- Email: [email protected]
SiO2 nanocomposite grating coupler
Optik - International Journal for Light and Electron Optics 182 (2019) 1143–1148
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Diffraction-distortion-induced deflection of guided waves in twodimensional Ag/SiO2 nanocomposite grating coupler
T
⁎
Jun Wanga, , Changlong Liub,c, Gang Wangb, Yongjie Sunb a b c
College of Science, China University of Petroleum (East China), Qingdao, 266580, China School of Science, Tianjin University, Tianjin, 300072, China Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparation Technology, Tianjin, 300072, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Grating coupler Waveguide slab Deflection of guided wave Diffraction distortion
Two-dimensional Ag/SiO2 nanocomposite grating coupler with a periodicity of 600 nm was fabricated by etching an Ag-ion-implanted SiO2 waveguide slab, which was evidenced to be able to convert a vertically incident beam in the wavelength range of 620–880 nm into four beams of guided waves without regard for the polarization of incident beam. Employing this coupler, the deflection of guided waves due to the diffraction distortion in the case of oblique incidence was clearly demonstrated. Moreover, to accurately predict the propagating direction of guided wave in the SiO2 waveguide layer, a simple relation of the deflected angle of guided wave to the polar and azimuth angles of incident beam was deduced according to the oblique coupling of a onedimensional Ag/SiO2 nanocomposite grating coupler. The calculated results by using the deduced relation revealed that increasing the polar angle and/or azimuth angle of incident beam could lead to an increase in deflected angle of guided wave. Especially, for an azimuth angle of 90°, the calculated results agreed well with the experimental data, justifying the deduced relation. The above findings might be useful for the packaging and applications of grating couplers.
1. Introduction In comparison with the end-facet (or edge illumination) and prism couplers [1,2], the grating couplers are more robust and convenient to couple light beams into or out of optical thin films or slabs [3]. Moreover, the grating couplers are more compatible with the planar device technology [4], and thereby, they have been considered as fundamental building blocks of large-scale photonic integrated circuits [5]. In an optical thin film or slab, the excitation of waveguide modes via a grating coupler means that the proper diffraction orders are converted into the propagating waves. This fact suggests that the propagating direction of a guided wave in the optical thin film or slab is absolutely governed by the corresponding diffraction order’s azimuth angle with respect to a specific coordinate axis in the grating plane. For a diffraction grating, when a light beam vertically strikes on it, the azimuth angles of diffraction orders are easy to predict. However, when a light beam obliquely strikes on it, the diffraction orders will be aberrant. That is to say, the oblique incidence of light beam at a polar angle with respect to the normal of grating plane and an azimuth angle with respect to a specific coordinate axis in the grating plane can make the diffraction orders present different azimuth angles from those corresponding to the normal incidence. The aberration of diffraction order, i.e., the diffraction distortion, can be explained on the basis of the phase difference of the high-order propagation factor in Fresnel diffraction [6]. As a fundamental and important phenomenon, the diffraction distortion of grating in the case of oblique incidence has been investigated theoretically and experimentally
⁎
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.ijleo.2019.01.107 Received 5 January 2019; Accepted 30 January 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 182 (2019) 1143–1148
J. Wang, et al.
[6–10], but its influence on the propagating directions of the waveguide modes excited via a grating coupler has not been touched upon as yet. In our opinion, the above influence may be crucial to the packaging and applications of grating couplers, and thus, it is worthy to be discussed in depth. In this work, two-dimensional (2D) Ag/SiO2 nanocomposite grating coupler (i.e., a square grid of Ag/SiO2 nanocomposite veins) with a periodicity of 600 nm is fabricated by etching an Ag-ion-implanted SiO2 waveguide slab, which is able to convert a vertically incident beam in the wavelength range of 620–880 nm into four beams of guided waves without regard for the polarization of incident beam. Using this coupler, the diffraction-distortion-induced deflection of guided waves in the case of oblique incidence is clearly demonstrated. Moreover, a relation of the deflected angle of guided wave to the polar and azimuth angles of incident beam is also deduced, which can be used to precisely predict the propagating direction of guided wave in the SiO2 waveguide layer. 2. Experimental 2D Ag/SiO2 nanocomposite grating coupler (i.e., Ag/SiO2 coupler) of 600 nm in periodicity was fabricated on a 0.5-mm-thick SiO2 waveguide slab with an area of 20 × 20 mm2 via the following five steps. Firstly, the SiO2 waveguide slab was implanted with 90 keV Ag ions to a dose of 6 × 1016 cm−2, and the Ag ion beam was tilted by 45° from the sample surface due to the limit of implanter. Under these conditions, a subsurface Ag/SiO2 nanocomposite layer could be synthesized in a depth range of 0–100 nm according to a SRIM simulation [11]. Secondly, the Ag-ion-implanted SiO2 waveguide slab (i.e., Ag/SiO2 slab) was evenly coated with a layer of electron beam (EB) resist on a high-precision spin coater (CEE-200X-F, Brewer Sci. Co.). Thirdly, the EB resist layer was patterned with the given periodicity in a region of 4 × 4 mm2 on an EB lithography system (EBPG5000+, Vistec Co.). Fourthly, using the patterned EB resist layer as a mask, the Ag/SiO2 slab was etched for 38 s at −10 °C in CHF3 and Ar gases on an inductively coupled plasma reactive ion etching system (SI500, Sentech Co.). Such etching had been evidenced to be able to dislodge a 100 nm thick layer from an Ag/SiO2 slab without EB resist layer. Finally, the residual EB resist layer was removed in a 1:1 (v/v) solution of H2SO4 and H2O2. To reveal the vertical input coupling property of Ag/SiO2 coupler, the transmission spectra of Ag/SiO2 slab and coupler were recorded under the same conditions by using a double beam spectrophotometer (UV-3600, Shimadzu Co.). In addition, the inner structure of Ag/SiO2 slab and the surface morphology of Ag/SiO2 coupler were also examined by using a transmission electron microscope (TEM, G2 F20 S-Twin, Tecnai Co.) and a scanning electron microscopy (SEM, S4800, Hitachi Co.), respectively. To demonstrate the excitation of waveguide modes and the diffraction-distortion-induced deflection of guided waves, the Ag/SiO2 coupler was investigated by means of a simple setup as schematically shown in Fig. 1. In this setup, the Ag/SiO2 coupler was fastened to a sample holder and photographed with a digital camera fixed in the front of coupler. A laser diode of 650 nm in wavelength was used to offer an incident beam, and two linear polarizers were employed to transform the incident beam into the p- or s-polarized wave. The laser diode and linear polarizers were set to synchronously rotate around the coupler via a rocker arm (not shown here), and thereby, the polar angle of incident beam with respect to the normal of coupler could be altered continuously. To well conduct the observations at different polar angles, the digital camera was slightly higher than the laser diode and linear polarizers. 3. Results and discussion Fig. 2 shows the transmission spectra of Ag/SiO2 slab and coupler, and its insets (a) and (b) are the cross-sectional TEM image of Ag/SiO2 slab and the SEM image of Ag/SiO2 coupler, respectively. In the transmission spectrum of Ag/SiO2 slab, a steep transmittance attenuation band around a wavelength of 405 nm can be clearly found. According to the inset (a) and our previous work [12], one can know that this steep transmittance attenuation band is contributed by the localized surface plasmon resonance (LSPR)
Fig. 1. Schematic setup to observe the formation of guided waves and their deflection in the Ag/SiO2 coupler. 1144
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J. Wang, et al.
Fig. 2. Transmission spectra of Ag/SiO2 slab and coupler. Insets (a) and (b) exhibit the cross-sectional TEM image of Ag/SiO2 slab and the SEM image of Ag/SiO2 coupler, respectively.
absorption of the Ag nanoparticles (NPs) synthesized in the SiO2 waveguide slab. In the transmission spectrum of Ag/SiO2 coupler, a transmittance attenuation band induced by the LSPR absorption of Ag NPs can be also found, but it, compared to that appeared in the transmission spectrum of Ag/SiO2 slab, shifts to a longer wavelength (∼415 nm) and becomes weaker and more asymmetrical. Obviously, these spectral changes can be attributed to the formation of grating structure (refer to the inset (b) and Ref. [12]). Especially, the formation of grating structure can lead to another transmittance attenuation band, which is located between 620 and 880 nm in wavelength. The appearance of transmittance attenuation band in the wavelength range of 620–880 nm substantially indicates that an incident light beam in the corresponding wavelength range can be partly coupled into the SiO2 waveguide layer [13]. Owing to the introduction of Ag NPs, the grating teeth (i.e., nanocomposite veins) of Ag/SiO2 coupler not only are larger in refractivity than SiO2 [14], but also can act as effective scatterers [15]. Consequently, in the wavelength range of 620–880 nm, the Ag/SiO2 coupler can have a much higher coupling efficiency compared to an Ag-NP-free coupler with identical morphological parameters [16,17]. Such a feature makes the Ag/SiO2 coupler become a proper platform to demonstrate the formation of guided waves and their deflection in the case of oblique incidence. According to the coupling band revealed in Fig. 2, the Ag/SiO2 coupler was observed and photographed by means of the setup as schematically shown in Fig. 1 when it was illuminated by a laser beam of 650 nm in wavelength at different polar angles. Figs. 3(a) and (b) are the obtained typical photos for the incidence of p- and s-polarized waves, respectively. In the two figures, the sample surface is in the xoy plane, the incident beam is in the yoz plane, and the θI denotes the polar angle of incident beam with respect to the z axis. Fig. 3(a) clearly shows that in the case of θI = 0°, four light spots due to diffusion appear at the sample’s side walls. This phenomenon substantially reveals that four beams of guided waves are formed in the SiO2 waveguide layer, which propagate along the x axis (i.e., the column of grating) and the y axis (i.e., the row of grating), respectively. The formation of guided waves indicates that the phase matching condition is satisfied [4]. As known, the Ag/SiO2 coupler is of a square grid of Ag/SiO2 nanocomposite veins standing on the SiO2 waveguide layer, and thus, the phase matching condition can be simply described as
ns sinθD = sinθI + m
λ , Λ
(1)
where ns is the refractive index of SiO2, m is the diffraction order, θD is the polar angle of mth-order diffracted beam, λ is the wavelength of incident beam in the free space, and Λ is the periodicity of square grid. With ns = 1.46 [18], θI = 0°, λ = 650 nm, and Λ = 600 nm, again noting that the θD should be equal to or larger than sin−1 (1/ns) if a diffracted beam can become a propagating wave in the SiO2 waveguide layer, one can easily infer that only the first-order diffracted beams are converted into the guided waves. Moreover, Fig. 3(a) also shows that the increase of θI can give rise to three new phenomena. The first phenomenon is that the two light spots distributed in the x axis gradually depart from their respective initial positions with an identical rate, indicating that the correlative two guided waves synchronously deflect in anticlockwise and clockwise directions, respectively. In our opinion, similar phenomenon could be also observed for the two light spots distributed in the y axis if the incident beam were not in the yoz plane. From Eq. (1) and the related inference, one can draw a conclusion that the deflection of guided waves here is due to the aberrations of the first-order diffracted beams in the xoz plane. As to the dependence of deflected angle of guided wave on the polar angle of incident beam, it will be discussed in depth hereinafter. The second phenomenon is that owing to the phase mismatches at two specific polar angles of incident beam, the two light spots distributed in the y axis (or rather, the two guided waves propagating along the y axis) first become single and then disappear. The two specific polar angles of incident beam for the phase mismatches were measured to be about 5.5° and 20.5°, respectively. The phase mismatch at θI = 5.5° is due to θD < sin−1 (1/ns) for the diffraction order of m = −1, while the phase mismatch at θI = 20.5° is due to θD > 90° for the diffraction order of m = 1. The last phenomenon is that two new light spots appear at the sample’s side walls perpendicular to the x axis when θI ≈ 10°, and they gradually get close to the x axis with the increase of θI. The appearance of two new light spots should be related to the reflection of incident beam at the side walls of nanocomposite veins that are parallel to the x axis. Like the reflective gratings [10], the Ag/SiO2 coupler is believed to be able to produce the diffracted light fields due to an in-phase addition of the reflected light fields induced by the interaction between 1145
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J. Wang, et al.
Fig. 3. Typical photos of Ag/SiO2 coupler for the incidence of (a) p- and (b) s-polarized waves of 650 nm in wavelength at different polar angles θI.
the incident beam and the side walls of nanocomposite veins, and therefore, two new guided waves can be formed in the SiO2 waveguide layer when the Ag/SiO2 coupler is obliquely illuminated at a specific θI. Just because the two new light spots originate from the reflection rather than the transmission, increasing θI makes them gradually come near rather than depart from the x axis. It is worth noting that the above three phenomena for θI > 0° as well as that for θI = 0° can be also found in Fig. 3(b). This fact means that the coupling process of Ag/SiO2 coupler is quite insensitive to the polarization of incident beam. In our opinion, this insensitivity is not only due to the 2D orthogonal structure of coupling grating [19], but also due to the fact that the embedded Ag NPs in nanocomposite veins are globular and small in diameter [20]. The phenomena exhibited in Fig. 3 suggest that the 2D Ag/SiO2 coupler can be considered as an orthogonal overlapping of two 1D Ag/SiO2 coupler with an identical periodicity of Λ = 600 nm. On this basis, we suppose a 1D Ag/SiO2 coupler as schematically shown in Fig. 4 to reveal the dependence of deflection of guided wave on the direction of incident beam. In Fig. 4, kI and kD are the wave vector for incident beam and the wave vector for one of mth-order (in our case, m = ± 1) diffracted beams, respectively. Without loss of generality, the direction of kI is described with a polar angle of θI and an azimuth angle of ϕI. As a result of oblique incidence, the kD with a polar angle of θD deviates from the xoz plane by an azimuth angle of ϕD. This is the so-called diffraction distortion. Obviously, the ϕD is equal to the deflected angle φ of guided wave. According to the above descriptions, the wave vector β of guided wave in the SiO2 waveguide layer can be expressed in two forms:
2π 2π 2π β = ⎛ sinθI cosϕI + m ⎞ x 0 + ⎛ sinθI sinϕI ⎞ y0 , Λ⎠ ⎝ λ ⎝ λ ⎠
(2)
2π 2π β = ⎛ ns sinθD cosϕD ⎞ x 0 + ⎛ ns sinθDsinϕD ⎞ y0 , ⎝ λ ⎠ ⎝ λ ⎠
(3)
where x0 is the unit vector along the x axis, and y0 is the unit vector along the y axis. Eqs. (2) and (3) are related to the kI and kD, respectively. From them, the generalized grating formulae can be obtained as
ns sinθD cosϕD = sinθI cosϕI + m
λ , Λ
(4)
ns sinθDsinϕD = sinθI sinϕI .
(5) 1146
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Fig. 4. Diffraction-distortion-induced deflection of guided wave in a 1D Ag/SiO2 coupler.
Consequently, the deflected angle φ of guided wave can be given as
φ = ϕD = tan−1
sinθI sinϕI . sinθI cosϕI + mλ / Λ
(6)
With m = 1, λ = 650 nm, and Λ = 600 nm, the deflected angles of guided wave for the incidence at different polar and azimuth angles are calculated by using Eq. (6). The calculated results as shown in Fig. 5 clearly demonstrate that in the case of oblique incidence, increasing the polar angle and/or azimuth angle of incident beam can lead to an increase in deflected angle of guided wave. Especially, when ϕI = 90°, the calculated results are consistent well with the experimental data obtained from the photos of Ag/SiO2 coupler for the incidence of p-polarized wave (refer to Fig. 3(a)). This consistency substantially justifies Eq. (6). Eq. (6) does not involve any information on the embedded Ag NPs, and therefore, it can be expected to be used in other grating couplers to predict the propagating direction of guided wave in the waveguide layer. 4. Conclusions In summary, a vertically incident light beam in the wavelength range of 620–880 nm can be converted into four beams of guided waves via the Ag/SiO2 coupler, and the coupling process is insensitive to the polarization of incident beam. In the case of oblique incidence, partial (or all) guided waves can deflect from their propagating directions corresponding to the normal incidence owing to the diffraction distortion. The deflected angle of guided wave depends on the polar and azimuth angles of incident beam. Increasing the polar angle and/or azimuth angle of incident beam can lead to an increase in deflected angle of guided wave. The dependence of
Fig. 5. Deflected angles φ of guided wave for the incidence at different polar angles θI and azimuth angles ϕI. The experimental results are obtained from the photos of Ag/SiO2 coupler for the incidence of p-polarized wave (refer to Fig. 3(a)), and the theoretical results are calculated by using Eq. (6). 1147
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deflected angle of guided wave on the polar and azimuth angles of incident beam can be described with a simple equation (see Eq. (6)). The equation does not involve any information on the embedded Ag NPs, and thus, it can be expected to be used in other grating couplers to predict the propagating direction of guided wave in the waveguide layer. The above findings might be valuable for the packaging and applications of grating couplers. Funding This work was supported by the Natural Science Foundation of China [grant numbers 11675120, 11535008]. Acknowledgments Authors are grateful to the National Center for Nanoscience and Technology for the sample fabrication. References [1] R. Shubert, H. Harris, Optical surface waves on thin films and their application to integrated data processors, IEEE Trans. Microw. Theory Tech. 16 (1968) 1048–1054. [2] P.K. Tien, R. Ulrich, R.J. Martin, Modes of propagating light waves in thin deposited semiconductor films, Appl. Phys. Lett. 14 (1969) 291–294. [3] S.B. Mendes, S.S. Saavedra, N.R. Armstrong, Broadband spectroelectrochemical interrogation of molecular thin films by single-mode electro-active integrated optical waveguides, in: M. Zourob, A. Lakhtakia (Eds.), Optical Guided-Wave Chemical and Biosensors I, Springer, Berlin, 2010, pp. 101–129. [4] M.L. Dakss, L. Kuhn, P.F. Heidrich, B.A. Scott, Grating coupler for efficient excitation of optical guided waves in thin films, Appl. Phys. Lett. 16 (1970) 523–525. [5] D. Taillaert, F.V. Laere, M. Ayre, W. Bogaerts, D.V. Thourhout, P. Bienstman, R. Baets, Grating couplers for coupling between optical fibers and nanophotonic waveguides, Jpn. J. Appl. Phys. 45 (2006) 6071–6077. [6] J.E. Harvey, R.V. Shack, Aberrations of diffracted wave fields, Appl. Opt. 17 (1978) 3003–3009. [7] J.E. Harvey, C.L. Vernold, Description of diffraction grating behavior in direction cosine space, Appl. Opt. 37 (1998) 8158–8160. [8] J.E. Harvey, D. Bogunovic, A. Krywonos, Aberrations of diffracted wave fields: distortion, Appl. Opt. 42 (2003) 1167–1174. [9] G. Fortin, Graphical representation of the diffraction grating equation, Am. J. Phys. 76 (2008) 43–47. [10] S.Y. Teng, J.C. Zhang, C.F. Cheng, Optical scattering analysis of the diffraction distortion of a two-dimensional reflection grating, Appl. Opt. 48 (2009) 4519–4525. [11] J.F. Ziegler, M.D. Ziegler, J.P. Biersack, SRIM–the stopping and range of ions in matter, Nucl. Instrum. Methods Phys. Res. Sect. B 268 (2010) 1818–1823. [12] J. Wang, G. Wang, C.L. Liu, Plasmonic behaviors of two-dimensional Ag/SiO2 nanocomposite gratings: roles of gap diffraction and localized surface plasmon resonance absorption, Plasmonics (2018), https://doi.org/10.1007/s11468-018-0875-3. [13] J. Wang, X.Y. Mu, G. Wang, C.L. Liu, Two-dimensional Ag/SiO2 and Cu/SiO2 nanocomposite surface-relief grating couplers and their vertical input coupling properties, Opt. Mater. 73 (2017) 466–472. [14] U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Springer, Berlin, 1995. [15] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, New York, 1983. [16] C.C. Ghizoni, B.U. Chen, C.L. Tang, Theory and experiments on grating couplers for thin-film waveguides, IEEE J. Quantum Elect. 12 (1976) 69–73. [17] S. Scheerlinck, J. Schrauwen, F.V. Laere, D. Taillaert, D.V. Thourhout, R. Baets, Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides, Opt. Express 15 (2007) 9625. [18] H.R. Philipp, Silicon dioxide (SiO2) (glass), in: E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic, San Diego, 1985, pp. 749–763. [19] A.L. Fehrembach, D. Maystre, A. Sentenac, Phenomenological theory of filtering by resonant dielectric gratings, J. Opt. Soc. Am. A 19 (2002) 1136–1144. [20] K.L. Kelly, E. Coronado, L.L. Zhao, G.C. Schatz, The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment, J. Phys. Chem. B 107 (2003) 668–677.
1148
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Diffraction-distortion-induced deflection of guided waves in twodimensional Ag/SiO2 nanocomposite grating coupler
T
⁎
Jun Wanga, , Changlong Liub,c, Gang Wangb, Yongjie Sunb a b c
College of Science, China University of Petroleum (East China), Qingdao, 266580, China School of Science, Tianjin University, Tianjin, 300072, China Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparation Technology, Tianjin, 300072, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Grating coupler Waveguide slab Deflection of guided wave Diffraction distortion
Two-dimensional Ag/SiO2 nanocomposite grating coupler with a periodicity of 600 nm was fabricated by etching an Ag-ion-implanted SiO2 waveguide slab, which was evidenced to be able to convert a vertically incident beam in the wavelength range of 620–880 nm into four beams of guided waves without regard for the polarization of incident beam. Employing this coupler, the deflection of guided waves due to the diffraction distortion in the case of oblique incidence was clearly demonstrated. Moreover, to accurately predict the propagating direction of guided wave in the SiO2 waveguide layer, a simple relation of the deflected angle of guided wave to the polar and azimuth angles of incident beam was deduced according to the oblique coupling of a onedimensional Ag/SiO2 nanocomposite grating coupler. The calculated results by using the deduced relation revealed that increasing the polar angle and/or azimuth angle of incident beam could lead to an increase in deflected angle of guided wave. Especially, for an azimuth angle of 90°, the calculated results agreed well with the experimental data, justifying the deduced relation. The above findings might be useful for the packaging and applications of grating couplers.
1. Introduction In comparison with the end-facet (or edge illumination) and prism couplers [1,2], the grating couplers are more robust and convenient to couple light beams into or out of optical thin films or slabs [3]. Moreover, the grating couplers are more compatible with the planar device technology [4], and thereby, they have been considered as fundamental building blocks of large-scale photonic integrated circuits [5]. In an optical thin film or slab, the excitation of waveguide modes via a grating coupler means that the proper diffraction orders are converted into the propagating waves. This fact suggests that the propagating direction of a guided wave in the optical thin film or slab is absolutely governed by the corresponding diffraction order’s azimuth angle with respect to a specific coordinate axis in the grating plane. For a diffraction grating, when a light beam vertically strikes on it, the azimuth angles of diffraction orders are easy to predict. However, when a light beam obliquely strikes on it, the diffraction orders will be aberrant. That is to say, the oblique incidence of light beam at a polar angle with respect to the normal of grating plane and an azimuth angle with respect to a specific coordinate axis in the grating plane can make the diffraction orders present different azimuth angles from those corresponding to the normal incidence. The aberration of diffraction order, i.e., the diffraction distortion, can be explained on the basis of the phase difference of the high-order propagation factor in Fresnel diffraction [6]. As a fundamental and important phenomenon, the diffraction distortion of grating in the case of oblique incidence has been investigated theoretically and experimentally
⁎
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.ijleo.2019.01.107 Received 5 January 2019; Accepted 30 January 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 182 (2019) 1143–1148
J. Wang, et al.
[6–10], but its influence on the propagating directions of the waveguide modes excited via a grating coupler has not been touched upon as yet. In our opinion, the above influence may be crucial to the packaging and applications of grating couplers, and thus, it is worthy to be discussed in depth. In this work, two-dimensional (2D) Ag/SiO2 nanocomposite grating coupler (i.e., a square grid of Ag/SiO2 nanocomposite veins) with a periodicity of 600 nm is fabricated by etching an Ag-ion-implanted SiO2 waveguide slab, which is able to convert a vertically incident beam in the wavelength range of 620–880 nm into four beams of guided waves without regard for the polarization of incident beam. Using this coupler, the diffraction-distortion-induced deflection of guided waves in the case of oblique incidence is clearly demonstrated. Moreover, a relation of the deflected angle of guided wave to the polar and azimuth angles of incident beam is also deduced, which can be used to precisely predict the propagating direction of guided wave in the SiO2 waveguide layer. 2. Experimental 2D Ag/SiO2 nanocomposite grating coupler (i.e., Ag/SiO2 coupler) of 600 nm in periodicity was fabricated on a 0.5-mm-thick SiO2 waveguide slab with an area of 20 × 20 mm2 via the following five steps. Firstly, the SiO2 waveguide slab was implanted with 90 keV Ag ions to a dose of 6 × 1016 cm−2, and the Ag ion beam was tilted by 45° from the sample surface due to the limit of implanter. Under these conditions, a subsurface Ag/SiO2 nanocomposite layer could be synthesized in a depth range of 0–100 nm according to a SRIM simulation [11]. Secondly, the Ag-ion-implanted SiO2 waveguide slab (i.e., Ag/SiO2 slab) was evenly coated with a layer of electron beam (EB) resist on a high-precision spin coater (CEE-200X-F, Brewer Sci. Co.). Thirdly, the EB resist layer was patterned with the given periodicity in a region of 4 × 4 mm2 on an EB lithography system (EBPG5000+, Vistec Co.). Fourthly, using the patterned EB resist layer as a mask, the Ag/SiO2 slab was etched for 38 s at −10 °C in CHF3 and Ar gases on an inductively coupled plasma reactive ion etching system (SI500, Sentech Co.). Such etching had been evidenced to be able to dislodge a 100 nm thick layer from an Ag/SiO2 slab without EB resist layer. Finally, the residual EB resist layer was removed in a 1:1 (v/v) solution of H2SO4 and H2O2. To reveal the vertical input coupling property of Ag/SiO2 coupler, the transmission spectra of Ag/SiO2 slab and coupler were recorded under the same conditions by using a double beam spectrophotometer (UV-3600, Shimadzu Co.). In addition, the inner structure of Ag/SiO2 slab and the surface morphology of Ag/SiO2 coupler were also examined by using a transmission electron microscope (TEM, G2 F20 S-Twin, Tecnai Co.) and a scanning electron microscopy (SEM, S4800, Hitachi Co.), respectively. To demonstrate the excitation of waveguide modes and the diffraction-distortion-induced deflection of guided waves, the Ag/SiO2 coupler was investigated by means of a simple setup as schematically shown in Fig. 1. In this setup, the Ag/SiO2 coupler was fastened to a sample holder and photographed with a digital camera fixed in the front of coupler. A laser diode of 650 nm in wavelength was used to offer an incident beam, and two linear polarizers were employed to transform the incident beam into the p- or s-polarized wave. The laser diode and linear polarizers were set to synchronously rotate around the coupler via a rocker arm (not shown here), and thereby, the polar angle of incident beam with respect to the normal of coupler could be altered continuously. To well conduct the observations at different polar angles, the digital camera was slightly higher than the laser diode and linear polarizers. 3. Results and discussion Fig. 2 shows the transmission spectra of Ag/SiO2 slab and coupler, and its insets (a) and (b) are the cross-sectional TEM image of Ag/SiO2 slab and the SEM image of Ag/SiO2 coupler, respectively. In the transmission spectrum of Ag/SiO2 slab, a steep transmittance attenuation band around a wavelength of 405 nm can be clearly found. According to the inset (a) and our previous work [12], one can know that this steep transmittance attenuation band is contributed by the localized surface plasmon resonance (LSPR)
Fig. 1. Schematic setup to observe the formation of guided waves and their deflection in the Ag/SiO2 coupler. 1144
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Fig. 2. Transmission spectra of Ag/SiO2 slab and coupler. Insets (a) and (b) exhibit the cross-sectional TEM image of Ag/SiO2 slab and the SEM image of Ag/SiO2 coupler, respectively.
absorption of the Ag nanoparticles (NPs) synthesized in the SiO2 waveguide slab. In the transmission spectrum of Ag/SiO2 coupler, a transmittance attenuation band induced by the LSPR absorption of Ag NPs can be also found, but it, compared to that appeared in the transmission spectrum of Ag/SiO2 slab, shifts to a longer wavelength (∼415 nm) and becomes weaker and more asymmetrical. Obviously, these spectral changes can be attributed to the formation of grating structure (refer to the inset (b) and Ref. [12]). Especially, the formation of grating structure can lead to another transmittance attenuation band, which is located between 620 and 880 nm in wavelength. The appearance of transmittance attenuation band in the wavelength range of 620–880 nm substantially indicates that an incident light beam in the corresponding wavelength range can be partly coupled into the SiO2 waveguide layer [13]. Owing to the introduction of Ag NPs, the grating teeth (i.e., nanocomposite veins) of Ag/SiO2 coupler not only are larger in refractivity than SiO2 [14], but also can act as effective scatterers [15]. Consequently, in the wavelength range of 620–880 nm, the Ag/SiO2 coupler can have a much higher coupling efficiency compared to an Ag-NP-free coupler with identical morphological parameters [16,17]. Such a feature makes the Ag/SiO2 coupler become a proper platform to demonstrate the formation of guided waves and their deflection in the case of oblique incidence. According to the coupling band revealed in Fig. 2, the Ag/SiO2 coupler was observed and photographed by means of the setup as schematically shown in Fig. 1 when it was illuminated by a laser beam of 650 nm in wavelength at different polar angles. Figs. 3(a) and (b) are the obtained typical photos for the incidence of p- and s-polarized waves, respectively. In the two figures, the sample surface is in the xoy plane, the incident beam is in the yoz plane, and the θI denotes the polar angle of incident beam with respect to the z axis. Fig. 3(a) clearly shows that in the case of θI = 0°, four light spots due to diffusion appear at the sample’s side walls. This phenomenon substantially reveals that four beams of guided waves are formed in the SiO2 waveguide layer, which propagate along the x axis (i.e., the column of grating) and the y axis (i.e., the row of grating), respectively. The formation of guided waves indicates that the phase matching condition is satisfied [4]. As known, the Ag/SiO2 coupler is of a square grid of Ag/SiO2 nanocomposite veins standing on the SiO2 waveguide layer, and thus, the phase matching condition can be simply described as
ns sinθD = sinθI + m
λ , Λ
(1)
where ns is the refractive index of SiO2, m is the diffraction order, θD is the polar angle of mth-order diffracted beam, λ is the wavelength of incident beam in the free space, and Λ is the periodicity of square grid. With ns = 1.46 [18], θI = 0°, λ = 650 nm, and Λ = 600 nm, again noting that the θD should be equal to or larger than sin−1 (1/ns) if a diffracted beam can become a propagating wave in the SiO2 waveguide layer, one can easily infer that only the first-order diffracted beams are converted into the guided waves. Moreover, Fig. 3(a) also shows that the increase of θI can give rise to three new phenomena. The first phenomenon is that the two light spots distributed in the x axis gradually depart from their respective initial positions with an identical rate, indicating that the correlative two guided waves synchronously deflect in anticlockwise and clockwise directions, respectively. In our opinion, similar phenomenon could be also observed for the two light spots distributed in the y axis if the incident beam were not in the yoz plane. From Eq. (1) and the related inference, one can draw a conclusion that the deflection of guided waves here is due to the aberrations of the first-order diffracted beams in the xoz plane. As to the dependence of deflected angle of guided wave on the polar angle of incident beam, it will be discussed in depth hereinafter. The second phenomenon is that owing to the phase mismatches at two specific polar angles of incident beam, the two light spots distributed in the y axis (or rather, the two guided waves propagating along the y axis) first become single and then disappear. The two specific polar angles of incident beam for the phase mismatches were measured to be about 5.5° and 20.5°, respectively. The phase mismatch at θI = 5.5° is due to θD < sin−1 (1/ns) for the diffraction order of m = −1, while the phase mismatch at θI = 20.5° is due to θD > 90° for the diffraction order of m = 1. The last phenomenon is that two new light spots appear at the sample’s side walls perpendicular to the x axis when θI ≈ 10°, and they gradually get close to the x axis with the increase of θI. The appearance of two new light spots should be related to the reflection of incident beam at the side walls of nanocomposite veins that are parallel to the x axis. Like the reflective gratings [10], the Ag/SiO2 coupler is believed to be able to produce the diffracted light fields due to an in-phase addition of the reflected light fields induced by the interaction between 1145
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Fig. 3. Typical photos of Ag/SiO2 coupler for the incidence of (a) p- and (b) s-polarized waves of 650 nm in wavelength at different polar angles θI.
the incident beam and the side walls of nanocomposite veins, and therefore, two new guided waves can be formed in the SiO2 waveguide layer when the Ag/SiO2 coupler is obliquely illuminated at a specific θI. Just because the two new light spots originate from the reflection rather than the transmission, increasing θI makes them gradually come near rather than depart from the x axis. It is worth noting that the above three phenomena for θI > 0° as well as that for θI = 0° can be also found in Fig. 3(b). This fact means that the coupling process of Ag/SiO2 coupler is quite insensitive to the polarization of incident beam. In our opinion, this insensitivity is not only due to the 2D orthogonal structure of coupling grating [19], but also due to the fact that the embedded Ag NPs in nanocomposite veins are globular and small in diameter [20]. The phenomena exhibited in Fig. 3 suggest that the 2D Ag/SiO2 coupler can be considered as an orthogonal overlapping of two 1D Ag/SiO2 coupler with an identical periodicity of Λ = 600 nm. On this basis, we suppose a 1D Ag/SiO2 coupler as schematically shown in Fig. 4 to reveal the dependence of deflection of guided wave on the direction of incident beam. In Fig. 4, kI and kD are the wave vector for incident beam and the wave vector for one of mth-order (in our case, m = ± 1) diffracted beams, respectively. Without loss of generality, the direction of kI is described with a polar angle of θI and an azimuth angle of ϕI. As a result of oblique incidence, the kD with a polar angle of θD deviates from the xoz plane by an azimuth angle of ϕD. This is the so-called diffraction distortion. Obviously, the ϕD is equal to the deflected angle φ of guided wave. According to the above descriptions, the wave vector β of guided wave in the SiO2 waveguide layer can be expressed in two forms:
2π 2π 2π β = ⎛ sinθI cosϕI + m ⎞ x 0 + ⎛ sinθI sinϕI ⎞ y0 , Λ⎠ ⎝ λ ⎝ λ ⎠
(2)
2π 2π β = ⎛ ns sinθD cosϕD ⎞ x 0 + ⎛ ns sinθDsinϕD ⎞ y0 , ⎝ λ ⎠ ⎝ λ ⎠
(3)
where x0 is the unit vector along the x axis, and y0 is the unit vector along the y axis. Eqs. (2) and (3) are related to the kI and kD, respectively. From them, the generalized grating formulae can be obtained as
ns sinθD cosϕD = sinθI cosϕI + m
λ , Λ
(4)
ns sinθDsinϕD = sinθI sinϕI .
(5) 1146
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Fig. 4. Diffraction-distortion-induced deflection of guided wave in a 1D Ag/SiO2 coupler.
Consequently, the deflected angle φ of guided wave can be given as
φ = ϕD = tan−1
sinθI sinϕI . sinθI cosϕI + mλ / Λ
(6)
With m = 1, λ = 650 nm, and Λ = 600 nm, the deflected angles of guided wave for the incidence at different polar and azimuth angles are calculated by using Eq. (6). The calculated results as shown in Fig. 5 clearly demonstrate that in the case of oblique incidence, increasing the polar angle and/or azimuth angle of incident beam can lead to an increase in deflected angle of guided wave. Especially, when ϕI = 90°, the calculated results are consistent well with the experimental data obtained from the photos of Ag/SiO2 coupler for the incidence of p-polarized wave (refer to Fig. 3(a)). This consistency substantially justifies Eq. (6). Eq. (6) does not involve any information on the embedded Ag NPs, and therefore, it can be expected to be used in other grating couplers to predict the propagating direction of guided wave in the waveguide layer. 4. Conclusions In summary, a vertically incident light beam in the wavelength range of 620–880 nm can be converted into four beams of guided waves via the Ag/SiO2 coupler, and the coupling process is insensitive to the polarization of incident beam. In the case of oblique incidence, partial (or all) guided waves can deflect from their propagating directions corresponding to the normal incidence owing to the diffraction distortion. The deflected angle of guided wave depends on the polar and azimuth angles of incident beam. Increasing the polar angle and/or azimuth angle of incident beam can lead to an increase in deflected angle of guided wave. The dependence of
Fig. 5. Deflected angles φ of guided wave for the incidence at different polar angles θI and azimuth angles ϕI. The experimental results are obtained from the photos of Ag/SiO2 coupler for the incidence of p-polarized wave (refer to Fig. 3(a)), and the theoretical results are calculated by using Eq. (6). 1147
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deflected angle of guided wave on the polar and azimuth angles of incident beam can be described with a simple equation (see Eq. (6)). The equation does not involve any information on the embedded Ag NPs, and thus, it can be expected to be used in other grating couplers to predict the propagating direction of guided wave in the waveguide layer. The above findings might be valuable for the packaging and applications of grating couplers. Funding This work was supported by the Natural Science Foundation of China [grant numbers 11675120, 11535008]. Acknowledgments Authors are grateful to the National Center for Nanoscience and Technology for the sample fabrication. References [1] R. Shubert, H. Harris, Optical surface waves on thin films and their application to integrated data processors, IEEE Trans. Microw. Theory Tech. 16 (1968) 1048–1054. [2] P.K. Tien, R. Ulrich, R.J. Martin, Modes of propagating light waves in thin deposited semiconductor films, Appl. Phys. Lett. 14 (1969) 291–294. [3] S.B. Mendes, S.S. Saavedra, N.R. Armstrong, Broadband spectroelectrochemical interrogation of molecular thin films by single-mode electro-active integrated optical waveguides, in: M. Zourob, A. Lakhtakia (Eds.), Optical Guided-Wave Chemical and Biosensors I, Springer, Berlin, 2010, pp. 101–129. [4] M.L. Dakss, L. Kuhn, P.F. Heidrich, B.A. Scott, Grating coupler for efficient excitation of optical guided waves in thin films, Appl. Phys. Lett. 16 (1970) 523–525. [5] D. Taillaert, F.V. Laere, M. Ayre, W. Bogaerts, D.V. Thourhout, P. Bienstman, R. Baets, Grating couplers for coupling between optical fibers and nanophotonic waveguides, Jpn. J. Appl. Phys. 45 (2006) 6071–6077. [6] J.E. Harvey, R.V. Shack, Aberrations of diffracted wave fields, Appl. Opt. 17 (1978) 3003–3009. [7] J.E. Harvey, C.L. Vernold, Description of diffraction grating behavior in direction cosine space, Appl. Opt. 37 (1998) 8158–8160. [8] J.E. Harvey, D. Bogunovic, A. Krywonos, Aberrations of diffracted wave fields: distortion, Appl. Opt. 42 (2003) 1167–1174. [9] G. Fortin, Graphical representation of the diffraction grating equation, Am. J. Phys. 76 (2008) 43–47. [10] S.Y. Teng, J.C. Zhang, C.F. Cheng, Optical scattering analysis of the diffraction distortion of a two-dimensional reflection grating, Appl. Opt. 48 (2009) 4519–4525. [11] J.F. Ziegler, M.D. Ziegler, J.P. Biersack, SRIM–the stopping and range of ions in matter, Nucl. Instrum. Methods Phys. Res. Sect. B 268 (2010) 1818–1823. [12] J. Wang, G. Wang, C.L. Liu, Plasmonic behaviors of two-dimensional Ag/SiO2 nanocomposite gratings: roles of gap diffraction and localized surface plasmon resonance absorption, Plasmonics (2018), https://doi.org/10.1007/s11468-018-0875-3. [13] J. Wang, X.Y. Mu, G. Wang, C.L. Liu, Two-dimensional Ag/SiO2 and Cu/SiO2 nanocomposite surface-relief grating couplers and their vertical input coupling properties, Opt. Mater. 73 (2017) 466–472. [14] U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Springer, Berlin, 1995. [15] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, New York, 1983. [16] C.C. Ghizoni, B.U. Chen, C.L. Tang, Theory and experiments on grating couplers for thin-film waveguides, IEEE J. Quantum Elect. 12 (1976) 69–73. [17] S. Scheerlinck, J. Schrauwen, F.V. Laere, D. Taillaert, D.V. Thourhout, R. Baets, Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides, Opt. Express 15 (2007) 9625. [18] H.R. Philipp, Silicon dioxide (SiO2) (glass), in: E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic, San Diego, 1985, pp. 749–763. [19] A.L. Fehrembach, D. Maystre, A. Sentenac, Phenomenological theory of filtering by resonant dielectric gratings, J. Opt. Soc. Am. A 19 (2002) 1136–1144. [20] K.L. Kelly, E. Coronado, L.L. Zhao, G.C. Schatz, The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment, J. Phys. Chem. B 107 (2003) 668–677.
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