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RP Photonics has the powerful numerical software RP Fiber Power for the simulation of pulse propagation. Even the coherence of supercontinua can be simulated.
Definition: a nonlinear process for strong spectral broadening of light
Supercontinuum generation is a process where laser light is converted to light with a very broad spectral bandwidth (i.e., low temporal coherence), whereas the spatial coherence usually remains high. The spectral broadening is usually accomplished by propagating optical pulses through a strongly nonlinear device. For example, one may send an intense (amplified) ultrashort pulse through a piece of bulk glass. Alternatively, one can send pulses with much lower pulse energy through an optical fiber, having a much higher nonlinearity and also a waveguide structure which ensures a high beam quality. Of special interest are photonic crystal fibers, mainly due to their unusual chromatic dispersion characteristics, which can allow a strong nonlinear interaction over a significant length of fiber. Even with fairly moderate input powers, very broad spectra are achieved; this leads to a kind of “laser rainbow”. In some cases, tapered fibers can also be used.
Applications of supercontinua include coherence tomography, fluorescence microscopy, flow cytometry, the characterization of optical devices, the generation of multiple carrier waves in optical fiber communications systems, and the measurement of the carrier–envelope offset frequency of frequency combs.
The Physics of Supercontinuum Generation
The physical processes behind supercontinuum generation in fibers can be very different, depending particularly on the chromatic dispersion and length of the fiber (or other nonlinear medium), the pulse duration, the initial peak power and the pump wavelength. When femtosecond pulses are used, the spectral broadening can be dominantly caused by self-phase modulation. In the anomalous dispersion regime, the combination of self-phase modulation and dispersion can lead to complicated soliton dynamics, including the split-up of higher-order solitons into multiple fundamental solitons (soliton fission). For pumping with picosecond or nanosecond pulses, Raman scattering and four-wave mixing can be important. Supercontinuum generation is even possible with continuous-wave beams, when using multi-watt laser beams in long fibers; Raman scattering and four-wave mixing are very important in that regime.
The noise properties of the generated continua can also be very different in different parameter regions. In some cases, e.g. with self-phase modulation being the dominant mechanism and the dispersion being normal, the process is very deterministic, and the phase coherence of the generated supercontinuum pulses can be very high, even under conditions of strong spectral broadening. In other cases (e.g. involving higher-order soliton effects), the process can be extremely sensitive to the slightest fluctuations (including quantum noise) e.g. in the input pulses, so that the properties of the spectrally broadened pulses vary substantially from pulse to pulse.
The strongly nonlinear nature of supercontinuum generation makes it difficult to understand intuitively all the details of the interaction, or to predict relations with analytical tools. Therefore, numerical pulse propagation modeling (often with special precautions due to the extreme optical bandwidth) is required for the analysis of such processes. Intuitive pictures or analytical guidelines can be tested by comparison with results from such numerical models.
It is worth spending some thoughts on the coherence properties of supercontinua. The spatial coherence (considering the cross-spectral density) is usually very high, particularly when the source involves a single-mode fiber. On the other hand, the high spectral bandwidth suggests a very low temporal coherence. However, supercontinua generated from periodic pulse trains can still have a high temporal coherence in the sense that there can be strong correlations between the electric fields corresponding to different pulses, if the spectral broadening mechanism is highly reproducible. This kind of coherence is in fact very important for the generation of frequency combs in photonic crystal fibers, and it may or may not be achieved depending on parameters such as the seed pulse duration and energy, fiber length, and fiber dispersion.
The initially surprising discrepancy between high bandwidth and high temporal coherence can be resolved by realizing the shape of the field correlation function: it has a very narrow peak around zero time delay (with a width of e.g. a few femtoseconds), but there are also additional peaks with comparable height at time delays corresponding to integer multiples of the pulse period. Hence there is low temporal coherence in the sense of vanishing correlations for most time delays, but high temporal coherence in the sense of strong correlations for some large time delays.
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|||R. Paschotta, case study on supercontinuum generation in a photonic crystal fiber|
This encyclopedia is authored by Dr. Rüdiger Paschotta, the founder and executive of RP Photonics Consulting GmbH. Contact this distinguished expert in laser technology, nonlinear optics and fiber optics, and find out how his technical consulting services (e.g. product designs, problem solving, independent evaluations, or staff training) and software could become very valuable for your business!
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