Abstract

We theoretically investigate the use of Rayleigh surface acoustic waves (SAWs) for refractive index modulation in optical waveguides consisting of amorphous dielectrics. Considering low-loss Si3N4 waveguides with a standard core cross-section of 4.4×0.03 μm2 size, buried 8-μm deep in a SiO2 cladding, we compare surface acoustic wave generation in various different geometries via a piezo-active, lead zirconate titanate film placed on top of the surface and driven via an interdigitized transducer (IDT). Using numerical solutions of the acoustic and optical wave equations, we determine the strain distribution of the SAW under resonant excitation. From the overlap of the acoustic strain field with the optical mode field, we calculate and maximize the attainable amplitude of index modulation in the waveguide. For the example of a near-infrared wavelength of 840 nm, a maximum shift in relative effective refractive index of 0.7x10−3 was obtained for TE polarized light, using an IDT period of 30–35 μm, a film thickness of 2.5–3.5 μm, and an IDT voltage of 10 V. For these parameters, the resonant frequency is in the range of 70–85 MHz. The maximum shift increases to 1.2x10−3, with a corresponding resonant frequency of 87 MHz, when the height of the cladding above the core is reduced to 3 μm. The relative index change is about 300 times higher than in previous work based on non-resonant proximity piezo-actuation, and the modulation frequency is about 200 times higher. Exploiting the maximum relative index change of 1.2×10−3 in a low-loss, balanced Mach-Zehnder modulator should allow full-contrast modulation in devices as short as 120 μm (half-wave voltage length product = 0.24 Vcm).

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

K. Alexander, J. P. George, J. Verbist, K. Neyts, B. Kuyken, D. V. Thourhout, and J. Beeckman, “Nanophotonic pockels modulators on a silicon nitride platform,” Nat. Commun. 9, 3444 (2018).
[Crossref]

2017 (4)

L. Chang, M. H. P. Pfeiffer, N. Volet, M. Zervas, J. D. Peters, C. L. Manganelli, E. J. Stanton, Y. Li, T. J. Kippenberg, and J. E. Bowers, “Heterogeneous integration of lithium niobate and silicon nitride waveguides for wafer-scale photonic integrated circuits on silicon,” Opt. Lett. 42, 803–806 (2017).
[Crossref] [PubMed]

J. P. Epping, D. Marchenko, A. Leinse, R. Mateman, M. Hoekman, L. Wevers, E. J. Klein, C. G. H. Roeloffzen, M. Dekkers, and R. G. Heideman, “Ultra-low-power stress-optics modulator for microwave photonics,” Proc. SPIE 10106, 101060F (2017).

E. P. Haglund, S. Kumari, J. S. Gustavsson, E. Haglund, G. Roelkens, R. G. Baets, and A. Larsson, “Hybrid vertical-cavity laser integration on silicon,” Proc. SPIE 10122, 101220H (2017).
[Crossref]

Y. Shi, A. Cerjan, and S. Fan, “Acousto-optic finite-difference frequency-domain algorithm for first-principles simulations of on-chip acousto-optic devices,” APL Photonics 2, 020801 (2017).
[Crossref]

2016 (2)

D. J. Collins, A. Neild, and Y. Ai, “Highly focused high-frequency travelling surface acoustic waves (SAW) for rapid particle sorting,” Lab. Chip 16, 471–479 (2016).
[Crossref]

A. Ovvyan, N. Gruhler, S. Ferrari, and W. Pernice, “Cascaded Mach-Zehnder interferometer tunable filters,” J. Opt. 18, 064011 (2016).
[Crossref]

2015 (7)

J. P. Epping, T. Hellwig, M. Hoekman, R. Mateman, A. Leinse, R. G. Heideman, A. van Rees, P. J. M. van der Slot, C. J. Lee, C. Fallnich, and K.-J. Boller, “On-chip visible-to-infrared supercontinuum generation with more than 495 THz spectral bandwidth,” Opt. Express 23, 19596–19604 (2015).
[Crossref] [PubMed]

C. Xiong, X. Zhang, A. Mahendra, J. He, D.-Y. Choi, C. J. Chae, D. Marpaung, A. Leinse, R. G. Heideman, M. Hoekman, C. G. H. Roeloffzen, R. M. Oldenbeuving, P. W. L. van Dijk, C. Taddei, P. H. W. Leong, and B. J. Eggleton, “Compact and reconfigurable silicon nitride time-bin entanglement circuit,” Optica 2, 724–727 (2015).
[Crossref]

L. Zhuang, C. G. H. Roeloffzen, M. Hoekman, K.-J. Boller, and A. J. Lowery, “Programmable photonic signal processor chip for radiofrequency applications,” Optica 2, 854–859 (2015).
[Crossref]

K. Wörhoff, R. Heideman, A. Leinse, and M. Hoekman, “Triplex: A versatile dielectric photonic platform,” Adv. Opt. Techn. 4, 189–207 (2015).

N. Hosseini, R. Dekker, M. Hoekman, M. Dekkers, J. Bos, A. Leinse, and R. Heideman, “Stress-optic modulator in triplex platform using a piezoelectric lead zirconate titanate (pzt) thin film,” Opt. Express 23, 14018–14026 (2015).
[Crossref] [PubMed]

S. A. Tadesse, H. Li, Q. Liu, and M. Li, “Acousto-optic modulation of a photonic crystal nanocavity with lamb waves in microwave k band,” Appl. Phys. Lett. 107, 201113 (2015).

K. Luke, Y. Okawachi, M. R. E. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
[Crossref] [PubMed]

2014 (5)

L. Zhang, R. Barrett, P. Cloetens, C. Detlefs, and M. Sanchez del Rioa, “Anisotropic elasticity of silicon and its application to the modelling of x-ray optics,” J. Synchrotron Radiat. 21, 507–517 (2014).
[Crossref]

S. A. Tadesse and M. Li, “Sub-optical wavelength acoustic wave modulation of integrated photonic resonators at microwave frequencies,” Nat. Commun. 5, 5402 (2014).
[Crossref] [PubMed]

M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, and J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev. 8, 667–686 (2014).
[Crossref]

L. Zhuang, M. Hoekman, C. Taddei, A. Leinse, R. G. Heideman, A. Hulzinga, J. Verpoorte, R. M. Oldenbeuving, P. W. L. van Dijk, K.-J. Boller, and C. G. H. Roeloffzen, “On-chip microwave photonic beamformer circuits operating with phase modulation and direct detection,” Opt. Express 22, 17079–17091 (2014).
[Crossref] [PubMed]

S. M. Hendrickson, A. C. Foster, R. M. Camacho, and B. D. Clader, “Integrated nonlinear photonics: emerging applications and ongoing challenges,” J. Opt. Soc. Am. B 31, 3193–3203 (2014).
[Crossref]

2013 (4)

J. P. Epping, M. Kues, P. J. M. van der Slot, C. J. Lee, C. Fallnich, and K.-J. Boller, “Integrated CARS source based on seeded four-wave mixing in silicon nitride,” Opt. Express 21, 32123–32129 (2013).
[Crossref]

C. G. H. Roeloffzen, L. Zhuang, C. Taddei, A. Leinse, R. G. Heideman, P. W. L. van Dijk, R. M. Oldenbeuving, D. A. I. Marpaung, M. Burla, and K.-J. Boller, “Silicon nitride microwave photonic circuits,” Opt. Express 21, 22937–22961 (2013).
[Crossref] [PubMed]

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7, 506–538 (2013).
[Crossref]

R. M. Oldenbeuving, E. J. Klein, H. L. Offerhaus, C. J. Lee, H. Song, and K.-J. Boller, “25 khz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity,” Laser Phys. Lett. 10, 015804 (2013).
[Crossref]

2012 (3)

2011 (1)

2008 (2)

K. Zinoviev, L. G. Carrascosa, J. Sánchez del Río, B. Sepúlveda, C. Domínguez, and L. M. Lechuga, “Silicon Photonic Biosensors for Lab-on-a-Chip Applications,” Adv. Opt. Technol. 2008, 383927 (2008).
[Crossref]

A. B. Fallahkhair, K. S. Li, and T. E. Murphy, “Vector finite difference modesolver for anisotropic dielectric waveguides,” J. Light. Technol. 26, 1423–1431 (2008).
[Crossref]

2006 (1)

M. M. de Lima, M. Beck, R. Hey, and P. V. Santos, “Compact Mach-Zehnder acousto-optic modulator,” Appl. Phys. Lett. 89, 121104 (2006).
[Crossref]

2005 (3)

M. M. D. Lima and P. V. Santos, “Modulation of photonic structures by surface acoustic waves,” Rep. Prog. Phys. 68, 1639–1701 (2005).
[Crossref]

P. Tang, A. L. Meier, D. J. Towner, and B. W. Wessels, “Batio3 thin-film waveguide modulator with a low voltage–length product at near-infrared wavelengths of 0.98 and 1.55 μm,” Opt. Lett. 30, 254–256 (2005).
[Crossref]

P. Tang, A. L. Meier, D. J. Towner, and B. W. Wessels, “High-speed travelling-wave batio3 thin-film electro-optic modulators,” Electron. Lett. 41, 1296–1297 (2005).
[Crossref]

2004 (1)

Y. Saito, H. Takao, T. Tani, T. Nonoyama, K. Takatori, T. Homma, T. Nagaya, and M. Nakamura, “Lead-free piezoceramics,” Nature 432, 84–87 (2004).
[Crossref]

1992 (2)

D. Rebiére, J. Pistrè, M. Hoummady, D. Hauden, P. Cunin, and R. Planade, “Sensitivity comparison between gas sensors using saw and shear horizontal plate-mode oscillators,” Sens. Actuator B-Chem. 6, 274–278 (1992).
[Crossref]

V. Sundar and R. E. Newnham, “Electrostriction and polarization,” Ferroelectrics 135, 431–446 (1992).
[Crossref]

1988 (1)

A. Bertholds and R. Dandliker, “Determination of the individual strain-optic coefficients in single-mode optical fibres,” J. Light. Technol. 6, 17–20 (1988).
[Crossref]

1984 (1)

J. Fukushima, K. Kodaira, and T. Matsushita, “Preparation of ferroelectric pzt films by thermal decomposition of organometallic compounds,” J. Mater. Sci. 19, 595–598 (1984).
[Crossref]

1980 (1)

J. Schroeder, “Brillouin scattering and pockels coefficients in silicate glasses,” J. Non-Cryst. Solids 40, 549–566 (1980).
[Crossref]

1979 (1)

D. Heiman, D. Hamilton, and R. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[Crossref]

1968 (1)

1955 (1)

H. Kay, “Electrostriction,” Rep. Prog. Phys. 18, 230–250 (1955).
[Crossref]

1885 (1)

L. Rayleigh, “On waves propagated along the plane surface of an elastic solid,” Proc. Lond. Math. Soc. s1-17, 4–11 (1885).
[Crossref]

1815 (1)

D. Brewster, “On the effects of simple pressure in producing that species of crystallization which forms two oppositely polarised images, and exhibits the complementary colours by polarised light,” Phil. Trans. R. Soc. Lond. 105, 60–64 (1815).
[Crossref]

Ai, Y.

D. J. Collins, A. Neild, and Y. Ai, “Highly focused high-frequency travelling surface acoustic waves (SAW) for rapid particle sorting,” Lab. Chip 16, 471–479 (2016).
[Crossref]

Alexander, K.

K. Alexander, J. P. George, J. Verbist, K. Neyts, B. Kuyken, D. V. Thourhout, and J. Beeckman, “Nanophotonic pockels modulators on a silicon nitride platform,” Nat. Commun. 9, 3444 (2018).
[Crossref]

Baets, R. G.

E. P. Haglund, S. Kumari, J. S. Gustavsson, E. Haglund, G. Roelkens, R. G. Baets, and A. Larsson, “Hybrid vertical-cavity laser integration on silicon,” Proc. SPIE 10122, 101220H (2017).
[Crossref]

Barrett, R.

L. Zhang, R. Barrett, P. Cloetens, C. Detlefs, and M. Sanchez del Rioa, “Anisotropic elasticity of silicon and its application to the modelling of x-ray optics,” J. Synchrotron Radiat. 21, 507–517 (2014).
[Crossref]

Barton, J. S.

Bauters, J. F.

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M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, and J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev. 8, 667–686 (2014).
[Crossref]

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J. P. Epping, T. Hellwig, M. Hoekman, R. Mateman, A. Leinse, R. G. Heideman, A. van Rees, P. J. M. van der Slot, C. J. Lee, C. Fallnich, and K.-J. Boller, “On-chip visible-to-infrared supercontinuum generation with more than 495 THz spectral bandwidth,” Opt. Express 23, 19596–19604 (2015).
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[Crossref]

L. Zhuang, M. Hoekman, C. Taddei, A. Leinse, R. G. Heideman, A. Hulzinga, J. Verpoorte, R. M. Oldenbeuving, P. W. L. van Dijk, K.-J. Boller, and C. G. H. Roeloffzen, “On-chip microwave photonic beamformer circuits operating with phase modulation and direct detection,” Opt. Express 22, 17079–17091 (2014).
[Crossref] [PubMed]

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J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19, 3163–3174 (2011).
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Y. Fan, R. M. Oldenbeuving, C. G. Roeloffzen, M. Hoekman, D. Geskus, R. G. Heideman, and K.-J. Boller, “290 Hz intrinsic linewidth from an integrated optical chip-based widely tunable InP-Si3N4 hybrid laser,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), JTh5C.9.
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K. Wörhoff, R. Heideman, A. Leinse, and M. Hoekman, “Triplex: A versatile dielectric photonic platform,” Adv. Opt. Techn. 4, 189–207 (2015).

J. P. Epping, T. Hellwig, M. Hoekman, R. Mateman, A. Leinse, R. G. Heideman, A. van Rees, P. J. M. van der Slot, C. J. Lee, C. Fallnich, and K.-J. Boller, “On-chip visible-to-infrared supercontinuum generation with more than 495 THz spectral bandwidth,” Opt. Express 23, 19596–19604 (2015).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref]

L. Zhuang, C. G. H. Roeloffzen, M. Hoekman, K.-J. Boller, and A. J. Lowery, “Programmable photonic signal processor chip for radiofrequency applications,” Optica 2, 854–859 (2015).
[Crossref]

L. Zhuang, M. Hoekman, C. Taddei, A. Leinse, R. G. Heideman, A. Hulzinga, J. Verpoorte, R. M. Oldenbeuving, P. W. L. van Dijk, K.-J. Boller, and C. G. H. Roeloffzen, “On-chip microwave photonic beamformer circuits operating with phase modulation and direct detection,” Opt. Express 22, 17079–17091 (2014).
[Crossref] [PubMed]

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[Crossref]

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R. M. Oldenbeuving, E. J. Klein, H. L. Offerhaus, C. J. Lee, H. Song, and K.-J. Boller, “25 khz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity,” Laser Phys. Lett. 10, 015804 (2013).
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Figures (8)

Fig. 1
Fig. 1 Schematic view of a waveguide (in dark blue) based Mach-Zehnder interferometer. Half of the electrode structure (in yellow) and piezo layer (in green) is not shown to enable a full view on the interferometer (dark blue waveguides). The interferometer waveguides are buried in SiO2 (light gray) deposited on a silicon substrate (dark Grey).
Fig. 2
Fig. 2 (a) Schematic view of the geometry comprising a Si3N4 core (4.4x0.03 μm2, dark blue) centered in a 16-μm thick SiO2 cladding (light gray) on a Si substrate (dark gray). A crystalline PZT layer on top of the cladding (green)in combination with an IDT (yellow) is used for exciting surface acoustic waves (SAWs). (b) The cross-section shows the corresponding two-dimensional unit cell across a single period Λ of the IDT. The thickness of the Si layer included in the unit cell is proportional to Λ to ensure a negligible SAW amplitude at the lower boundary of the unit cell. The layer between the PZT and the SiO2 layers is either conductive (yellow) or dielectric (light blue) and functions as seed layer for the crystalline growth of the PZT layer on top of the amorphous SiO2 or IDT electrode. (c)-(f) Illustrate the various combinations of IDT locations with and without opposite conductive layer, following the same color coding. (c) ETC, (d) ETD,(e) EBC,(f) EBD. Features are not to scale.
Fig. 3
Fig. 3 Resonant acoustic frequency, f R, of the fundamental Rayleigh wave for the IDT configuration ETD, and, for clarity, the frequency difference Δ f R with regard to the reference IDT configuration ETD, for the remaining IDT configurations EBD, ETC and EBC.The frequency is displayed as function of the period of the acoustic wave, which is equal to the period Λ of the IDT for a fixed PZT thickness d = 2 μm (a), and as a function of the thickness d of the PZT layer for an IDT period of Λ = 30 μm (b).
Fig. 4
Fig. 4 Strain distribution in the horizontal, Sx, (a) and vertical, Sy, (b) directions as generated by the fundamental Rayleigh wave when Λ = 30 μm and d = 2 μm. The Si3N4 waveguide core is shown in black at scale.
Fig. 5
Fig. 5 Strain in the x-direction (a) at the center of the core, S x ( 0 , 0 ), and corresponding strain in the y-direction (b), S y ( 0 , 0 ) as a function of Λ for d=1.5, 2.5 and 3.5 μm. Strain in the y-direction at the center of the core, S y ( 0 , 0 ) versus Λ for d = 1.5 μm (c) and versus d for Λ = 25 μm (d) for the four IDT configurations. A sinusoidal voltage with a resonant frequency and an amplitude of 10 V is applied to the IDT electrode.
Fig. 6
Fig. 6 Distribution of the Ex component (in arbitrary units) of the fundamental quasi-TE eigenmode for a wavelength of 840 nm. The Si3N4 core with dimensions of 30 nm by 4.4 μm is centered at the origin of the coordinate system and is indicated by the white line. The drawing is to scale.
Fig. 7
Fig. 7 Relative change in the effective refractive index, Δ n / n eff, for the quasi-TE mode (a) and quasi-TM mode (b) as a function of IDT period, Λ, for three different PZT-layer thicknesses, d = 1.5, 2.5 and 3.5 μm and as a function of d for Λ = 20, 25, 30 and 35 μm for the quasi-TE mode (c) and for the quasi-TM mode (d). The IDT configuration is EBC and the vacuum wavelength is λ = 840 nm.
Fig. 8
Fig. 8 Relative change in the effective refractive index, Δ n / n eff, as a function thickness of the cladding layer above the core, d cl for the fundamental mode with TE polarization (red line) and TM polarization (dashed black line). The IDT configuration is EBC, d = 2.5 μm, Λ = 30 μm and a voltage signal with an amplitude of 10 V and the appropriate resonant frequency is applied to the IDT electrodes. The vacuum wavelength is λ = 840 nm.

Tables (1)

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Table 1 Material constants used in calculating the SAW properties. Parameters not included in the model are denoted as (NI). Parameters included in tensor form are shown as (-).

Equations (10)

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[ Δ ( ε 1 ) ] i j = ( p S ) i j = k l p i j k l S k l ,
Δ n x = 1 2 n 0 3 ( p 11 S x + p 12 S y ) .
Δ n y = 1 2 n 0 3 ( p 12 S x + p 11 S y ) .
Δ φ = 2 π Δ n L λ ,
Δ φ t = 4 π | Δ n | L λ .
L = λ 4 | Δ n | ,
C = ( c 11 c 12 c 21 0 0 0 c 12 c 11 c 21 0 0 0 c 21 c 21 c 33 0 0 0 0 0 0 c 44 0 0 0 0 0 0 c 44 0 0 0 0 0 0 c 66 ) ,
d = ( 0 0 0 0 440 0 0 0 0 440 0 0 60 60 152 0 0 0 ) × 10 12 C N ,
ε T = ( 990 0 0 0 990 0 0 0 450 ) ,
f R = v R / Λ ,

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