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Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 9 — May. 2, 2005
  • pp: 3230–3235
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99% efficiency measured in the -1st order of a resonant grating

N. Destouches, A. V. Tishchenko, J. C. Pommier, S. Reynaud, O. Parriaux, S. Tonchev, and M. Abdou Ahmed  »View Author Affiliations


Optics Express, Vol. 13, Issue 9, pp. 3230-3235 (2005)
http://dx.doi.org/10.1364/OPEX.13.003230


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Abstract

A resonant diffraction grating comprising a mirror, a dielectric layer and a high index corrugation at the layer-air interface is shown to exhibit off-Littrow the record diffraction efficiency of 99% in the -1st reflected order at 1064 nm wavelength thanks to the excitation of a leaky mode of the layer. Such high figure is obtained by a grating 5 to 10 times shallower than in current attempts to realize high efficiency all-dielectric gratings.

© 2005 Optical Society of America

1. Introduction

Unlike their standard metallic counterparts, resonant all-dielectric gratings are capable of diffracting an incident free space wave with a diffraction efficiency of up to 100% theoretically [1

1. G.A. Golubenko, A.S. Svakhin, A.V. Tishchenko, and V.A Sychugov, “Total reflection of light from the corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985). [CrossRef]

2

2. A.V. Tishchenko and V.A. Sychugov, “High grating efficiency by energy accumulation in a leaky mode,” Opt. and Quantum Electron. 32, 1027–1031 (2000). [CrossRef]

]. They are composed of a dielectric film and of a surface corrugation or film index modulation. Since diffraction in resonant gratings involves the excitation of a waveguide mode, the efficiency possibly exhibits high polarization, angular and wavelength selectivity, which offers new functions and performances to the field of optical filtering.

There are mainly two types of resonant phenomena taking place in a dielectric slab associated with a periodical corrugation. The first type relies upon the excitation of a propagating mode of the dielectric layer used as a slab waveguide. Under the condition αD≫2π (D is the incident beam diameter, α is the radiation coefficient of the considered mode of the grating waveguide [3

3. V.A. Sychugov and A.V. Tishchenko, “Light emission from a corrugated dielectric waveguide,” Sov. J. Quantum Electron. 10 (2), 186–189 (1980). [CrossRef]

4

4. I.A. Avrutsky and V. A. Sychugov “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527 (1989) [CrossRef]

]), and in the neighbourhood of the waveguide mode synchronism condition, the corrugated waveguide exhibits close to 100% reflection of a finite beam in the direction of the zeroth order [1

1. G.A. Golubenko, A.S. Svakhin, A.V. Tishchenko, and V.A Sychugov, “Total reflection of light from the corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985). [CrossRef]

]. This resonant effect [4

4. I.A. Avrutsky and V. A. Sychugov “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527 (1989) [CrossRef]

], called anomalous reflection [5

5. O. Parriaux, V. A. Sychugov, and A. V. Tishchenko, “Coupling gratings as functional elements,” Pure Appl. Opt. 5, 453–469 (1996) [CrossRef]

], or resonant reflection [6

6. S.S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993). [CrossRef] [PubMed]

], can be understood phenomenologically as a destructive interference in the transmission medium between the wave crossing the waveguide grating without being diffracted (the zeroth transmitted order) and the wave trapped in the slab waveguide by +1st or −1st order coupling, and re-radiated out into the transmission medium.

The second type of resonant grating is the subject of the experimental result of the present paper. The mechanism is quite different and much less known in the scientific community although implicitly used sometimes as the result of numerical computing [7

7. K. Hehl, J. Bischoff, U. Mohaupt, M. Palme, B. Schnabel, L Wenke, R. Boedefeld, W. Theobald, E. Welsch, R. Sauerbrey, and H. Heyer, “High-efficiency dielectric reflection gratings: design, fabrication and analysis,” Appl. Opt. 38, 6257–6271 (1999). [CrossRef]

]. No truly guided mode is involved. The field trapping is achieved here by the refractive excitation of a leaky mode of a mirror based layer [8

8. R. Ulrich and W. Prettl, “Planar leaky light-guides and couplers,” Appl. Phys. 1, 55–68 (1973). [CrossRef]

9

9. J.D. Decotignie, O. Parriaux, and F.E. Gardiol, “Wave propagation in lossy and leaky planar optical waveguides,” AEÜ, Band 35, 201–204 (1981).

]. The grating acts as a valve allowing the cancellation of the Fresnel reflection and thus imposing in principle 100% diffraction efficiency in the −1st order [2

2. A.V. Tishchenko and V.A. Sychugov, “High grating efficiency by energy accumulation in a leaky mode,” Opt. and Quantum Electron. 32, 1027–1031 (2000). [CrossRef]

;10

10. I.F. Salakhutdinov, V.A. Sychugov, and O. Parriaux, “Highly efficient diffraction gratings for use in the Littman-Metcalf mounting,” Quantum Electron. 28, 983–986 (1998). [CrossRef]

]. We are reporting here the record experimental value of more than 99% diffraction efficiency (a comparable result was recently reported [11

11. T. Clausnitzer, T. Schreiber, F. Röser, J. Limpert, E.-B. Kley, H.- J. Fuchs, and A. Tuennermann, “Highly efficient dielectric gratings for high power ultrafast fiberlaser systems,” SPIE Photonics West 22–27 January, 2005, Conference Proceeding No 5714 Commercial and Biomedical Applications of Ultrafast Lasers VII (in print), Paper No 49.

] for a similar structure under the Littrow mounting which is known to always permit close to 100% diffraction efficiency [12

12. H. Wei and L. Li, “All-dielectric reflection gratings: a study of the physical mechanism for achieving high efficiency,” Appl. Opt. 42 (31), 6255–6260 (2003). [CrossRef] [PubMed]

]; the present result is obtained off-Littrow). A further achievement reported here is that the grating is made in the last high index layer of a multilayer stack which permits maximum efficiency to be obtained by 5 to 10 times shallower grating grooves.

2. Operation principle and structure design

Let an incident free space wave impinge under incidence angle θi onto a dielectric layer placed on a mirror. If the refraction angle θf in the layer of refractive index nf, the average layer thickness h and the wavelength λ satisfy the condition

k0nfhcosθf+ϕm+ϕc2=mπ
(1)

the incident wave excites a leaky mode resonance of order m [10

10. I.F. Salakhutdinov, V.A. Sychugov, and O. Parriaux, “Highly efficient diffraction gratings for use in the Littman-Metcalf mounting,” Quantum Electron. 28, 983–986 (1998). [CrossRef]

] in the mirror layer. The incident field is trapped in the layer with some rate of leakage into the cover medium, which can be controlled by the reflection coefficient at the film-cover interface. k0=2π/λ is the vacuum wave number, ϕm is the reflection phase shift at the mirror and ϕc is the reflection phase shift at the layer-cover interface in case of incidence from the layer. In the absence of grating there are two contributions to the Fresnel reflection : the wave firstly reflected at the layer surface, and the trapped leaky mode field re-radiating into the cover. The presence of a grating, as sketched in figure 1, modifies the balance between these two reflection contributions through its 0th order; furthermore, its −1st order represents an additional output port for the field trapped in the layer. The second contribution results from a resonance. Under the hypothesis that dispersion equation (1) is fulfilled, its phase is opposite to the phase of the first contribution. There is consequently the possibility of cancelling the overall reflection in the Fresnel reflection direction by rendering the modulus of the two contributions equal. If moreover the −1st diffraction order is the only one which can propagate, the light has nowhere else to propagate but to be diffracted with 100% efficiency (minus the metal loss if the mirror is metallic). This resonant diffraction effect is polarization selective since ϕm and ϕc are usually polarization dependent. It can be highly wavelength selective if the leaky mode resonance is sharp, i.e., if the incidence angle θi is large and if the mirror is essentially lossless.

Fig. 1. Fresnel reflection mechanism on a mirror based corrugated dielectric film : direct reflection, field trapping, leaky mode propagation and re-radiation. The corrugation balances the direct reflected and the re-radiated field modulus ensuring 100% −1st order efficiency. The inset represents the fabricated multilayer grating structure.

The grating structure firstly comprises a multilayer mirror made of eighteen quarter wave layers for the prescribed incidence angle. The low index (nL) and high index (nH) layers are respectively made of SiO2 and Ta2O5 (nL=1.48 and nH=2.18 at λ=1064 nm in the case of ion plating layer deposition technology). The quarter wave layer thicknesses are wL=λ4nLcosθL and wH=λ4nHcosθH where θL and θH are the refracted angles which the incident wave makes in the low and high index quarter wave layers with respect to the normal. The multilayer mirror has a wide angular width; its role is primarily to act as the mirror for the leaky mode. It should however also reflect the −1st diffraction order of the grating propagating towards the substrate. The incident and diffracted beams being not far off angularly in the present case, a single periodic multilayer with wH=131 nm and wL=223 nm was used.

The leaky mode guiding corrugated layer lies on top of the multilayer mirror. It can be of low or of high index, or even of composite index provided the dispersion equation (1) or that given in ref. [9

9. J.D. Decotignie, O. Parriaux, and F.E. Gardiol, “Wave propagation in lossy and leaky planar optical waveguides,” AEÜ, Band 35, 201–204 (1981).

] is satisfied. The solution which was engineered in the present case was to combine a low index leaky mode guiding layer with a high index grating layer made of Ta2O5 as sketched in the inset of Fig. 1. This represents the very beneficial advantage of achieving a high efficiency grating with quite shallow grooves (hardly some tens of nanometers deep against several hundreds of nanometers if the leaky mode guiding layer was a unique silica layer). The reflection phase shift terms ϕs and ϕc in the leaky mode dispersion equation (1) applied to the leaky mode guiding layer for the TE polarization are in the present case ϕs=π, because the first layer of the mirror is a high index layer, and ϕc=0. Equation (1) for the fundamental mode (m=1) writes

k0nfhcosθf=π2
(2)

which means that the leaky mode guiding layer must be a quarter wave layer. The fundamental leaky mode exhibits zero field amplitude at the multilayer mirror surface, but a field maximum at the air boundary where the corrugation is made.

However, the leaky mode guiding layer is here composed of two sub-layers: the low index layer (152 nm) and the average thickness of the high index corrugation. The latter consists of 50 nm deep quasi-rectangular grooves of close to 50/50 line/space ratio etched into a Ta2O5 layer of initial thickness of 70 nm; this is equivalent for the TE polarization to a uniform Ta2O5 layer of 20+25=45 nm thickness. The sum of the two contributions is equivalent to a single low index layer of 230 nm which is close to the thickness of a quarter wave layer at 1064 nm wavelength and under 73° incidence.

3. Grating technology and experimental results

The multilayer was deposited by ion plating (Tafelmaier, Rosenheim, Germany) onto a 6.35 mm thick quartz wafer of 50 mm diameter. The grating was firstly created by exposing the resist coated multilayer mirror to an interferogramme at 442 nm wavelength, then transferred into the last high index layer by ion beam etching. As illustrated in Fig. 2 an AFM scan of the resulting corrugation shows a quasi-rectangular profile with a line/space ratio of 0.85 and a groove depth of 52 nm meaning that a 18 nm thick Ta2O5 layer remains under the grating. The theoretical diffraction efficiency in the −1st order of such a grating structure calculated at 1064 nm wavelength under an incidence angle of 73 ° is more than 99.7 %. Under these incidence and diffraction conditions the only propagating non-zero diffraction order is the −1st order. A microchip Nd:YAG laser was used to measure the angular spectrum of the −1st order diffraction of the device at 1064 nm wavelength.

Fig. 2. AFM scan of the 560 nm period grating etched into the last Ta2O5 layer of 70 nm thickness.
Fig. 3. Comparison of the experimental and the theoretical diffraction efficiencies of the −1st order for the TE polarization. Calculations are performed taking into account the groove depth experimental value of 52 nm and a line/space ratio of 0.85. Both experiments and calculations are performed at a wavelength of 1064 nm with a variable incidence angle. The diffraction efficiency is defined as the ratio between the diffracted power and the incident power.

The curves of Fig. 4 illustrate the diffraction efficiency of the TM polarization; as expected, the efficiency is practically zero because the TM leaky mode excitation condition is not fulfilled. Moreover, the multilayer is no perfect reflector for the TM orders and part of the incident power is transmitted in the 0th and −1st orders of the substrate. This explains why the sum of the two theoretical curves is not unity.

Fig. 4. Comparison of the experimental and the theoretical diffraction efficiencies in the 0th order in TM polarization. Both experiments and calculations are performed at a wavelength of 1064 nm with a variable incidence angle. In this case, TM leaky mode excitation condition is not fulfilled and −1st order efficiency is practically zero.

4. Conclusion

It was shown that an all-dielectric reflection grating can reach diffraction efficiencies above 99%, i.e., above the reflection coefficient of the best metal mirrors, and close to that of multilayer dielectric mirrors. This means that such element can now be envisaged for the low loss performance of a complex optical function usually requiring at least one standard mirror and one or more discrete optical elements such as a Lyot filter.

The phenomenological understanding proposed for this type of resonant grating has been explained and was shown to easily lead to a design, which is naturally capable of best satisfying the specifications under given constraints prior to any numerical modelling effort. It was shown in particular that such high efficiency can be obtained by the moderate technological effort of etching a few tens of nanometers deep grooves, i.e., between 5 and 10 times less than in the best known endeavours. The applicability of such resonant gratings goes well beyond the present application, still to be demonstrated, as a highly dispersive mirror. Systematic results concerning the grating uniformity, attempts of applying the technique of scatterometry for contactless, high resolution testing, as well as laser damage threshold investigation on this second type of resonant gratings will be reported in an extended paper.

Acknowledgments

The R&D as well as the applicative endeavours on resonant gratings are now performed within the Network of Excellence NEMO.

References and links

1.

G.A. Golubenko, A.S. Svakhin, A.V. Tishchenko, and V.A Sychugov, “Total reflection of light from the corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985). [CrossRef]

2.

A.V. Tishchenko and V.A. Sychugov, “High grating efficiency by energy accumulation in a leaky mode,” Opt. and Quantum Electron. 32, 1027–1031 (2000). [CrossRef]

3.

V.A. Sychugov and A.V. Tishchenko, “Light emission from a corrugated dielectric waveguide,” Sov. J. Quantum Electron. 10 (2), 186–189 (1980). [CrossRef]

4.

I.A. Avrutsky and V. A. Sychugov “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527 (1989) [CrossRef]

5.

O. Parriaux, V. A. Sychugov, and A. V. Tishchenko, “Coupling gratings as functional elements,” Pure Appl. Opt. 5, 453–469 (1996) [CrossRef]

6.

S.S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993). [CrossRef] [PubMed]

7.

K. Hehl, J. Bischoff, U. Mohaupt, M. Palme, B. Schnabel, L Wenke, R. Boedefeld, W. Theobald, E. Welsch, R. Sauerbrey, and H. Heyer, “High-efficiency dielectric reflection gratings: design, fabrication and analysis,” Appl. Opt. 38, 6257–6271 (1999). [CrossRef]

8.

R. Ulrich and W. Prettl, “Planar leaky light-guides and couplers,” Appl. Phys. 1, 55–68 (1973). [CrossRef]

9.

J.D. Decotignie, O. Parriaux, and F.E. Gardiol, “Wave propagation in lossy and leaky planar optical waveguides,” AEÜ, Band 35, 201–204 (1981).

10.

I.F. Salakhutdinov, V.A. Sychugov, and O. Parriaux, “Highly efficient diffraction gratings for use in the Littman-Metcalf mounting,” Quantum Electron. 28, 983–986 (1998). [CrossRef]

11.

T. Clausnitzer, T. Schreiber, F. Röser, J. Limpert, E.-B. Kley, H.- J. Fuchs, and A. Tuennermann, “Highly efficient dielectric gratings for high power ultrafast fiberlaser systems,” SPIE Photonics West 22–27 January, 2005, Conference Proceeding No 5714 Commercial and Biomedical Applications of Ultrafast Lasers VII (in print), Paper No 49.

12.

H. Wei and L. Li, “All-dielectric reflection gratings: a study of the physical mechanism for achieving high efficiency,” Appl. Opt. 42 (31), 6255–6260 (2003). [CrossRef] [PubMed]

13.

M. D. Perry, R.D. Boyd, J.A. Decker, B.W. Shore, C. Shannon, and E. Shults, “High-efficiency multilayer dielectric diffraction gratings,” Opt. Lett. 20, 940–942 (1995). [CrossRef] [PubMed]

14.

B. Touzet and J. R. Gilchrist, “Multilayer dielectric gratings enable more-powerful high-energy lasers,” Photonics Spectra, 68–75, Sept 2003.

15.

M. A. Ahmed, J.-C. Pommier, F. Pigeon, and O. Parriaux, “Flux resistance degradation in resonant grating multilayer mirror,” SPIE 5250, 27 (2003).

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(140.3570) Lasers and laser optics : Lasers, single-mode
(230.4000) Optical devices : Microstructure fabrication
(310.2790) Thin films : Guided waves
(310.6860) Thin films : Thin films, optical properties

ToC Category:
Research Papers

History
Original Manuscript: March 18, 2005
Revised Manuscript: April 13, 2005
Published: May 2, 2005

Citation
N. Destouches, A. Tishchenko, J. Pommier, S. Reynaud, O. Parriaux, S. Tonchev, and M. Ahmed, "99% efficiency measured in the -1st order of a resonant grating," Opt. Express 13, 3230-3235 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-9-3230


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References

  1. G.A. Golubenko, A.S. Svakhin, A.V. Tishchenko, V.A Sychugov, �??Total reflection of light from the corrugated surface of a dielectric waveguide,�?? Sov. J. Quantum Electron. 15, 886-887 (1985). [CrossRef]
  2. A.V. Tishchenko, V.A. Sychugov, �??High grating efficiency by energy accumulation in a leaky mode,�?? Opt. and Quantum Electron. 32, 1027-1031 (2000). [CrossRef]
  3. V.A. Sychugov, A.V. Tishchenko, �??Light emission from a corrugated dielectric waveguide,�?? Sov. J. Quantum Electron. 10 (2), 186-189 (1980). [CrossRef]
  4. I.A. Avrutsky, V. A. Sychugov �??Reflection of a beam of finite size from a corrugated waveguide,�?? J. Mod. Opt. 36, 1527 (1989). [CrossRef]
  5. O. Parriaux, V. A. Sychugov, A. V. Tishchenko, �??Coupling gratings as functional elements,�?? Pure Appl. Opt. 5, 453-469 (1996). [CrossRef]
  6. S.S. Wang, R. Magnusson, �??Theory and applications of guided-mode resonance filters,�?? Appl. Opt. 32, 2606-2613 (1993). [CrossRef] [PubMed]
  7. K. Hehl, J. Bischoff, U. Mohaupt, M. Palme, B. Schnabel, L, Wenke, R. Boedefeld, W. Theobald, E. Welsch, R. Sauerbrey, H. Heyer, �??High-efficiency dielectric reflection gratings: design, fabrication and analysis,�?? Appl. Opt. 38, 6257-6271 (1999). [CrossRef]
  8. R. Ulrich, W. Prettl, �??Planar leaky light-guides and couplers,�?? Appl. Phys. 1, 55-68 (1973). [CrossRef]
  9. J.D. Decotignie, O. Parriaux, F.E. Gardiol, �??Wave propagation in lossy and leaky planar optical waveguides,�?? AE�?, Band 35, 201-204 (1981).
  10. I.F. Salakhutdinov, V.A. Sychugov, O. Parriaux, �??Highly efficient diffraction gratings for use in the Littman-Metcalf mounting,�?? Quantum Electron. 28, 983-986 (1998). [CrossRef]
  11. T. Clausnitzer, T. Schreiber, F. Röser, J. Limpert, E.-B. Kley, H.- J. Fuchs, A. Tuennermann, �??Highly efficient dielectric gratings for high power ultrafast fiberlaser systems,�?? SPIE Photonics West 22-27 January, 2005, Conference Proceeding No 5714 Commercial and Biomedical Applications of Ultrafast Lasers VII (in print), Paper No 49.
  12. H. Wei, L. Li, �??All-dielectric reflection gratings: a study of the physical mechanism for achieving high efficiency,�?? Appl. Opt. 42 (31), 6255-6260 (2003). [CrossRef] [PubMed]
  13. M. D. Perry, R.D. Boyd, J.A. Decker, B.W. Shore, C. Shannon, E. Shults, �??High-efficiency multilayer dielectric diffraction gratings,�?? Opt. Lett. 20, 940-942 (1995). [CrossRef] [PubMed]
  14. B. Touzet, J. R. Gilchrist, �??Multilayer dielectric gratings enable more-powerful high-energy lasers,�?? Photonics Spectra, 68-75, Sept 2003.
  15. M. A. Ahmed, J.-C. Pommier, F. Pigeon, O. Parriaux, �??Flux resistance degradation in resonant grating multilayer mirror,�?? SPIE 5250, 27 (2003).

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