Virtually imaged phased array

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.

VIPA was proposed and named by Shirasaki in 1996.{{Cite journal |last=Shirasaki |first=M. |year=1996 |title=Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer |journal=Optics Letters |volume=21 |issue=5 |pages=366–8 |bibcode=1996OptL...21..366S |doi=10.1364/OL.21.000366 |pmid=19865407}} Prior to the publication in the paper, a preliminary presentation was given by Shirasaki at a conference.{{Cite conference |last=Shirasaki |first=M. |date=October 1995 |title=Large angular-dispersion by virtually-imaged phased-array (VIPA) and its application to wavelength demultiplexing |url=https://drive.google.com/file/d/1YJqOeHxxMFIaF2_jaZ97NUAmIk6tYJRD/view?usp=sharing |conference=5th Microoptics Conference (MOC'95) |location=Hiroshima, Japan |id=Paper PD3 |archive-url=https://web.archive.org/web/20231118061930/https://drive.google.com/file/d/1YJqOeHxxMFIaF2_jaZ97NUAmIk6tYJRD/view?usp=sharing |archive-date=2023-11-18 |access-date=2024-10-08 |url-status=live}} This presentation was reported in Laser Focus World.{{Cite journal |date=December 1995 |title=Virtual imaging array splits light into ten wavelengths |url=https://www.laserfocusworld.com/optics/article/16553339/optoelectronic-components-virtual-imaging-array-splits-light-into-ten-wavelengths |url-status=live |journal=Laser Focus World |volume=31 |issue=12 |pages=30–33 |archive-url=https://web.archive.org/web/20240527211612/https://www.laserfocusworld.com/optics/article/16553339/optoelectronic-components-virtual-imaging-array-splits-light-into-ten-wavelengths |archive-date=2024-05-27 |access-date=2024-10-08}} The details of this new approach to producing angular dispersion were described in the patent.{{cite patent | country=US | number=5,999,320 | status=patent | title=Virtually imaged phased array as a wavelength demultiplexer | fdate=1996-07-24 | pridate=1995-07-26 | invent1=Shirasaki, M. | url=https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/5999320 }} {{Webarchive|url=https://web.archive.org/web/20231119095337/https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/5999320 |date=2023-11-19 }} 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, 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.{{Cite journal |last1=Xiao |first1=S. |last2=Weiner |first2=A. M. |year=2005 |title=An eight-channel hyperfine wavelength demultiplexer using a virtually imaged phased-array (VIPA) |journal=IEEE Photonics Technology Letters |volume=17 |issue=2 |pages=372 |bibcode=2005IPTL...17..372X |doi=10.1109/LPT.2004.839017 |s2cid=37277234}} 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).{{Cite conference |last=Shirasaki |first=M. |date=July 1997 |title=Chromatic dispersion compensation using virtually imaged phased array |url=https://doi.org/10.1364/OAA.1997.SD17 |conference=Optical Amplifiers and Their Applications |location=Victoria, Canada |doi=10.1364/OAA.1997.SD17 |id=Paper PDP-8|url-access=subscription }}{{Cite journal |last=Shirasaki |first=M. |year=1997 |title=Chromatic-dispersion compensator using virtually imaged phased array |journal=IEEE Photonics Technology Letters |volume=9 |issue=12 |pages=1598–1600 |bibcode=1997IPTL....9.1598S |doi=10.1109/68.643280 |s2cid=25043474}}{{Cite conference |last1=Shirasaki |first1=M. |last2=Cao |first2=S. |date=March 2001 |title=Compensation of chromatic dispersion and dispersion slope using a virtually imaged phased array |url=https://www.osapublishing.org/abstract.cfm?uri=OFC-2001-TuS1 |conference=2001 Optical Fiber Communication Conference |location=Anaheim, CA |id=Paper TuS1 |archive-url=https://web.archive.org/web/20200317234912/https://www.osapublishing.org/abstract.cfm?uri=OFC-2001-TuS1 |archive-date=2020-03-17 |access-date=2019-05-15 |url-status=live}} The compensation was further developed for tunable systems by using adjustable mirrors{{Cite conference |last1=Shirasaki |first1=M. |last2=Kawahata |first2=Y. |last3=Cao |first3=S. |last4=Ooi |first4=H. |last5=Mitamura |first5=N. |last6=Isono |first6=H. |last7=Ishikawa |first7=G. |last8=Barbarossa |first8=G. |last9=Yang |first9=C. |date=September 2000 |title=Variable dispersion compensator using the virtually imaged phased array (VIPA) for 40-Gbit/s WDM transmission systems |conference=2000 European Conference on Optical Communication |location=Munich, Germany |id=Paper PD-2.3 |last10=Lin |first10=C.}}{{Cite conference |last1=Garrett |first1=L. D. |last2=Gnauck |first2=A. H. |last3=Eiselt |first3=M. H. |last4=Tkach |first4=R. W. |last5=Yang |first5=C. |last6=Mao |first6=C. |last7=Cao |first7=S. |date=March 2000 |title=Demonstration of virtually-imaged phased-array device for tunable dispersion compensation in 16 X10 Gb/s WDM transmission over 480 km standard fiber |url=https://www.osapublishing.org/abstract.cfm?uri=OFC-2000-PD7 |conference=2000 Optical Fiber Communication Conference |location=Baltimore, MD |id=Paper PD7 |archive-url=https://web.archive.org/web/20200310054904/https://www.osapublishing.org/abstract.cfm?uri=OFC-2000-PD7 |archive-date=2020-03-10 |access-date=2019-05-15 |url-status=live}}{{Cite conference |last1=Cao |first1=S. |last2=Lin |first2=C. |last3=Barbarossa |first3=G. |last4=Yang |first4=C. |date=July 2001 |title=Dynamically tunable dispersion slope compensation using a virtually imaged phased array (VIPA) |conference=2001 LEOS Summer Topical Meetings Tech. Dig. |location=Copper Mountain, CO}} or a spatial light modulator (Weiner, 2006).{{Cite journal |last1=Lee |first1=G-H |last2=Xiao |first2=S. |last3=Weiner |first3=A. M. |year=2006 |title=Optical dispersion compensator with >4000-ps/nm tuning range using a virtually imaged phased array (VIPA) and spatial light modulator (SLM) |journal=IEEE Photonics Technology Letters |volume=18 |issue=17 |pages=1819 |bibcode=2006IPTL...18.1819L |doi=10.1109/LPT.2006.880732 |s2cid=2418483}} Using the VIPA, compensation of polarization mode dispersion was also achieved (Weiner, 2008).{{Cite journal |last1=Miao |first1=H. |last2=Weiner |first2=A. M. |last3=Mirkin |first3=L. |last4=Miller |first4=P. J. |year=2008 |title=AII-order polarization-mode dispersion (PMD) compensation via virtually imaged phased array (VIPA) - based pulse shaper |journal=IEEE Photonics Technology Letters |volume=20 |issue=8 |pages=545 |bibcode=2008IPTL...20..545M |doi=10.1109/LPT.2008.918893 |s2cid=26711798}} Furthermore, pulse shaping using the combination of a VIPA for high-resolution wavelength splitting/recombining and a SLM was demonstrated (Weiner, 2010).{{Cite journal |last1=Supradeepa |first1=V. R. |last2=Hamidi |first2=E. |last3=Leaird |first3=D. E. |last4=Weiner |first4=A. M. |year=2010 |title=New aspects of temporal dispersion in high resolution Fourier pulse shaping: A quantitative description with virtually imaged phased array pulse shapers |journal=Journal of the Optical Society of America B |volume=27 |issue=9 |pages=1833 |arxiv=1004.4693 |bibcode=2010JOSAB..27.1833S |doi=10.1364/JOSAB.27.001833 |s2cid=15594268}}

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.{{cite patent | country=US | number=5,973,838 | status=patent | title=Apparatus which includes a virtually imaged phased array (VIPA) in combination with a wavelength splitter to demultiplex wavelength division multiplexed (WDM) light | fdate=1997-10-10 | pridate=1995-07-26 | invent1=Shirasaki, M. | url=https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/5973838 }} {{Webarchive|url=https://web.archive.org/web/20241008092249/https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/5973838 |date=2024-10-08 }} 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),{{Cite journal |last1=Xiao |first1=S. |last2=Weiner |first2=A. W. |year=2004 |title=2-D wavelength demultiplexer with potential for >1000 channels in the C-band |journal=Optics Express |volume=12 |issue=13 |pages=2895–902 |bibcode=2004OExpr..12.2895X |doi=10.1364/OPEX.12.002895 |pmid=19483805 |s2cid=22626277 |doi-access=free|url=http://pdfs.semanticscholar.org/a102/68128c423cef9697138ae98e9016a2c601a8.pdf }} a laser frequency comb (Diddams, 2007),{{Cite journal |last1=Diddams |first1=S. A. |last2=Hollberg |first2=L. |last3=Mbele |first3=V. |year=2007 |title=Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb |journal=Nature |volume=445 |issue=7128 |pages=627–630 |doi=10.1038/nature05524 |pmid=17287805 |s2cid=4420945}} a spectrometer (Nugent-Glandorf, 2012),{{Cite journal |last1=Nugent-Glandorf |first1=L. |last2=Neely |first2=T. |last3=Adler |first3=F. |last4=Fleisher |first4=A. J. |last5=Cossel |first5=K. C. |last6=Bjork |first6=B. |last7=Dinneen |first7=T. |last8=Ye |first8=J. |last9=Diddams |first9=S. A. |year=2012 |title=Mid-infrared virtually imaged phased array spectrometer for rapid and broadband trace gas detection |journal=Optics Letters |volume=37 |issue=15 |pages=3285–7 |arxiv=1206.1316 |bibcode=2012OptL...37.3285N |doi=10.1364/OL.37.003285 |pmid=22859160 |s2cid=16831767}} astrophysical instruments (Le Coarer, 2017, Bourdarot, 2018, Delboulbé, 2022, and Stacey, 2024),{{Cite journal |last1=Bourdarot |first1=G. |last2=Coarer |first2=E. L. |last3=Bonfils |first3=X. |last4=Alecian |first4=E. |last5=Rabou |first5=P. |last6=Magnard |first6=Y. |year=2017 |title=NanoVipa: a miniaturized high-resolution echelle spectrometer, for the monitoring of young stars from a 6U Cubesat |journal=CEAS Space Journal |volume=9 |issue=4 |pages=411 |bibcode=2017CEAS....9..411B |doi=10.1007/s12567-017-0168-2 |s2cid=125787048}}{{Cite conference |last1=Bourdarot |first1=G. |last2=Le Coarer |first2=E. |last3=Mouillet |first3=D. |last4=Correia |first4=J. |last5=Jocou |first5=L. |last6=Rabou |first6=P. |last7=Carlotti |first7=A. |last8=Bonfils |first8=X. |last9=Artigau |first9=E. |year=2018 |title=Experimental test of a 40 cm-long R=100000 spectrometer for exoplanet characterisation |url=https://doi.org/10.1117/12.2311696 |conference=SPIE Astronomical Telescopes + Instrumentation 2018 |location=Austin, TX |id=Paper 10702-217 |last10=Vallee |first10=P. |last11=Doyon |first11=R. |last12=Forveille |first12=T. |last13=Stadler |first13=E. |last14=Magnard |first14=Y. |last15=Vigan |first15=A.|doi=10.1117/12.2311696 |arxiv=1812.09272 }}{{Cite conference |last1=Carlotti |first1=A. |last2=Bidot |first2=A. |last3=Mouillet |first3=D. |last4=Correia |first4=J. J. |last5=Jocou |first5=L. |last6=Curaba |first6=S. |last7=Delboulbé |first7=A. |last8=Le-Coarer |first8=E. |last9=Rabou |first9=P. |year=2022 |title=On-sky demonstration at Palomar Observatory of the near-IR, high-resolution VIPA spectrometer |url=https://doi.org/10.1117/12.2628937 |conference=SPIE Astronomical Telescopes + Instrumentation 2022 |location=Montréal, Canada |id=Paper 12184 |last10=Bourdarot |first10=G. |last11=Forveille |first11=T. |last12=Bonfils |first12=X. |last13=Vasisht |first13=G. |last14=Mawet |first14=D. |last15=Burruss |first15=R. S. |last16=Oppenheimer |first16=R. |last17=Doyon |first17=R. |last18=Artigau |first18=E. |last19=Vallée |first19=P.|doi=10.1117/12.2628937 |arxiv=2305.19736 }}{{Cite conference |last1=Nikola |first1=T. |last2=Zou |first2=B. |last3=Stacey |first3=G. |last4=Connors |first4=J. |last5=Cothard |first5=N. |last6=Kutyrev |first6=A. |last7=Mentzell |first7=E. |last8=Rostem |first8=K. |last9=Wollack |first9=E. |year=2024 |title=Virtually image phased array (VIPA): demonstration of the next generation direct detection spectrometer for velocity resolved spectroscopy in the far-infrared |url=https://doi.org/10.1117/12.3020350 |conference=SPIE Astronomical Telescopes + Instrumentation 2024 |location=Yokohama, Japan |id=Paper 13102-33 |last10=Jellema |first10=W. |last11=Kao |first11=T. |last12=Lee |first12=A.|doi=10.1117/12.3020350 |url-access=subscription }} Brillouin spectroscopy in biomechanics (Scarcelli, 2008, Rosa, 2018, and Margueritat, 2020),{{Cite journal |last1=Scarcelli |first1=G. |last2=Yun |first2=S. H. |year=2008 |title=Confocal Brillouin microscopy for three-dimensional mechanical imaging |journal=Nature Photonics |volume=2 |issue=1 |pages=39–43 |bibcode=2008NaPho...2...39S |doi=10.1038/nphoton.2007.250 |pmc=2757783 |pmid=19812712}}{{Cite journal |last1=Antonacci |first1=G. |last2=de Turris |first2=V. |last3=Rosa |first3=A. |last4=Ruocco |first4=G. |year=2018 |title=Background-deflection Brillouin microscopy reveals altered biomechanics of intracellular stress granules by ALS protein FUS |journal=Communications Biology |volume=10 |issue=139 |pages=139 |doi=10.1038/s42003-018-0148-x |pmc=6131551 |pmid=30272018}}{{Cite journal |last1=Yan |first1=G |last2=Bazir |first2=A |last3=Margueritat |first3=J |last4=Dehoux |first4=T |year=2020 |title=Evaluation of commercial virtually imaged phase array and Fabry-Pérot based Brillouin spectrometers for applications to biology |journal=Biomedical Optics Express |volume=11 |issue=12 |pages=6933–6944 |doi=10.1364/BOE.401087 |pmc=7747923 |pmid=33408971 |doi-access=free}} other Brillouin spectroscopy (Loubeyre, 2022 and Wu, 2023),{{Cite journal |last1=Forestier |first1=A |last2=Weck |first2=G |last3=Datchi |first3=F |last4=Loubeyre |first4=P |year=2022 |title=Performances of a VIPA-based spectrometer for Brillouin scattering experiments in the diamond anvil cell under laser heating |url=https://hal.science/hal-03866581/document |url-status=live |journal=High Pressure Research |volume=42 |issue=3 |pages=259–277 |bibcode=2022HPR....42..259F |doi=10.1080/08957959.2022.2109968 |archive-url=https://web.archive.org/web/20241008091014/https://hal.science/hal-03866581/document |archive-date=2024-10-08 |access-date=2024-10-08}}{{Cite journal |last1=Salzenstein |first1=P |last2=Wu |first2=T |year=2023 |title=Uncertainty estimation for the Brillouin frequency shift measurement using a scanning tandem Fabry–Pérot interferometer |journal=Micromachines |volume=14 |issue=7 |page=1429 |doi=10.3390/mi14071429 |pmc=10386179 |pmid=37512740 |doi-access=free}} beam scanning (Ford, 2008),{{Cite journal |last1=Chan |first1=T. |last2=Myslivet |first2=E. |last3=Ford |first3=J. E. |year=2008 |title=2-Dimensional beamsteering using dispersive deflectors and wavelength tuning |journal=Optics Express |volume=16 |issue=19 |pages=14617–28 |bibcode=2008OExpr..1614617C |doi=10.1364/OE.16.014617 |pmid=18794998 |s2cid=24244961 |doi-access=free}} microscopy (Jalali, 2009),{{Cite journal |last1=Tsia |first1=K. K. |last2=Goda |first2=K. |last3=Capewell |first3=D. |last4=Jalali |first4=B. |year=2009 |title=Simultaneous mechanical-scan-free confocal microscopy and laser microsurgery |journal=Optics Letters |volume=34 |issue=14 |pages=2099–101 |bibcode=2009OptL...34.2099T |doi=10.1364/OL.34.002099 |pmid=19823514 |s2cid=6265532 |hdl-access=free |hdl=10722/91309}} tomography imaging (Ellerbee, 2014),{{Cite journal |last1=Lee |first1=H. Y. |last2=Marvdashti |first2=T. |last3=Duan |first3=L. |last4=Khan |first4=S. A. |last5=Ellerbee |first5=A. K. |year=2014 |title=Scalable multiplexing for parallel imaging with interleaved optical coherence tomography |journal=Biomedical Optics Express |volume=5 |issue=9 |pages=3192–203 |doi=10.1364/BOE.5.003192 |pmc=4230859 |pmid=25401031}} metrology (Bhattacharya, 2015),{{Cite journal |last1=Berg |first1=S. A. |last2=Eldik |first2=S. |last3=Bhattacharya |first3=N. |year=2015 |title=Mode-resolved frequency comb interferometry for high-accuracy long distance measurement |journal=Scientific Reports |volume=5 |pages=14661 |bibcode=2015NatSR...514661V |doi=10.1038/srep14661 |pmc=4588503 |pmid=26419282}} fiber laser (Xu, 2020),{{Cite journal |last1=Chen |first1=X |last2=Gao |first2=Y |last3=Jiang |first3=J |last4=Liu |first4=M |last5=Luo |first5=A |last6=Luo |first6=Z |last7=Xu |first7=W |year=2020 |title=High-repetition-rate pulsed fiber laser based on virtually imaged phased array |journal=Chinese Optics Letters |volume=18 |issue=7 |pages=071403 |bibcode=2020ChOpL..18g1403C |doi=10.3788/COL202018.071403}} LiDAR (Fu, 2021),{{Cite journal |last1=Li |first1=Z |last2=Zang |first2=Z |last3=Han |first3=Y |last4=Wu |first4=L |last5=Fu |first5=H |year=2021 |title=Solid-state FMCW LiDAR with two-dimensional spectral scanning using a virtually imaged phased array |journal=Optics Express |volume=29 |issue=11 |pages=16547–16562 |bibcode=2021OExpr..2916547L |doi=10.1364/OE.418003 |pmid=34154215 |doi-access=free}} and surface measurement (Zhu, 2022).{{Cite journal |last1=Zou |first1=W |last2=Peng |first2=C |last3=Liu |first3=A |last4=Zhu |first4=R |last5=Ma |first5=J |last6=Gao |first6=L |year=2022 |title=Ultrafast two-dimensional imaging for surface defects measurement of mirrors based on a virtually imaged phased-array |journal=Optics Express |volume=30 |issue=21 |pages=37235–37244 |bibcode=2022OExpr..3037235Z |doi=10.1364/OE.469315 |pmid=36258315 |doi-access=free}}

File:Modified Operational principle of VIPA.jpg

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. 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.

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.

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).{{Cite journal |last1=Metz |first1=P. |last2=Block |first2=H. |last3=Behnke |first3=C. |last4=Krantz |first4=M. |last5=Gerken |first5=M. |last6=Adam |first6=J. |year=2013 |title=Tunable elastomer-based virtually imaged phased array |journal=Optics Express |volume=21 |issue=3 |pages=3324–35 |bibcode=2013OExpr..21.3324M |doi=10.1364/OE.21.003324 |pmid=23481792 |doi-access=free}}

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.{{Cite journal |last1=Shirasaki |first1=M. |last2=Akhter |first2=A. N. |last3=Lin |first3=C. |year=1999 |title=Virtually imaged phased array with graded reflectivity |journal=IEEE Photonics Technology Letters |volume=11 |issue=11 |pages=1443 |bibcode=1999IPTL...11.1443S |doi=10.1109/68.803073 |s2cid=8915803}}

An analytical calculation of the VIPA was first performed by Vega and Weiner in 2003 {{Cite journal |last1=Vega |first1=A. |last2=Weiner |first2=A. M. |last3=Lin |first3=C. |year=2003 |title=Generalized grating equation for virtually-imaged phased-array spectral dispersers |journal=Applied Optics |volume=42 |issue=20 |pages=4152–5 |bibcode=2003ApOpt..42.4152V |doi=10.1364/AO.42.004152 |pmid=12856727}} 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.{{cite journal |last1=Xiao |first1=S. |last2=Weiner |first2=A. M. |last3=Lin |first3=C. |title=A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory |journal=IEEE Journal of Quantum Electronics |date=2004 |volume=40 |issue=4 |pages=420 |bibcode=2004IJQE...40..420X |doi=10.1109/JQE.2004.825210 |s2cid=1352376 }}

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

{{Reflist}}

Category:Spectroscopy

Category:Optical components

Category:Interferometry