# Propagation Losses

Definition: losses of optical energy during propagation of light

More specific terms: bend losses, depolarization loss, insertion loss, return loss, photoinduced losses

German: Ausbreitungsverluste, Propagationsverluste

Categories: general optics, physical foundations

Author: Dr. RĂ¼diger Paschotta

When light propagates in a transparent medium, some of its optical power may be lost due to different physical effects:

- Some of the light may be absorbed. The corresponding energy will often be converted into heat, but it may also lead to fluorescence at other optical wavelengths.
- Light can also be scattered (often in the form of Rayleigh scattering), i.e., it is sent to other directions. Although that does not reduce the total amount of light, it reduces the amount which propagates along the original path. Therefore, scattered light is usually considered to be lost. In some situations, however, a significant part of the scattered light may be sent to approximately the original propagation direction by multiple scattering. It may then be more difficult to appropriately define a propagation loss coefficient.
- In some situations, there are losses due to nonlinear frequency conversion; for example, energy may be transferred to a wave with twice the optical frequency (→
*frequency doubling*). - For light propagation in waveguides (e.g. optical fibers), there can be losses due to mode coupling between guided and unguided modes. (Power transferred into unguided modes is usually considered as lost.) For example, they can be caused by strong bending (→
*bend losses*).

With propagation losses, one usually means only those losses which are distributed in the medium – not localized losses, such as those arising from Fresnel reflections at optical interfaces.

In some situations, propagation losses may be compensated or over-compensated by gain e.g. in a laser gain medium or by nonlinear effects (e.g. optical parametric amplification).

## Loss Coefficients

The propagation losses in a medium can be quantified with a propagation loss coefficient <$\alpha$>, which is the sum of contributions from absorption and scattering and has units of m^{−1}. If the loss coefficient is constant, the optical power is proportional to <$\exp(-\alpha z)$> where <$z$> is the propagation distance.

Alternatively, the losses can be quantified in decibels per meter (dB/m); the numerical values are then ≈4.34 times higher than those of the loss coefficient in m^{−1}. (See the first paragraph in the article on decibel for an explanation of the factor 4.34.) It is also possible to describe propagation losses with a complex refractive index, where the losses are expressed in the imaginary part. Similarly, the evolution power and optical phase can be described with a complex propagation constant.

## Intrinsic and Extrinsic losses

Propagation losses are called *intrinsic* when they inevitably arise from the basic properties of the material. On the other hand, *extrinsic losses* are those which arise from circumstances which can in principle be avoided.

For example, silica fibers exhibit some intrinsic losses due to infrared absorption and also due to Rayleigh scattering at unavoidable inhomogeneities of the glass. (Note that a glass, having an amorphous structure, can never be completely optically homogeneous, even for perfectly optimized fabrication conditions.) On the other hand, there can be additional extrinsic losses due to impurities or non-perfect fabrication conditions.

## Dependencies

The propagation loss coefficient is generally wavelength-dependent. In the case of a waveguide, it can also be strongly mode-dependent.

Generally, propagation losses in waveguides are larger than those in homogeneous media, mostly because non-perfect interfaces can lead to increased scattering. However, optimized single-mode fibers (used e.g. as telecom fibers) can have losses below 0.2 dB/km in the 1.5-μm spectral region because highly purified silica (even when doped e.g. with germania) exhibits very little absorption and scattering in that wavelength region.

For low enough optical intensities, the propagation loss is independent of the intensity. For higher intensities, optical nonlinearities can come into play. For example, the propagation loss may be increased by two-photon absorption or by nonlinear frequency conversion as mentioned above.

See also: propagation constant, absorption coefficient, scattering

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2022-03-28

What would be the power loss for a 1-kW laser beam due to propagation in a vacuum through a 1 km distance?

The author's answer:

Zero! Why should there be any power loss?