The resonant reflection of a free-space beam from a slab waveguide grating is rendered high bandwidth and angularly robust by using a bimodal high index waveguide. A deep double-sided corrugation gives rise to the coalescence of the resonant reflection peaks resulting in a top-hat reflection spectrum. A low-cost waveguide technology based on solar cell amorphous silicon is demonstrated in the near infrared in a polarizer application.
©2012 Optical Society of America
Since its discovery in 1985 , and the explanation of its waveguide mechanism , resonant grating reflection has been used with beams of high spatial coherence, usually narrow band laser beams. In its applications in biosensors  or in lasers mirrors  the width of the reflection peak is of the order of one nanometer and the peak position is very sensitive angularly. There have been attempts to broaden the spectral width of the reflection peak as in polarizing laser mirrors where polarization resolved reflection must be high over the full gain bandwidth of a Yb:YAG laser . There have also been attempts to broaden the angular spectrum of resonant reflection by enhancing the second diffraction order of the grating which couples the forward-propagating waveguide mode to its backward-propagating counterpart either by tailoring the duty cycle of a binary corrugation  or by resorting to a doubly-periodic grating . None of these designs can however achieve the resonant reflection of a wide bandwidth and wide angular spectrum beam like that emitted by a lensed LED for instance, and yet it would be very useful in many practical low-end applications to benefit from the polarization selectivity of this effect and from a wide but definite spectral width, for instance for coarse (de)multiplexing.
The present paper reports on a waveguide grating structure which leads under essentially normal incidence to a polarization selective resonant reflection peak of wide spectral width and which exhibits a high angular robustness preventing in particular the formation of the well-known reflection dip in the middle of the spectrum for rays impinging slightly off-normal incidence . These features result from the strong coupling between the modes of a very high index bimodal waveguide causing the coalescence of the otherwise two separate resonant reflection peaks. The same objective of suppressing the reflection dip under an angular tilt in the incidence plane was pursued by using a single-mode segmented waveguide in the form of a subwavelength binary grating of high index contrast : the reflection peak splitting is prevented and the wavelength and angular spectra are shown to be widened. However, the reflection maximum remains a peak of Lorentzian aspect whereas resonant reflection applications with white light sources or LEDs require top-hat spectra. The solution developed in the present paper rests on the coalescence of two modes of a continuous (non-segmented) waveguide layer whose both boundaries are undulated and which exhibits resonant reflection spectra in the form of a plateau rather than a peak; furthermore, the fabrication technology is notably simpler than reactive ion etching as in . In the present article the rationale of the solution will first be explained from a phenomenological standpoint, then exact numerical simulations will illustrate the coalescence effect and the properties of the resulting single reflection peak. The chosen technology for the experimental model is that of an amorphous silicon waveguide layer deposited onto a corrugated polymer substrate which is ideally suited for low-cost near infrared optoelectronic systems. Then, experimental spectra will be shown and SEM scans of FIB slices will illustrate the conditions to be fulfilled for obtaining the expected high reflection of the TE polarized light. The example of a polarizer will be shown where the element has been optimized to also lead to close to 100% transmission of the TM polarization.
2. Reflection peak splitting under normal incidence
Under strictly normal incidence of a plane wave, a grating waveguide of period Λ as illustrated in Fig. 1(b) , reflects a single wavelength component λ as it is shown in the reflection spectrum of Fig. 1(a), since the mode coupling condition is the same for both + and −1st grating orders: Kg = nek0 where Kg = 2π/Λ, k0 = 2π/λ, and ne is the effective index of the coupled mode. In the spectra of Fig. 1(a) the slab waveguide structure is that which corresponds to usual biosensors [3, 9]: the waveguide index is 2.12 at 850 nm wavelength (HfO2 deposited by ion plating) with a period Λ = 550 nm and an undulation depth h = 40 nm, with a thickness w = 100 nm as illustrated in Fig. 1(b).
Under normal incidence this mode is usually the fundamental TE0 mode of the transverse electric polarization since its radiation coefficient can be large whereas that of the TM0 mode would be vanishingly small since the vibration of its electric field in the grating corrugation is essentially normal to the waveguide plane. If the incident wave k-vector gets slightly tilted in the incidence plane normal to the grating lines (1 degree for instance), the resonant reflection peak splits as shown in Fig. 1(a), the short (long) wavelength peak corresponding to contradirectional (codirectional) mode coupling by the −1st and + 1st orders. This means that some wavelength components of an imperfectly collimated wave will be resonantly reflected whereas some will be transmitted, precluding therefore the resonant reflection of a whole light beam of non-zero angular aperture.
One might think that considering a larger index contrast waveguide, like the structure presented in Fig. 2 (b) , and larger grating radiation coefficient could prevent peak splitting. As spectrum a) of Fig. 2 (a) shows in the case of an amorphous silicon (a-Si) waveguide (index ng = 3.7 at λ = 850 nm) deposited onto a substrate of index ns = 1.5 sinusoidally corrugated at period Λ = 330 nm and depth h = 25 nm, the reflection resonance is broader, but the peak splitting is still there as illustrated in spectrum b) of Fig. 2(a). This reflection peak splitting always occurs in a single-mode grating waveguide regardless of the undulation being defined at the bottom or upper, or at both waveguide sides. As a matter of fact, there is a double-benefit which can be drawn from defining the corrugation at both sides: first, this double-sided undulation corresponds to what naturally comes out of a low cost fabrication technology where a polymer substrate is first embossed or injection moulded with the corrugation formed at its surface, and a high index layer is deposited on top of the latter. The second advantage pertains to the electromagnetic problem itself: in a double-sided undulated waveguide, the radiation coefficient of a propagating mode results as the vectorial sum of the fields radiated in the adjacent substrate and cover media by each undulation. If this sum is constructive, the radiation coefficient can be large even though the undulation amplitude remains shallow. Section 3 will make use of a third advantage of a double-sided undulation when the waveguide is bimodal.
3. Angularly robust resonant reflection with coalesced modes
A remarkable property of double-sided corrugated slab waveguides of very high index propagating a second mode close to its cutoff, here the TE1 mode, is to exhibit a gradual coalescence of the fundamental TE0 and TE1 modes as the corrugation amplitude increases: the effective index of the TE0 mode decreases and that of the TE1 mode increases to finally merge. This is illustrated in Fig. 3(a) where an a-Si slab waveguide is given a thickness large enough, t = 130 nm, to propagate the TE1 mode at the wavelength λ = 850 nm. The different curves correspond to different undulation amplitudes h taken as a parameter. The abscissa is the grating period in a numerical experiment at constant wavelength and waveguide thickness, the incidence being strictly normal, and the ordinate is the reflection coefficient. Figure 3 (b) is the 3D representation of Fig. 3(a) in a false color scale representing the TE reflection versus both period and grating depth, which illustrates clearly the coalescence phenomenon: the 100% reflection condition forms an arc with the two separate mode peaks at small grating depth, and a single broad plateau at about 120 nm grating depth. As expected, a shallow grating of increasing period couples the TE0 mode first, then, at larger period, the TE1 mode with the resulting two narrow resonant reflection peaks. From the graphs of Fig. 3(a) the effective index of the modes can be retrieved as ne = λ/Λ. Increasing the grating depth brings the two effective index closer to each other up to the grating depth of 140 nm where the two modes have coalesced in a single grating waveguide resonance.
As from this result, the “C”-method used for the modeling of this structure  calculates the reflection spectrum with the grating depth having led to the mode coalescence in Fig. 3. The spectrum of Fig. 4 , curve A), corresponding to a grating depth of 120 nm and 330 nm period exhibits a very wide reflection plateau of close to 100% reflection. The fact that it is a plateau and not a peak any more implies that all spectral components of a relatively wide spectrum light beam under normal incidence experience close to 100% reflection. The other curves correspond to a tilted incidence in the incidence plane. Remarkably, the wavelength spectrum remains essentially unchanged up to an incidence angle of 15 degrees. This roughly corresponds to the angular width of a lensed LED. Consequently, the designed structure represents a high contrast resonant mirror for incoherent light sources of the LED type. Adding into Fig. 4 curve E) representing the TM reflection in the very same element, exhibiting a broad transmission peak next to a sharp reflection peak, one has realized an angularly and spectrally robust high contrast polarizer.
A phenomenological understanding can be given of this coalescence effect which only takes place if the waveguide/substrate index ratio is large enough (larger than about 2). Going back to curve A) of Fig. 3 corresponding to a shallow grating, one realizes that a grating which would couple a normally incident wave to the TE1 mode of effective index close to the substrate index of 1.5 would also couple the TE1 mode to the TE0 mode of index close to 3. This fulfills a double coupling synchronism condition. Furthermore, the intraguide coupling coefficient between TE0 and TE1 modes given as the overlap integral of the transverse modal electric field in the undulated parts of the slab is very large since the parity of both the field of the TE1 mode and that of the dielectric perturbation which the double-sided undulation represents is odd. The free-space wave and mode coupling situation is thus characterized by a high degree of synchronism and a large coupling coefficient. Getting off this characteristic situation, for instance by using a high index oxide waveguide (e.g. TiO2, diamond or ZnS of about 2.4 index), or even by increasing the a-Si waveguide thickness, thus modifying the effective index ratio and the synchronism condition between TE modes, suppresses the coalescence effect. It is therefore a quite unique coincidence that, in this spectral range between 700 and 1000 nm, one finds the cheapest and most efficient LED light sources, the best silicon-based photodetectors, together with the so well controlled a-Si of solar cell technology for optical purposes.
4. Demonstrator of a wide angular and wavelength spectrum polarizer
Usual polymer-based polarizers do have a large spectral width and a wide angular aperture with high extinction in the range of −40 dB. They however do not withstand the temperature conditions that prevail in most industrial systems. This is a big technical problem and the alternatives are only few. The functionality demonstration of the design described in the last section was first made as modeled in the form of a sinusoidally corrugated substrate with a conformal amorphous silicon layer on top. The experimental model of the undulated substrate is a glass plate with about 1 μm thick Shipley 505A photoresist film on top. This optical substrate was sinusoidally undulated by submitting the resist-coated glass substrate to a flood exposure first to set the photoresist in its linear regime, then to a 442 nm wavelength interferogram of 330 nm period to obtain after development an undulation depth of 120 nm. The photoresist layer was then post-backed to withstand the a-Si deposition conditions. These are not so harsh as a-Si solar cells can now be deposited by low temperature PECVD [11, 12] on polymer foils. The deposition of the hydrogenated amorphous silicon layers were carried out at 150°C. The radio-frequency (RF) glow discharge deposition system used here is an industrial Plasma Enhanced Chemical Vapor Deposition (PECVD) KAI-M reactor. It is a parallel-plate capacitively-coupled reactor driven at a plasma excitation frequency of 40.68 MHz. The silane/hydrogen process gases are introduced through a showerhead incorporated within the RF-powered electrode in the plasma at a deposition pressure of 0.5 mbar. Figure 5 (a) is the picture of the glass/resist/silicon structure. And Fig. 5(b) is the SEM picture of a FIB (focused ion beam) slice of the structure.
It reveals a very uniform silicon coverage and a perfect resist/silicon interface without local delamination or hot spots which might occur like in metal evaporation. Remarkable however is a slight non-uniformity of the corrugation depth in this picture which might explain why the experimental results do not match so well with the modeling expectations of Fig. 4 according to experimental results of the TE and TM transmission spectra of Fig. 6 .
Resonant reflection relies upon perfect uniformity of the waveguide thickness, i.e., of the mode effective index, at the scale of the incident beam diameter. The reason for such non-uniformity lies in the resist grating recording conditions: the resist being set in its linear regime by the initial flood exposure, any reflection, any scattering from the substrate and its surrounding is printed coherently . The recording of a free-space hologram does not suffer that much from scattering and reflections since the light crossing it does not stay there nor comes back, but the same background light may in the present structure alter the grating waveguide uniformity and strongly perturb the phase of the waves trapped and propagating locally in the waveguide. It was therefore decided to go from a sinusoidal undulation to a binary resist profile, the resist being set in its standard nonlinear operation point. Under such conditions, small reflections and scattering still superpose to the main interferogram but remain sub-threshold and do not get recorded. Figure 7 is the SEM picture of the new structure showing that the initially rectangular resist lines have experienced notable edge rounding during the a-Si deposition.
However, the corrugation uniformity is better which translates into a reflection spectrum whose pattern is closer to the modeling expectations as shown in Fig. 8 . The reflection peak is shifted to a slightly larger wavelength, 880 nm instead of 850 nm which is just a question of calibration, the actual dielectric structure of Fig. 7 being difficult to model exactly as the two undulations are not exactly conformal. The main result obtained at this stage is that the TE transmission is acceptably low, below 6% and that the TM transmission is larger than 90% over the typical spectral width of a LED.
The angular robustness of the element was also checked and measured as illustrated in the TE/TM transmitted spectra in Fig. 9 . High frequency noises in the 870-950 nm wavelength range is due to instabilities of the spectrophotometer and must not be taken into account.
The curves exhibit no trace of reflection peak splitting and show that the polarization function is very tolerant (variation below 5%) within 30 degrees around normal incidence in the 850-880 nm range, which is compatible with the emission diagram of most well collimated lensed LED. This confirms experimentally the phenomenological expectation of a broad-band and angularly robust resonant-grating reflection which a dual-mode slab waveguide may exhibit and that this resonance is present in waveguides with a non-sinusoidal grating profile which implies that a simple binary glass corrugation coated with an a-Si layer (or any other semiconductor in its transparency domain) defines a high thermal resistance element.
A new property of mode coalescence was discovered in very high index contrast bimodal grating coupled slab waveguides whereby a deep corrugation makes the two modes to coalesce in a single waveguide resonance. This resonance does not exhibit the usual reflection peak splitting in the neighborhood of normal incidence and can therefore be at the basis of a family of resonant optical elements using low temporal and spatial coherence light sources like LEDs. The optical function that was demonstrated is an angularly robust, wide band polarizer using the unique properties of an amorphous silicon waveguide fabricated by the highly reliable solar cell technology. This is a scientific breakthrough in that optical waveguide resonances with their inherent selectivity characteristics can act with high contrast on a beam of high NA and large bandwidth. To what extent this waveguide grating technology can compete with the usual free-space wave microoptical elements used so far to process incoherent light is not known yet, nevertheless the present achievement is setting a date for a new player relying on waveguide resonances.
Kroll Thin Film Technologies are gratefully acknowledged for the high optical quality of their solar cell amorphous silicon layers and their reliable fabrication service. The authors thank David Troadec, IEMN CNRS, for SEM analysis of the resist based FIB slices of the undulated amorphous silicon.
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