Concepts for the Temporal Characterization of Short Optical Pulses
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Concepts for the Temporal Characterization of Short Optical Pulses Christophe Dorrer Bell Laboratories, Lucent Technologies, 791 Keyport-Holmdel Road, Holmdel, NJ 07733, USA Email: [email protected]
Ian A. Walmsley Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom Email: [email protected] Received 1 April 2004; Revised 15 September 2004 Methods for the characterization of the time-dependent electric field of short optical pulses are reviewed. The representation of these pulses in terms of correlation functions and time-frequency distributions is discussed, and the strategies for their characterization are explained using these representations. Examples of the experimental implementations of the concepts of spectrography, interferometry, and tomography for the characterization of pulses in the optical telecommunications environment are presented. Keywords and phrases: optical pulse characterization, time-frequency distribution, Wigner function, spectrogram, tomography, interferometry.
1.
INTRODUCTION
Ultrashort optical pulses are used in areas of science and engineering as diverse as spectroscopy, medical research, plasma physics, quantum optics, and optical telecommunications. In optical telecommunications, information is encoded in the amplitude and/or phase of an optical wave [1]. While information encoding in digital telecommunications is based on a finite number of values of a physical quantity (e.g., the presence or absence of energy in a given bit slot), the ability to measure in detail the waveform of the optical wave itself is crucial for optimizing the properties of the systems that generate the signal, and understanding the linear and nonlinear properties of the systems through which the pulses propagate. This information is critical in developing strategies to overcome the current limitations of current optical networks. For example, dispersion management compensates for the chromatic dispersion induced by linear propagation and can also be used to mitigate nonlinear effects. Similarly, the phase distortion imposed on a pulse by the modulators used in carving the pulse out of a cw- or quasi-cw source can impact the propagation of the pulse. Finally, measurements of the electric field can be used to characterize the linear or nonlinear properties of a device. There are various approaches for temporal waveform measurements. We only consider here techniques that provide self-referencing characterization of an unknown pulse or a train of unknown but
identical pulses, that is, that do not use a well-characterized pulse as a reference. While test-plus-reference techniques, such as spectral interferometry [2, 3, 4], can be easier to implement in some cases, they require a well-characterized reference pulse mutually coherent with the pulse under test. Although this can be difficult to achieve over long distances, they have been used to characterize pulses in the telecommunication environment [5]. We will not deal either with sampling techniques. These techniques can provide samples of the
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