Short address: rpp-con.com
Dr. Paschotta, the founder of RP Photonics, supports your R & D with his deep expertise. Save time and money with efficient support!
Short address: rpp-soft.com
Powerful simulation software for fiber lasers and amplifiers, resonator design, pulse propagation and multilayer coating design.
Short address: rpp-enc.com
The famous Encyclopedia of Laser Physics and Technology provides a wealth of high-quality scientific and technical information.
Short address: rpp-bg.com
In the RP Photonics Buyer's Guide, you easily find suppliers for photonics products. As a supplier, you can profit from enhanced entries!
Learn on lasers and photonics every day!
||part of the|
In the RP Photonics Buyer's Guide you can find plenty of suppliers for hundreds of photonics products.
Definition: the distance from a beam waist where the mode radius increased by a factor square root of 2
The Rayleigh length (or Rayleigh range) of a laser beam is the distance from the beam waist (in the propagation direction) where the beam radius is increased by a factor of the square root of 2.
For a circular beam, this means that the mode area is doubled at this point.
For Gaussian beams, the Rayleigh length is determined by the waist radius w0 and the wavelength λ:
where the wavelength λ is the vacuum wavelength divided by the refractive index n of the material.
For beams with imperfect beam quality and a given waist radius, the Rayleigh length is effectively decreased by the so-called M2 factor.
This implies that such beams have a larger beam divergence for a given beam waist radius.
The Rayleigh length is a convenient quantity for calculations in the context of focused laser beams.
Essentially, it determines the depth of focus.
There can thus be a trade-off between a more strongly focused beam with higher optical intensity in the focus, and a less strongly focused beam with longer Rayleigh length, i.e. larger depth of focus.
For example, the highest laser gain in a laser medium can be achieved when the focused pump beam has a Rayleigh length of the order of the length of the gain medium: weaker focusing reduces the pump intensity, whereas stronger focusing leads to a strong divergence, which limits the effective interaction length.
Similar arguments apply to nonlinear interactions, e.g. frequency doubling, even though some more sophisticated aspects such as the Gouy phase shift come into play in such situations, where phase matching is important.
The older literature often uses the confocal parameter b, which is two times the Rayleigh length.
See also: Gaussian beams, laser beams, collimated beams, Gouy phase shift, beam quality, M2 factor
Category: general optics
Have you seen the
RP Photonics Buyer's Guide?
It lists many hundreds of suppliers for photonics products, and is just one mouse click away from the extremely popular Encyclopedia of Laser Physics and Technology:
- In any product-related encyclopedia article, you find a box for the Buyer's Guide.
- Alternatively, click on the heading which your mouse pointer has just touched.
Our Buyer's Guide is what you need:
- easy handling, clear layout
- high-quality information
- additional technical information in the encyclopedia
And surely you will remember where to find this useful resource again!
Suppliers: get your free entries, and enhanced visibility with paid entries.
Free Fiber Optics Software!
RP Fiber Calculator – a convenient tool for calculations on optical fibers -- offered for free –
let us celebrate the 10-year anniversary of RP Photonics!
Laser Design Services
Fast and efficient laser development is possible with the competent design services of RP Photonics, based on extensive experience, deep scientific knowledge and advanced software.
Thin-film Optics Software
Analyze and optimize dichroic and dispersive mirrors, AR coatings, filters, thin-film polarizers, rugate filters, VECSELs etc. with RP Coating!
RP Photonics Buyer's Guide
Do you know a better place to find suppliers for photonics items?
Search by product or by supplier.
Suppliers, show your products with free or enhanced entries!
The Encyclopedia in Book Form
The two-volume print version of the encyclopedia would deserve a place in your institute or group library!
Click on the image to get to Wiley-VCH.