Coherence Length And Coherence Time PdfBy Doccardiac In and pdf 15.04.2021 at 11:21 5 min read
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- Coherence control spans 12 orders of magnitude
- Coherence Length of Ultrashort Pulses
Gaps in the coherence spectrum of diode lasers have been known to hinder research. Anselm Deninger and Thomas Renner look at how these gaps are being filled and the applications that are benefiting from access to previously unachievable linewidths and coherence lengths. The ability to control the coherence properties of laser light is a major success factor in applications as diverse as spectroscopy, optical pumping of atoms, nonlinear frequency conversion, interferometry and laser-based imaging.
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Gaps in the coherence spectrum of diode lasers have been known to hinder research. Anselm Deninger and Thomas Renner look at how these gaps are being filled and the applications that are benefiting from access to previously unachievable linewidths and coherence lengths.
The ability to control the coherence properties of laser light is a major success factor in applications as diverse as spectroscopy, optical pumping of atoms, nonlinear frequency conversion, interferometry and laser-based imaging.
The stumbling block for researchers however has been the gaps that exist in the coherence length spectrum of diode lasers. Now, new electronic techniques for laser coherence control are filling the gaps and enabling the controlled manipulation of the linewidth and coherence length of diode lasers over 12 orders of magnitude from the micron range to hundreds of thousands of kilometres.
Linewidth and coherence The term "coherence" is derived from the Latin verb cohaerere meaning to join together. A light wave is considered to be coherent if two joint parts of the wave exhibit interference. In laser physics, it is important to distinguish between spatial and temporal coherence. Spatial coherence denotes the distance between two points on a wave over which they still interfere with one another and governs factors such as the laser beam quality.
Temporal coherence, on the other hand, describes the ability of a wave to interfere with a time-shifted copy of itself. The time during which the phase of the wave changes by a significant amount reducing the interference is known as the coherence time. The corresponding propagation length during this time is called the coherence length. In this article, "coherence" only refers to the temporal coherence properties.
The larger the range of frequencies in any given wave, the faster the phase correlation is lost. In mathematical terms, the linewidth and the coherence length of a laser are inversely proportional and information about the laser's temporal coherence can be expressed in linewidth units of either megahertz or pm. Without any frequency stabilization, the spectrum has a width of approximately 0.
If the diode laser is used in an external-cavity configuration, a diffraction grating narrows the diode's spectrum and the effect is dramatic: the typical linewidth is now 0. The grating effectively changes the coherence properties by almost six orders of magnitude. Unfortunately, this simple trick cannot be adopted universally and the intermediate range has long been considered a gap in the coherence length spectrum of diode lasers.
In this article, we will present technologies to close this gap and extend the coherence length spectrum to even longer — and shorter — values. Influences on the coherence length The coherence length of an ideal theoretical laser can be derived from the Schawlow—Townes formula and is proportional to the output power divided by the square of the resonator bandwidth.
In reality, this limit is usually not achieved due to the influence of various noise sources. If this noise is due primarily to spontaneous emission quantum noise , then high intracavity power, long resonator length and low resonator losses will all increase the coherence length and, consequently, reduce the laser's linewidth.
In a real-world diode laser, the coherence is further influenced by drift factors and technical excess noise. Temperature drifts, environmental factors such as air pressure and humidity, and, in the case of external-cavity lasers piezo creep, all cause long-term drifts on timescales of seconds to hours.
Figure 1 On the other hand, current noise and acoustic perturbations influence the linewidth on a timescale of milliseconds or microseconds. Efficient coherence control must be performed on the correct timescale, or in other words, bandwidth is the key to linewidth narrowing and broadening concepts.
The ability to apply high-frequency electric fields directly to the laser chip distinguishes diode lasers from other laser types, where a controlled coherence variation usually involves intricate external modulation schemes involving, for example, acousto-optic or electro-optic modulators. Typical values Operating regimes Diode lasers can be operated in a variety of different configurations.
Free-running diodes without any spectrally selective means are used in applications where spectral control is either not necessary at all, or comes second to a diffraction-limited beam. Examples include laser microscopy, flow cytometry, disc mastering and microlithography. Grating-stabilized external-cavity geometries are used if single-frequency emission and spectral tunability are required. As outlined above, the gain in coherence due to spectral filtering by a grating can span up to six orders of magnitude.
Unfortunately, this increase in coherence is usually paid for in terms of output power. Figure 2 Narrowing the linewidth Narrow laser linewidths are required in precision spectroscopy, quantum optics and metrology. So-called "forbidden" transitions between long-lived atomic energy levels have linewidths between a few tens of kilohertz and a few hertz.
In order to match these narrow lineshapes, the laser linewidth must be several decades smaller than that of common external-cavity systems. Narrowing a diode laser's output to these levels requires both ultrastable high-finesse reference cavities and extremely fast locking circuitry. A second, slower loop also cancels out long-term frequency drifts by acting on the grating piezo of the laser cavity. Figure 3 Whilst linewidth narrowing techniques have traditionally been the backbone of TOPTICA's development of laser control electronics, a growing number of applications demand just the opposite: increasing the laser linewidth in a stable and reproducible way.
Here, one prefers an artificially broadened laser linewidth, which has been virtually impossible to achieve with diode lasers: external-cavity systems are spectrally too narrow while free-running diodes are far too broad. The LCC employs a proprietary high-bandwidth current modulation scheme to increase the spectral line profile of an external-cavity or distributed feedback diode laser. Changing the amplitude of the modulation permits a precise adjustment of the laser linewidth.
The spectral profile of a diode laser can therefore be matched to a given absorption profile while the laser remains tuned to the resonance frequency. Aligning the tiny nuclear magnets renders the gas magnetic, which enables in vivo imaging of human lungs and airways. This technique has been used to identify ventilation defects caused by smoking; to visualize gas inflow through the trachea and bronchi; and to measure oxygen concentrations within the lungs.
Optical pumping is used to magnetize the gas and this process is most efficient when the laser linewidth matches the Doppler-broadened absorption profile of the gas. At the far end of the scale, the spectral width of a diode laser is limited only by its gain profile. SLEDs are used in applications such as optical coherence tomography OCT , where an increase in spatial resolution is obtained by means of a low temporal coherence and high spatial coherence.
Even if this spectral width is not sufficient, a supercontinuum can be generated by ultrashort pulse lasers. The attainable coherence spectrum of semiconductor lasers now covers more than 12 orders of magnitude and has resulted in spectrally broad violet diodes and new records in frequency resolution. Applications ranging from laser-based imaging to precision studies of hydrogen transitions are now a reality. Optical and electronic feedback, short signal processing times and high operating bandwidths are the main tools that laser engineers resort to.
Coherence control spans 12 orders of magnitude
For an electromagnetic wave , the coherence time is the time over which a propagating wave especially a laser or maser beam may be considered coherent , meaning that its phase is, on average, predictable. In long-distance transmission systems , the coherence time may be reduced by propagation factors such as dispersion , scattering , and diffraction. A single mode fiber laser has a linewidth of a few kHz, corresponding to a coherence time of a few hundred microseconds. From Wikipedia, the free encyclopedia. For the similar concept in communication systems, see Coherence time communications systems. Physics portal.
Coherence Length of Ultrashort Pulses
Coherent Optics pp Cite as. In optics, the original sense of the word coherence was attributed to the ability of radiation to produce interference phenomena. Today, the notion of coherence is defined more generally by the correlation properties between quantities of an optical field.
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