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`THOMAS SWAN 2006
`Finisar v. Thomas Swan
`|PR2014-00461
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`THOMAS SWAN 2006
`Finisar v. Thomas Swan
`IPR2014-00461
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`DIFFRACTION
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`GRATING
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`HANDBOOK
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`fourth edition
`
`Christopher Palmer
`
`Erwin Loewen, Editor (first edition)
`
`’ The Difli‘action Grating Handbook is supplemented by the
`Richardson Grating Laboratory’s Grating Catalog, which lists the
`standard plane and concave gratings available. If the Catalog does
`not offer a diffraction grating that meets your requirements, please
`contact us for a listing of new gratings or a quotation for a custom-
`designed and ‘—_fabricated grating.
`
`,
`
`The Richardson Grating Laboratory remains committed to main-
`taining its proud traditions — using the most advanced technology
`available to produce high-quality precision diffraction gratings, and
`providing competent technical assistance in the choice and use of
`these gratings.
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`RICHARDSON GRATING LABORATORY
`
`705 St. Paul Street, Rochester, New York 14605 USA
`
`tel: 716/262—1331, fax: 716/454-1568, e—mail: gratings@spectronic.com
`
`http://www.grating1ab.com/
`
`Copyright 2000, Richardson u‘rating Laboratory, All Rights Reserved
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`the light of wavelength xi
`for any grating instrument configuration,
`that,
`diffracted in the m = 1 order will coincide with the light of wavelength xl/Z
`diffracted in the m = 2 order, etc., for all in satisfying inequality (2—7).
`In this
`example,
`the red light (600 nm) in the‘first spectral order will overlap the
`ultraviolet light (300 nm) in the second order. A detector sensitive at both
`wavelengths would see both
`simultaneously. This superposition of wave-
`lengths, which would lead to ambiguous spectroscopic data, is inherent in the
`grating equation itself and must be prevented‘by suitable filtering (called order
`sorting), since the detector cannot generally distinguish between light of differ-
`ent wavelengths incident on it (within its range of sensitivity).
`[See also Section
`2.7. below,]
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`2.3. " DISPERSION
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`The primary purpose of a diffraction grating is to disperse light spatially by
`wavelength. A beam of White light incident on a grating will be separated into'
`its component colors upon diffraction from the grating, with each color
`diffracted along a different direction. Dispersion is a measure of the separation
`(either angular or spatial) between diffracted light of different wavelengths.
`Angular dispersion expresses the spectral range per unit angle, and linear reso-
`lution expresses the spectral range per unit length.
`'
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`2.3.1. Angular dispersion.
`
`The angular spread dfl of a spectrum of order m between the wavelength/t
`and xi + d/l can be obtained by differentiating the grating equation, assuming the
`incidence angle a to be constant. The change D in diffraction angle per unit
`wavelength is therefore
`i
`-
`
`J
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`p
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`8,6
`D = —— =
`6/1
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`
`m
`dcos ,5
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`m
`= ——
`d secfl
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`'
`.= G
`,
`msecfl
`
`‘
`
`2-9
`(
`)
`
`where ,6 is given by Eq; (2-2). The ratio D = dfl/d/t is called the angular
`dispersion. As the groove frequency G = l/d increases, the angular dispersion
`increases (meaning that the angular separation between wavelengths increases
`for a given order m).
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`In Eq. (2-9), it is important to realize that the quantity m/d is not a ratio
`Which may be chosen independently of other parameters; substitution of the
`grating equation into Eq. (2-9) yields the following general equation for the
`angular dispersion:
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`l9
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`4. HOLOGRAPHIC GRATINGS
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`_____________—_————————
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`4.0.
`
`INTRODUCTION
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`Since the late 19605, a method distinct from mechanical ruling has also been
`used to manufacture diffraction gratings. This method involves the photographic
`recording of a stationary interference fringe field. Such interference gratings,
`more commonly (though inaccurately) known as holographic gratings, have
`several characteristics that distinguish them from ruled gratings.
`
`interference gratings, fifty
`In 1901 Aime Cotton produced experimental
`years before the concepts of holography were developed by Gabon A few
`decades later, Michelson considered the interferometric generation of diffraction
`gratings obvious, but recognized that an intense monochromatic light source and
`a photosensitive material of sufficiently, fine granularity did not then exist.
`In
`the mid 19605, ion lasers and photoresists
`(grainless photosensitive materials)
`became available;. the former provided a strong monochromatic line, and the
`latter was photoactive at the molecular level, rather than at the crystalline level
`(unlike, for example, photographic film).
`In 1967 D. Rudolph and G. Schmahl
`at the University of Gettingen and'A. Labeyrie and J. Flamand in France.
`independently produced the first holographic diffraction gratings of spectro-
`scopic quality.
`‘
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`4.1.-
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`PRINCIPLE OF MANUFACTURE
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`4.1.1. Formation of an interference pattern
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`When two sets of coherent equally polarized monochromatic optical plane
`waves of equal intensity intersect each other, a standing wave pattern will be
`formed in the region of intersection if both sets of waves are of the same
`wavelength it (see Figure 4-1). The combined intensity distribution forms a set
`of straight equally-spaced fringes (bright and dark lines). Thus a photographic
`plate would record a fringe pattern, since the regions of zero field intensity»
`would leave the film unexposed while the regions of maximum intensity would
`leave the film maximally exposed. Regions between these extremes, for which
`the combined intensity is neither maximal nor zero, would leave the film
`partially exposed. The combined intensity varies sinusoidally with position as
`the interference pattern is sCanned along a line.
`If the beams are not of equal
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