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OPTICS LETTERS / Vol. 39, No. 1 / January 1, 2014
Widely tunable grating-assisted heterogeneous silicon nitride/polymer waveguide coupler Ziyang Zhang,* Garri Genrich, Norbert Keil, and Norbert Grote Fraunhofer Heinrich-Hertz Institute, Einsteinufer 37, Berlin 10587, Germany *Corresponding author: [email protected] Received November 15, 2013; revised November 29, 2013; accepted November 29, 2013; posted December 3, 2013 (Doc. ID 200966); published December 24, 2013 A grating-assisted heterogeneous waveguide coupler is designed, fabricated, and demonstrated on a polymer platform. The parallel silicon nitrite core and polymer core are horizontally placed with vertical center alignment accuracy of 5 nm. The coupler is differentially thermally tunable. The temperature gradient distribution, introduced by offset micro-heaters, is studied by thermal simulations. A total tuning range of 82 nm is demonstrated experimentally. © 2013 Optical Society of America OCIS codes: (130.5460) Polymer waveguides; (050.2770) Gratings; (130.7408) Wavelength filtering devices. http://dx.doi.org/10.1364/OL.39.000162
Low-cost and power-efficient wide-band tunable devices are highly desired for long-haul and metro communication systems, where a multitude of wavelengths are being utilized for signal multiplexing, switching, and network reconfiguring. Under this demand, there has been much research on the development of widely tunable filters as building blocks for various photonic devices, such as tunable lasers [1,2] and wavelength multiplexers [3,4]. Over the years, optical polymers have been shown to form a viable waveguide platform for hybrid photonic integration [5,6]. Polymer materials generally feature both fairly high thermo-optic coefficients, in the range of −1–3 × 10−4 K−1 , and low thermal conductivity, which makes them attractive for implementing power-efficient thermally tunable devices [7–9]. To increase the waveguide index contrast and bring down the device footprint, silicon nitride (SiNx ) has been introduced on the polymer platform to build heterogeneous SiNx/polymer waveguides. Low-loss waveguides and related tunable filters have been reported [10,11]. In this Letter, we take a step further to develop a widely tunable filter, relying on the grating-assisted codirectional coupler scheme. Basically, it comprises two parallel asymmetric waveguides, one with a SiNx core and the other with a polymer core. Long-period gratings are formed along the SiNx waveguide to provide phase matching and wavelength filtering. Coupled mode theory is applied to study the behavior of this filter, which can be tuned by the temperature difference between the two waveguides. Thermal simulations are carried out to design a heating scheme that induces a temperature gradient between the two waveguides. The fabricated devices are characterized to verify the design. The advantages of the coupler, such as bi-directional tunability, a broad tuning range, and high tuning efficiency are experimentally demonstrated. The schematic of the grating-assisted coupler is shown in Fig. 1. The polymer cladding exhibits an index of 1.45 and the core of 1.47; whereas, that of the SiNx film was determined to be 1.83 at 1550 nm. The polymer waveguide core has a dimension of 3.5 μm × 3.5 μm and the SiNx core measures 2.8 μm wide × 135 nm (thick). The heater–electrodes, P and N, are placed on top of 0146-9592/14/010162-04$15.00/0
the waveguides with an offset with respect to the center of the gap to create a temperature gradient. We refer to the polymer waveguide as WGP and the SiNx waveguide as WGN. np and nn are the effective indices of WGP and WGN, respectively, assuming np to be smaller. Λ is the period of the grating. The coupling coefficient κ depends on the mode overlap between WGP and WGN. The detuning of the propagation constants is defined as Δk
2π 2π n − np − : λ n Λ
(1)
Assuming weak coupling, the coupled mode equations can be written as: 8 dAz > < −jκ exp−jΔkzBz dz ; > : dBz −jκ expjΔkzAz dz
2
Fig. 1. Schematic of the grating-assisted SiNx and polymer waveguide coupler filter: (a) side view and (b) central top view. © 2014 Optical Society of America
January 1, 2014 / Vol. 39, No. 1 / OPTICS LETTERS
where Az and Bz represent the slow varying waveguide mode field in WGP and WGN, respectively. With proper boundary conditions, the intensity variation of the WGP mode can be derived as, P A λ; z jAzj2
κ2 1 − cos2σz ; 2 σ2
(3)
where r Δk2 σ κ2 : 2
(4)
The central wavelength of the coupler, λ0 , can be obtained from the phase matching condition when Δk 0: λ0 nn − np Λ:
(5)
The transmission spectra are numerically studied using Eq. (3). An example is plotted as the central green curve in Fig. 2(a). Taking the temperature derivative of Eq. (5), the tuning of the central wavelength can be expressed by: Δλ0
∂nn ∂np − ΛΔT Γn ΔT n − Γp ΔT p Λ: ∂T n ∂T p
(6)
ΔT denotes temperature change in the coupler region in general. It can be decomposed into two parts, emphasizing the separate temperature change ΔT p in WGP and ΔT n in WGN, respectively. Since the polymer core and cladding are made of chemically similar materials with almost identical thermal optic coefficient (TOC), it is
Fig. 2. (a) Channel transfer spectra at various heating conditions and (b) intensity snapshot in the central horizontal plane of the waveguides, indicating 100% channel transfer from WGN to WGP.
163
convenient to assume that Γp is the polymer material TOCp itself, measured as −1.14 × 10−4 K−1 · Γn , on the other hand, depends on the mode confinement factor (ρ) of WGN.: Γn 1 − ρΓP ρTOCn :
(7)
WGN features a very thin SiNx core, resulting in a weakly confined mode, with ρ (TE) typically being around 16%. Despite the positive value of SiNx material TOCn 3.0 × 10−5 K−1 , Γn still has a negative sign and is calculated to be −9.1 × 10−5 K−1 . Note that, in Eq. (6), if one waveguide region has an overall temperature gradient over the other, then λ0 will either increase when WGP is “hotter” (due to the negative sign of Γp ), or decrease when WGN is “hotter”. Figure 2(a) summarizes the situation. When ΔT p 5 K, while ΔT n 0, the central wavelength increases by about 40 nm. When the heating condition is reversed, λ0 drops by about 32 nm. However, in the situation where the heating is uniform among the two waveguides, i.e., ΔT p ΔT n 5 K, the tuning tends to cancel out and λ0 only increases by 8 nm. The numerical study is verified by simulations using the commercial software Fimmwave. An intensity snapshot, taken at the central wavelength (without tuning), is shown in Fig. 2(b) and indicates 100% channel transfer from WGN to WGP. From Eq. (6), the temperature dependent wavelength shift can be seen to be proportional to the grating period Λ, which again is determined by the effective index contrast of the two waveguides, as described in Eq. (5). At a given wavelength, two similar waveguides will lead to a rather long grating period. This, though beneficial for realizing extremely temperature gradient sensitive devices, will inevitably result in a very bulky device. The index contrast, in a series of chemically compatible polymer materials, is usually limited to only a few percent. A heterogeneous waveguide made of material with a higher index, such as SiNx , is well-suited to overcome this issue and offers a much higher design freedom for finding a reasonable trade-off between tuning sensitivity and device geometry. Crucial to the proposed tunable filter is the creation of an appropriate temperature gradient between the two waveguides. One solution is to apply a heat current through only one of two alternate electrodes while leaving the other unbiased. Thermal simulations are presented in Fig. 3. The heater–electrode measures 8 μm in width and is assumed to generate a power density of 20 mW∕mm, amounting to a 168°C heat source, compared to the 25°C base temperature. Each isothermal contour indicates a 5°C temperature drop. In both Figs. 3(a) and 3(b), the electrode center is displaced by 8 μm from the center of the waveguide gap. The integral of the gradient lines across the modal area gives an effective temperature difference of 7.5°C. Placing the electrode symmetrically above the two waveguides, as in Fig. 3(c), results in a close to zero temperature difference. Sidewall electrodes in Fig. 3(d) can enhance this gradient to 10.5°C.
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OPTICS LETTERS / Vol. 39, No. 1 / January 1, 2014
Fig. 3. Thermal simulations: (a) and (b) displaced heaterelectrode, (c) center symmetric heater–electrode, and (d) sidewall electrode.
During the fabrication, both the SiNx and the polymer layers are formed at low temperature (
OPTICS LETTERS / Vol. 39, No. 1 / January 1, 2014
Widely tunable grating-assisted heterogeneous silicon nitride/polymer waveguide coupler Ziyang Zhang,* Garri Genrich, Norbert Keil, and Norbert Grote Fraunhofer Heinrich-Hertz Institute, Einsteinufer 37, Berlin 10587, Germany *Corresponding author: [email protected] Received November 15, 2013; revised November 29, 2013; accepted November 29, 2013; posted December 3, 2013 (Doc. ID 200966); published December 24, 2013 A grating-assisted heterogeneous waveguide coupler is designed, fabricated, and demonstrated on a polymer platform. The parallel silicon nitrite core and polymer core are horizontally placed with vertical center alignment accuracy of 5 nm. The coupler is differentially thermally tunable. The temperature gradient distribution, introduced by offset micro-heaters, is studied by thermal simulations. A total tuning range of 82 nm is demonstrated experimentally. © 2013 Optical Society of America OCIS codes: (130.5460) Polymer waveguides; (050.2770) Gratings; (130.7408) Wavelength filtering devices. http://dx.doi.org/10.1364/OL.39.000162
Low-cost and power-efficient wide-band tunable devices are highly desired for long-haul and metro communication systems, where a multitude of wavelengths are being utilized for signal multiplexing, switching, and network reconfiguring. Under this demand, there has been much research on the development of widely tunable filters as building blocks for various photonic devices, such as tunable lasers [1,2] and wavelength multiplexers [3,4]. Over the years, optical polymers have been shown to form a viable waveguide platform for hybrid photonic integration [5,6]. Polymer materials generally feature both fairly high thermo-optic coefficients, in the range of −1–3 × 10−4 K−1 , and low thermal conductivity, which makes them attractive for implementing power-efficient thermally tunable devices [7–9]. To increase the waveguide index contrast and bring down the device footprint, silicon nitride (SiNx ) has been introduced on the polymer platform to build heterogeneous SiNx/polymer waveguides. Low-loss waveguides and related tunable filters have been reported [10,11]. In this Letter, we take a step further to develop a widely tunable filter, relying on the grating-assisted codirectional coupler scheme. Basically, it comprises two parallel asymmetric waveguides, one with a SiNx core and the other with a polymer core. Long-period gratings are formed along the SiNx waveguide to provide phase matching and wavelength filtering. Coupled mode theory is applied to study the behavior of this filter, which can be tuned by the temperature difference between the two waveguides. Thermal simulations are carried out to design a heating scheme that induces a temperature gradient between the two waveguides. The fabricated devices are characterized to verify the design. The advantages of the coupler, such as bi-directional tunability, a broad tuning range, and high tuning efficiency are experimentally demonstrated. The schematic of the grating-assisted coupler is shown in Fig. 1. The polymer cladding exhibits an index of 1.45 and the core of 1.47; whereas, that of the SiNx film was determined to be 1.83 at 1550 nm. The polymer waveguide core has a dimension of 3.5 μm × 3.5 μm and the SiNx core measures 2.8 μm wide × 135 nm (thick). The heater–electrodes, P and N, are placed on top of 0146-9592/14/010162-04$15.00/0
the waveguides with an offset with respect to the center of the gap to create a temperature gradient. We refer to the polymer waveguide as WGP and the SiNx waveguide as WGN. np and nn are the effective indices of WGP and WGN, respectively, assuming np to be smaller. Λ is the period of the grating. The coupling coefficient κ depends on the mode overlap between WGP and WGN. The detuning of the propagation constants is defined as Δk
2π 2π n − np − : λ n Λ
(1)
Assuming weak coupling, the coupled mode equations can be written as: 8 dAz > < −jκ exp−jΔkzBz dz ; > : dBz −jκ expjΔkzAz dz
2
Fig. 1. Schematic of the grating-assisted SiNx and polymer waveguide coupler filter: (a) side view and (b) central top view. © 2014 Optical Society of America
January 1, 2014 / Vol. 39, No. 1 / OPTICS LETTERS
where Az and Bz represent the slow varying waveguide mode field in WGP and WGN, respectively. With proper boundary conditions, the intensity variation of the WGP mode can be derived as, P A λ; z jAzj2
κ2 1 − cos2σz ; 2 σ2
(3)
where r Δk2 σ κ2 : 2
(4)
The central wavelength of the coupler, λ0 , can be obtained from the phase matching condition when Δk 0: λ0 nn − np Λ:
(5)
The transmission spectra are numerically studied using Eq. (3). An example is plotted as the central green curve in Fig. 2(a). Taking the temperature derivative of Eq. (5), the tuning of the central wavelength can be expressed by: Δλ0
∂nn ∂np − ΛΔT Γn ΔT n − Γp ΔT p Λ: ∂T n ∂T p
(6)
ΔT denotes temperature change in the coupler region in general. It can be decomposed into two parts, emphasizing the separate temperature change ΔT p in WGP and ΔT n in WGN, respectively. Since the polymer core and cladding are made of chemically similar materials with almost identical thermal optic coefficient (TOC), it is
Fig. 2. (a) Channel transfer spectra at various heating conditions and (b) intensity snapshot in the central horizontal plane of the waveguides, indicating 100% channel transfer from WGN to WGP.
163
convenient to assume that Γp is the polymer material TOCp itself, measured as −1.14 × 10−4 K−1 · Γn , on the other hand, depends on the mode confinement factor (ρ) of WGN.: Γn 1 − ρΓP ρTOCn :
(7)
WGN features a very thin SiNx core, resulting in a weakly confined mode, with ρ (TE) typically being around 16%. Despite the positive value of SiNx material TOCn 3.0 × 10−5 K−1 , Γn still has a negative sign and is calculated to be −9.1 × 10−5 K−1 . Note that, in Eq. (6), if one waveguide region has an overall temperature gradient over the other, then λ0 will either increase when WGP is “hotter” (due to the negative sign of Γp ), or decrease when WGN is “hotter”. Figure 2(a) summarizes the situation. When ΔT p 5 K, while ΔT n 0, the central wavelength increases by about 40 nm. When the heating condition is reversed, λ0 drops by about 32 nm. However, in the situation where the heating is uniform among the two waveguides, i.e., ΔT p ΔT n 5 K, the tuning tends to cancel out and λ0 only increases by 8 nm. The numerical study is verified by simulations using the commercial software Fimmwave. An intensity snapshot, taken at the central wavelength (without tuning), is shown in Fig. 2(b) and indicates 100% channel transfer from WGN to WGP. From Eq. (6), the temperature dependent wavelength shift can be seen to be proportional to the grating period Λ, which again is determined by the effective index contrast of the two waveguides, as described in Eq. (5). At a given wavelength, two similar waveguides will lead to a rather long grating period. This, though beneficial for realizing extremely temperature gradient sensitive devices, will inevitably result in a very bulky device. The index contrast, in a series of chemically compatible polymer materials, is usually limited to only a few percent. A heterogeneous waveguide made of material with a higher index, such as SiNx , is well-suited to overcome this issue and offers a much higher design freedom for finding a reasonable trade-off between tuning sensitivity and device geometry. Crucial to the proposed tunable filter is the creation of an appropriate temperature gradient between the two waveguides. One solution is to apply a heat current through only one of two alternate electrodes while leaving the other unbiased. Thermal simulations are presented in Fig. 3. The heater–electrode measures 8 μm in width and is assumed to generate a power density of 20 mW∕mm, amounting to a 168°C heat source, compared to the 25°C base temperature. Each isothermal contour indicates a 5°C temperature drop. In both Figs. 3(a) and 3(b), the electrode center is displaced by 8 μm from the center of the waveguide gap. The integral of the gradient lines across the modal area gives an effective temperature difference of 7.5°C. Placing the electrode symmetrically above the two waveguides, as in Fig. 3(c), results in a close to zero temperature difference. Sidewall electrodes in Fig. 3(d) can enhance this gradient to 10.5°C.
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OPTICS LETTERS / Vol. 39, No. 1 / January 1, 2014
Fig. 3. Thermal simulations: (a) and (b) displaced heaterelectrode, (c) center symmetric heater–electrode, and (d) sidewall electrode.
During the fabrication, both the SiNx and the polymer layers are formed at low temperature (
