Changes

[[File:lighterstill.jpg]][[File:Penetration_ingo_cover.jpg|right|frame]]]]

[[File:lighterstill.jpg]][[File:Penetration_ingo_cover.jpg|right|frame]]

==Origin==

==Origin==

When [[electromagnetic]] [[radiation]] is incident on the [[surface]] of a material, it may be (partly) [[reflected]] from that surface and there will be a field  containing [[energy]] [[transmitted]] into the material. This [[electromagnetic]] field [[interacts]] with the [[atoms]] and [[electrons]] inside the [[material]]. Depending on the [[nature]] of the [[material]], the electromagnetic field might [[travel]] very far into the material, or may die out very quickly. For a given [[material]], penetration depth will generally be a [[function]] of [[wavelength]].

When [[electromagnetic]] [[radiation]] is incident on the [[surface]] of a material, it may be (partly) [[reflected]] from that surface and there will be a field  containing [[energy]] [[transmitted]] into the material. This [[electromagnetic]] field [[interacts]] with the [[atoms]] and [[electrons]] inside the [[material]]. Depending on the [[nature]] of the [[material]], the electromagnetic field might [[travel]] very far into the material, or may die out very quickly. For a given [[material]], penetration depth will generally be a [[function]] of [[wavelength]].

According to [http://en.wikipedia.org/wiki/Beer-Lambert_law Beer-Lambert law], the [[intensity]] of an [[electromagnetic]] [[wave]] inside a material falls off [[exponentially]] from the [[surface]] as

According to [https://en.wikipedia.org/wiki/Beer-Lambert_law Beer-Lambert law], the [[intensity]] of an [[electromagnetic]] [[wave]] inside a material falls off [[exponentially]] from the [[surface]] as

[[File:Penetration_1.jpg]]

[[File:Penetration_1.jpg]]

[[File:Penetration3b.jpg]]

[[File:Penetration3b.jpg]]

Note that δe is identical to the [http://en.wikipedia.org/wiki/Skin_depth skin depth], the latter term usually applying to metals in [[reference]] to the [[decay]] of [[electrical]] currents (which follow the decay in the electric or [[magnetic]] field due to a plane wave incident on a bulk conductor). The attenuation constant α / 2 is also identical to the (negative) real part of the [http://en.wikipedia.org/wiki/Propagation_constant propagation constant], which may also be referred to as α using a notation inconsistent with the above use. When referencing a source one must always be careful to note whether a [[number]] such as α or δ refers to the decay of the field itself, or of the [[intensity]] ([[power]]) associated with that field. It can also be [[ambiguous]] as to whether a positive number describes [http://en.wikipedia.org/wiki/Attenuation attenuation] (reduction of the field) or gain; this is usually obvious from the [[context]].

Note that δe is identical to the [https://en.wikipedia.org/wiki/Skin_depth skin depth], the latter term usually applying to metals in [[reference]] to the [[decay]] of [[electrical]] currents (which follow the decay in the electric or [[magnetic]] field due to a plane wave incident on a bulk conductor). The attenuation constant α / 2 is also identical to the (negative) real part of the [https://en.wikipedia.org/wiki/Propagation_constant propagation constant], which may also be referred to as α using a notation inconsistent with the above use. When referencing a source one must always be careful to note whether a [[number]] such as α or δ refers to the decay of the field itself, or of the [[intensity]] ([[power]]) associated with that field. It can also be [[ambiguous]] as to whether a positive number describes [https://en.wikipedia.org/wiki/Attenuation attenuation] (reduction of the field) or gain; this is usually obvious from the [[context]].

The [http://en.wikipedia.org/wiki/Propagation_constant#Attenuation_constant attenuation constant] for an [[electromagnetic]] [[wave]] at [[normal]] incidence on a [[material]] is also [[proportional]] to the imaginary part of the material's refractive index n. Using the above [[definition]] of α (based on [[intensity]]) the following [[relationship]] holds:

The [https://en.wikipedia.org/wiki/Propagation_constant#Attenuation_constant attenuation constant] for an [[electromagnetic]] [[wave]] at [[normal]] incidence on a [[material]] is also [[proportional]] to the imaginary part of the material's refractive index n. Using the above [[definition]] of α (based on [[intensity]]) the following [[relationship]] holds:

[[File:Penetration_3b.jpg]]

[[File:Penetration_3b.jpg]]

where [[File:Tilde_n.jpg]] denotes the complex [http://en.wikipedia.org/wiki/Index_of_refraction#Dispersion_and_absorption index of refraction], ω is the radian frequency of the radiation, and c is the speed of light in vacuum. Note that [[File:Nw.jpg]] is very much a [[function]] of [[frequency]], as is its imaginary part which is often not mentioned (it is essentially zero for [[transparent]] dielectrics). The complex refractive index of metals is also infrequently mentioned but has the same signficance, leading to a penetration depth (or [http://en.wikipedia.org/wiki/Skin_depth skin depth] δe) accurately given by a [[formula]] which is valid up to microwave frequencies.

where [[File:Tilde_n.jpg]] denotes the complex [https://en.wikipedia.org/wiki/Index_of_refraction#Dispersion_and_absorption index of refraction], ω is the radian frequency of the radiation, and c is the speed of light in vacuum. Note that [[File:Nw.jpg]] is very much a [[function]] of [[frequency]], as is its imaginary part which is often not mentioned (it is essentially zero for [[transparent]] dielectrics). The complex refractive index of metals is also infrequently mentioned but has the same signficance, leading to a penetration depth (or [https://en.wikipedia.org/wiki/Skin_depth skin depth] δe) accurately given by a [[formula]] which is valid up to microwave frequencies.

[[Relationships]] between these and other ways of specifying the [[decay]] of an [[electromagnetic]] field are further detailed in the article: [http://en.wikipedia.org/wiki/Mathematical_descriptions_of_opacity Mathematical descriptions of opacity].[http://en.wikipedia.org/wiki/Penetration_depth]

[[Relationships]] between these and other ways of specifying the [[decay]] of an [[electromagnetic]] field are further detailed in the article: [https://en.wikipedia.org/wiki/Mathematical_descriptions_of_opacity Mathematical descriptions of opacity].[https://en.wikipedia.org/wiki/Penetration_depth]

[[Category: Physics]]

[[Category: Physics]]

[[Category: General Reference]]

[[Category: General Reference]]