The development of methods to fabricate micro-optical devices, and more particularly diffractive el-ements to direct light or separate wavelengths, hasbecome an active and productive area of research inrecent years.1–3 Miniaturization brings opportuni-ties to introduce new technologies, new fabricationtechniques, and new materials. The optical proper-ties of a material with a refractive index modulated atthe scale of the wavelength may strongly differ fromthose of a material whose refractive index is modu-lated at the scale of a fraction of the wavelength.Efficient components can be achieved with tech-niques such as photolithography, electron-beamwriting, reactive ion etching, diamond turning of op-tical surfaces, or replication.4 But titanium-ionmplantation5–7 constitutes a suitable technique for
making refractive-index gratings.8,9 Indeed, ion im-lantation permits one to modify refractive index of
L. Esoubas [email protected]!, F. Flory, F.Lemarchand, E. Drouard, and G. Albrand are with the Equipe“Composants Optiques Microstructures,” Laboratoire d’Optiquedes Surfaces et des Couches Minces, Centre National de la Recher-che Scientifique, Unite Propre de Recherche 6080, Ecole NationaleSuperieure de Physique de Marseille, Domaine Universitaire deSaint Jerome, 13397 Marseille Cedex 20, France. L. Roux and S.Tisserand are with Ion Beam Services, rue Imbert prolongee,13790 Peynier, France.
Received 26 June 2000; revised manuscript received 23 October2000.
bulk or thin-film silica without patterning the sur-face. Refractive-index changes are well controlledthrough the implanted dose of ions, and the in-depthindex profile can be adjusted by the ion energy. Un-like with other techniques, we obtain componentswith quasi-plane surfaces, which permits us to de-posit coatings on top of them with a perfect planarsurface. Thus ion implantation, which is a well-mastered process in microelectronics, might be usefulfor fabricating an extended class of diffractive opticalelements ~such as blazed gratings, Fresnel lenses,and so on!. But first the diffraction efficiency ofndex-modulated binary gratings obtained by ion im-lantation has to be increased. Thus our purpose inhis study is to demonstrate that diffraction efficiencyan be strongly increased.
In previous research,9 it was theoretically shownthat one could enhance the free-space diffraction ef-ficiency of gratings made by titanium-ion implanta-tion by inserting them into multilayer dielectricFabry–Perot cavities. More precisely, a computerprogram was developed that was able to calculate thediffraction efficiencies of single-phase gratings orphase gratings embedded in multilayer optical inter-ference coatings with a differential method.10–12
Even if the refractive-index variation between im-planted and nonimplanted areas is high ~0.7 at l 50.6328 mm!, single gratings made in silica exhibit a
iffraction efficiency in the 11 transmitted order un-er TE illumination of only 0.78% ~at l 5 0.6328 mm!,ecause the implanted material is only 120 nm thicksee Fig. 1!.
A thin-film Fabry–Perot cavity was considered.
1 April 2001 y Vol. 40, No. 10 y APPLIED OPTICS 1587
totsfi
mfeeFrna
tcttlcgc
oWtl
cN
s
1
The grating was positioned in the spacer layer of theFabry–Perot cavity ~see Fig. 2! to benefit from theelectromagnetic field resonance and to increase, bythis means, the diffraction efficiency. Various de-signs of the Fabry–Perot multilayer were considered.Efficiencies of the 11 TE order of diffraction werecomputed for dielectric mirrors with p alternate lay-ers of low ~SiO2! and high ~Ta2O5! refractive index.p 5 1, 3, 5, 7, 9, 11. Layers had quarter-wave opti-cal thickness at a manufacturing wavelength lf~0.4 , lf , 0.8 mm!, and the thickness t of the non-implanted part of the spacer was between 0 and 2 mm~Fig. 3!. Then we demonstrated by computationthat a maximal diffraction efficiency of 18.8% wasreached at l 5 0.6328 mm when p 5 11, t 5 1467 nmand, lf 5 751 nm ~Figs. 3 and 4!. The efficiency washus increased to as much as 24 times the efficiencyf the single grating. The maximal 11 TE transmit-ed order efficiency was found for thickness t of thepacer for which the Fabry–Perot cavity is resonantor the two directions of diffraction and for the normalncidence. The numerical study showed that the
Fig. 1. In-depth index profile of a titanium implanted silica layer.
Fig. 2. Grating embedded in a Fabry–Perot cavity.
Fig. 3. Diffraction efficiency of the 11 TE transmitted order ver-us the thickness of the nonimplanted part of the spacer.
588 APPLIED OPTICS y Vol. 40, No. 10 y 1 April 2001
aximal diffraction efficiency was lower than 18.8%or structures whose mirrors have more than 11 lay-rs. Indeed, it was necessary to have a maximallectromagnetic field on the grating, inside theabry–Perot cavity. This condition had to beeached for the two directions of diffraction and forormal incidence. Such a double condition requiredcompromise from the structures considered.In the following study we first present the sensi-
ivity of the diffraction efficiency to the optogeometri-al parameters of the structures. Then we describehe process used to insert a grating made byitanium-ion implantation in the spacer of a multi-ayer dielectric Fabry–Perot cavity. Finally, we dis-uss efficiency measurements versus period dx of therating and versus angle of incidence u of light on theomponent.
2. Dependence of the Diffraction Efficiency on theOptogeometrical Parameters
As we have previously seen, the most efficient struc-ture is obtained with 11-layer mirrors, and it reachesa theoretical efficiency of 18.8%. We are here con-cerned with a structure with 7-layer mirrors, which iseasier to manufacture than those with 9- or 11-layermirrors. The calculations show that, for maximumefficiency of the 11 TE transmitted order, t 5 1711nm and lf of the mirrors is 751 nm. This efficiencyreaches 14.2%, i.e., 18 times that obtained for theuncoated grating.
The efficiency depends on many optogeometricalparameters: maximal refractive index Nmax, width sand depth m of the maximal refractive-index value ofimplanted areas ~see Fig. 1!, fill factor a and period dxf the grating, and the angle of incidence of light u.e compute the influence of each parameter, keeping
he others constant. The optimal parameters areisted in Table 1.
Since the implanted dose of titanium can be pre-isely set, the maximum value of the refractive indexmax is controlled at 2.17 with an accuracy of
62 3 1022. Computations ~Fig. 5! show that in thiscase the efficiency remains higher than 14%.
Moreover, because the ion implantation techniqueis well mastered, s ~in-depth width of implanted ar-
Fig. 4. Maximal diffraction efficiency of the 11 TE transmittedorder versus the number of dielectric layers p of the mirrors.
vi
vc
itp0
a
s
s
Table 1. Optogeometrical Parameters
eas! and m ~position of the maximal refractive-indexalue! can be considered to remain close to their nom-nal values of 0.097 and 0.060 mm, respectively. We
deduce, from the calculations ~Figs. 6 and 7!, that forvariations of s between 0.075 and 0.120 mm and forariations of m between 0.03 and 0.073 mm the effi-iency remains higher than 12%.
If fill factor a of the grating is controlled within thenterval @0.45, 0.55# the efficiency remains higherhan 13% ~Fig. 8!. By using a holographic setup forhotolithography,13 one easily obtains a fill factor of.5 with an accuracy of better than 60.05.The value of dx ~1 mm! must be well controlled to
within 610 nm to keep the efficiency above 10% ~Fig.9!. By means of calibrating the holographic setupwe developed, the period dx is controlled with a63-nm accuracy.
Fig. 5. Diffraction efficiency of the 11 TE transmitted order ver-us Nmax.
Fig. 6. Diffraction efficiency of the 11 TE transmitted order ver-us s.
RaUs
Maximal refractive index, Nmax
Half-width of the index profile, sDepth of Nmax, mFill factor, aGrating period, dxIncident angle, u 2
The angle of incidence u on the component must beaccurately set ~20.1° , u ,0.1°! to yield an efficiencyhigher than 10% ~Fig. 10!. For incident anglesgreater than 1.5° or less than 21.5° the efficiency islower than 2%. One can note that a maximum effi-ciency of 20% is reached for an incident angle of 0.3°,which precisely corresponds to the resonance of thestructure.
3. Experimental Results
To demonstrate the feasibility of components withenhanced diffraction efficiency, we make a Fabry–Perot cavity composed of seven-layer mirrors.
A. Process
A dielectric mirror made of Ta2O5 and SiO2 layersnd the spacer made of SiO2 are first deposited by
Fig. 7. Diffraction efficiency of the 11 TE transmitted order ver-sus m.
Fig. 8. Diffraction efficiency of the 11 TE transmitted order ver-sus a.
of ParametersOptimization Optimal Parameters
–2.5 2.175–0.120 mm 0.097 mm–0.09 mm 0.060 mm–0.9 0.5–1.2 mm 1 mmto 11.5° 0°
ngesed in
20.070.030.10.8
1.5°
1 April 2001 y Vol. 40, No. 10 y APPLIED OPTICS 1589
~s
n~h
rod
dfal~~mtltwasnpnop
s
1
ion plating. During the deposition process we op-tically monitor the layer thicknesses to make a mir-ror centered at lf 5 751 nm. Then the gratingperiod, 1 mm; fill factor, 0.5! is implanted in thepacer by use of the process described in Fig. 11.The photoresist ~Shipley S1805! is spun in a 500-
m-thick layer ~30 s at 4000 rpm! on the spacerstep I of Fig. 11! and exposed with an argon laserolographic interference setup ~step II of Fig. 11!13
to pattern the grating. Indeed, when two coherentand monochromatic optical plane waves intersecteach other with the same intensity, wavelength,and polarization state, interference fringes areformed in the region of intersection ~Fig. 12!. Theesultant intensity distributions ~Fig. 12! form a setf straight and equally spaced fringes ~bright andark lines!.14 This fringe pattern is recorded in
the photoresist, since the regions of zero field inten-sity leave the resist unexposed, whereas regions ofmaximum intensity leave the resist maximally ex-posed. With our setup, the period of the resultantinterference fringes is given by dx 5 llasery2 sin a~where a is the angle of incidence on the sample!.Hence a small angle between the beams produces awidely spaced fringe pattern, whereas a large oneproduces a fine fringe pattern. Thus we select theangle corresponding to a fringe pattern with dx 5 1mm, and we expose the photoresist during 60 s with
Fig. 9. Diffraction efficiency of the 11 TE transmitted order ver-us dx.
Fig. 10. Diffraction efficiency of the 11 TE transmitted orderversus u.
590 APPLIED OPTICS y Vol. 40, No. 10 y 1 April 2001
105 mWycm2 at l 5 457.9 nm. The photoresist iseveloped ~step III of Fig. 11! after the laser inter-erence patterning. The exposed regions ~Fig. 12!re removed during the development. A chromiumayer is then deposited on the surface componentstep IV of Fig. 11!. After removing the photoresistlift-off; step V of Fig. 11!, we obtain a chromiumask for titanium implantation ~Fig. 13!. The
hickness of the chromium layer is 100 nm, which isarge enough to stop titanium ions in our implan-ation conditions. Then titanium is implantedith adequate dose and energy ~step VI of Fig. 11!,nd the chromium layer is etched with Chrometcholution ~step VII of Fig. 11!. Finally, the compo-ent is annealed to oxidize the titanium, and ahase grating is obtained. The implantation doesot pattern the surface of the spacer; thus the sec-nd seven-layer mirror is easily deposited to com-lete the Fabry–Perot cavity ~see Fig. 2!.
Fig. 11. Grating manufacturing.
B. Efficiency Measurements
Three different phase gratings embedded in thespacer of seven-layer mirror Fabry–Perot structureshave been fabricated. The holographic setup wasset to make grating periods of dx 5 0.982, 1.000, and1.013 mm, respectively.
By accurately measuring the angles of diffractionof the 11 TE transmitted orders in a Littrow config-uration, we obtain the values of the grating periods:0.982, 1.000, and 1.010 mm, respectively. Thus, bymeans of calibrating the holographic setup, the grat-
Fig. 12. Holographic setup and in
Fig. 13. SEM image of the chromium mask.
ing period is precisely controlled within a few nano-meters’ accuracy.
We measured 11 TE transmitted order diffractionefficiencies of the gratings in the multilayer struc-tures in normal incidence, using a photodetector.Figure 14 shows that the measured efficiencies of thethree structures are in good agreement with the the-oretical efficiency versus dx.
In Fig. 15 the calculated efficiency versus the inci-dent angle of light is compared with measurementson the structure that has a grating period dx 5 1 mm.
ty distributions in the photoresist.
Fig. 14. Measured and theoretical diffraction efficiencies of the11 TE transmitted order versus dx.
tensi
1 April 2001 y Vol. 40, No. 10 y APPLIED OPTICS 1591
1
The discrepancy between calculated and measuredefficiencies is not well understood but may be attrib-uted to differences between expected and real valuesof the optogeometrical parameters.
4. Conclusions
In conclusion, it is clear from the numerical study ofthe diffraction efficiency stability that the period dx ofthe grating is a critical parameter for obtaining effi-cient components. However, dx is controlled towithin a few nanometers’ accuracy by calibration ofthe holographic setup. Moreover, parameters suchas maximal refractive index Nmax, width s and depthm of implanted areas, and fill factor a of the gratingare not critical. Moreover, the incident angle of lighton the component must be accurately controlled toobtain a resonance. Furthermore, titanium-ion im-plantation has been used to insert a phase gratingwith a micrometric period in the spacer of a multi-layer Fabry–Perot cavity, and the enhancement ofthe free-space diffraction efficiency has been experi-mentally demonstrated.
Such components based on refractive-index modu-lations, at the wavelength scale, obtained withtitanium-ion implantation associated with well-designed multilayer optical interference coatingsmay also be useful for applications dedicated to min-
Fig. 15. Measured and theoretical diffraction efficiencies of the11 TE transmitted order versus u.
592 APPLIED OPTICS y Vol. 40, No. 10 y 1 April 2001
imizing the diffracted intensity of light, such as fur-tivity.
References1. W. B. Veldkamp and T. J. McHugh, “Binary optics,” Sci. Am.
~May, 1992!, pp. 92–97.2. D. H. Raguin and G. M. Morris, “Structured surfaces mimic
coating performance,” Laser Focus World ~April, 1997!, pp.113–117.
3. S. Astilean, P. Lalanne, P. Chavel, E. Cambril, and H. Launois,“High-efficiency subwavelength diffractive element patternedin high-refractive-index material for 633 nm,” Opt. Lett. 23,552–554 ~1998!.
4. H. P. Herzig, Micro-Optics Elements, Systems and Applications~Taylor & Francis, London, 1997!.
5. F. Flory, S. Tisserand, L. Brasse, and L. Roux, “Integratedoptics devices made by Ti implantation in SiO2 layers,” pre-sented at the 1996 OSA Annual Meeting, Rochester, N.Y.,20–25 October 1996.
6. S. Tisserand, F. Flory, A. Gatto, L. Roux, M. Adamik, and I.Kovacs, “Titanium implantation in bulk and thin film amor-phous silica,” J. Appl. Phys. 83, 5150–5153 ~1998!.
7. P. N. Favennec, L’implantation ionique pour la microelectron-ique et l’optique ~Masson, Paris, 1993!.
8. F. Flory, L. Escoubas, S. Tisserand, E. Nicolas, G. Albrand, F.Lemarchand, and L. Roux, “Enhancement of the diffractionefficiency of titanium implanted gratings by associating themwith optical interference coatings,” in Advances in OpticalInterference Coatings, C. Amra and H. Macleod, eds., Proc.SPIE 3738, 306–315 ~1999!.
9. L. Escoubas, F. Flory, F. Lemarchand, A. During, and L. Roux,“Enhanced diffraction efficiency of gratings in multilayers,”Opt. Lett. 25, 194–196 ~2000!.
10. P. Vincent, “Differential methods,” in Electromagnetic Theoryof Grating, R. Petit, ed. ~Springer-Verlag, Berlin, 1980!, pp.101–121.
11. F. Lemarchand, A. Sentenac, and H. Giovannini, “Increasingthe angular tolerance of resonant grating filters with doublyperiodic structures,” Opt. Lett. 23, 1149–1151 ~1998!.
12. M. Neviere, D. Maystre, and P. Vincent, “Application du calculdes modes de propagation a l’etude theorique des anomaliesdes reseaux recouverts de dielectrique,” J. Opt. ~Paris! 8, 231–242 ~1977!.
13. F.-L. Xu, Y.-L. Lam, Y.-C. Chan, and Y. Zhou, “Development oflaser holographic interference system for optical grating fab-rication,” in Automatic Inspection and Novel Instrumentation,A. T. Ho, S. Rao, and L. Cheng, eds., Proc. SPIE 3185, 110–116~1997!.
14. M. Born and E. Wolf, Principles of Optics, 6th ed. ~Pergamon,New York, 1983!, pp. 256–268.
