Abstract

The performances of triangular groove photoresist gratings used in transmission are studied in the visible and near-infrared regions with the electromagnetic theory. The mounting considered here associates triangular groove gratings on the hypotenuse face of a right-angle prism in a configuration, usually called a grism, in such a way that for a chosen wavelength the deviations of the prism and the grating compensate. To assist designers of spectrometric systems, we have covered a complete range of blaze wavelengths and, consequently, of blaze angles. We studied the influence on grating efficiencies when the line density is increased, and the optimal choice angle of incidence is discussed.

© 1991 Optical Society of America

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References

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  1. M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating couplers, waveguide systems,” Opt. Commun. 8, 113—117 (1973).
    [CrossRef]
  2. M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  3. T. Tamir, S. T. Peng, “Analysis and design of gratings couplers,” Appl. Phys. 14, 235–242 (1977).
    [CrossRef]
  4. D. Marcuse, ed., Integrated Optics (IEEE Press, New York, 1973).
  5. T. Tamir, ed., Integrated Optics, 2nd ed. (Springer-Verlag, Berlin, 1979).
  6. E. G. Loewen, M. Nevière, D. Maystre, “Grating efficiency theory as it applies to blazed and holographic gratings,” Appl. Opt. 16, 2711–2721 (1977).
    [CrossRef] [PubMed]
  7. D. Maystre, M. Nevière, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  8. M. Nevière, P. Vincent, R. Petit, “Sur la théorie du réseau conducteur et ses applications à l'Optique,” Nouv. Rev. Opt. 5, 65–77 (1974).
    [CrossRef]
  9. P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  10. M. Nevière, D. Maystre, J. P. Laude, “Perfect blazing for transmission gratings,” J. Opt. Soc. Am. A 7, 1736–1739 (1990).
    [CrossRef]
  11. E. G. Loewen, Milton Roy Analytical Products Division, 820 Linden Avenue, Rochester, N.Y. 14625 (personal communication);Diffraction Grating Handbook, 2nd ed. (Bausch & Lomb, Rochester, N.Y., 1972).
  12. H. Dekker, S. D'Odorico, R. Arsenault, “First results with a transmission echelle grating on the ESO Faint Object Spectrograph: observations of the SN1986a in NGC3367 and of the nucleus of the galaxy,” Astron. Astrophys. 189, 353–360 (1988).
  13. S. Sebillotte, “Holographic optical backplane for boards interconnection,” in Microelectronic Interconnects and Packaging: Optical and Electrical Technologies, G. Arjavalingam, J. Pazaris, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1389 (to be published).
  14. A. Baranne, “Sur l'emploi des réseaux par transmission en optique astronomique,” C. R. Acad. Sci. Ser. B 291, 205–207 (1980).

1990 (1)

1988 (1)

H. Dekker, S. D'Odorico, R. Arsenault, “First results with a transmission echelle grating on the ESO Faint Object Spectrograph: observations of the SN1986a in NGC3367 and of the nucleus of the galaxy,” Astron. Astrophys. 189, 353–360 (1988).

1980 (1)

A. Baranne, “Sur l'emploi des réseaux par transmission en optique astronomique,” C. R. Acad. Sci. Ser. B 291, 205–207 (1980).

1977 (2)

1974 (1)

M. Nevière, P. Vincent, R. Petit, “Sur la théorie du réseau conducteur et ses applications à l'Optique,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

1973 (1)

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating couplers, waveguide systems,” Opt. Commun. 8, 113—117 (1973).
[CrossRef]

Arsenault, R.

H. Dekker, S. D'Odorico, R. Arsenault, “First results with a transmission echelle grating on the ESO Faint Object Spectrograph: observations of the SN1986a in NGC3367 and of the nucleus of the galaxy,” Astron. Astrophys. 189, 353–360 (1988).

Baranne, A.

A. Baranne, “Sur l'emploi des réseaux par transmission en optique astronomique,” C. R. Acad. Sci. Ser. B 291, 205–207 (1980).

Cadilhac, M.

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating couplers, waveguide systems,” Opt. Commun. 8, 113—117 (1973).
[CrossRef]

Dekker, H.

H. Dekker, S. D'Odorico, R. Arsenault, “First results with a transmission echelle grating on the ESO Faint Object Spectrograph: observations of the SN1986a in NGC3367 and of the nucleus of the galaxy,” Astron. Astrophys. 189, 353–360 (1988).

D'Odorico, S.

H. Dekker, S. D'Odorico, R. Arsenault, “First results with a transmission echelle grating on the ESO Faint Object Spectrograph: observations of the SN1986a in NGC3367 and of the nucleus of the galaxy,” Astron. Astrophys. 189, 353–360 (1988).

Laude, J. P.

Loewen, E. G.

E. G. Loewen, M. Nevière, D. Maystre, “Grating efficiency theory as it applies to blazed and holographic gratings,” Appl. Opt. 16, 2711–2721 (1977).
[CrossRef] [PubMed]

E. G. Loewen, Milton Roy Analytical Products Division, 820 Linden Avenue, Rochester, N.Y. 14625 (personal communication);Diffraction Grating Handbook, 2nd ed. (Bausch & Lomb, Rochester, N.Y., 1972).

Maystre, D.

Nevière, M.

M. Nevière, D. Maystre, J. P. Laude, “Perfect blazing for transmission gratings,” J. Opt. Soc. Am. A 7, 1736–1739 (1990).
[CrossRef]

E. G. Loewen, M. Nevière, D. Maystre, “Grating efficiency theory as it applies to blazed and holographic gratings,” Appl. Opt. 16, 2711–2721 (1977).
[CrossRef] [PubMed]

M. Nevière, P. Vincent, R. Petit, “Sur la théorie du réseau conducteur et ses applications à l'Optique,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating couplers, waveguide systems,” Opt. Commun. 8, 113—117 (1973).
[CrossRef]

M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
[CrossRef]

D. Maystre, M. Nevière, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
[CrossRef]

Peng, S. T.

T. Tamir, S. T. Peng, “Analysis and design of gratings couplers,” Appl. Phys. 14, 235–242 (1977).
[CrossRef]

Petit, R.

M. Nevière, P. Vincent, R. Petit, “Sur la théorie du réseau conducteur et ses applications à l'Optique,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating couplers, waveguide systems,” Opt. Commun. 8, 113—117 (1973).
[CrossRef]

D. Maystre, M. Nevière, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
[CrossRef]

Sebillotte, S.

S. Sebillotte, “Holographic optical backplane for boards interconnection,” in Microelectronic Interconnects and Packaging: Optical and Electrical Technologies, G. Arjavalingam, J. Pazaris, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1389 (to be published).

Tamir, T.

T. Tamir, S. T. Peng, “Analysis and design of gratings couplers,” Appl. Phys. 14, 235–242 (1977).
[CrossRef]

Vincent, P.

M. Nevière, P. Vincent, R. Petit, “Sur la théorie du réseau conducteur et ses applications à l'Optique,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

T. Tamir, S. T. Peng, “Analysis and design of gratings couplers,” Appl. Phys. 14, 235–242 (1977).
[CrossRef]

Astron. Astrophys. (1)

H. Dekker, S. D'Odorico, R. Arsenault, “First results with a transmission echelle grating on the ESO Faint Object Spectrograph: observations of the SN1986a in NGC3367 and of the nucleus of the galaxy,” Astron. Astrophys. 189, 353–360 (1988).

C. R. Acad. Sci. Ser. B (1)

A. Baranne, “Sur l'emploi des réseaux par transmission en optique astronomique,” C. R. Acad. Sci. Ser. B 291, 205–207 (1980).

J. Opt. Soc. Am. A (1)

Nouv. Rev. Opt. (1)

M. Nevière, P. Vincent, R. Petit, “Sur la théorie du réseau conducteur et ses applications à l'Optique,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

Opt. Commun. (1)

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating couplers, waveguide systems,” Opt. Commun. 8, 113—117 (1973).
[CrossRef]

Other (7)

M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
[CrossRef]

D. Marcuse, ed., Integrated Optics (IEEE Press, New York, 1973).

T. Tamir, ed., Integrated Optics, 2nd ed. (Springer-Verlag, Berlin, 1979).

P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
[CrossRef]

D. Maystre, M. Nevière, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
[CrossRef]

E. G. Loewen, Milton Roy Analytical Products Division, 820 Linden Avenue, Rochester, N.Y. 14625 (personal communication);Diffraction Grating Handbook, 2nd ed. (Bausch & Lomb, Rochester, N.Y., 1972).

S. Sebillotte, “Holographic optical backplane for boards interconnection,” in Microelectronic Interconnects and Packaging: Optical and Electrical Technologies, G. Arjavalingam, J. Pazaris, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1389 (to be published).

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Figures (26)

Fig. 1
Fig. 1

Schematic representation of a grism.

Fig. 2
Fig. 2

Transmission grating on the hypotenuse face of the prism.

Fig. 3
Fig. 3

Efficiencies in TE polarization, TM polarization, and for natural light as functions of wavelength λ (in micrometers) for a 300-groove/mm transmission grating with α = 11.345° (λc = 0.4 μm).

Fig. 4
Fig. 4

Same as Fig. 3 but with α = 14.552° (λc = 0.5 μm).

Fig. 5
Fig. 5

Same as Fig. 3 but with α = 17.763° (λc = 0.6 μm).

Fig. 6
Fig. 6

Same as Fig. 3 but with α = 21.075° (λc = 0.7 μm).

Fig. 7
Fig. 7

Same as Fig. 3 but with α = 24.443° (λc = 0.8 μm).

Fig. 8
Fig. 8

Same as Fig. 3 but with α = 27.916° (λc = 0.9 μm).

Fig. 9
Fig. 9

Efficiencies as functions of wavelength for a 600-groove/mm transmission grating with α = 23.169° (λc = 0.4 μm).

Fig. 10
Fig. 10

Same as Fig. 9 but with α = 30.166° (λc = 0.5 μm).

Fig. 11
Fig. 11

Same as Fig. 9 but with α = 37.602° (λc = 0.6 μm).

Fig. 12
Fig. 12

Same as Fig. 9 but with α = 45.987° (λc = 0.7 μm).

Fig. 13
Fig. 13

Same as Fig. 9 but with α = 55.851° (λc = 0.8 μm).

Fig. 14
Fig. 14

Efficiencies as functions of wavelength for a 900-groove/mm transmission grating with α = 36.169° (λc = 0.4 μm).

Fig. 15
Fig. 15

Same as Fig. 14 but with α = 48.918° (λc = 0.5 μm).

Fig. 16
Fig. 16

Same as Fig. 14 but with α = 66.242° (λc = 0.6 μm).

Fig. 17
Fig. 17

Efficiencies as functions of wavelength for a 1200-groove/mm transmission grating with α = 51.896° (λc,. = 0.4 μm).

Fig. 18
Fig. 18

Efficiencies as functions of angle of incidence θ (in degrees) for the grating of Fig. 13 (α = 55.851°, 600 grooves/mm) at wavelength λ = 0.8 μm.

Fig. 19
Fig. 19

Efficiencies as functions of angle of incidence θ for the grating of Fig. 9 (α = 23.169°, 600 grooves/mm) at wavelength λ = 0.4 μm.

Fig. 20
Fig. 20

Efficiencies as functions of groove depth h for a 600-groove/mm sinusoidal grating (θ = 30.166°, λ = 0.5 μm).

Fig. 21
Fig. 21

Efficiencies as functions of wavelength for a 600-groove/mm transmission grating with a 23.169° blaze angle illuminated under normal incidence. Dashed curve: TE polarization; dotted curve: TM polarization; solid curve: natural light.

Fig. 22
Fig. 22

Same as Fig. 21 but with α = 30.166°.

Fig. 23
Fig. 23

Same as Fig. 21 but with α = 37.602°.

Fig. 24
Fig. 24

Same as Fig. 21 but with α = 45.987°.

Fig. 25
Fig. 25

Same as Fig. 21 but with α = 55.851°.

Fig. 26
Fig. 26

Efficiencies as functions of wavelength for a 300-groove/mm transmission grating with a 21.075° blaze angle illuminated under normal incidence. Dashed curve: TE polarization; dotted curve: TM polarization; solid curve: natural light.

Tables (1)

Tables Icon

Table I Blaze Angles Corresponding to Wavelengths λc and Four Groove Frequencies for a Resin with Refractive Index ν, Deduced from the Grism Equation

Equations (3)

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a = λ ν 1 .
sin θ j = ν sin α + j λ d ,
( ν 1 ) sin α = λ d .

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