A prism coupler is a
prism
Prism usually refers to:
* Prism (optics), a transparent optical component with flat surfaces that refract light
* Prism (geometry), a kind of polyhedron
Prism may also refer to:
Science and mathematics
* Prism (geology), a type of sedimentary ...
designed to couple a substantial fraction of the power contained in a beam of light (e.g., a laser beam) into a thin film to be used as a
waveguide
A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities de ...
without the need for precision polishing of the edge of the film, without the need for sub-
micrometer Micrometer can mean:
* Micrometer (device), used for accurate measurements by means of a calibrated screw
* American spelling of micrometre
The micrometre ( international spelling as used by the International Bureau of Weights and Measures; ...
alignment precision of the beam and the edge of the film, and without the need for matching the
numerical aperture
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the proper ...
of the beam to the film. Using a prism coupler, a beam coupled into a thin film can have a diameter hundreds of times the thickness of the film. Invention of the coupler contributed to the initiation of a field of study known as
integrated optics
A photonic integrated circuit (PIC) or integrated optical circuit is a microchip containing two or more photonic components which form a functioning circuit. This technology detects, generates, transports, and processes light. Photonic integrated c ...
.
History
The theory underlying the prism coupler was first published in the
Soviet Union
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...
. This work was not known in the US. Starting in 1969, Shubert, Harris, and Polky at the
University of Washington
The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington.
Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle a ...
, and, independently, Tien, Ulrich, and Martin, at
Bell Laboratories
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984),
then AT&T Bell Laboratories (1984–1996)
and Bell Labs Innovations (1996–2007),
is an American industrial research and scientific development company owned by mult ...
described the first experiments with prism coupling and its underlying theory. This was done with a view toward device applications of thin films.
Configuration
A prism coupler is used to couple the power from an incident laser beam into a thin film. The film lies on a substrate such as a glass microscope slide and might have a thickness of the order of the wavelength of the
incident light
In optics a ray is an idealized geometrical model of light, obtained by choosing a curve that is perpendicular to the ''wavefronts'' of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation o ...
(0.550 μm for green light). The refractive index of the film is made greater than that of the glass slide, the film can serve as a dielectric planar waveguide for light via
total internal reflection
Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...
off the film–glass interface (and film–air interface). The prism coupler consists of a near cube of high–
refractive-index glass and a second thin film at the bottom that contacts the
waveguide film and serves the function of partially containing the guided wave over the coupling distance. The thin film at the bottom of the prism is referred to as the ''tunneling layer''. The tunneling layer must have a lower
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, or ...
than the waveguide film and may actually be implemented as a layer of air. The thickness of the tunneling layer will be on the order of a fraction of a wavelength (tens to hundreds of nanometers for visible light).
The prism and tunneling layer are pressed against the waveguide film. The beam enters the front face of the prism and strikes the tunneling layer somewhat more than half a beam width away from the face opposite the entry face of the prism. The ranking of refractive indices of the four regions of the combined coupler and waveguide structure must be as follows: the refractive index of the glass slide and the tunneling layer must be lowest, next is the refractive index of the guide film, and highest is the index of the prism.
Theory
A prism coupler may be explained in terms of the
reciprocity theorem. The reciprocity theorem permits the relative power coupled into the thin film by an incident beam to be computed from the solution to a reciprocal problem. In the reciprocal problem, a waveguide mode in the film (travelling to the left in the first figure) is incident on the prism coupler. Barring significant scattering at the prism interface, the waveguide mode in the reciprocal problem retains its form as a mode and propagates under the prism, losing power as it propagates due to radiation into the prism. The power in the prism emerges as a
collimated beam
A collimated beam of light or other electromagnetic radiation has parallel rays, and therefore will spread minimally as it propagates. A perfectly collimated light beam, with no divergence, would not disperse with distance. However, diffraction pr ...
at an angle determined by the propagation constant of the waveguide mode and the refractive index of the prism. Radiation into the prism occurs because the evanescent tail of the waveguide mode touches the bottom of the prism. The waveguide mode
tunnels
A tunnel is an underground passageway, dug through surrounding soil, earth or rock, and enclosed except for the entrance and exit, commonly at each end. A pipeline is not a tunnel, though some recent tunnels have used immersed tube constr ...
through the tunneling layer.
Efficient coupling of light into the film occurs when the
incident beam (arriving from the left shown in the first figure), evaluated at the bottom face of the prism, has the same shape as the radiated beam in the reciprocal problem. When the power in both the incident beam and the reciprocal waveguide mode is normalized, the fractional coupling amplitude is expressed as an
integral
In mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...
over the product of the incident wave and the radiated reciprocal field. The integral is a surface integral taken over the bottom face of the prism. From such an integral we deduce three key features:
# To couple in a significant fraction of the incident power, the incident beam must arrive at the angle that renders it phase matched to the waveguide mode.
# The transverse behavior of the waveguide mode launched in the film (
transverse
Transverse may refer to:
*Transverse engine, an engine in which the crankshaft is oriented side-to-side relative to the wheels of the vehicle
*Transverse flute, a flute that is held horizontally
* Transverse force (or ''Euler force''), the tangen ...
to the direction of propagation) will be essentially that of the incident beam.
# If the thickness of the tunneling layer is adjusted appropriately, it is possible, in principle, to couple nearly all the light in the beam into the waveguide film.
Suppressing the transverse part of the representation for the fields, and taking x as direction to the left in Fig. 1, the waveguide mode in the reciprocal problem takes the monotonically decreasing form
:
where α(''x'') is the attenuation rate and
is the
propagation constant
The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a cir ...
of the waveguide mode.
The associated transverse field at the bottom of the prism takes the form
:
with ''A'' a
normalization constant
The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics. The normalizing constant is used to reduce any probability function to a probability density function with total probability of one.
...
.
The transverse field of the incident beam will have the form
:
where ''f''(''x'') is a normalized
Gaussian
Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below.
There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...
, or other beam form, and β
in is the longitudinal component of the propagation constant of the incident beam.
When β
in = β
''w'', integration of
:
yields the coupling amplitude. Adjusting α(''x'') permits the coupling to approach unity, barring significant geometry-dependent diffractive effects.
Remarks
The
Goos-Hänchen shift describes the displacement of the center point of an optical beam when it undergoes total reflection from the interface between two semi-infinite regions of different
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, or ...
. The displacement is generally of the order of the wavelength of light. If the reflection of a beam from a sandwich structure that consists of a semi-infinite prism, a tunneling layer, a waveguide film layer, and a semi-infinite glass slide is investigated, the shift will be found to be much larger as a consequence of the excitation of the guided wave. Terminating the upper (prism) region just beyond the midpoint of the incident beam traps the light of the beam in the waveguide mode in the film.
Excitation of the guided wave by an incident beam can also be viewed as a problem in coupled modes, the modes being the waveguide mode and a representation for the incident beam. Power introduced into one branch of a coupled mode structure can transfer to the other branch along the structure.
Measurement applications
Prism couplers are instruments used to measure the
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, or ...
/
birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
and thickness of
dielectric
In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
and
polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part")
is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
films. Since refractive indices of a material depend upon the
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, tro ...
of the
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
transmitted, a monochromatic
laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
is used in conjunction with a prism of known refractive index. The laser beam is directed through a side of the prism, bent, and is normally reflected back out the opposite side into a photo detector. However, at certain values of the incident angle theta, the beam does not reflect back out, but instead is transmitted through the base into the film sample. These angles are called "mode angles". A computer-driven rotary table varies the incident angle of the
laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
. The first mode angle found determines the refractive index, and the angle difference from one mode to the next determines the sample thickness.
Prism couplers also allow for coupling light in and out of a waveguide without exposing the cross-section of the waveguide (edge coupling). To achieve this a
phase matching
Phase or phases may refer to:
Science
*State of matter, or phase, one of the distinct forms in which matter can exist
*Phase (matter), a region of space throughout which all physical properties are essentially uniform
*Phase space, a mathematica ...
condition is required between the propagation constant of the mth mode in the waveguide
and the
incident light
In optics a ray is an idealized geometrical model of light, obtained by choosing a curve that is perpendicular to the ''wavefronts'' of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation o ...
at an angle
normal from the waveguide surface.
:
where
is the
index of refraction
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, or ...
of the prism.
:
where
is the index of air (~1) and
is the
propagation constant
The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a cir ...
of the waveguide. In order to have a guided mode,
. This would imply that
, which is not possible.
[R. Hunsperger. Integrated Optics. Springer. 1995.]
References
{{reflist
Prisms (optics)