mode matching (original) (raw)
Definition: the precise spatial matching of the electric field distributions of laser beams and resonator modes or waveguide modes
Categories: 
general optics, 
optical resonators
- modes
- guided modes
- cladding modes
- tunelling modes = leaky modes
- resonator modes
- Hermite–Gaussian modes
- Laguerre-Gaussian modes
- LP modes
- higher-order modes
- mode competition
- mode coupling
- mode hopping
- mode matching
- mode radius
- V-number
- (more topics)
Related: modescavitieslaser beamsdiffraction-limited beams
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DOI: 10.61835/x1d Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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What is Mode Matching?
In many situations, it is necessary to spatially match a laser beam precisely to another beam or a mode to obtain some kind of efficient coupling. Examples are:
- A beam from a laser has to be coupled into an optical fiber or some other type of waveguide.
- A laser beam must be matched to a mode (often the fundamental mode) of a passive optical resonator which should act, e.g., as a spatial and/or spectral filter (→ mode cleaner cavities) or for resonant frequency doubling.
- For injection locking, the mode of a master laser has to be matched to that of the slave laser.
The necessary matching of modes means not only creating a good spatial overlap of the intensity profiles, but also matching the optical phase profiles. In other words, the wavefronts of the beams will then be matched. If the complex amplitude profiles of two beams (having the same optical frequency) are well matched in a certain plane, they will remain well matched during further propagation.
Mode matching can be achieved by using suitable relay optics (typically some combination of curved mirrors or lenses), provided that the beam quality of the initial beam is close to diffraction-limited.
Mathematically, the quality of mode matching can be quantified with an overlap integral. The following formula, involving the square of such an overlap integral, calculates the coupling efficiency: \eta = \frac{{{{\left| {\int {E_1^*{E_2}\;{\rm{d}}A} } \right|}^2}}}{{\int {{{\left| {{E_1}} \right|}^2}{\rm{d}}A\;\int {{{\left| {{E_2}} \right|}^2}{\rm{d}}A} } }}$$
where ($E_1$) and ($E_2$) are the complex electric fields in a plane, referring e.g. to a laser beam and the field of a resonator or waveguide mode, and the integration spans the whole beam cross-section. This formula can be applied for the scalar case (assuming constant polarization over the beam cross-section), but also in the vectorial case, where the electric field phasors are vectors with ($x$) and ($y$) components.
Note that the overlap as calculated above is preserved during propagation in free space.
A similar overlap integral can be used for calculating complex mode amplitudes.
The equation above can be used to calculate, for example, which fraction of the optical power of a Gaussian laser beam can be launched into a single-mode fiber. This efficiency can be close to 100% if the fiber's guided mode is close to Gaussian.
Mode Matching Calculations
The software RP Resonator is a particularly flexible tool for calculating all kinds of resonator mode properties. With a little script code (which we are happy to provide), you can also calculate mode overlap integrals. For example, calculate how efficiently a Gaussian input beam can be coupled to a resonator under conditions of misalignment.
If the beam from a frequency-tunable single-frequency laser hits a symmetric Fabry–Pérot interferometer and the laser frequency is tuned over the whole free spectral range of the resonator, the transmitted light can be used to analyze the degree of mode matching. For perfect matching to a cavity mode (typically the fundamental Gaussian mode), complete transmission of the resonator can be observed when the resonance condition is met, whereas other resonances (corresponding to other resonator modes) cannot be excited.
When trying to launch light into a waveguide without perfect mode matching, one may get part of the light into cladding modes of the waveguide, rather than the desired guided modes.
Frequently Asked Questions
What does 'mode matching' mean in optics?
Mode matching is the process of spatially adapting a laser beam to match the mode of another system, such as an optical fiber or a resonator. This requires matching both the intensity and phase profiles (i.e., wavefronts) of the light to ensure efficient power transfer.
For which applications is mode matching required?
Mode matching is essential for applications like efficiently coupling a laser beam into a single-mode optical fiber, injecting light into a resonant optical cavity (e.g., a mode cleaner), or for the injection locking of one laser to another.
How can the quality of mode matching be calculated?
The quality is quantified by the power coupling efficiency ($\eta$), which is calculated with an overlap integral of the two complex electric field profiles ($E_1$) and ($E_2$). A value of 1 corresponds to a perfect match.
Suppliers
Sponsored content: The RP Photonics Buyer's Guide contains 14 suppliers for Fabry–Pérot interferometers. Among them:
âš™ hardware
LightMachinery manufactures the world's finest solid and air spaced etalons. Our fluid jet polishing systems allow us to routinely create surfaces that are better than λ/100 peak to valley.
Solid etalons, air spaced etalons, piezo tunable etalons, Gires–Tournois etalons — LightMachinery has extensive expertise in the manufacturing and testing of all kinds of Fabry–Pérot etalons from 1 mm square to 100 mm in diameter. These devices require high quality, very flat optical surfaces and extreme parallelism to achieve high performance, making them a good match for the polishing and metrology at LightMachinery.
âš™ hardware
The FPI 100 is a confocal, scanning Fabry–Pérot interferometer with a built-in photodetector unit, designed for measuring and controlling the mode profiles of continuous wave (cw) lasers. The FPI is available with different mirror sets and photodetectors for wavelength ranges between 330 nm and 3000 nm.
âš™ hardware
Hamamatsu Photonics offer MEMS-FPI spectroscopic modules, compact near-infrared spectrometers that incorporate a MEMS-FPI spectrum sensor and a light source.
âš™ hardware
The Fabry–Pérot interferometers offered by ALPHALAS are high-resolution spectroscopic instruments having applications in spectral analysis of narrowband light sources like gas discharge lamps and lasers. These are especially useful for analyzing the spectral content of pulsed lasers, because they allow for single-shot measurements.
The interferometers consist of two high-precision mirrors with a flatness better than λ/40 over 90% of the aperture, having broadband coatings and spacers of different thickness. The working aperture is either 22 mm or 48 mm, and the reflectivity finesse is > 120. The standard spectral range is 450 nm … 1100 nm, others on request. Combined with our CCD linear array, the interferometers form a versatile spectral analysis system.
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