Novel dispersive devices, such as chirped fiber Bragg gratings (CFBGs), can be used to temporally process broadband opti
© 2008 OSA / CLEO/QELS 2008 a559_1.pdf CMII3.pdf
Compensation Algorithm for Deterministic Phase Ripple Josh A. Conway, George A. Sefler, George C. Valley and Jason Chou Electronics and Photonics Laboratory, The Aerospace Corporation, 355 South Douglas, El Segundo, CA 90245
[email protected]
Abstract: Phase ripple arising from imperfections in novel dispersive devices can severely distort broadband optical signals. We experimentally and theoretically demonstrate an algorithm that corrects for these distortions while simultaneously reducing the effects of additive noise.
©2008 Optical Society of America
OCIS codes: 060.5625 (RF Photonics), 060.3735 (Fiber Bragg Gratings)
Novel dispersive devices, such as chirped fiber Bragg gratings (CFBGs), can be used to temporally process broadband optical signals. Unlike optical fiber, these devices exhibit very low loss and custom dispersion profiles. However, CFBGs introduce higher order distortions such as phase ripple [1]. Phase ripple typically represents a small perturbation to the total transfer function of a CFBG and would seem to require only a high-order correction. In the time domain, however, sinusoidal phase ripple translates to an impulse response that creates time-delayed copies of the original signal. A device with sinusoidal phase ripple is equivalent to a low-Q Fabry-Perot cavity and arbitrary phase ripple is equivalent to a series of cavities by Fourier analysis. The interference between the various time delays creates a highly structured time-domain signal after square-law detection, analogous to laser speckle patterns in the spatial domain. Correcting this distortion would seem to require knowledge of both the optical phase and amplitude. Herein we describe a simple algorithm that corrects for phase ripple using only the measured optical intensity and a thorough characterization of the CFBG transfer function. This algorithm is then demonstrated in a photonic time-stretch application where the SNR is improved by over 9 dB. While the transfer function of most broadband devices exhibits phase variation, ripple is particularly egregious in CFBGs. Because they operate in reflection mode, CFBGs implicitly have one facet of the Fabry-Perot cavity that generates phase ripple. Simple errors in fabrication then produce the other cavity reflector through the superstructure effect [2]. The severity of phase ripple is demonstrated by the results of Fig. 1. In this experiment, a 1.5-ps, C band fiber laser (Precision Photonics) source goes into a Proximion CFBG (2 ns/nm dispersion), followed by a 3nm bandpass filter (Bookham), and finally into a photodetector. The signal is digitized by a real-time oscilloscope with 16 GHz of analogue bandwidth (Tektronix 7204) and then averaged over 64 traces to remove the effects of noise. A comparison with simulation illustrates the signal corruption induced by chirp ripple. To generate the simulation shown in Fig. 1a, the optical spectrum was measured at the output of the bandpass filter using a spectrometer. This empirical power spectral density was mapped to a frequency domain electric field for the simulation input. At this stage, the field is represented only by its slowly varying envelope and no phase information is used in the source. The field was then multiplied by the manufacturer-supplied grating transfer function (with and without ripple), Fourier transformed to the time domain, and finally multiplied by its complex conjugate. The correspondence between measurement and simulation reveals the extent to which chirp ripple corrupts broadband signals. Note that this 'phase-only' effect produces features with 25% modulation depth and at frequencies up to the scope bandwidth.
Fig. 1. (a) Comparison of time averaged measurement versus simulation with and without chirp ripple. The output of the correction algorithm is also shown. (b) Block diagram of the experiment.
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© 2008 OSA / CLEO/QELS 2008 a559_1.pdf CMII3.pdf
The agreement between simulation and experiment suggests that the correction the effects of phase ripple may be reversible through post processing. If the complex field were directly detected at the output, correction would be a simple matter of dividing by the transfer function. The square-law detection, however, strips away the requisite phase information. Fortunately, the phase information can be retrieved from the system characteristics that created the distortion. Deterministic interference amongst the various spectral components is assured by the picosecond timescale of the input pulse. The rest of the system is static and adds a known phase in the time domain. Therefore the complex time-domain field envelope can be obtained by taking the square-root of the intensity measured in the physical system and multiplying it by the phase determined from simulation. Temporal alignment of the simulated phase with intensity, which is required for correction, is facilitated by the sharp features generated by the phase ripple itself. The output field is now known and the problem reduces to a simple linear system that can be solved by dividing out the ripple in the frequency domain. Transforming back to the time domain and multiplying by the complex conjugate returns the undistorted signal. The problem is analogous to an optical system with spatial aberrations that is illuminated by a point source whose transfer function is known exactly. This technique has been applied to the measured data of Fig. 1a, and the result of the algorithm is shown by the top curve. The results have very low dependence on the spectrum of the simulated source. Note that the noise remaining after correction is of the order of the lease significant read-out bit of the 8-bit oscilloscope, which is the noise floor of our system.
Fig. 2. (a) Comparison of time averaged measurement before and after the algorithm and filtering. (b) Block diagram of the experiment.
Potential applications of this algorithm go far beyond the system described above, and include any device that adds static phase in the time domain. These include zero-chirp modulators and devices of arbitrary dispersion. To demonstrate this, we apply the algorithm to the photonic time-stretch system [3] depicted in Fig. 2(b) that employs a CFBG as the high dispersion stage. This system uses dispersion to stretch RF signals in time, thereby compressing the RF bandwidth [4], by a factor of three. A 3-GHz tone was applied to the pulse with a push-pull modulator of modulation depth of 0.28. A delay and recombination stage is used to capture the complimentary output from both modulator arms which allows for pulse envelope correction. Single-pulse data in Fig. 2(a) shows a stretched frequency of 1 GHz. No averaging was employed so the distortion comes from both noise and the CFBG. The phase-ripple correction algorithm was applied to this data without any assumptions about the RF modulation. After low pass filtering at 1.7 GHz, we obtain the corrected signal. The dual outputs are then manipulated to remove the pulse envelope. A sine fit test on the recovered signal shows more than 9 dB SNR improvement over identical processing and filtering without phase-ripple correction. This SNR is also higher than equivalent experiments using ripple-free dispersion compensated fiber (DCF) in place of the CFBG because DCF has more loss and hence requires more amplifier gain. In addition, the ripple correction algorithm maps additive noise out of band, which has been shown through extensive simulation. Thus the algorithm provides noise reduction, rather than amplification as is standard in image recovery algorithms [5]. These results show that the strong phase distortions found in CFBGs can be corrected, allowing their use in a variety of high resolution photonic applications. References [1] C. Scheerer, C. Glingener, G. Fischer, M. Bohn, and W. Rosenkranz, ICTON, 33-36 (1999). [2] M. Sumetsky, B. Eggleton and C. de Sterke, Opt. Express, 10, 332-40 (2002). [3] J. Conway, G.C. Valley and J. Chou, IEEE Trans. Microw. Theory Tech., 2270-71 (2007). [4] Y. Han and B. Jalali, IEEE/OSA J. Lightwave Tech. 21, 3085-3103 (2003). [5] R.C. Puetter, T.R. Gosnell and A. Yahil, Annu. Rev. Astron. Astrophys. 43, 139-94 (2005).
