A rugate filter, also known as a gradient-index filter, is an optical filter based on a dielectric mirror that selectively reflects specific wavelength ranges of light. This effect is achieved by a periodic, continuous change of the refractive index of the dielectric coating. [2] The word "rugate" is derived from corrugated structures found in nature, which also selectively reflect certain wavelength ranges of light, [3] for example the wings of the Morpho butterfly. [4]
In rugate filters the refractive index varies periodically and continuously as a function of the depth of the mirror coating. This is similar to Bragg mirrors with the difference that the refractive index profile of a Bragg mirror is discontinuous. The refractive index profiles of a Rugate and a Bragg mirror are shown in the graph on the right. In Bragg mirrors, the discontinuous transitions are responsible for reflection of incident light, whereas in rugate filters, incident light is reflected throughout the thickness of the coating. According to the Fresnel equations, however, the reflection coefficient is greatest where the greatest change in refractive index occurs. For rugate filters, these are the inflection points in the refractive index profile. The theory of the Bragg mirror leads to a calculation of the wavelength at which the reflection of a rugate filter is greatest. For an alternating sequence in the Bragg mirror, the maximum reflection at a wavelength is:
In this equation and stand for the high and low refractive indices of the Bragg mirror while and are the respective thicknesses of these layers. For the more general case that the refractive index changes continuously, the previous equation can be rewritten as:
On the left hand side is the integral over the refractive index over one period of the refractive index profile divided by the period length . This term corresponds to the mean value of the refractive index profile. [5] As a sanity check for the correctness of this equation, one can solve the integral for a discrete refractive index profile and substitute the period of a Bragg mirror .
The figure on the right shows the reflection spectra calculated by the transfer-matrix method for the refractive index profiles of a Bragg and Rugate filter. It can be seen that both mirrors have their maximum reflectivity at 700 nm, whereas the rugate filter has a lower bandwidth. For this reason rugate filters are often used as optical notch filters. Furthermore, one can see a smaller peak in the spectrum of the rugate filter at . This peak is not present in the spectrum of the Bragg mirror because of its discrete layer system, which causes destructive interference at this wavelength. However, Bragg mirrors have secondary maxima at wavelengths of , which may be undesirable if you only want to filter out a certain wavelength. Rugate filters are better suited for this purpose because the sinusoidal refractive index profile has anti-reflection properties similar to those of black silicon. This reduces the intensity of the secondary maxima. [5]
Rugate filters can be produced by sputtering [6] and chemical vapor deposition. [7] A special challenge is the creation of the continuous refractive index profile. To achieve this, the chemical composition of the mirror must also change continuously as a function of the layer thickness. This can be achieved by continuously changing the gas composition during the deposition process. Another possibility for the production of rugate filters is electrochemical porosification of silicon. Here, the current density during the etching process is selected so that the resulting porosity and thus the refractive index varies sinusoidally with the layer thickness. [8]
In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
In optics, a diffraction grating is an optical grating with a periodic structure that diffracts light into several beams traveling in different directions. The emerging coloration is a form of structural coloration. The directions or diffraction angles of these beams depend on the wave (light) incident angle to the diffraction grating, the spacing or distance between adjacent diffracting elements on the grating, and the wavelength of the incident light. The grating acts as a dispersive element. Because of this, diffraction gratings are commonly used in monochromators and spectrometers, but other applications are also possible such as optical encoders for high-precision motion control and wavefront measurement.
In physics and chemistry, Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a large crystal lattice. It encompasses the superposition of wave fronts scattered by lattice planes, leading to a strict relation between wavelength and scattering angle, or else to the wavevector transfer with respect to the crystal lattice. Such law had initially been formulated for X-rays upon crystals. However, it applies to all sorts of quantum beams, including neutron and electron waves at atomic distances if there are a large number of atoms, as well as visible light with artificial periodic microscale lattices.
An optical coating is one or more thin layers of material deposited on an optical component such as a lens, prism or mirror, which alters the way in which the optic reflects and transmits light. These coatings have become a key technology in the field of optics. One type of optical coating is an anti-reflective coating, which reduces unwanted reflections from surfaces, and is commonly used on spectacle and camera lenses. Another type is the high-reflector coating, which can be used to produce mirrors that reflect greater than 99.99% of the light that falls on them. More complex optical coatings exhibit high reflection over some range of wavelengths, and anti-reflection over another range, allowing the production of dichroic thin-film filters.
An optical ring resonator is a set of waveguides in which at least one is a closed loop coupled to some sort of light input and output. The concepts behind optical ring resonators are the same as those behind whispering galleries except that they use light and obey the properties behind constructive interference and total internal reflection. When light of the resonant wavelength is passed through the loop from the input waveguide, the light builds up in intensity over multiple round-trips owing to constructive interference and is output to the output bus waveguide which serves as a detector waveguide. Because only a select few wavelengths will be at resonance within the loop, the optical ring resonator functions as a filter. Additionally, as implied earlier, two or more ring waveguides can be coupled to each other to form an add/drop optical filter.
In optics, an ARROW is a type of waveguide that uses the principle of thin-film interference to guide light with low loss. It is formed from an anti-resonant Fabry–Pérot reflector. The optical mode is leaky, but relatively low-loss propagation can be achieved by making the Fabry–Pérot reflector of sufficiently high quality or small size.
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 efficiency since less light is lost due to reflection. In complex systems such as cameras, binoculars, telescopes, and microscopes the reduction in reflections also improves the contrast of the image by elimination of stray light. This is especially important in planetary astronomy. In other applications, the primary benefit is the elimination of the reflection itself, such as a coating on eyeglass lenses that makes the eyes of the wearer more visible to others, or a coating to reduce the glint from a covert viewer's binoculars or telescopic sight.
A dielectric mirror, also known as a Bragg mirror, is a type of mirror composed of multiple thin layers of dielectric material, typically deposited on a substrate of glass or some other optical material. By careful choice of the type and thickness of the dielectric layers, one can design an optical coating with specified reflectivity at different wavelengths of light. Dielectric mirrors are also used to produce ultra-high reflectivity mirrors: values of 99.999% or better over a narrow range of wavelengths can be produced using special techniques. Alternatively, they can be made to reflect a broad spectrum of light, such as the entire visible range or the spectrum of the Ti-sapphire laser.
A fiber Bragg grating (FBG) is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by creating a periodic variation in the refractive index of the fiber core, which generates a wavelength-specific dielectric mirror. Hence a fiber Bragg grating can be used as an inline optical fiber to block certain wavelengths, can be used for sensing applications, or it can be used as wavelength-specific reflector.
A distributed Bragg reflector (DBR) is a reflector used in waveguides, such as optical fibers. It is a structure formed from multiple layers of alternating materials with different refractive index, or by periodic variation of some characteristic of a dielectric waveguide, resulting in periodic variation in the effective refractive index in the guide. Each layer boundary causes a partial reflection and refraction of an optical wave. For waves whose vacuum wavelength is close to four times the optical thickness of the layers, the interaction between these beams generates constructive interference, and the layers act as a high-quality reflector. The range of wavelengths that are reflected is called the photonic stopband. Within this range of wavelengths, light is "forbidden" to propagate in the structure.
X-ray optics is the branch of optics that manipulates X-rays instead of visible light. It deals with focusing and other ways of manipulating the X-ray beams for research techniques such as X-ray crystallography, X-ray fluorescence, small-angle X-ray scattering, X-ray microscopy, X-ray phase-contrast imaging, and X-ray astronomy.
Fluorescence interference contrast (FLIC) microscopy is a microscopic technique developed to achieve z-resolution on the nanometer scale.
Athermalization, in the field of optics, is the process of achieving optothermal stability in optomechanical systems. This is done by minimizing variations in optical performance over a range of temperatures.
Acousto-optics is a branch of physics that studies the interactions between sound waves and light waves, especially the diffraction of laser light by ultrasound through an ultrasonic grating.
Volume holograms are holograms where the thickness of the recording material is much larger than the light wavelength used for recording. In this case diffraction of light from the hologram is possible only as Bragg diffraction, i.e., the light has to have the right wavelength (color) and the wave must have the right shape. Volume holograms are also called thick holograms or Bragg holograms.
The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium; a stack of thin films. This is, for example, relevant for the design of anti-reflective coatings and dielectric mirrors.
Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film 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 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 bubbles and oil films on water. It is also the mechanism behind the action of antireflection coatings used on glasses and camera lenses. 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 of the light source.
Resonant-cavity-enhanced photodetectors, also known as RCE photodetectors, sensors designed to detect light or other forms of electromagnetic radiation. They achieve this by employing an optical cavity, a configuration of mirrors or other optical elements that forms a cavity resonator for light waves, allowing more efficient targeting of specific wavelengths.
Holographic optical element (HOE) is an optical component (mirror, lens, directional diffuser, etc.) that produces holographic images using principles of diffraction. HOE is most commonly used in transparent displays, 3D imaging, and certain scanning technologies. The shape and structure of the HOE is dependent on the piece of hardware it is needed for, and the coupled wave theory is a common tool used to calculate the diffraction efficiency or grating volume that helps with the design of an HOE. Early concepts of the holographic optical element can be traced back to the mid-1900s, coinciding closely with the start of holography coined by Dennis Gabor. The application of 3D visualization and displays is ultimately the end goal of the HOE; however, the cost and complexity of the device has hindered the rapid development toward full 3D visualization. The HOE is also used in the development of augmented reality(AR) by companies such as Google with Google Glass or in research universities that look to utilize HOEs to create 3D imaging without the use of eye-wear or head-wear. Furthermore, the ability of the HOE to allow for transparent displays have caught the attention of the US military in its development of better head-up displays (HUD) which is used to display crucial information for aircraft pilots.
A nanophotonic resonator or nanocavity is an optical cavity which is on the order of tens to hundreds of nanometers in size. Optical cavities are a major component of all lasers, they are responsible for providing amplification of a light source via positive feedback, a process known as amplified spontaneous emission or ASE. Nanophotonic resonators offer inherently higher light energy confinement than ordinary cavities, which means stronger light-material interactions, and therefore lower lasing threshold provided the quality factor of the resonator is high. Nanophotonic resonators can be made with photonic crystals, silicon, diamond, or metals such as gold.
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