optical path length (original) (raw)

Author: the photonics expert (RP)

Definition: product of physical path length and refractive index

Alternative term: optical length

Category: article belongs to category general optics general optics

Related: optical phase wavelength

Units: m

Formula symbol: OPL, ($\Lambda$)

Page views in 12 months: 2615

DOI: 10.61835/2m5 Cite the article: BibTex BibLaTex plain text HTML Link to this page! LinkedIn

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What is an Optical Path Length?

Optical Path Length (OPL) is a fundamental concept in the field of optics. It refers to the product of the physical path length that light travels through a medium and the refractive index of that medium. This implies that light on that path acquires the same change in optical phase as it would when traveling that distance (the OPL) in vacuum.

In a simple case with light traveling through a homogeneous medium, we have the simple equation \Lambda = n \cdot d$$

where ($n$) is the refractive index and ($d$) the geometric path length. This can be generalized, for example, to situations where light passes through different media in some sequence (e.g., in a multilayer dielectric coating), or even to cases where the ray path is curved. Note, however, that simply using a line integral involving the refractive index along the path may not be accurate. For example, for light propagation through an optical waveguide (e.g. a fiber), the phase delay per unit distance is not governed by the ordinary kind of refractive index, but rather by the effective refractive index, which is a non-local property and also takes into account waveguiding effects. In such a context, where also the application of geometrical optics becomes inaccurate, the naive application of the original concept of optical path length may lead to wrong results concerning the phase delay, which is often the crucial quantity.

Optical path lengths are usually considered only for (quasi-)monochromatic light, i.e., for light with a well-defined wavelength.

According to Fermat's principle, light always takes the path between two points such that the minimum possible optical path length (i.e., the minimum phase delay) results.

Applications

The concept of optical path length is particularly significant in the following fields:

Interferometry: The interference conditions in an interferometer are basically determined by some difference in optical path lengths in the interferometer arms. Therefore, an interferometer can be used to detect very small changes in optical path length.
Optics design: An optical lens should be designed such that the optical path length difference for different rays is minimized. For example, for a lens used for focusing a collimated beam, the path lengths of rays from a plane before the lens to a focal plane (with different distances from the beam axis) should be very similar (differing much less than by one wavelength). In that way, optical aberrations are minimized. Such optimization is important, for example, for obtaining optimal beam focusing or optical image quality in some imaging system.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is the optical path length (OPL)?

The optical path length is the product of the geometric distance light travels through a medium and that medium's refractive index. The light acquires the same optical phase change as it would when traveling a distance equal to the OPL in a vacuum.

How does one calculate the optical path length?

In a homogeneous medium, it is calculated with the formula ($\Lambda = n \cdot d$), where ($\Lambda$) is the optical path length, ($n$) is the refractive index, and ($d$) is the geometric path length. For propagation in a waveguide, one must use the effective refractive index instead of ($n$).

Where is the concept of optical path length applied?

It is essential in interferometry, where interference patterns are determined by differences in optical path lengths. It is also fundamental in the design of optical systems like lenses, where minimizing optical aberrations often involves equalizing the optical path lengths for different light rays.

What is Fermat's principle in relation to optical path length?

According to Fermat's principle, when light travels between two points, it follows the path which has the minimum possible optical path length.

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