Embedded metallic focus grating for silicon nitride waveguide with enhanced coupling and directive radiation

We design a compact embedded metallic elliptical focus grating coupler based on gold or silver that efficiently interconnects free space with silicon nitride waveguide at 632.8nm wavelength. The 3D far-field radiation pattern for the proposed grating coupler shows much higher gain and directivity towards free space coupling than that of the etched grating coupler. Specifically the free space transmission efficiency achieves 65% for silver grating coupler. It can also further enhance the fluorescence signal detection for Cy-5 fluorophore by isolating peak diffraction angle for 10°. The dense system integration capability shows the application potential for on-chip interfacing sub-wavelength light processing circuits and near-field fluorescent biosensors with far-field detection of superb radiation directivity and coupling efficiency. ©2012 Optical Society of America OCIS codes: (130.0130) Integrated optics; (050.2770) Gratings. References and links 1. F. Ay, A. Kocabas, C. Kocabas, A. 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Introduction
Conventional light coupling technologies to sub-wavelength waveguide include bulky back plate prism coupling, which is not suitable for compact dense system integration [1], and optical fiber end fire coupling with waveguide facet, which requires stringent alignment accuracy [2,3], especially at visible wavelength range due to the even smaller waveguide core size.The concept of on-chip grating coupler design has been extensively researched at longer infra-red (IR) communication wavelength due to the rapid development of telecommunication industry and the silicon-on-insulator (SOI) fabrication technologies during the last several decades.The grating structure is defined by either metal lift-off on top of the waveguide layer [4], or etching the grating grooves partially or fully into the higher index waveguide layer from the top [5,6].The partial etching approach suffers from inaccuracy in etching depth control due to non-stopping layer etching, since etching depth plays a critical role in both coupling efficiency and beam pattern control.In the fully etched grating case, which requires less on etching depth control, however, at least half of the light will unavoidably propagate into the substrate layer which strongly decreases the transmission efficiency into the optical fiber or free space.In many grating designs, the high coupling efficiency with free space is the utmost design goal, and the light scattering into the substrate layer should be well managed to minimize the energy loss.For example, in the silicon-oninsulator (SOI) grating design at IR wavelength, usually multiple oxide layers are stacked under waveguide layer to form distributed Bragg reflector to reduce light coupling into substrate [7].The metal lift-off approach excels for its relative easy fabrication and low absorption loss of the thin metal layer thickness (usually less than tenth of the wavelength) involved.
However their counterpart at visible wavelength did not share equal attention and met greater challenge, because of even smaller feature size restriction on fabrication and nontransparent property of silicon at visible range.And the finite difference time domain (FDTD) modeling of metal in optical range requires extensive dispersion modeling due to the negative real part of its permittivity property.Sub-wavelength optical detection, such as in near field optical scanning microscopy (NSOM) [8][9][10][11] or through nano-optical antennas [12], mandates efficient and compact light coupling from sub-wavelength light processing circuits.Previously, we have demonstrated silicon nitride photonic crystal and nano-resonator on probe tip for near field light localization [13,14].
In this paper, we report a compact noble metal grating coupler design for free space directional light coupling from or into sub-wavelength silicon nitride optical waveguide working at HeNe laser wavelength at 632.8nm.We aim to fill the research gap from device modeling perspective for noble metal grating by placing it just below the waveguide layer to block coupling loss into the substrate.The fabrication of the proposed noble metal grating coupler is compatible with silicon micro-machining technology and it offers a new concept of light coupling at 632.8nm wavelength, with comparable coupling efficiency as the IR wavelength counterpart.A Cavity Modeling Framework (CAMFR) optimized model for simple etched silicon nitride grating coupler is demonstrated through its 3D far field directivity pattern for comparison purpose.A 2D FDTD model of the embedded metallic grating coupler estimates much higher transmission efficiency than the etched one.Based on the theoretical first order diffraction and effective refraction index of the waveguide, the elliptic patterned grating lines are demonstrated to further reduce the coupler size by enhanced focusing capability on the lateral plane through 3D FDTD simulation.Far field radiation pattern, derived from the 3D FDTD model, indicates its high directivity that is suitable for angular far field light detection.This paper also exploits the possible fluorescence signal enhancement by the proposed metallic grating coupler.The current state of the art in the fluorescence detection strongly depends on directive light propagation property and the surface modification techniques that control the affinity between fluorescent molecule and the active light emit surface.However most of the fluorescence detection modifies the metal surface, such as gold or silver, which weakens the fluorescence signal due to the quenching effects [15].The proposed light coupling device can overcome the quenching issue through isolating the metal layer and the active affinity surface by dielectric material of silicon nitride.And the surface modification can be realized in top of the silicon nitride surface [16].Due to the 1st order diffraction angle dependence on light wavelength, the fluorescence signal can be further extracted and distinguished from the excitation source through radiation pattern difference by low aperture objective lens in free space.By separating the fluorescent light propagation and exciting source light coupling with large angle at 10°, the background light noise can be greatly suppressed to enhance the weak fluorescence light detection.
Compared to large scale non-focusing grating design [17][18][19], the proposed compact metallic focus grating size makes large scale nano-system integration possible to provide a mechanism for both light coupling and fluorescence signal extraction to detect large quantities of the nano scale localized protein or DNA binding process simultaneously within one single silicon chip.The far field radiation patterns of silver or gold at both excitation and fluorescence wavelengths are quantified through FDTD simulation results, and it agrees well with grating diffraction theory.

Design of the etched silicon nitride grating coupler
Before we discuss the embedded metal grating design, it is beneficial to analyze the partial etched grating coupler and evaluate its performance.The partially etched grating coupler can be fabricated using electron beam lithography and dry etching method [7].Other grating fabrication methods, such as polymer based grating [20], deep UV lithography [21], and achromatic interferometry lithography [22], have also been utilized.The grating coupler also achieves beam spot converting from the grating square into the narrow ridged waveguide.The eigenmode expansion technique can be used to greatly simplify the model to yield the reflection resonance peak in the 1D grating structures.In this research, we use CAMFR, an eigenmode expansion frequency domain modeling tool, to obtain the optimal grating period and groove depth for the 1D grating in the 2D simulation [23].Only TE polarization (E-field parallel to the grating grooves) is considered in this study.As illustrated in Fig. 1(a), the reflection rate R and transmission T rate can be calculated by finding the eigenmode of each discretized slab in the vertical direction.The total out-of-plane light coupling can be expressed as 1 C R T = − − .The peak reflection corresponds to the grating coupler resonance condition that maximum out-of-plane coupling radiates in the vertical direction.Silicon nitride of 250nm thickness is chosen as the waveguide layer due to its transparent optical property at 632.8nm wavelength.Silicon dioxide serves as the substrate layer.The CAMFR calculation domain is surrounded in upper and bottom boundaries with sufficient perfect matched layer (PML) thickness to reduce the light reflection at the calculation boundaries.
The reflection and out-of-plane radiation efficiency is shown in Fig. 2 by sweeping the pitch size within the range from 300nm to 400nm and the etching depth from 70nm to grating 120nm in 10nm interval with 50% grating duty cycle.At the reflection resonance pitch period Ʌ p the out-of-plane light coupling curve also shows the minimum value due to strong reflection.At the same time, we also need to increase the out-of-plane coupling rate to increase the free space coupling rate.By finding out the pitch period that corresponds to the maximum out-of-plane coupling at the reflection resonance, the effective index of the waveguide grating composite structure can be estimated using effective index equation under vertical radiation condition [7] 0 .It is found that 110nm etching depth with 361nm pitch period gives the maximum out-ofplane coupling rate with effective index of 1.7529 at the reflection resonance pitch period.For arbitrary out-of-plane coupling angle θ 1 , the effective index can be estimated from the 1st order grating diffraction equation [20] where n 0 is the refraction of top cover material (free space in the proposed grating coupler), Ʌ is the grating pitch period, and λ 0 is the wavelength in free space.CAMFR provides a convenient way to predict the effective index for maximum out-of-plane coupling under vertical radiation condition.However for arbitrary 3D grating coupler design for radiation angles other than vertical direction, the light coupling distribution has to be verified through 3D FDTD modeling.We choose the compact focusing grating coupler as 3D FDTD simulation example.For polarized plane wave light source, the wave vector front is regulated by constructive interference according to the first order Bragg's diffraction theory.The focusing capability is realized by constructive interference of the wave front phase between the wave coming from the dielectric waveguide and the scattered wave from grating groove lines into the free space at the 1st order diffraction angle.The 3D constructive interference on the center xy plane of the silicon nitride waveguide layer can be described by the phase matching equation below where q is the grating line numbers [20].Detail expansion of Eq. (3) in elliptical curve form is also presented in Eq. ( 5).Such a 3D compact focusing grating coupler with 110nm etching depth and 361nm pitch period of effective index 1.7529 is modeled as in Fig. 1(b) with azimuth angle φ and polar angle θ as indicated.A waveguide port with broadband excitation centered at 632.8nm wavelength is used as excitation source which is located at the single mode silicon nitride ridge waveguide with TE mode linear polarization.All the boundaries are set up as open space with PML to reduce the back reflection calculation error.The size of the grating coupler is 10µm in y direction and 7µm in x direction which would fit the approximate core size of single mode optical fiber at 632.8nm wavelength.The overall relative small size of the grating coupler also helps greatly reduce FDTD calculation time.The grating coupler FDTD simulation problem can be treated as a typical antenna radiation pattern problem by converting the near field to far-field.The far-field directivity of the etched compact grating coupler is shown in Fig. 3, in which both vertical out-of-plane coupling of the peak reflection resonance case and the 10 0 tilted radiation of the same effective index are plotted.There are two radiation lobes for both vertical radiation coupler and 10 0 tilted coupler.Since there is no special treatment for blocking the radiation into substrate, almost half of the light energy is lost into the bottom.Based on the CAMFR calculation, under maximal vertical radiation case, the total out-of-plane light coupling is 45% and the free space coupling rate is about slightly more than half of it as estimated from the far field pattern.So the free space coupling is quite low as compared to that of the embedded metal ones as shown in later sections.The main design requirement on the free space grating coupler is to reduce the secondary radiation lobe into the substrate layer for enhanced free space coupling.The reduction of the radiation into the substrate can be realized by introducing a distributed Bragg reflector in the substrate layer as in the IR grating coupler on SOI platform, but with extra burden on fabrication process [7].Also as shown in the Fig. 2, the grating etching depth is also very critical as it would also change coupling efficiency and beam pattern dramatically.Another novel way to reduce substrate coupling and still have higher directivity towards free space will be introduced next by placing the metal grating on top of the substrate layer.

Grating coupler overview and 2D FDTD numerical analysis
As demonstrate in [4] for IR wavelength, a metal grating can be placed on top of the waveguide layer to form a grating coupler on SOI platform.However the free space coupling efficiency is greatly related to the buried oxide thickness, since maximum upward coupling only happens when constructive interference forms between wave reflection from oxide substrate interface and the upward light propagation [4].In order to avoid the oxide thickness A metal grating layer of 40nm is placed on top of the silicon dioxide layer with duty cycle of 50%, which can be defined by electron beam lithography and fabricated by metal lift-off method.
Only one electron beam lithography alignment is needed to align the silicon nitride waveguide pattern that is finalized by dry etching.Silicon nitride with thickness of 250nm is chosen to form the single mode (TE 0 , E field polarized in y direction) rib waveguide with cross section width of 500nm working at 632.8nm for its relative high index (n ≈2.02) and near zero absorption loss.Other transparent waveguide layer material with relative high index like ITO can also be used.Also silicon nitride is compatible with silicon fabrication technology and can be deposited by either low pressure chemical vapor deposition (LPCVD) or plasma enhanced chemical vapor deposition (PECVD).The annealing temperature for silicon nitride can be achieved at around 800°C [24].So gold and silver are compatible with silicon nitride deposition since their melting points are 1064°C and 962°C respectively [25].Also the fused silica can be used as the SiO 2 substrate material for its low thermal expansion and annealing temperature above 1000°C [25].The bottom placement of the metal layer under the waveguide layer also further enhances the free space light coupling efficiency by reducing the light energy diffracted with higher order modes into the silicon dioxide substrate given by the penetrating properties of such noble metals.The top conformal grooves pattern is also modeled to simulate the uniform conformal silicon nitride deposition.The top silicon nitride grooves does not serve as an active grating element due to its thin thickness.
The compatibilities with the electron beam lithography, stable chemical properties at ambient environment, and low light absorption make silver and gold excellent candidates for grating materials at visible wavelengths.For the noble metals, the real part of permittivity is negative (well less than −10) throughout the visible range, and the imaginary part is weakly positive [26].The metallic grating grooves serves as the diffraction element leading to the directional radiation due to its refraction index contrast with that of the waveguide layer material.Also due to the high negative permittivity, the surface plasmonic resonance waves exist on top of the metal surface [27].Therefore the propagation distance of the waves on the lateral grating plane is greatly restricted.The main lobe size in the far-field radiation pattern is also reduced which enhances the far-field directivity.The absorption loss for 632.8nm wavelength for gold and silver are even smaller due to the smaller loss tangent, as compared ( ) where ω D is the plasma frequency, γ D is the damping term, γ n represents spectral width, ω n represents oscillator strength of the Lorentz oscillators, and σ n stands for weighting factor [28][29][30].The DL model with two Lorentzian terms for both metals is calculated by leastsquares nonlinear curve-fitting method with experiment data in [26] for optical wavelength range from 500 nm to 1000 nm which cover the interested wavelength of 632.8nm as listed in Table 1 with data plotted in Fig. 5.At the wavelength of 632.8nm, the imaginary part of both metals, especially gold, shows minimal value as compared to other wavelengths.A 2D FDTD model that requires less computing time, other than CAMFR (CAMFR is not yet ready for dispersive metal with negative real part of permittivity) or computational intensive and time consuming 3D FDTD, has been implemented to estimate free space coupling efficiency before extending it to the 3D model [31].In this 2D FDTD model as illustrated in Fig. 4(a) and also in Fig. 7(a), a light source of TE 0 mode is launched from the silicon nitride rib waveguide ending at x = 0.For each pitch period, FDTD calculations are performed twice to separate the incident and reflected field.The first FDTD calculates field distribution of a simple silicon nitride waveguide without grating coupler perturbation to separate out the incident fields.The second FDTD calculates the field distribution of the grating coupler [32].The free space transmission efficiency, as shown in Fig. 6, is calculated using the ratio between flux of electromagnetic energy through 5µm line along x direction at 4µm above the grating coupler center and the incident flux energy at the waveguide input.The 5µm line length in x direction models a typical single mode optical fiber at 632.8nm wavelength, though the 2D FDTD model does not count the coupling loss into the optical fiber.A Gaussian broadband current signal with center wavelength at 632.8nm is used as the excitation signal with metal dispersive permittivity property described by the DL model.The flux of the electromagnetic energy is derived from the Fourier-transformed field into frequency domain [31].In this 2D FDTD model, PML layers are surrounded the calculation domain to avoid back reflection error.Since only the total flux across the defined line in x direction is involved in this calculation, the free space transmission efficiency only quantifies the energy flux without taking account of the directional radiation information.The directional radiation pattern will be quantified through far field directivity by 3D FDTD model as shown in the next section.The silver grating and the gold grating give peak free space coupling efficiencies of 68% and 55% respectively.The free space coupling for both metals grating couplers are much higher than those of the etched grating coupler as shown in section 2. The smaller loss tangent of silver explains the higher transmission rate than that of the gold one.The higher transmission rate for silver grating is also demonstrated by the higher free space radiation directivity calculation in the following 3D FDTD simulation.Fig. 6.Free space transmission efficiencies by sweeping grating pitch period from 355 nm to 420 nm for Au and Ag through 2D FDTD model.

Compact focus grating coupler design and far field pattern
The design of the grating coupler needs to achieve two aims, efficient light coupling and compact coupler size.Also the size of the grating coupler needs to match that of the free space source or detector for maximal coupling efficiency.At the cross section plane of y = 0, the elliptical grating pitch period is a constant as defined in the 2D FDTD model.The effective index of the silicon nitride dielectric waveguide can be calculated from Eq. (2).Following similar design ideology as the etched grating coupler for compact focusing on xy center plane at the waveguide layer, Eq. ( 3) can be further expanded in elliptical curve form as follows to design the embedded metallic grating coupler.Equation ( 5) describes a set of ellipses that share a common focal point at (0, 0) on xy plane.By fixing the grating pitch period and the diffraction angle in free space, the focus grating curves can be exactly determined by Eq. ( 5).The size of the grating coupler is determined by the starting grating number of q, and can be adjusted for different free space source size or detector size.To achieve focusing effects on xy plane, the silicon nitride waveguide ending facet needs to be positioned at the focal point of the ellipse curves.
To verify the field distribution and far-field radiation pattern, a 3D FDTD model is carried out in this research by CST microwave studio and one term DL model has been used to simplify the 3D model [33].The size of the focusing grating coupler is set as 10µm in y direction with 20 grating grooves of 50% duty cycle and the distance from the nearest grating line center to the waveguide is set as 7µm to cover the optical fiber ending facet size.An E y waveguide port current source with broad wavelength range of center wavelength of 632.8nm is modeled as the excitation source for the 3D structure.The surrounding boundaries of the calculation domain are set as open absorbing boundary condition.And the E y field distribution are plotted in Fig. 7, based on the 3D FDTD simulation results of gold focusing grating coupler with center pitch period of Λ = 397.5nm.The center pitch period in 3D FDTD model is chosen by optimizing the directional radiation angle at θ 1 = 10°.Figure 7(a) demonstrates the directional radiation along the 10° tilt direction as designed.Shown in Fig. 7(b), the light exit from the waveguide facet has matched wave front that collides with the grating curvatures on the lateral center plane.The silver grating coupler has similar field distribution but with slightly higher field intensity in the free space direction radiation which will be demonstrated in the following far field distribution patterns discussion.To quantify the radiation difference, the 3D far-field radiation pattern is derived from near to far-field conversion for these two materials as shown in Fig. 8.The effective refraction indexes of silver and gold grating coupler are 1.7711 (397.5nmcenter pitch) and 1.7611 (400nm center pitch) respectively for optimized directional radiation for the 1st order diffraction angle θ 1 = 10°.The far-field radiation pattern shows strong directional angular radiation pattern oriented in θ 1 = 10° for 1st diffraction angle.As it can be seen, the pitch period for peak free space coupling as calculated by 2D FDTD model is not used for the 3D FDTD model due to the fact that 2D FDTD does not take account of the directional radiation information.Thus correspondingly the 2D free space coupling efficiencies for the 3D designs are reduced to be 65% and 50% for silver and gold respectively as read from Fig. 6.As expected, there is also a side lobe pointing towards the substrate layer which counts for the light coupling loss but with much smaller magnitude as compared to the etched one.The peak free space directivity is also greatly increased for both metallic grating designs.This phenomenon also echoes with the initial design discussion for bottom placement of the (C) 2012 OSA metallic grating.The radiation intensity difference is not apparent as shown in the directivity plot in Fig. 8(c) due to the dBi unit used.However both grating structures show a 4.2° 3dB angular width for the main lobe radiation pattern.From radiation antenna point of view, this kind of far radiation pattern corresponds to the super high gain or directivity antenna, which is suitable for directional light coupling or detection with minimal sway light loss.

Cy-5 fluorescence radiation signal extraction analysis
Cy-5 is a common cyanine based fluorescent dye that can be excited by HeNe laser (632.8nm) and has emission max around 690nm [17,34].Also Cy-5, as water soluble, can be immobilized to the silicon nitride surface evenly through covalent bonding with DNA or antibody probe [16].Thus it is very useful to study the radiation pattern for fluorescence signal at wavelength of 690nm.Based on the effective refraction index Eq.( 2), the 1st order diffraction angle relates to the light wavelength in a way that the increase of wavelength reduces the coupling angle.The peak radiation angle is predicted to be around θ f = 0° by Eq.
(2).Through 3D FDTD modeling of the exact same grating coupler structure as in section 4, the radiation patterns are presented in Fig. 9 for incident light wavelength at 690nm for TE mode.The peak directivities of both metallic grating couplers are pointing towards vertical direction into free space, which would reduce the source light coupling contamination at θ 1 = 10° and enhance the signal to noise ratio by utilizing a low numerical aperture objective lens.Similar to the case of the 632.8nm wavelength, due to the material loss difference, the silver grating coupler still has slightly higher radiation intensity at the 1st order diffraction angle.

Conclusions
In conclusion, we propose a novel focus grating coupler design concept using noble metals for directional light coupling at 632.8nm wavelength for silicon nitride waveguide.Our modeling and simulations show that this focusing grating structure yields free space coupling efficiency as high as 63% with minimal material loss.The noble metal grating is compatible with silicon fabrication technology through metal lift-off, electron beam lithography and dry etching process.The far-field radiation pattern as derived from 3D FDTD demonstrates the angular light coupling capability for sub-wavelength light processing circuit.Also the fluorescence vertical radiation pattern can be further utilized to enhance fluorescence signal extraction for Cy-5 fluorescent dye.

1 Fig. 1 .
Fig. 1.Design of etched silicon nitride grating coupler.(a) CAMFR calculation model on eigenmodes of the 1D partially etched grating on silicon nitride waveguide layer on top of the silicon dioxide substrate; (b) 3D FDTD model with spherical axis as labeled.

Fig. 2 .
Fig.2.Reflection (bottom solid lines) and out-of-plane coupling (top dashed lines) rates as function of grating pitch period for etching depth ranging from 70nm to 120nm.

Fig. 3 .
Fig. 3. Far-field directivity plots of 3D focusing grating coupler fabricated by etching method for polar angle θ on φ = 0° plane.The grating etching depth is 110nm with effective grating index of 1.7529.(a) Coupler with peak reflection resonance with peak directivity of 504 towards free space; (b) Same effective grating coupler index but with tilted radiation angle of θ1 = 10 0 .It achieves free space directivity of 567.

Fig. 4 .
Fig.4.Noble metal grating on top of the silicon dioxide layer for interfacing far-field free space and silicon nitride dielectric rib waveguide (geometry not to scale).(a) Vertical cross section view on xz plane where the 1st order diffraction angle is θ from z axis; (b) 3D illustration of the coupler including the metal focus grating ellipses and silicon nitride single mode dielectric rib waveguide.

Fig. 7 .
Fig. 7. Ey field plots of an optimized gold focusing grating coupler excited by 632.8nmTE0 waveguide source on the center cross section planes of the coupler.(a) Field plot on xz center plane; (b) Field plot on xy plane along the silicon nitride slab center.The focusing point at (0, 0) on xy plane is as indicated.Grating pitch period Λ = 397.5nm,thickness of gold layer = 40nm, silicon nitride waveguide layer thickness = 250nm.

Fig. 8 .
Fig. 8. Far-field radiation pattern for incident waveguide source light at wavelength 632.8nm.(a) 3D directivity pattern as functions of spherical angles for Ag grating coupler with peak directivity of 841; (b) Normalized far-field power radiation pattern as function of θ on φ = 0 plane; (c) Far-field directivity as function of θ on φ = 0 plane in unit of dBi.The black curve represents silver grating and red one is for gold grating.

Fig. 9 .
Fig. 9. Far-field radiation pattern for fluorescence wavelength at 690nm.(a) 3D directivity pattern as functions of spherical angles for Ag grating coupler with peak directivity of 345; (b) Normalized far field power radiation pattern as function of θ on φ = 0 plane; (b) Far-field directivity as function of θ on φ = 0 plane in unit of dBi.The black curve represents silver grating and red one is for gold grating.

Table 1 . Drude-Lorentz Parameters Optimized for Dispersive Dielectric Properties of Gold and Silver in 500 nm to 1000 nm Wavelength Range for FDTD Modeling
Fig. 5. Relative permittivity as calculated by Drude-Lorentz (DL) model as compared with the experiment data in [26] by Johnson and Christy (JC) for both gold and silver for wavelength range from 500 nm to 1000 nm.(a) real part of permittivity; (b) imaginary part permittivity.