Torres-Company, J. Lancis, P. Andrés and L.R. Chen I n recent years, advances in pulseshaping technology have shown great potential for applications in microwave photonics.1,2 Researchers’ interest is partly motivated by the fact that the generation of arbitrary electromagnetic signals with 1-50 GHz frequency content is a challenge for purely electronic systems. Broad bandwidth signals could have a positive impact on high-speed wireless communication systems and find interesting applications in radar, remote sensing and electronic-equipment test measurements.1 Previously demonstrated photonicbased arbitrary waveform generators (AWGs) fall easily within the desired frequency range. Their principle of operation is based on the following general scheme. First, a broadband coherent signal (e.g., from a mode-locked laser) is synthesized in a user-defined way in the optical domain. Usually, pulse shapers based on spatial light modulators are preferred to all-fiber configurations because they provide reconfiguration capabilities.2 Once the synthesis is performed, the light intensity is transferred to the electrical domain simply by using a highspeed photodetector. In this way, the detector sets the upper limit on the achievable electrical bandwidth. Therefore, while obtaining highfrequency electrical signals is a relatively straightforward task with mode-locked lasers, reaching the low-frequency regime remains a challenge. In 2003, this problem was circumvented thanks to the coherent “wavelength-to-time mapping technique” demonstrated by Jalali’s group at UCLA.3 This scheme consists of synthesizing the energy spectrum of a coherent broadband signal with a Fourier-transform pulse shaper and later transferring the designed spectral shape into the electrical domain by stretching the optical pulse 38 | OPN December 2008 Lens Reflective SLM Grating Synthesized spectrum Mirror ASE light 1,554 1,552 1,560 Wavelength (nm) Pattern generator EOM Bias Experimental results Clock 0.5 ns Fiber O/E conversion Example of generating a chirped sinusoidal signal: The incoherent radiation is spectrally shaped with a Fourier transform pulse shaper. Once the spectrum is synthesized, the radiation is modulated with an external modulator. Finally, the light is stretched in a fiber long enough so that the output-averaged intensity becomes a scaled replica of the synthesized energy spectrum. The scaling factor is exactly the same as in the coherent version and, therefore, the previous advantageous features are preserved. in a dispersive medium (e.g., fiber) and subsequently detecting it. Accordingly, the scaling factor of the resulting electromagnetic waveform can be tunable by adjusting the amount of dispersion. We have gone one step further and shown that this widely used system can be operated with a spectrally incoherent light source such as amplified spontaneous emission (ASE). The physical mechanism behind this configuration relies on the temporal version of the vanCittertZernike theorem formulated by Dorrer in 2004.4 This theorem extends the previous wavelength-to-time mapping to the incoherent regime. In 2006, we suggested a theory of how this could be used for AWG. This year, we achieved the first experimental results.5 The setup is shown in the figure. The main goal is to avoid the use of a mode-locked laser. Apart from being an interesting economic alternative, this allows us to control the repetition rate of the electromagnetic waveform with an external clock. This is a key feature to perform continuously operating radiofrequency waveforms. To date, we have generated arbitrary electrical signals with frequency content around 1-10 GHz using standard 10 Gb/s telecommunications equipment. t V. Torres-Company ([email protected]) and J. Lancis are with the departament de fisica, Universitat Jaume I, in Castello, Spain. P. Andrés is with the departamento de Optica, Universitat Valencia, in Burjassot, Spain. L.R. Chen is with the department of electrical and computer engineering at McGill University in Montreal, Canada. References 1. J. Capmany and D. Novak. Nature Photon. 1, 319 (2007). 2. J.D. McKinney et al. Opt. Photon. News 17, 24 (2006). 3. J. Chou et al. IEEE Photon. Technol. Lett. 15, 581 (2003). 4. C. Dorrer. J. Opt. Soc. Am. B 21, 1417 (2004). 5. V. Torres-Company et al. J. Lightwave Technol. 26, 2476 (2008).