Abstract

The physical mechanism for the all-dielectric reflection gratings to achieve high efficiency in the -1st-order Littrow mounting is studied. The all-dielectric gratings consist of two parts, a surface-relief grating and a highly reflecting dielectric stack. The surface-relief grating sits on top of the reflecting stack. A simple analytical expression for diffraction efficiency is obtained in terms of the S-matrix elements of the two parts. By analyzing the expression we show that the diffraction can be interpreted as the interference of a symmetric wave and an antisymmetric wave. The conditions for achieving high diffraction efficiency are also identified. The analytical results are illustrated by numerical computations.

© 2003 Optical Society of America

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References

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  1. D. Strickland, G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef]
  2. M. D. Perry, G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917–924 (1994).
    [CrossRef] [PubMed]
  3. A. S. Svakhin, V. A. Sychugov, A. E. Tikhomirov, “Diffraction gratings with high optical strength for laser resonators,” Quantum Electron. 24, 233–235 (1994).
    [CrossRef]
  4. M. D. Perry, R. D. Boyd, J. A. Britten, D. Decker, B. W. Shore, C. Shannon, E. Shults, L. Li, “High-efficiency multilayer dielectric diffraction gratings,” Opt. Lett. 20, 940–942 (1995); erratum, Opt. Lett. 20, 1513 (1995).
    [CrossRef] [PubMed]
  5. B. W. Shore, M. D. Perry, J. A. Britten, R. D. Boyd, M. D. Feit, H. T. Nguyen, R. Chow, G. E. Loomis, L. Li, “Design of high-efficiency dielectric reflection gratings,” J. Opt. Soc. Am. A 14, 1124–1136 (1997).
    [CrossRef]
  6. K. Hehl, J. Bischoff, U. Mohaupt, M. Palme, B. Schnabel, L. Wenke, R. Bödefeld, W. Theobald, E. Welsch, R. Sauerbrey, H. Heyer, “High-efficiency dielectric reflection gratings: design, fabrication, and analysis,” Appl. Opt. 38, 6257–6271 (1999).
    [CrossRef]
  7. L. Li, H. Wei, “High-efficiency reflection gratings made on a highly reflecting multilayer thin-film system: a physical description,” in Diffractive Optics 2001, Vol. 30 of European Optical Society Technical Meetings Digest Series (European Optical Society, Hanover, Germany, 2001), pp. 16–17.
  8. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
    [CrossRef]
  9. M. Nevière, P. Vincent, “Sur une propriété de symétrie des réseaux diélectriques,” Opt. Acta 23, 557–568 (1976).
    [CrossRef]
  10. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
    [CrossRef]

1999 (1)

1997 (1)

1996 (1)

1995 (1)

1994 (2)

M. D. Perry, G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917–924 (1994).
[CrossRef] [PubMed]

A. S. Svakhin, V. A. Sychugov, A. E. Tikhomirov, “Diffraction gratings with high optical strength for laser resonators,” Quantum Electron. 24, 233–235 (1994).
[CrossRef]

1985 (1)

D. Strickland, G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

1978 (1)

1976 (1)

M. Nevière, P. Vincent, “Sur une propriété de symétrie des réseaux diélectriques,” Opt. Acta 23, 557–568 (1976).
[CrossRef]

Bischoff, J.

Bödefeld, R.

Boyd, R. D.

Britten, J. A.

Chow, R.

Decker, D.

Feit, M. D.

Hehl, K.

Heyer, H.

Knop, K.

Li, L.

Loomis, G. E.

Mohaupt, U.

Mourou, G.

M. D. Perry, G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917–924 (1994).
[CrossRef] [PubMed]

D. Strickland, G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Nevière, M.

M. Nevière, P. Vincent, “Sur une propriété de symétrie des réseaux diélectriques,” Opt. Acta 23, 557–568 (1976).
[CrossRef]

Nguyen, H. T.

Palme, M.

Perry, M. D.

Sauerbrey, R.

Schnabel, B.

Shannon, C.

Shore, B. W.

Shults, E.

Strickland, D.

D. Strickland, G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Svakhin, A. S.

A. S. Svakhin, V. A. Sychugov, A. E. Tikhomirov, “Diffraction gratings with high optical strength for laser resonators,” Quantum Electron. 24, 233–235 (1994).
[CrossRef]

Sychugov, V. A.

A. S. Svakhin, V. A. Sychugov, A. E. Tikhomirov, “Diffraction gratings with high optical strength for laser resonators,” Quantum Electron. 24, 233–235 (1994).
[CrossRef]

Theobald, W.

Tikhomirov, A. E.

A. S. Svakhin, V. A. Sychugov, A. E. Tikhomirov, “Diffraction gratings with high optical strength for laser resonators,” Quantum Electron. 24, 233–235 (1994).
[CrossRef]

Vincent, P.

M. Nevière, P. Vincent, “Sur une propriété de symétrie des réseaux diélectriques,” Opt. Acta 23, 557–568 (1976).
[CrossRef]

Wei, H.

L. Li, H. Wei, “High-efficiency reflection gratings made on a highly reflecting multilayer thin-film system: a physical description,” in Diffractive Optics 2001, Vol. 30 of European Optical Society Technical Meetings Digest Series (European Optical Society, Hanover, Germany, 2001), pp. 16–17.

Welsch, E.

Wenke, L.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Acta (1)

M. Nevière, P. Vincent, “Sur une propriété de symétrie des réseaux diélectriques,” Opt. Acta 23, 557–568 (1976).
[CrossRef]

Opt. Commun. (1)

D. Strickland, G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Opt. Lett. (1)

Quantum Electron. (1)

A. S. Svakhin, V. A. Sychugov, A. E. Tikhomirov, “Diffraction gratings with high optical strength for laser resonators,” Quantum Electron. 24, 233–235 (1994).
[CrossRef]

Science (1)

M. D. Perry, G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917–924 (1994).
[CrossRef] [PubMed]

Other (1)

L. Li, H. Wei, “High-efficiency reflection gratings made on a highly reflecting multilayer thin-film system: a physical description,” in Diffractive Optics 2001, Vol. 30 of European Optical Society Technical Meetings Digest Series (European Optical Society, Hanover, Germany, 2001), pp. 16–17.

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Figures (5)

Fig. 1
Fig. 1

All-dielectric, multilayer-substrate reflection grating analyzed as a combination of two subsystems, a surface-relief grating and a multilayer HR stack, as depicted by the two dashed rectangular boxes: h and h c denote the groove depth and the thickness of the connecting layer, and u and d denote amplitude vectors of waves that propagate upward and downward, respectively. S denotes the scattering matrices.

Fig. 2
Fig. 2

Incidence and diffraction of a symmetric and an antisymmetric wave and those of their superposition. (a), (c), (e) Incidence configurations; (b), (d), (f) diffraction configurations. Suppose that the two right incident waves in (a) and (c) are in phase; then the condition for achieving the situation in (e) and (f) is that the two left (right) diffracted waves in (b) and (d) be in (180° out of) phase.

Fig. 3
Fig. 3

Phase analysis of the mechanism for achieving high efficiency. The condition for the superposition of the four diffracted plane waves in (b) to produce only a net left diffracted plane wave is that the two transmitted diffracted waves in (a) have the same magnitude and be 90° out of phase.

Fig. 4
Fig. 4

Diffraction efficiency (-1st-order in reflection) versus groove depth. The data of the approximate model are almost the same as those of the rigorous model.

Fig. 5
Fig. 5

Relationship between grating efficiency and two eigenvalues a ±, and two transmission coefficients of the corrugated interface τ and τ′. (a) Grating efficiency (-1st-order in reflection) versus groove depth and thickness of the connecting layer; (b) magnitude of a +/a - versus groove depth and thickness of the connecting layer; (c) phase of a +/a - versus groove depth and thickness of the connecting layer, with phase range [-π, π]; (d) magnitude of τ, τ′ and phase of τ/τ′ versus groove depth.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

uidgc=Sgugcdi, ugcdrc=Scurcdgc, urcds=Srusdrc.
Sc=expiβmc+hc00exp-iβmc-hc,
uidgc=tuugrudgrdugtddgugcdi, urcds=tuurrudrrdurtddrusdrc.
S=Sg * Sc * Sr,
S12=rud+tuuR˜1-rduR˜-1tdd.
rud=ρρρρ, rdu=rrrr, tdd=ττττ, tuu=tttt.
S12=aaaa.
a±=a±a, v±=12±11,
S12v±=a±v±.
vinc=01=12v++v-.
S12vinc=12S12v++v-=12a+-a-a++a-.
a±=ρ±+t±R˜1-r±R˜-1τ±.
a±t±R˜τ±.
a+a-t+R˜τ+t-R˜τ-=τ/τ+1τ/τ-12.
τ/τ=±i.

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