Thin-film interference is a natural phenomenon in which
light wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) l ...
s reflected by the upper and lower boundaries of a
thin film
A thin film is a layer of material 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, either enhancing or reducing the
reflected light. When the thickness of the film is an odd multiple of one quarter-
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
of the light on it, the reflected waves from both surfaces interfere to cancel each other. Since the wave cannot be reflected, it is completely
transmitted instead. When the thickness is a multiple of a half-wavelength of the light, the two reflected waves reinforce each other, increasing the reflection and reducing the transmission. Thus when white light, which consists of a range of wavelengths, is incident on the film, certain wavelengths (colors) are intensified while others are
attenuated. Thin-film interference explains the multiple colors seen in light reflected from
soap bubble
A soap bubble is an extremely thin 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 before bursting, either on their own or on contact wi ...
s and
oil films on
water
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
. It is also the mechanism behind the action of
antireflection coatings used on
glasses
Glasses, also known as eyeglasses or spectacles, are vision eyewear, with lenses (clear or tinted) mounted in a frame that holds them in front of a person's eyes, typically utilizing a bridge over the nose and hinged arms (known as temples ...
and
camera lens
A camera lens (also known as photographic lens or photographic objective) is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media cap ...
es. If the thickness of the film is much larger than the
coherence length
In physics, coherence length is the propagation distance over which a coherent wave (e.g. an electromagnetic wave) maintains a specified degree of coherence. Wave interference is strong when the paths taken by all of the interfering waves di ...
of the incident light, then the interference pattern will be washed out due to the
linewidth
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to ident ...
of the light source.
The true thickness of the film depends on both its refractive index and on the
angle of incidence of the light. The speed of light is slower in a higher-index medium; thus a film is manufactured in proportion to the wavelength as it passes through the film. At a normal angle of incidence, the thickness will typically be a quarter or half multiple of the center wavelength, but at an oblique angle of incidence, the thickness will be equal to the
cosine of the angle at the quarter or half-wavelength positions, which accounts for the changing colors as the viewing angle changes. (For any certain thickness, the color will shift from a shorter to a longer wavelength as the angle changes from normal to oblique.) This constructive/destructive interference produces narrow reflection/transmission bandwidths, so the observed colors are rarely separate wavelengths, such as produced by a
diffraction grating
In optics, a diffraction grating is an optical component with a periodic structure that diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structur ...
or
prism, but a mixture of various wavelengths absent of others in the spectrum. Therefore, the colors observed are rarely those of the rainbow, but 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 a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, ...
of the film medium. Thin films have many commercial applications including
anti-reflection coatings,
mirror
A mirror or looking glass is an object that reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the direction of the im ...
s, and
optical filters.
Theory
In optics, a
thin film
A thin film is a layer of material 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 molecular scale.
The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re, ...
to
micron
The micrometre ( international spelling as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American spelling), also commonly known as a micron, is a unit of length in the International System of Un ...
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 Augustin-Jean Fres ...
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 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
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
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:
:
Where,
:
:
Using
Snell's law
Snell's law (also known as Snell–Descartes law and 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 throug ...
,
:
Interference will be constructive if the optical path difference is equal to an integer multiple of the wavelength of light,
.
:
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, monochro ...
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 ...
," 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 optical-grade piece of glass lapped and 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 light to determine the flatn ...
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 is an extremely thin 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 before bursting, either on their own or on contact wi ...
, light travels through air and strikes a soap film. The air has a refractive index of 1 (
) and the film has an index that is larger than 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 (
). 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
. The condition for interference for a soap bubble is the following:
:
for constructive interference of reflected light
:
for destructive interference of reflected light
Where
is the film thickness,
is the refractive index of the film,
is the angle of incidence of the wave on the lower boundary,
is an integer, and
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.
. There will be a phase shift upon reflection from the upper boundary because