Virtually imaged phased array

Last updated
Function and structure of VIPA Modified Function and structure of VIPA .jpg
Function and structure of VIPA

A virtually imaged phased array (VIPA) is an angular dispersive device that, like a prism or a diffraction grating, splits light into its spectral components. The device works almost independently of polarization. In contrast to prisms or regular diffraction gratings, the VIPA has a much higher angular dispersion but has a smaller free spectral range. This aspect is similar to that of an Echelle grating, since it also uses high diffraction orders. To overcome this disadvantage, the VIPA can be combined with a diffraction grating. The VIPA is a compact spectral disperser with high wavelength resolving power.

Contents

Basic mechanism

In a virtually imaged phased array, the phased array is the optical analogue of a phased array antenna at radio frequencies. Unlike a diffraction grating which can be interpreted as a real phased array, in a virtually imaged phased array the phased array is created in a virtual image. More specifically, the optical phased array is virtually formed with multiple virtual images of a light source. This is the fundamental difference from an Echelle grating, where a similar phased array is formed in the real space. The virtual images of a light source in the VIPA are automatically aligned exactly at a constant interval, which is critical for optical interference. This is an advantage of the VIPA over an Echelle grating. When the output light is observed, the virtually imaged phased array works as if light were emitted from a real phased array.

History and applications

VIPA was proposed and named by Shirasaki in 1996. [1] Prior to the publication in the paper, a preliminary presentation was given by Shirasaki at a conference. [2] This presentation was reported in Laser Focus World. [3] The details of this new approach to producing angular dispersion were described in the patent. [4] Since then, in the first ten years, the VIPA was of particular interest in the field of optical fiber communication technology. The VIPA was first applied to optical wavelength division multiplexing (WDM) and a wavelength demultiplexer was demonstrated for a channel spacing of 0.8 nm, [1] which was a standard channel spacing at the time. Later, a much smaller channel separation of 24 pm and a 3 dB bandwidth of 6 pm were achieved by Weiner in 2005 at 1550 nm wavelength range. [5] For another application, by utilizing the wavelength-dependent length of the light path due to the angular dispersion of the VIPA, the compensation of chromatic dispersion of fibers was studied and demonstrated (Shirasaki, 1997). [6] [7] [8] The compensation was further developed for tunable systems by using adjustable mirrors [9] [10] [11] or a spatial light modulator (Weiner, 2006). [12] Using the VIPA, compensation of polarization mode dispersion was also achieved (Weiner, 2008). [13] Furthermore, pulse shaping using the combination of a VIPA for high-resolution wavelength splitting/recombining and a SLM was demonstrated (Weiner, 2010). [14]

A drawback of the VIPA is its limited free spectral range due to the high diffraction order. To expand the functional wavelength range, Shirasaki combined a VIPA with a regular diffraction grating in 1997 to provide a broadband two-dimensional spectral disperser. [15] This configuration can be a high performance substitute for diffraction gratings in many grating applications. After the mid 2000s, the two-dimensional VIPA disperser has been used in various fields and devices, such as high-resolution WDM (Weiner, 2004), [16] a laser frequency comb (Diddams, 2007), [17] a spectrometer (Nugent-Glandorf, 2012), [18] astrophysical instruments (Le Coarer, 2017, Bourdarot, 2018, and Stacey, 2024), [19] [20] [21] Brillouin spectroscopy in biomechanics (Scarcelli, 2008, Rosa, 2018, and Margueritat, 2020), [22] [23] [24] other Brillouin spectroscopy (Loubeyre, 2022 and Wu, 2023), [25] [26] beam scanning (Ford, 2008), [27] microscopy (Jalali, 2009), [28] tomography imaging (Ellerbee, 2014), [29] metrology (Bhattacharya, 2015), [30] fiber laser (Xu, 2020), [31] LiDAR (Fu, 2021), [32] and surface measurement (Zhu, 2022). [33]

Structure and operational principle

Operational principle of VIPA Modified Operational principle of VIPA.jpg
Operational principle of VIPA

The main component of a VIPA is a glass plate whose normal is slightly tilted with respect to the input light. One side (light input side) of the glass plate is coated with a 100% reflective mirror and the other side (light output side) is coated with a highly reflective but partially transmissive mirror. The side with the 100% reflective mirror has an anti-reflection coated light entrance area, through which a light beam enters the glass plate. The input light is line-focused to a line (focal line) on the partially transmissive mirror on the light output side. A typical line-focusing lens is a cylindrical lens, which is also part of the VIPA. The light beam is diverging after the beam waist located at the line-focused position.

After the light enters the glass plate through the light entrance area, the light is reflected at the partially transmissive mirror and the 100% reflective mirror, and thus the light travels back and forth between the partially transmissive mirror and the 100% reflective mirror.

It is noted that the glass plate is tilted as a result of its slight rotation where the axis of rotation is the focal line. This rotation/tilt prevents the light from leaving the glass plate out of the light entrance area. Therefore, in order for the optical system to work as a VIPA, there is a critical minimum angle of tilt that allows the light entering through the light entrance area to return only to the 100% reflective mirror. [1] Below this angle, the function of the VIPA is severely impaired. If the tilting angle were zero, the reflected light from the partially transmissive mirror would travel exactly in reverse and exit the glass plate through the light entrance area without being reflected by the 100% reflective mirror. In the figure, refraction at the surfaces of the glass plate was ignored for simplicity. [1]

When the light beam is reflected each time at the partially transmissive mirror, a small portion of the light power passes through the mirror and travels away from the glass plate. For a light beam passing through the mirror after multiple reflections, the position of the line-focus can be seen in the virtual image when observed from the light output side. Therefore, this light beam travels as if it originated at a virtual light source located at the position of the line-focus and diverged from the virtual light source. The positions of the virtual light sources for all the transmitted light beams automatically align along the normal to the glass plate with a constant spacing, that is, a number of virtual light sources are superimposed to create an optical phased array. Due to the interference of all the light beams, the phased array emits a collimated light beam in one direction, which is at a wavelength dependent angle, and therefore, an angular dispersion is produced.

Wavelength resolution

Similarly to the resolving power of a diffraction grating, which is determined by the number of the illuminated grating elements and the order of diffraction, the resolving power of a VIPA is determined by the reflectivity of the back surface of the VIPA and the thickness of the glass plate. For a fixed thickness, a high reflectivity causes light to stay longer in the VIPA. This creates more virtual sources of light and thus increases the resolving power. On the other hand, with a lower reflectivity, the light in the VIPA is quickly lost, meaning fewer virtual sources of light are superimposed. This results in lower resolving power.

For large angular dispersion with high resolving power, the dimensions of the VIPA should be accurately controlled. Fine tuning of the VIPA characteristics was demonstrated by developing an elastomer-based structure (Metz, 2013). [34]

A constant reflectivity of the partially transmissive mirror in the VIPA produces a Lorentzian power distribution when the output light is imaged onto a screen, which has a negative effect on the wavelength selectivity. This can be improved by providing the partially transmissive mirror with a linearly decreasing reflectivity. This leads to a Gaussian-like power distribution on a screen and improves the wavelength selectivity or the resolving power. [35]

Spectral dispersion law

An analytical calculation of the VIPA was first performed by Vega and Weiner in 2003 [36] based on the theory of plane waves and an improved model based on the Fresnel diffraction theory was developed by Xiao and Weiner in 2004. [37]

Commercialization of the VIPA

VIPA devices have been commercialized by LightMachinery as spectral disperser devices or components with various customized design parameters.

Related Research Articles

<span class="mw-page-title-main">Optical spectrometer</span> Instrument to measure the properties of visible light

An optical spectrometer is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum, typically used in spectroscopic analysis to identify materials. The variable measured is most often the irradiance of the light but could also, for instance, be the polarization state. The independent variable is usually the wavelength of the light or a closely derived physical quantity, such as the corresponding wavenumber or the photon energy, in units of measurement such as centimeters, reciprocal centimeters, or electron volts, respectively.

<span class="mw-page-title-main">Diffraction grating</span> Optical component which splits light into several beams

In optics, a diffraction grating is an optical grating with a periodic structure that diffracts light, or another type of electromagnetic radiation, 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 periodic 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.

<span class="mw-page-title-main">Chromatic aberration</span> Failure of a lens to focus all colors on the same point

In optics, chromatic aberration (CA), also called chromatic distortion, color aberration, color fringing, or purple fringing, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the wavelength of light. The refractive index of most transparent materials decreases with increasing wavelength. Since the focal length of a lens depends on the refractive index, this variation in refractive index affects focusing. Since the focal length of the lens varies with the color of the light different colors of light are brought to focus at different distances from the lens or with different levels of magnification. Chromatic aberration manifests itself as "fringes" of color along boundaries that separate dark and bright parts of the image.

<span class="mw-page-title-main">Prism (optics)</span> Transparent optical element with flat, polished surfaces that refract light

An optical prism is a transparent optical element with flat, polished surfaces that are designed to refract light. At least one surface must be angled — elements with two parallel surfaces are not prisms. The most familiar type of optical prism is the triangular prism, which has a triangular base and rectangular sides. Not all optical prisms are geometric prisms, and not all geometric prisms would count as an optical prism. Prisms can be made from any material that is transparent to the wavelengths for which they are designed. Typical materials include glass, acrylic and fluorite.

<span class="mw-page-title-main">Photonic crystal</span> Periodic optical nanostructure that affects the motion of photons

A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of natural crystals gives rise to X-ray diffraction and that the atomic lattices of semiconductors affect their conductivity of electrons. Photonic crystals occur in nature in the form of structural coloration and animal reflectors, and, as artificially produced, promise to be useful in a range of applications.

Liquid crystal on silicon is a miniaturized reflective active-matrix liquid-crystal display or "microdisplay" using a liquid crystal layer on top of a silicon backplane. It is also known as a spatial light modulator. LCoS initially was developed for projection televisions, but has since found additional uses in wavelength selective switching, structured illumination, near-eye displays and optical pulse shaping.

<span class="mw-page-title-main">Monochromator</span> Optical device which allows selection of a narrow band of wavelengths from a wider spectrum

A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input. The name is from Greek mono- 'single' chroma 'colour' and Latin -ator 'denoting an agent'.

<span class="mw-page-title-main">Michelson interferometer</span> Common configuration for optical interferometry

The Michelson interferometer is a common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson. Using a beam splitter, a light source is split into two arms. Each of those light beams is reflected back toward the beamsplitter which then combines their amplitudes using the superposition principle. The resulting interference pattern that is not directed back toward the source is typically directed to some type of photoelectric detector or camera. For different applications of the interferometer, the two light paths can be with different lengths or incorporate optical elements or even materials under test.

<span class="mw-page-title-main">Tunable laser</span> Laser with a variable wavelength

A tunable laser is a laser whose wavelength of operation can be altered in a controlled manner. While all laser gain media allow small shifts in output wavelength, only a few types of lasers allow continuous tuning over a significant wavelength range.

Chirped pulse amplification (CPA) is a technique for amplifying an ultrashort laser pulse up to the petawatt level, with the laser pulse being stretched out temporally and spectrally, then amplified, and then compressed again. The stretching and compression uses devices that ensure that the different color components of the pulse travel different distances.

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 diffraction, X-ray crystallography, X-ray fluorescence, small-angle X-ray scattering, X-ray microscopy, X-ray phase-contrast imaging, and X-ray astronomy.

Optical axis gratings (OAGs) are gratings of optical axis of a birefringent material. In OAGs, the birefringence of the material is constant, while the direction of optical axis is periodically modulated in a fixed direction. In this way they are different from the regular phase gratings, in which the refractive index is modulated and the direction of the optical axis is constant.

Digital holography is the acquisition and processing of holograms with a digital sensor array, typically a CCD camera or a similar device. Image rendering, or reconstruction of object data is performed numerically from digitized interferograms. Digital holography offers a means of measuring optical phase data and typically delivers three-dimensional surface or optical thickness images. Several recording and processing schemes have been developed to assess optical wave characteristics such as amplitude, phase, and polarization state, which make digital holography a very powerful method for metrology applications .

<span class="mw-page-title-main">Dispersive prism</span> Device used to disperse light

In optics, a dispersive prism is an optical prism that is used to disperse light, that is, to separate light into its spectral components. Different wavelengths (colors) of light will be deflected by the prism at different angles. This is a result of the prism material's index of refraction varying with wavelength (dispersion). Generally, longer wavelengths (red) undergo a smaller deviation than shorter wavelengths (blue). The dispersion of white light into colors by a prism led Sir Isaac Newton to conclude that white light consisted of a mixture of different colors.

<span class="mw-page-title-main">Echelle grating</span> Type of diffraction grating used in spectrometers

An echelle grating is a type of diffraction grating characterised by a relatively low groove density, but a groove shape which is optimized for use at high incidence angles and therefore in high diffraction orders. Higher diffraction orders allow for increased dispersion (spacing) of spectral features at the detector, enabling increased differentiation of these features. Echelle gratings are, like other types of diffraction gratings, used in spectrometers and similar instruments. They are most useful in cross-dispersed high resolution spectrographs, such as HARPS, PARAS, and numerous other astronomical instruments.

Wavelength selective switching components are used in WDM optical communications networks to route (switch) signals between optical fibres on a per-wavelength basis.

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.

Incoherent broad band cavity enhanced absorption spectroscopy (IBBCEAS), sometimes called broadband cavity enhanced extinction spectroscopy (IBBCEES), measures the transmission of light intensity through a stable optical cavity consisting of high reflectance mirrors (typically R>99.9%). The technique is realized using incoherent sources of radiation e.g. Xenon arc lamps, LEDs or supercontinuum (SC) lasers, hence the name.

In physics, a high contrast grating is a single layer near-wavelength grating physical structure where the grating material has a large contrast in index of refraction with its surroundings. The term near-wavelength refers to the grating period, which has a value between one optical wavelength in the grating material and that in its surrounding materials.

<span class="mw-page-title-main">Electromagnetic metasurface</span>

An electromagnetic metasurface refers to a kind of artificial sheet material with sub-wavelength features. Metasurfaces can be either structured or unstructured with subwavelength-scaled patterns.

References

  1. 1 2 3 4 Shirasaki, M. (1996). "Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer". Optics Letters. 21 (5): 366–8. Bibcode:1996OptL...21..366S. doi:10.1364/OL.21.000366. PMID   19865407.
  2. ↑ Shirasaki, M. (October 1995). Large angular-dispersion by virtually-imaged phased-array (VIPA) and its application to wavelength demultiplexing. 5th Microoptics Conference (MOC'95). Hiroshima, Japan. Paper PD3. Archived from the original on 2023-11-18. Retrieved 2024-10-08.
  3. ↑ "Virtual imaging array splits light into ten wavelengths". Laser Focus World. 31 (12): 30–33. December 1995. Archived from the original on 2024-05-27. Retrieved 2024-10-08.
  4. ↑ USpatent 5,999,320,Shirasaki, M.,"Virtually imaged phased array as a wavelength demultiplexer" Archived 2023-11-19 at the Wayback Machine
  5. ↑ Xiao, S.; Weiner, A. M. (2005). "An eight-channel hyperfine wavelength demultiplexer using a virtually imaged phased-array (VIPA)". IEEE Photonics Technology Letters. 17 (2): 372. Bibcode:2005IPTL...17..372X. doi:10.1109/LPT.2004.839017. S2CID   37277234.
  6. ↑ Shirasaki, M. (July 1997). Chromatic dispersion compensation using virtually imaged phased array. Optical Amplifiers and Their Applications. Victoria, Canada. Paper PDP-8.
  7. ↑ Shirasaki, M. (1997). "Chromatic-dispersion compensator using virtually imaged phased array". IEEE Photonics Technology Letters. 9 (12): 1598–1600. Bibcode:1997IPTL....9.1598S. doi:10.1109/68.643280. S2CID   25043474.
  8. ↑ Shirasaki, M.; Cao, S. (March 2001). Compensation of chromatic dispersion and dispersion slope using a virtually imaged phased array. 2001 Optical Fiber Communication Conference. Anaheim, CA. Paper TuS1. Archived from the original on 2020-03-17. Retrieved 2019-05-15.
  9. ↑ Shirasaki, M.; Kawahata, Y.; Cao, S.; Ooi, H.; Mitamura, N.; Isono, H.; Ishikawa, G.; Barbarossa, G.; Yang, C.; Lin, C. (September 2000). Variable dispersion compensator using the virtually imaged phased array (VIPA) for 40-Gbit/s WDM transmission systems. 2000 European Conference on Optical Communication. Munich, Germany. Paper PD-2.3.
  10. ↑ Garrett, L. D.; Gnauck, A. H.; Eiselt, M. H.; Tkach, R. W.; Yang, C.; Mao, C.; Cao, S. (March 2000). Demonstration of virtually-imaged phased-array device for tunable dispersion compensation in 16 X10 Gb/s WDM transmission over 480 km standard fiber. 2000 Optical Fiber Communication Conference. Baltimore, MD. Paper PD7. Archived from the original on 2020-03-10. Retrieved 2019-05-15.
  11. ↑ Cao, S.; Lin, C.; Barbarossa, G.; Yang, C. (July 2001). Dynamically tunable dispersion slope compensation using a virtually imaged phased array (VIPA). 2001 LEOS Summer Topical Meetings Tech. Dig. Copper Mountain, CO.
  12. ↑ Lee, G-H; Xiao, S.; Weiner, A. M. (2006). "Optical dispersion compensator with >4000-ps/nm tuning range using a virtually imaged phased array (VIPA) and spatial light modulator (SLM)". IEEE Photonics Technology Letters. 18 (17): 1819. Bibcode:2006IPTL...18.1819L. doi:10.1109/LPT.2006.880732. S2CID   2418483.
  13. ↑ Miao, H.; Weiner, A. M.; Mirkin, L.; Miller, P. J. (2008). "AII-order polarization-mode dispersion (PMD) compensation via virtually imaged phased array (VIPA) - based pulse shaper". IEEE Photonics Technology Letters. 20 (8): 545. Bibcode:2008IPTL...20..545M. doi:10.1109/LPT.2008.918893. S2CID   26711798.
  14. ↑ Supradeepa, V. R.; Hamidi, E.; Leaird, D. E.; Weiner, A. M. (2010). "New aspects of temporal dispersion in high resolution Fourier pulse shaping: A quantitative description with virtually imaged phased array pulse shapers". Journal of the Optical Society of America B. 27 (9): 1833. arXiv: 1004.4693 . Bibcode:2010JOSAB..27.1833S. doi:10.1364/JOSAB.27.001833. S2CID   15594268.
  15. ↑ USpatent 5,973,838,Shirasaki, M.,"Apparatus which includes a virtually imaged phased array (VIPA) in combination with a wavelength splitter to demultiplex wavelength division multiplexed (WDM) light" Archived 2024-10-08 at the Wayback Machine
  16. ↑ Xiao, S.; Weiner, A. W. (2004). "2-D wavelength demultiplexer with potential for >1000 channels in the C-band". Optics Express. 12 (13): 2895–902. Bibcode:2004OExpr..12.2895X. doi: 10.1364/OPEX.12.002895 . PMID   19483805. S2CID   22626277.
  17. ↑ Diddams, S. A.; Hollberg, L.; Mbele, V. (2007). "Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb". Nature (journal). 445 (7128): 627–630. doi:10.1038/nature05524. PMID   17287805. S2CID   4420945.
  18. ↑ Nugent-Glandorf, L.; Neely, T.; Adler, F.; Fleisher, A. J.; Cossel, K. C.; Bjork, B.; Dinneen, T.; Ye, J.; Diddams, S. A. (2012). "Mid-infrared virtually imaged phased array spectrometer for rapid and broadband trace gas detection". Optics Letters. 37 (15): 3285–7. arXiv: 1206.1316 . Bibcode:2012OptL...37.3285N. doi:10.1364/OL.37.003285. PMID   22859160. S2CID   16831767.
  19. ↑ Bourdarot, G.; Coarer, E. L.; Bonfils, X.; Alecian, E.; Rabou, P.; Magnard, Y. (2017). "NanoVipa: a miniaturized high-resolution echelle spectrometer, for the monitoring of young stars from a 6U Cubesat". CEAS Space Journal. 9 (4): 411. Bibcode:2017CEAS....9..411B. doi:10.1007/s12567-017-0168-2. S2CID   125787048.
  20. ↑ Bourdarot, G.; Le Coarer, E.; Mouillet, D.; Correia, J.; Jocou, L.; Rabou, P.; Carlotti, A.; Bonfils, X.; Artigau, E.; Vallee, P.; Doyon, R.; Forveille, T.; Stadler, E.; Magnard, Y.; Vigan, A. (2018). Experimental test of a 40 cm-long R=100000 spectrometer for exoplanet characterisation. SPIE Astronomical Telescopes + Instrumentation 2018. Austin, TX. Paper 10702-217.
  21. ↑ Nikola, T.; Zou, B.; Stacey, G.; Connors, J.; Cothard, N.; Kutyrev, A.; Mentzell, E.; Rostem, K.; Wollack, E.; Jellema, W.; Kao, T.; Lee, A. (2024). Virtually image phased array (VIPA): demonstration of the next generation direct detection spectrometer for velocity resolved spectroscopy in the far-infrared. SPIE Astronomical Telescopes + Instrumentation 2024. Yokohama, Japan. Paper 13102-33.
  22. ↑ Scarcelli, G.; Yun, S. H. (2008). "Confocal Brillouin microscopy for three-dimensional mechanical imaging". Nature Photonics. 2 (1): 39–43. Bibcode:2008NaPho...2...39S. doi:10.1038/nphoton.2007.250. PMC   2757783 . PMID   19812712.
  23. ↑ Antonacci, G.; de Turris, V.; Rosa, A.; Ruocco, G. (2018). "Background-deflection Brillouin microscopy reveals altered biomechanics of intracellular stress granules by ALS protein FUS". Communications Biology. 10 (139): 139. doi:10.1038/s42003-018-0148-x. PMC   6131551 . PMID   30272018.
  24. ↑ Yan, G; Bazir, A; Margueritat, J; Dehoux, T (2020). "Evaluation of commercial virtually imaged phase array and Fabry-Pérot based Brillouin spectrometers for applications to biology". Biomedical Optics Express. 11 (12): 6933–6944. doi: 10.1364/BOE.401087 . PMC   7747923 . PMID   33408971.
  25. ↑ Forestier, A; Weck, G; Datchi, F; Loubeyre, P (2022). "Performances of a VIPA-based spectrometer for Brillouin scattering experiments in the diamond anvil cell under laser heating". High Pressure Research. 42 (3): 259–277. Bibcode:2022HPR....42..259F. doi:10.1080/08957959.2022.2109968. Archived from the original on 2024-10-08. Retrieved 2024-10-08.
  26. ↑ Salzenstein, P; Wu, T (2023). "Uncertainty estimation for the Brillouin frequency shift measurement using a scanning tandem Fabry–Pérot interferometer". Micromachines. 14 (7): 1429. doi: 10.3390/mi14071429 . PMC   10386179 . PMID   37512740.
  27. ↑ Chan, T.; Myslivet, E.; Ford, J. E. (2008). "2-Dimensional beamsteering using dispersive deflectors and wavelength tuning". Optics Express. 16 (19): 14617–28. Bibcode:2008OExpr..1614617C. doi: 10.1364/OE.16.014617 . PMID   18794998. S2CID   24244961.
  28. ↑ Tsia, K. K.; Goda, K.; Capewell, D.; Jalali, B. (2009). "Simultaneous mechanical-scan-free confocal microscopy and laser microsurgery". Optics Letters. 34 (14): 2099–101. Bibcode:2009OptL...34.2099T. doi:10.1364/OL.34.002099. hdl: 10722/91309 . PMID   19823514. S2CID   6265532.
  29. ↑ Lee, H. Y.; Marvdashti, T.; Duan, L.; Khan, S. A.; Ellerbee, A. K. (2014). "Scalable multiplexing for parallel imaging with interleaved optical coherence tomography". Biomedical Optics Express. 5 (9): 3192–203. doi:10.1364/BOE.5.003192. PMC   4230859 . PMID   25401031.
  30. ↑ Berg, S. A.; Eldik, S.; Bhattacharya, N. (2015). "Mode-resolved frequency comb interferometry for high-accuracy long distance measurement". Scientific Reports. 5: 14661. Bibcode:2015NatSR...514661V. doi:10.1038/srep14661. PMC   4588503 . PMID   26419282.
  31. ↑ Chen, X; Gao, Y; Jiang, J; Liu, M; Luo, A; Luo, Z; Xu, W (2020). "High-repetition-rate pulsed fiber laser based on virtually imaged phased array". Chinese Optics Letters. 18 (7): 071403. Bibcode:2020ChOpL..18g1403C. doi:10.3788/COL202018.071403.
  32. ↑ Li, Z; Zang, Z; Han, Y; Wu, L; Fu, H (2021). "Solid-state FMCW LiDAR with two-dimensional spectral scanning using a virtually imaged phased array". Optics Express. 29 (11): 16547–16562. Bibcode:2021OExpr..2916547L. doi: 10.1364/OE.418003 . PMID   34154215.
  33. ↑ Zou, W; Peng, C; Liu, A; Zhu, R; Ma, J; Gao, L (2022). "Ultrafast two-dimensional imaging for surface defects measurement of mirrors based on a virtually imaged phased-array". Optics Express. 30 (21): 37235–37244. Bibcode:2022OExpr..3037235Z. doi: 10.1364/OE.469315 . PMID   36258315.
  34. ↑ Metz, P.; Block, H.; Behnke, C.; Krantz, M.; Gerken, M.; Adam, J. (2013). "Tunable elastomer-based virtually imaged phased array". Optics Express. 21 (3): 3324–35. Bibcode:2013OExpr..21.3324M. doi: 10.1364/OE.21.003324 . PMID   23481792.
  35. ↑ Shirasaki, M.; Akhter, A. N.; Lin, C. (1999). "Virtually imaged phased array with graded reflectivity". IEEE Photonics Technology Letters. 11 (11): 1443. Bibcode:1999IPTL...11.1443S. doi:10.1109/68.803073. S2CID   8915803.
  36. ↑ Vega, A.; Weiner, A. M.; Lin, C. (2003). "Generalized grating equation for virtually-imaged phased-array spectral dispersers". Applied Optics. 42 (20): 4152–5. Bibcode:2003ApOpt..42.4152V. doi:10.1364/AO.42.004152. PMID   12856727.
  37. ↑ Xiao, S.; Weiner, A. M.; Lin, C. (2004). "A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory". IEEE Journal of Quantum Electronics. 40 (4): 420. Bibcode:2004IJQE...40..420X. doi:10.1109/JQE.2004.825210. S2CID   1352376.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.