Thin-film Interference
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Thin-film interference is a natural phenomenon in which
light wave In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ra ...
s reflected by the upper and lower boundaries of a
thin film A thin film is a layer of materials ranging from fractions of a nanometer ( monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many ...
interfere with one another, increasing reflection at some
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
s and decreasing it at others. When white light is incident on a thin film, this effect produces colorful reflections. Thin-film interference explains the multiple colors seen in light reflected from
soap bubble A soap bubble (commonly referred to as simply a bubble) is an extremely thin soap film, film of soap or detergent and water enclosing air that forms a hollow sphere with an iridescent surface. Soap bubbles usually last for only a few seconds b ...
s and oil films on
water Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known liv ...
. It is also the mechanism behind the action of antireflection coatings used on
glasses Glasses, also known as eyeglasses (American English), spectacles (Commonwealth English), or colloquially as specs, are vision eyewear with clear or tinted lenses mounted in a frame that holds them in front of a person's eyes, typically u ...
and
camera lens A camera lens, photographic lens or photographic objective is an optical lens (optics), lens or assembly of lenses (compound lens) used in conjunction with a camera body and mechanism to Imaging, make images of objects either on photographic film ...
es. If the thickness of the film is much larger than the coherence length of the incident light, then the interference pattern will be washed out due to the
linewidth A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used ...
of the light source. The reflection from a thin film is typically not individual wavelengths as produced by a
diffraction grating In optics, a diffraction grating is an optical grating with a periodic structure that diffraction, diffracts light, or another type of electromagnetic radiation, into several beams traveling in different directions (i.e., different diffractio ...
or
prism PRISM is a code name for a program under which the United States National Security Agency (NSA) collects internet communications from various U.S. internet companies. The program is also known by the SIGAD . PRISM collects stored internet ...
, but rather are a mixture of various wavelengths. Therefore, the colors observed are rarely those of the rainbow, but rather browns, golds, turquoises, teals, bright blues, purples, and magentas. Studying the light reflected or transmitted by a thin film can reveal information about the thickness of the film or the effective
refractive index In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
of the film medium. Thin films have many commercial applications including
anti-reflection coating An antireflective, antiglare or anti-reflection (AR) coating is a type of optical coating applied to the surface of lenses, other optical elements, and photovoltaic cells to reduce reflection. In typical imaging systems, this improves the effi ...
s,
mirror A mirror, also known as a looking glass, is an object that Reflection (physics), reflects an image. Light that bounces off a mirror forms an image of whatever is in front of it, which is then focused through the lens of the eye or a camera ...
s, and
optical filter An optical filter is a device that selectively transmits light of different wavelengths, usually implemented as a glass plane or plastic device in the optical path, which are either dyed in the bulk or have interference coatings. The optic ...
s.


Theory

In optics, a
thin film A thin film is a layer of materials ranging from fractions of a nanometer ( monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many ...
is a layer of material with thickness in the sub-
nanometer 330px, Different lengths as in respect to the Molecule">molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm), or nanometer (American spelling Despite the va ...
to
micron The micrometre (English in the Commonwealth of Nations, Commonwealth English as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American English), also commonly known by the non-SI term micron, is a uni ...
range. As light strikes the surface of a film, it is either transmitted or reflected at the upper surface. Light that is transmitted reaches the bottom surface and may once again be transmitted or reflected. The
Fresnel equations The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by French engineer and ...
provide a quantitative description of how much of the light will be transmitted or reflected at an interface. The light reflected from the upper and lower surfaces will interfere. The degree of constructive or destructive
interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or disrupts a message * Adjacent-channel interference, caused by extra ...
between the two light waves depends on the difference in their phase. This difference in turn depends on the thickness of the film layer, the refractive index of the film, and the angle of incidence of the original wave on the film. Additionally, a phase shift of 180° or \pi radians may be introduced upon reflection at a boundary depending on the refractive indices of the materials on either side of the boundary. This phase shift occurs if the refractive index of the medium the light is travelling through is less than the refractive index of the material it is striking. In other words, if n_1 < n_2 and the light is travelling from material 1 to material 2, then a phase shift occurs upon reflection. The pattern of light that results from this interference can appear either as light and dark bands or as colorful bands depending upon the source of the incident light. Consider light incident on a thin film and reflected by both the upper and lower boundaries. The optical path difference (OPD) of the reflected light must be calculated in order to determine the condition for interference. Referring to the ray diagram above, the OPD between the two waves is the following: :OPD = n_2 (\overline + \overline)- n_1(\overline) Where, :\overline = \overline = \frac :\overline = 2d\tan(\theta_2)\sin(\theta_1) Using
Snell's law Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing th ...
, n_1\sin(\theta_1)=n_2\sin(\theta_2) :\beginOPD &= n_2\left(\frac\right) - 2d\tan(\theta_2)n_2\sin(\theta_2)\\&= 2n_2d\left(\frac\right)\\&= 2n_2d\cos\big(\theta_2)\\\end Interference will be constructive if the optical path difference is equal to an integer multiple of the wavelength of light, \lambda. :2n_2d\cos\big(\theta_2)=m\lambda This condition may change after considering possible phase shifts that occur upon reflection.


Monochromatic source

Where incident light is
monochromatic A monochrome or monochromatic image, object or palette is composed of one color (or values of one color). Images using only shades of grey are called grayscale (typically digital) or black-and-white (typically analog). In physics, mon ...
in nature, interference patterns appear as light and dark bands. Light bands correspond to regions at which constructive interference is occurring between the reflected waves and dark bands correspond to destructive interference regions. As the thickness of the film varies from one location to another, the interference may change from constructive to destructive. A good example of this phenomenon, termed "
Newton's rings Newton's rings is a phenomenon in which an interference pattern is created by the reflection of light between two surfaces, typically a spherical surface and an adjacent touching flat surface. It is named after Isaac Newton, who investigated th ...
", demonstrates the interference pattern that results when light is reflected from a spherical surface adjacent to a flat surface. Concentric rings are observed when the surface is illuminated with monochromatic light. This phenomenon is used with
optical flat An optical flat is an Optics, optical-grade piece of glass lapping, lapped and polishing, polished to be extremely flat on one or both sides, usually within a few tens of nanometres (billionths of a metre). They are used with a monochromatic li ...
s to measure the shape and flatness of surfaces.


Broadband source

If the incident light is broadband, or white, such as light from the sun, interference patterns appear as colorful bands. Different wavelengths of light create constructive interference for different film thicknesses. Different regions of the film appear in different colors depending on the local film thickness.


Phase interaction

The figures show two incident light beams (A and B). Each beam produces a reflected beam (dashed). The reflections of interest are beam A’s reflection off of the lower surface and beam B’s reflection off of the upper surface. These reflected beams combine to produce a resultant beam (C). If the reflected beams are in phase (as in the first figure) the resultant beam is relatively strong. If, on the other hand, the reflected beams have opposite phase, the resulting beam is attenuated (as in the second figure). The phase relationship of the two reflected beams depends on the relationship between the wavelength of beam A in the film, and the film's thickness. If the total distance beam A travels in the film is an integer multiple of the wavelength of the beam in the film, then the two reflected beams are in phase and constructively interfere (as depicted in the first figure). If the distance traveled by beam A is an odd integer multiple of the half wavelength of light in the film, the beams destructively interfere (as in the second figure). Thus, the film shown in these figures reflects more strongly at the wavelength of the light beam in the first figure, and less strongly at that of the beam in the second figure.


Examples

The type of interference that occurs when light is reflected from a thin film is dependent upon the wavelength and angle of the incident light, the thickness of the film, the refractive indices of the material on either side of the film, and the index of the film medium. Various possible film configurations and the related equations are explained in more detail in the examples below.


Soap bubble

In the case of a
soap bubble A soap bubble (commonly referred to as simply a bubble) is an extremely thin soap film, film of soap or detergent and water enclosing air that forms a hollow sphere with an iridescent surface. Soap bubbles usually last for only a few seconds b ...
, light travels through air and strikes a soap film. The air has a refractive index of 1 (n_ = 1) and the film has an index that is larger than 1 (n_ > 1). The reflection that occurs at the upper boundary of the film (the air-film boundary) will introduce a 180° phase shift in the reflected wave because the refractive index of the air is less than the index of the film (n_ < n_). Light that is transmitted at the upper air-film interface will continue to the lower film-air interface where it can be reflected or transmitted. The reflection that occurs at this boundary will not change the phase of the reflected wave because n_ > n_. The condition for interference for a soap bubble is the following: :2n_d\cos(\theta_2)=\left(m-\frac\right)\lambda for constructive interference of reflected light :2n_d\cos\big(\theta_2)=m\lambda for destructive interference of reflected light Where d is the film thickness, n_ is the refractive index of the film, \theta_2 is the angle of incidence of the wave on the lower boundary, m is an integer, and \lambda is the wavelength of light.


Oil film

In the case of a thin oil film, a layer of oil sits on top of a layer of water. The oil may have an index of refraction near 1.5 and the water has an index of 1.33. As in the case of the soap bubble, the materials on either side of the oil film (air and water) both have refractive indices that are less than the index of the film. n_ < n_ < n_. There will be a phase shift upon reflection from the upper boundary because n_ but no shift upon reflection from the lower boundary because n_>n_. The equations for interference will be the same. :2n_d\cos(\theta_2)=\left(m-\frac\right)\lambda for constructive interference of reflected light :2n_d\cos\big(\theta_2)=m\lambda for destructive interference of reflected light


Anti-reflection coatings

An anti-reflection coating eliminates reflected light and maximizes transmitted light in an optical system. A film is designed such that reflected light produces destructive interference and transmitted light produces constructive interference for a given wavelength of light. In the simplest implementation of such a coating, the film is created so that its optical thickness d n_ is a quarter-wavelength of the incident light and its refractive index is greater than the index of air and less than the index of glass. :n_ :d=\lambda/(4 n_) A 180° phase shift will be induced upon reflection at both the top and bottom interfaces of the film because n_ and n_. The equations for interference of the reflected light are: :2n_d\cos\big(\theta_2)=m\lambda for constructive interference :2n_d\cos(\theta_2)=\left(m-\frac\right)\lambda for destructive interference If the optical thickness d n_ is equal to a quarter-wavelength of the incident light and if the light strikes the film at normal incidence (\theta_2 = 0), the reflected waves will be completely out of phase and will destructively interfere. Further reduction in reflection is possible by adding more layers, each designed to match a specific wavelength of light. Interference of transmitted light is completely constructive for these films.


In nature

Structural coloration Structural coloration in animals, and a few plants, is the production of colour by microscopically structured surfaces fine enough to interfere with visible light instead of Biological pigment, pigments, although some structural coloration occu ...
due to thin-film layers is common in the natural world. The wings of many insects act as thin films because of their minimal thickness. This is clearly visible in the wings of many flies and wasps. In butterflies, the thin-film optics are visible when the wing itself is not covered by pigmented wing scales, which is the case in the blue wing spots of the ''
Aglais io ''Aglais io'', the European peacock, or the peacock butterfly, is a colourful butterfly, found in Europe and temperate Asia as far east as Japan. The peacock butterfly is resident in much of its range, often wintering in buildings or trees. It th ...
'' butterfly. The glossy appearance of buttercup flowers is also due to a thin film as well as the shiny breast feathers of the bird of paradise. File:Peacock butterfly (inachis io) 2.jpg, The blue wing patches of the European peacock butterfly (''Aglais io'') are due to thin-film interference. File:Ranunculus macro.jpg, The gloss of
buttercup ''Ranunculus'' is a large genus of about 1750 species of flowering plants in the family Ranunculaceae. Members of the genus are known as buttercups, spearworts and water crowfoots. The genus is distributed worldwide, primarily in temperate an ...
flowers is due to thin-film interference.


Applications

Thin films are used commercially in anti-reflection coatings, mirrors, and optical filters. They can be engineered to control the amount of light reflected or transmitted at a surface for a given wavelength. A Fabry–Pérot etalon takes advantage of thin film interference to selectively choose which wavelengths of light are allowed to transmit through the device. These films are created through deposition processes in which material is added to a substrate in a controlled manner. Methods include
chemical vapor deposition Chemical vapor deposition (CVD) is a vacuum deposition method used to produce high-quality, and high-performance, solid materials. The process is often used in the semiconductor industry to produce thin films. In typical CVD, the wafer (electro ...
and various
physical vapor deposition Physical vapor deposition (PVD), sometimes called physical vapor transport (PVT), describes a variety of vacuum deposition methods which can be used to produce thin films and coatings on substrates including metals, ceramics, glass, and polym ...
techniques. Thin films are also found in nature. Many animals have a layer of tissue behind the
retina The retina (; or retinas) is the innermost, photosensitivity, light-sensitive layer of tissue (biology), tissue of the eye of most vertebrates and some Mollusca, molluscs. The optics of the eye create a focus (optics), focused two-dimensional ...
, the
Tapetum lucidum The ; ; : tapeta lucida) is a layer of tissue in the eye of many vertebrates and some other animals. Lying immediately behind the retina, it is a retroreflector. It Reflection (physics), reflects visible light back through the retina, increas ...
, that aids in light collecting. The effects of thin-film interference can also be seen in oil slicks and soap bubbles. The reflectance spectrum of a thin-film features distinct oscillations and the extrema of the spectrum can be used to calculate the thickness of the thin-film.
Ellipsometry Ellipsometry is an optical technique for investigating the dielectric properties (complex refractive index or dielectric function) of thin films. Ellipsometry measures the change of polarization upon reflection or transmission and compares it ...
is a technique that is often used to measure properties of thin films. In a typical ellipsometry experiment polarized light is reflected off a film surface and is measured by a detector. The complex reflectance ratio, \rho, of the system is measured. A model analysis is then conducted, in which the information is used to determine film layer thicknesses and refractive indices.
Dual polarisation interferometry Dual-polarization interferometry (DPI) is an analytical technique that probes molecular layers adsorbed to the surface of a waveguide using the evanescent wave of a laser beam. It is used to measure the conformational change in proteins, or o ...
is an emerging technique for measuring refractive index and thickness of molecular scale thin films and how these change when stimulated.


History

Iridescence Iridescence (also known as goniochromism) is the phenomenon of certain surfaces that appear gradually to change colour as the angle of view or the angle of illumination changes. Iridescence is caused by wave interference of light in microstru ...
caused by thin-film interference is a commonly observed phenomenon in nature, being found in a variety of plants and animals. One of the first known studies of this phenomenon was conducted by
Robert Hooke Robert Hooke (; 18 July 16353 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist, and architect. He is credited as one of the first scientists to investigate living ...
in 1665. In ''
Micrographia ''Micrographia: or Some Physiological Descriptions of Minute Bodies Made by Magnifying Glasses. With Observations and Inquiries Thereupon'' is a historically significant book by Robert Hooke about his observations through various lenses. It wa ...
'', Hooke postulated that the iridescence in
peacock Peafowl is a common name for two bird species of the genus '' Pavo'' and one species of the closely related genus '' Afropavo'' within the tribe Pavonini of the family Phasianidae (the pheasants and their allies). Male peafowl are referred t ...
feathers was caused by thin, alternating layers of plate and air. In 1704,
Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
stated in his book, ''
Opticks ''Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light'' is a collection of three books by Isaac Newton that was published in English language, English in 1704 (a scholarly Latin translation appeared in 1706). ...
'', that the iridescence in a peacock feather was due to the fact that the transparent layers in the feather were so thin.''Structural colors in the realm of nature'' By Shūichi Kinoshita – World Scientific Publishing 2008 pages 3–6 In 1801, Thomas Young provided the first explanation of constructive and destructive interference. Young's contribution went largely unnoticed until the work of
Augustin Fresnel Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Isaac Newton, Newton's c ...
, who helped to establish the wave theory of light in 1816.''Thin-film optical filters'' By Hugh Angus Macleod – Institute of Physics Publishing 2001 Pages 1–4 However, very little explanation could be made of the iridescence until the 1870s, when James Maxwell and
Heinrich Hertz Heinrich Rudolf Hertz (; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's equations of electromagnetism. Biography Heinri ...
helped to explain the electromagnetic nature of light. After the invention of the Fabry–Perot interferometer, in 1899, the mechanisms of thin-film interference could be demonstrated on a larger scale. In much of the early work, scientists tried to explain iridescence, in animals like peacocks and
scarab beetle The family Scarabaeidae, as currently defined, consists of over 35,000 species of beetles worldwide; they are often called scarabs or scarab beetles. The classification of this family has undergone significant change. Several groups formerly tre ...
s, as some form of surface color, such as a dye or pigment that might alter the light when reflected from different angles. In 1919,
Lord Rayleigh John William Strutt, 3rd Baron Rayleigh ( ; 12 November 1842 – 30 June 1919), was an English physicist who received the Nobel Prize in Physics in 1904 "for his investigations of the densities of the most important gases and for his discovery ...
proposed that the bright, changing colors were not caused by dyes or pigments, but by microscopic structures, which he termed " structural colors." In 1923, C. W. Mason noted that the barbules in the peacock feather were made from very thin layers. Some of these layers were colored while others were transparent. He noticed that pressing the barbule would shift the color toward the blue, while swelling it with a chemical would shift it toward the red. He also found that bleaching the pigments from the feathers did not remove the iridescence. This helped to dispel the surface color theory and reinforce the structural color theory.''Structural colors in the realm of nature'' By Shūichi Kinoshita - World Scientific Publishing 2008 Page 165–167 In 1925, Ernest Merritt, in his paper ''A Spectrophotometric Study of Certain Cases of Structural Color'', first described the process of thin-film interference as an explanation for the iridescence. The first examination of iridescent feathers by an
electron microscope An electron microscope is a microscope that uses a beam of electrons as a source of illumination. It uses electron optics that are analogous to the glass lenses of an optical light microscope to control the electron beam, for instance focusing it ...
occurred in 1939, revealing complex thin-film structures, while an examination of the
morpho Morpho may refer to: * ''Morpho'' (genus), a genus of butterflies * Morpho (VTOL), a Swiss prototype drone * Morpho (company) IDEMIA (formerly known as OT-Morpho) is a French multinational technology company headquartered in Courbevoie, Fra ...
butterfly Butterflies are winged insects from the lepidopteran superfamily Papilionoidea, characterized by large, often brightly coloured wings that often fold together when at rest, and a conspicuous, fluttering flight. The oldest butterfly fossi ...
, in 1942, revealed an extremely tiny array of thin-film structures on the nanometer scale. The first production of thin-film coatings occurred quite by accident. In 1817,
Joseph Fraunhofer Joseph Ritter von Fraunhofer (; ; 6 March 1787 – 7 June 1826) was a German physicist and optical lens manufacturer. He made optical glass, an achromatic telescope, and objective lenses. He developed diffraction grating and also invented the s ...
discovered that, by tarnishing
glass Glass is an amorphous (non-crystalline solid, non-crystalline) solid. Because it is often transparency and translucency, transparent and chemically inert, glass has found widespread practical, technological, and decorative use in window pane ...
with
nitric acid Nitric acid is an inorganic compound with the formula . It is a highly corrosive mineral acid. The compound is colorless, but samples tend to acquire a yellow cast over time due to decomposition into nitrogen oxide, oxides of nitrogen. Most com ...
, he could reduce the reflections on the surface. In 1819, after watching a layer of alcohol evaporate from a sheet of glass, Fraunhofer noted that colors appeared just before the liquid evaporated completely, deducing that any thin film of transparent material will produce colors. Little advancement was made in thin-film coating technology until 1936, when John Strong began evaporating
fluorite Fluorite (also called fluorspar) is the mineral form of calcium fluoride, CaF2. It belongs to the halide minerals. It crystallizes in isometric cubic habit, although octahedral and more complex isometric forms are not uncommon. The Mohs scal ...
in order to make anti-reflection coatings on glass. During the 1930s, improvements in
vacuum pump A vacuum pump is a type of pump device that draws gas particles from a sealed volume in order to leave behind a partial vacuum. The first vacuum pump was invented in 1650 by Otto von Guericke, and was preceded by the suction pump, which dates to ...
s made
vacuum deposition Vacuum deposition is a group of processes used to deposit layers of material atom-by-atom or molecule-by-molecule on a solid surface. These processes operate at pressures well below atmospheric pressure (i.e., vacuum). The deposited layers can r ...
methods, like
sputtering In physics, sputtering is a phenomenon in which microscopic particles of a solid material are ejected from its surface, after the material is itself bombarded by energetic particles of a plasma or gas. It occurs naturally in outer space, and c ...
, possible. In 1939, Walter H. Geffcken created the first
interference filter An interference filter, dichroic filter, or thin-film filter is an optical filter that Reflection (physics), reflects some wavelengths (colors) of light and transmits others, with almost no absorption (optics), absorption for all wavelengths of i ...
s using
dielectric In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...
coatings.


See also

*
Reflectometric interference spectroscopy Reflectometric interference spectroscopy (RIfS) is a physical method based on the interference of white light at thin films, which is used to investigate molecular interaction. Principle The underlying measuring principle corresponds to that of the ...
*
Thin-film optics Thin-film optics is the branch of optics that deals with very thin structured layers of different materials. In order to exhibit thin-film optics, the thickness of the layers of material must be similar to the coherence length; for visible ...
*
Transfer-matrix method (optics) The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic wave, electromagnetic or acoustic waves through a stratified medium; a stack of thin films. This is, for example, relevant for the ...


References


Further reading

* * * * {{Citation , last = Knittl , first = Zdeněk , title=Optics of Thin Films; An Optical Multilayer Theory , year = 1976 , publisher = Wiley, bibcode = 1976otf..book.....K * D.G. Stavenga
Thin film and multilayer optics cause structural colors of many insects and birds
Materials today: Proceedings, 1S, 109 – 121 (2014). Thin-film optics