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Abstract
In integrated optical circuits light typically travels in waveguides which provide both vertical and horizontal confinement, enabling efficient routing between different parts of the chip. However, for a variety of applications, including on-chip wireless communications, steerable phased arrays or free-space inspired integrated optics, optical beams that can freely propagate in the horizontal plane of a 2D slab waveguide are advantageous. Here we present a distributed Bragg deflector that enables well controlled coupling from a waveguide mode to such a 2D on-chip beam. The device consists of a channel waveguide and a slab waveguide region separated by a subwavelength metamaterial spacer to prevent uncontrolled leakage of the guided mode. A blazed grating in the waveguide sidewall is used to gradually diffract light into the slab region. We develop a computationally efficient strategy for designing gratings that generate arbitrarily shaped beams. As a proof-of-concept we design, in the silicon-on-insulator platform, a compact $\times 75$ Gaussian beam expander and a partial beam deflector. For the latter, we also demonstrate a prototype device with experimental results showing good agreement with our theoretical predictions. We also demonstrate via a rigorous simulation that two such couplers in a back-to-back configuration efficiently couple light, suggesting that these devices can be used as highly directive antennas in the chip plane.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In planar lightwave circuits light is typically guided and manipulated in waveguide devices that provide both horizontal and vertical confinement, thereby restricting the possible field configurations to a discrete set of waveguide modes. Single-mode waveguides offer an efficient and well controlled means for routing light to various parts of the circuit. Directional couplers and multimode interference couplers [1] are typically used to transfer energy between waveguides modes, thereby providing the foundation for more complex devices such as optical modulators [2], coherent receivers [3], wavelength multiplexers and filters [4–6], among other applications. Gratings etched into a waveguide sidewall are a versatile tool for controlling the coupling between waveguide modes and have been used in high performance wavelength selective reflectors [7–9] and contra-directional couplers [10,11]. Typically, gratings working in the diffractive regime are used for fiber-chip coupling [12], where the waveguide mode is diffracted out of the chip as a free-space beam.
The use of free-space-like beams propagating within the plane of the chip (slab waveguide) can offer interesting opportunities for applications such as wireless on-chip optical communications [13,14], steerable optical phased arrays [15,16], and on-chip integrated lenses that are inspired by free-space optics design [17]. However, few works have addressed lateral coupling of light from a channel waveguide mode to a vertically confined beam in a slab waveguide (see Fig. 1). In [18,19] a diffractive grating, that was etched in the sidewall of a curved waveguide, was used in a wavelength demultiplexer in the silicon-on-insulator platform. The more general concept of a distributed Bragg deflector (DBD) [20,21], namely a channel waveguide that is periodically perturbed to produce well-controlled diffraction into a one-dimensionally confined slab waveguide, was originally envisioned for a variety of applications, including beam expansion, power division and polarization splitting, but has barely been explored.
Fig. 1. Sidewall-grating based distributed Bragg deflector that converts a conventional silicon wire mode (In) to a vertically confined Gaussian beam that propagates in the chip plane (Out). Light is diffracted out of the Si-wire waveguide with a blazed sidewall grating and couples into the slab free-propagation region (FPR). The subwavelength grating facilitates efficient coupling while minimizing lateral leakage of the waveguide mode. A detailed diagram of the diffractive element is also shown. Note: the geometry is not to scale; the total footprint is about $7\mu m \times 80\mu m$. The upper cladding is not shown for clarity.
Here, we use blazed sidewall gratings in silicon-on-insulator waveguides to implement a sidewall-grating distributed Bragg deflector (sidewall grating deflector, SGD) and develop an efficient Floquet-Bloch mode design procedure for shaping the diffracted beams at will. Then, we develop a beam deflector, as illustrated in Fig. 1, which converts a silicon wire waveguide mode, with a ${0.38 \,\mu {\textrm {m}}}$ mode field diameter, into a near-Gaussian beam with a ${30 \,\mu {\textrm {m}}}$ mode field diameter. In addition, we demonstrate that by placing two such deflectors facing one another in a back-to-back configuration, it is possible to transfer light from one waveguide to another via the diffracted beam, thereby opening a new path toward wireless on-chip communications in which the transmitting and receiving antennas are implemented via beam deflectors. Finally, we experimentally demonstrate a partial deflector, that redirects $10\,\%$ of the waveguide power into the slab mode, while keeping more than $80\,\%$ in the channel waveguide, yielding excellent agreement with simulation results.
The paper is organized as follows. In Section 2, the basic geometry and operation of the deflector are described. In Section 3, we discuss the design methodology and in Section 4, we present simulation results of the complete devices and the experimental validation. The conclusions of this work are presented in Section 5.
2. Deflector geometry and operation principle
The geometry of the device is illustrated in Fig. 1. Light that enters through a silicon wire fundamental TE mode is coupled to a Gaussian beam vertically confined in the slab free propagation region (FPR). The key part of the device is the diffractive SGD, which is composed of quasi-periodic diffractive elements of period $\Lambda$ (slowly varying with $z$) that progressively couple the Si-wire TE fundamental mode (with effective refractive index ${n_{\textrm {wire}}}$) to the vertically confined mode radiating with angle ${\theta _{m}}$ into the FPR slab. The grating equation for this geometry is as follows:
where ${n_{\textrm {wire}}}$ is the effective index of the silicon wire waveguide mode, ${n_{\textrm {slab}}}$ is the effective index of the FPR slab (${n_{\textrm {slab}}=2.97}$ for the in-plane polarization and silicon thickness of 260 nm) and $m$ is the diffraction order. Approximate values of these parameters are as follows: near-normal radiation of the $- 1^{st}$ diffraction order (${\theta _{-1}=-5^{\circ}}$) at ${\lambda _0=1.55\,\mu m}$, for a value of ${n_{\textrm {wire}}\sim 2.55}$ would require a pitch value on the order of $\Lambda \sim 551 \,nm$. Then, the radiation angle of the $0^{th}$ order beam coupled to the FPR would be ${\theta _0={\textrm {asin}}(n_{\textrm {wire}}}/{n_{\textrm {slab}}) \sim 59^{\circ}}$.The diffractive element, which is illustrated in the detail view of Fig. 1, comprises a blazed sidewall grating etched in the Si-wire core whose radiation strength $\alpha$, i.e. the rate at which the light propagating in the waveguide is radiated per unit length, can be adjusted through the blazing angle ($\beta$), the waveguide width $W_g$ and the etch ratio $\gamma$. The FPR and the Si-wire are connected through a sub-wavelength grating (SWG) metamaterial of width ${W_{\textrm {SWG}}}$ that has a periodic structure with pitch ${\Lambda _{\textrm {SWG}}}$ and duty cycle ${DC_{\textrm {SWG}}}$. Here we use the SWG metamaterial to provide sufficient isolation between the Si-wire and the FPR slab for minimizing the direct coupling through $0^{th}$-order diffraction, while at the same time providing a bridging layer between the Si-wire and the FPR slab so that most of the diffracted field is captured in the SWG region and then coupled to the slab with minimum radiation losses. The $0^{th}$ order couples to the lateral slab by the exponentially decaying evanescent field tail of the fundamental mode propagating in the channel waveguide (z axis as shown in Fig. 1). Hence, subwavelength grating trench effectively acts as an isolation layer, preventing the coupling of the evanescent tail of the channel waveguide mode to the FPR slab. For this reason, ${W_{\textrm {SWG}}}$ needs to be designed wide enough to mitigate this $0^{th}$ order leakage. On the other hand, the $-1^{st}$ order is diffracted by sidewall waveguide grating in a direction perpendicular to the channel waveguide, hence propagates in the SWG region (along x axis in Fig. 1) as a fundamental vertically confined mode (of the SWG region). Therefore, for the $-1^{st}$ diffraction order, the SWG region effectively acts as a waveguide, that is, a bridging region between the Si-wire and the FPR slab to minimize out-off-plane radiation loss. The SWG period has been set to ${\Lambda _{\textrm {SWG}}} = {\Lambda /2}$. This period is sufficiently small for ensuring the sub-wavelength regime and, thus, for synthesizing an effective medium [22,23]. We set ${\Lambda _{\textrm {SWG}}}$ as a submultiple of the diffractive period $\Lambda$ so that the Floquet-Bloch analysis of the individual diffractive elements can be efficiently performed. We also set the duty cycle of the SWG medium to ${DC_{\textrm {SWG}} = 0.5}$, thereby maximizing the minimum feature size. The SWG region is connected to a bidimensional free propagation region through an adiabatic taper that increases ${DC_{\textrm {SWG}}}$ linearly from the nominal value ($0.5$) to $1$ within a width of ${W_{\textrm {adapt}}}$. This taper forms a graded index (GRIN) region that realizes adaptation between the SWG and the FPR region, and hence mitigates both radiation loss due to vertical mode mismatch of the two regions and Fresnel reflection due to effective index mismatch. Once within the FPR, the light is vertically confined in the z direction but free to propagate in virtually any direction in the XZ-plane.
The device also includes input and output adaptation tapers for maximizing the power transfer from the Si-wire input mode to the diffractive Floquet-Bloch mode region. Without these tapers, losses would occur due to mode mismatch and possible excitation of radiation modes. The tapers are implemented by progressively introducing the sub-wavelength features of the diffractive region by increasing the pillars width as illustrated in Fig. 1(a).
2.1 Grating apodization
The design target is to create a Gaussian beam profile $r(z)$ with a constant phase front. Thus, the grating strength must be apodized while keeping the radiation angle $\theta (z)$ constant along the grating. Following [24], the leakage profile $\alpha (z)$ (radiation losses per unit length) required for synthesizing the radiated field profile $r(z)$ can be expressed as
where $r(z)$ is the desired radiated field profile (normalized as $\int _{-\infty }^{+\infty } r^{2}(z)dz=1$) and ${C_{\textrm {rad}}}$ is the fraction of input power that is radiated. This approximation holds if all propagation losses are due to radiation and there is only one diffraction order, which is also assumed for our design. Application of Eq. (2) yields the results in Fig. 2, which shows the required normalized radiation strength profile for radiating a Gaussian beam, defined by its mode field diameter (MFD) for three values of ${C_{\textrm {rad}}}$ (0.95, 0.98, and 0.99). Obtaining values of ${C_{\textrm {rad}}}$ that are closer to 1 requires increased dynamic range for the leakage coefficients. We selected ${C_{\textrm {rad}}=0.98}$ for our design as a suitable compromise between low losses and low dynamic range. This selection requires a maximum normalized radiation strength value of ${MFD\cdot \alpha _{\textrm {max}}=3}$. For our case, ${MFD=30 \,\mu {\textrm {m}}}$, ${\alpha _{\textrm {max}}=0.1\,{\mu {\textrm {m}}}^{-1}}$ and the total grating length is ${60 \,\mu {\textrm {m}}}$. Note that this maximum radiation strength is three orders of magnitude higher than the values that were reported for previous DBD designs [20,21].Fig. 2. Normalized radiated field profile (left axis) and the required grating radiation strength (right axis) for ${C_{\textrm {rad}}}$ = 0.95, 0.98, and 0.99 as a function of the normalized position.
2.2 Floquet-Bloch mode analysis
Once the desired radiation strength profile is calculated, the grating local geometry needs to be designed. Here, we assume that since the waveguide grating is quasi-periodic, i.e. slowly varying with z, the local behavior at any position of the structure can be approximated by a periodic structure that is characterized by its Floquet-Bloch mode [25, Chap. 3]. This assumption enables the independent design of the geometry of the diffractive element at a specific position ($z$) from the desired radiation strength $\alpha (z)$ and radiation angle $\theta (z)$ at that position. Thus, the design methodology is based on a 3D FDTD simulator with periodic boundary conditions to identify the diffractive element geometry that realizes the desired radiation strength and angle for each element. Via this approach, high computational efficiency is realized because during the design stage, the computational domain comprises of a single period of the structure, while computationally demanding 3D FDTD simulation of the complete structure will only be conducted once, at the check-out validation stage, to verify the device behavior.
3. Design methodology
Using the proposed Floquet-Bloch approach, the design of the complete device relies on the design of individual diffraction elements. However, the overall diffractive element geometry (see Fig. 1) is rather complex and a judicious design methodology needs to be utilized. The design objective for each element is to simultaneously attain the desired radiation strength $\alpha (z)$ and angle $\theta (z)$ while minimizing the power radiated into undesired directions. Furthermore, the guided Si-wire mode is initially radiated into the SWG region and subsequently coupled to the FPR slab via an adaptation taper. Therefore, the proposed design flow is as follows: a) design the SWG adaptation taper length (${W_{\textrm {adapt}}}$) to minimize the out-of-plane radiation loss; b) select the SWG width (${W_{\textrm {SWG}}}$) to reduce the leakage of the $0^{th}$ order to a negligible level; c) design the waveguide width ($W_g$) and the blazed diffractive trenches (with angle $\beta$ and etch ratio ${\gamma = W_{\textrm {etch}} /W_g}$) to obtain the desired grating strength $\alpha (z)$ with the maximum coupling efficiency; and d) slightly modify the structure pitch ($\Lambda$) to obtain the desired radiation angle ${\theta (z)={\textrm {constant}}}$ along the sidewall grating.
3.1 Subwavelength grating region design
According to the preliminary simulations, a substantial index mismatch occurs at the transition from the SWG region to the FPR slab, resulting in Fresnel reflection and out-of-plane radiation of the $-1^{st}$ diffraction order of the sidewall grating propagating as the fundamental TE mode of the SWG region, and then coupled to the FPR slab via a taper. Thus, following an approach that is similar to [19], a taper of length ${W_{\textrm {adapt}}}$ has been incorporated to provide a gradual transition between the SWG and FPR regions. The taper was designed using a 3D FDTD simulator and periodic boundary conditions for an SWG-to-FPR transition, as illustrated in the inset of Fig. 3 (the red colored cell represents the simulation period). A vertically confined plane wave that is normal to the SWG-FPR interface ($\theta =0$) is launched at the left side of the structure and the transmission and reflection coefficients are computed.
Fig. 3. a) The transmitted, reflected and radiated power at the junction between the SWG medium to the FPR slab as function of the adaptation taper length ${W_{\textrm {adapt}}}$. Inset: The geometry of the analyzed periodic structure and the unit cell (in red) which is effectively simulated. The electric field distributions for b) ${W_{\textrm {adapt}}=0}$ and c) ${W_{\textrm {adapt}}=2\,\mu m}$.
Figure 3 shows the transmitted power from the SWG fundamental TE mode to the FPR as a function of the length of the linear adaptation taper ${W_{\textrm {adapt}}}$. As expected, the transmitted power increases with ${W_{\textrm {adapt}}}$, which is further investigated by examining the field distribution. Figure 3(b) shows the total electric field for an abrupt transition, namely ${W_{\textrm {adapt}}=0}$. The power loss is mainly due to radiation, as a consequence of the vertical mode profile mismatch between the FPR slab and the SWG region. Figure 3(c) shows the electric field amplitude distribution for ${W_{\textrm {adapt}}={2 \,\mu {\textrm {m}}}}$. This adiabatic transition changes the mode profile progressively, thereby reducing both the reflection and radiation losses. We select ${W_{\textrm {adapt}}={1.5 \,\mu {\textrm {m}}}}$, which ensures that power that is lost due to radiation in the transition is less than 0.1 dB.
The SWG metamaterial trench is also required for laterally isolating the mode propagating in the silicon wire core from the FPR region, thereby avoiding leakage to a radiated FPR slab mode via the $0^{th}$-order. The SWG region is optimized to minimize lateral ($0^{th}$ order) mode leakage to the FPR slab. This leakage is primarily controlled by the SWG region width $W_{SWG}$ and the channel waveguide mode confinement. On the other hand, the diffraction to the $-1^{st}$ order is determined by the geometry of the blazed sidewall grating, without being substantially affected by the SWG region design. While the sidewall grating is blazed to maximize diffraction into $-1^{st}$ order towards the FPR slab, the light diffracted by the grating propagates in a direction approximately perpendicular to the channel waveguide, being vertically confined as a fundamental TE mode of the SWG region connected with the FPR slab via a taper. This SWG region is designed in subwavelength metamaterial regime to suppress diffraction effects, hence effectively operates in the $0^{th}$ order regime. Indeed, this is a fundamentally different mechanism compared to the $0^{th}$ order mode leakage effect discussed above. To study the effect of ${W_{\textrm {SWG}}}$ on the $0^{th}$-order leakage losses, the non-diffractive periodic structure that is illustrated in the inset of Fig. 4 is analyzed. In this simulation, the diffractive sidewall grating was excluded (${W_{\textrm {etch}}=0}$), as the $0^{th}$-order leakage losses are non-diffractive and depend only on the effective indices of the propagating mode which in turn determine the evanescent decay rate of the Si-wire in the SWG lateral cladding region. Using Floquet-Bloch mode analysis over this structure the leakage losses (${\alpha _{\textrm {leak}}}$) can be readily obtained. Figure 4 shows the $0^{th}$-order leakage parameter as a function of ${W_{\textrm {SWG}}}$ for various Si-wire widths $W_g$. As expected, due to the evanescent nature of the coupling mechanism, the dependence on ${W_{\textrm {SWG}}}$ is exponential and the decay rate increases with the wire width as this corresponds to higher confinement, and higher mode effective indices. According to this graph, selecting ${W_{\textrm {SWG}} ={2 \,\mu {\textrm {m}}}}$ is sufficient for maintaining the leakage losses below $1\%$ of the maximum radiation strength ${\alpha _{\textrm {max}}}$ that is required for the design.
Fig. 4. Leakage losses to the FPR region due to $0^{th}$-order coupling to lateral cladding as a function of the SWG region width ${W_{\textrm {SWG}}}$, for various Si-wire widths. The inset shows a schematic diagram of the analyzed structure.
3.2 Sidewall waveguide grating design
At this point, ${W_{\textrm {SWG}}}$ and ${W_{\textrm {adapt}}}$ have been optimized such that the $0^{th}$-order leakage losses and transition losses from the SWG slab to the FPR slab are negligible. Now, the geometry of the waveguide core ($W_g$) and the blazed trenches ($\beta$ and $\gamma$) will be designed to yield the targeted radiation strength $\alpha (z)$ for the $-1^{st}$ diffraction order, while simultaneously maintaining constant Floquet-Bloch modal effective index (for a constant radiation angle along the grating) and achieving optimal efficiency.
The radiation strength is mainly controlled by the etch ratio $\gamma$. To confirm this, we use a typical grating blazing angle of $\beta =45^{\circ}$ [19] and study the radiation strength as a function of the trench etch ratio $\gamma$ and the width $W_g$. The radiation strength is plotted in Fig. 5, according to which it mainly depends on the trench etch ratio $\gamma$, while the waveguide width $W_g$ has a minor impact on the radiation strength. Thus, we will use the value of $\gamma$ yielding the desired radiation strength while optimizing the remaining parameters ($\beta$ and $W_g$ ) for efficiency $\eta$. In this work, the efficiency ($\eta$) of a diffractive element is defined as the fraction of the radiated power that enters the FPR slab as the order -1. At the same time, our goal is to minimize the power loss due to radiation out of the chip and the leakage to the FPR slab through the $0^{th}$ order.
Fig. 5. Radiation strength versus waveguide width $W_g$ and etch ratio $\gamma$ for blazing angle $\beta$ of ${45^{\circ}}$.
To do this, we perform the Floquet-Bloch analysis of various diffractive elements by varying the three parameters, $\gamma$, $W_g$ and $\beta$, in the following ranges defining our design space: $\gamma \in [0.2,\, 0.8 ]$, ${W_g\in [450\,{\textrm {nm}},\ 750 \, {\textrm {nm}} ]}$ and $\beta \in [20^{\circ},\,70^{\circ}]$. From the Floquet-Bloch analysis, we compute the efficiency function $\eta (\gamma ,\beta ,W_g )$ for the permutations of these three parameters within the design space. Then, for each $\gamma$ we find the optimal $W_g$ and $\beta$ that maximize the efficiency. This process is done in two steps: first, we find the optimal angle for every ($W_g$, $\gamma$) pair within our design space. Figure 6(a) shows the efficiency maximized with respect to $\beta$ and Fig. 6(b) shows the optimal angle $\beta$. Second, we use the efficiency map obtained in the previous step to find the optimal $W_g$ for each $\gamma$. This gives us the optimal path $W_g( \gamma )$ that achieves a wide range of radiation strengths at a high efficiency, this path is plotted in Fig. 6(a) as a black line on top of the efficiency map. The obtained design geometries are shown in Fig. 6(c). These curves yield an optimum trench design for various values of the trench etch ratio $\gamma$, that is, for various radiation strengths. For the lowest values of the radiation strength the width $W_g$ was set to 450 nm and only the etch ratio $\gamma$ was varied. For clarity, a top view of the geometry of the trenched diffractive elements is also shown in this figure at several positions along the grating that correspond to $\gamma =[0.1,\, 0.25,\, 0.5,\, 0.7]$.
Fig. 6. Optimal geometries. a) The efficiency versus $\gamma$ and $W_g$, for optimal $\beta$. Pink circles indicate the optimal $W_g$ and $\gamma$ pairs. The path fitting curve that yields the waveguide width $W_g$ for a specified etch ratio $\gamma$ is shown as a solid black line. b) The optimal value of $\beta$ that achieves the maximum efficiency for each pair of $\gamma$ and $W_g$. c) Geometric parameters of the optimized blazed trenches versus $\gamma$ and top a view of selected elements.
As a result of the previous design steps, diffractive elements can be designed with arbitrary radiation strength and maximum efficiency. The phase profile was not engineered in this work., but small phase profile tuning was performed in the last step of the design to achieve constant radiation angle along the grating. Specifically, because of small variations in the mode effective index ${\Delta n_{\textrm {eff}}}$ along the grating, small corrections $\Delta \Lambda$ (${< 20\,{\textrm {nm}}}$) in the diffractive element period were necessary to ensure a constant Floquet-Bloch mode index along the grating. As a result, all grating teeth were designed to radiate exactly in the same direction, ${\theta _{\textrm {rad}}=-8.4^{\circ}}$. No extra simulation work was required for this correction, as the pitch adjustment can be directly calculated from Eq. (1) as
The final design curves are plotted in Fig. 7, which shows the radiation strength and efficiency for each of the designed optimal diffractive elements. Diffractive elements that produce radiation strengths in the range ${[0.002, 0.1] \,{\mu {\textrm {m}}}^{-1}}$ can be designed by varying the etch depth ratio with efficiencies that range from ${60\%}$ to ${80\%}$. The figure also includes the losses due to radiation out of the chip (${P_{\textrm {Out-of-chip}}}/{P_{\textrm {rad}}}$). Most of the efficiency penalty is attributed to losses that are due to out-of-chip radiation which are inherent to the proposed device.Fig. 7. Diffraction efficiency to the -1 diffraction order, out of chip radiation and radiation strength versus the etch ratio $\gamma$.
4. Device simulation and experimental evaluation
Via Eq. (2), Fig. 6(c) and Fig. 7, it is straightforward to synthesize an arbitrary radiation field intensity. We compute the required $\alpha (z)$ for synthesizing the desired field and we select the geometries from the optimal set that has already been designed to implement $\alpha (z)$. This procedure yields a succession of diffractive elements that implement the desired radiation field. These elements constitute the core of the proposed SGD. However, to connect it to the standard Si-wire without incurring high mode mismatch losses, appropriate adaptation structures are required. An adiabatic taper has been designed that starts with the Si-wire and introduces progressively the SWG pillars while adjusting the waveguide width to maximize the mode overlap (see Fig. 8(a)). To avoid radiation losses in the taper the period has been chosen to be equal to the SWG period ${\Lambda _{\textrm {SWG}}}$; hence, diffraction is frustrated. This taper was designed using 3D FDTD simulation of a back-to-back configuration for various grating lengths. The simulations demonstrated that for a length of ${13.75\,\mu {\textrm {m}}}$, the reflections were negligible and almost all the power was transmitted to the fundamental mode of the unperturbed straight waveguide with SWG pillars.
Fig. 8. a) A schematic diagram of the SGD device that is used to synthesize a quasi-Gaussian radiation profile with $MFD=30\,\mu m$. b) The magnetic field magnitude $|{\textbf{H}}_\textbf {y}|$ in the XZ plane at the center of the silicon layer. c) The magnetic field magnitude $|{\textbf{H}}_\textbf{y}(z)|$ along the dashed line in b).
Following this strategy, an SGD has been designed to generate a radiated Gaussian beam with $MFD=30\,\mu m$. However, since the minimum gap size was set to 50 nm ($\gamma =0.11$) for compatibility with the fabrication process, the minimum attainable radiation strength is ${\alpha _{\textrm {min}}=0.001\,{\textrm {Np}/\mu m}}$. Consequently, we cannot synthesize a perfect Gaussian beam since it requires a smaller ${\alpha _{\textrm {min}}}$ value. Hence, the designed field has a small section (${z\in [0, 14\, {\mu \textrm {m}}]}$) were it is exponentially decaying as shown in Fig. 8(c). The calculated field for a design with no constraint on the minimum feature size is also included in the figure (yellow curve).
The full structure has been simulated using 3D FDTD. The magnetic field magnitude at the center of the silicon layer, plotted in Fig. 8(b), clearly show that the power entering from the silicon wire (input on the left) is radiated towards the $-x$-direction as a Gaussian beam that propagates in the FPR slab. Figure 8(c) shows the magnetic field profile along the dashed line that is plotted in Fig. 8(b). According to Fig. 8(c) the radiated field is in good agreement with the designed field,which is further supported by the high overlap efficiency of 96% with the desired Gaussian profile. The total insertion loss of the device, which is defined as the Si-wire input power fraction that is transferred to the radiated Gaussian beam, is ${2.15\,\textrm{dB}}$ (61%), of which 1.87 dB corresponds to out-of-plane radiation loss in the diffractive elements (see Fig. 7), 0.18 dB to the field mismatch and 0.1 dB is due to the residual transmitted power (remaining in the waveguide at the end of the grating region).
In the second step, two identical previously designed SGDs have been arranged in a back-to-back configuration, as illustrated in Fig. 9(b). In this configuration, one of the deflectors has been rotated 180° and a small offset $\Delta z$ has been included to compensate for the radiation angle ${\theta _{\textrm {rad}}}$. This configuration demonstrates how SGDs can enable wireless on-chip communications in the SOI platform. For this purpose, an SGD that is designed to act as a transmitting antenna, is engineered to generate a focusing Gaussian beam that can propagate in any direction inside the slab. The same deflector (reversed or flipped back) is positioned hundreds of micrometers apart to capture this beam and transform it again into a guided mode, thereby acting as a receiving antenna. This configuration, which is illustrated in Fig. 9(a), can pave the way towards on-chip circuits with reconfigurable light paths, optical interconnects and low crosstalk crossings, to name a few.
Fig. 9. a) An on-chip free-space link based on two SGDs. b) The back-to-back SGD structure. c) The power at the through and cross ports and the power that is radiated out of the chip (normalized to the input power) as a function of the wavelength.
A full 3D FDTD simulation of the complete back-to-back architecture was performed to evaluate the device performance. Figure 9(c) shows the power transmitted to the through and cross ports and the power lost due to out-of-chip radiation as a function of the wavelength. Cross port insertion losses of ${4.5\,{\textrm {dB}}\,(37\%)}$ are observed at the central wavelength. This value is only ${0.2\,{\textrm {dB}}}$ higher than that in previous standalone simulation (${2\cdot 2.15\,{\textrm {dB}}} = {4.3\,{\textrm {dB}}}$).
Noticeably, the deflector exhibits a remarkably broad 1 dB bandwidth of 150 nm, which seems counter-intuitive due to the strong wavelength dependency of the radiation angle of a single device [19]. However, since one of the deflectors has been flipped back, both the transmitting and receiving deflectors scan synchronously with the wavelength and the two deflectors working in tandem compensate the wavelength dependence of each other.
As a third structure, we designed a uniform SGD that comprises 25 identical periods ($15\,\mu m$), as illustrated in Fig. 10. Hence, a constant radiation strength ($\alpha = 0.01\, {\mu m}^{-1}$) is obtained along the entire SGD. The deflector is designed such that 13% of the input power is radiated to the FPR slab and guided to the output port (cross port), while the remaining input power (72%) remains in the Si-wire waveguide, terminated with an antireflective structure. The beam that is radiated to the FPR slab is captured by a wide waveguide, rotated to ensure normal beam incidence at the central wavelength (see Fig. 10). The waveguide width (${21 \,\mu {\textrm {m}}}$) was chosen to maximize the field coupling efficiency.
4.1 Experimental results
For the proof-of-concept experimental evaluation, we selected our uniform SGD design (see Fig. 10). The structure was fabricated in a standard SOI wafer using 100 keV electron beam lithography patterning and reactive ion etching. A scanning electron microscope (SEM) image of the fabricated device is shown in Fig. 11(a).
Fig. 11. a) SEM image of the measured SGD and zoom of the diffractive elements. b) Simulated and measured response of the device.
To characterize our device we used the Agilent 81600B tunable laser as the light source. The light is carried to the chip edge by a lensed polarization-maintaining fiber. To ensure that only in-plane (TE) polarized light enters the chip, we used a high-precision fiber rotator. The light enters the chip edge through an SWG broadband fiber-chip coupler [26], which is connected to a 500-nm-wide interconnecting waveguide. The light exits the chip through another SWG edge coupler and the light is collimated by a micro-objective, filtered by Glan-Thompson polarizer and intercepted by a germanium photodetector connected to a digital power meter.
The transmittance of our device was determined by referencing the transmitted power of the device under test to that of a straight Si-wire waveguide terminated by fiber-chip couplers. This way, we calibrated out the input and output coupling losses and the waveguide propagation loss. Figure 11(b) shows the measured transmittance. The transmittance is slightly lower (${\sim }0.1$) than the designed value (0.13), which was found to be due to smoothing effect of the patterning process. This was confirmed by simulating a device with parameters determined by using SEM measurement. The expected theoretical behavior of the structure that was extracted from the SEM image is included in Fig. 11(b). The simulation and measurement yield similar values of the maximum transmittance (${\sim }0.1$), the central wavelength ($1.565\,\mu m$) and the bandwidth (${\sim } 40\,{\textrm {nm}}$), demonstrating that the SGD performs as designed. The fabricated deflector is radiating in the desired direction and the radiation strength is as expected for the geometry determined by SEM, thus validating our overall design strategy. This specific deflector is not aimed to show a significant performance improvement compared to conventional devices (e.g., directional couplers), but it is the prerequisite for implementing the back-to-back configuration presented in Section 4. The latter offers an interesting advantage of a substantially increased spectral bandwidth compared to conventional directional couplers.
5. Conclusions
We investigated new type of couplers for the silicon-on-insulator platform, operating as the sidewall grating distributed Bragg deflector. The nanophotonic beam deflector opens promising prospects for generation of arbitrarily shaped beams in the chip plane. Using a Floquet-Bloch mode analysis a compact 75-fold beam expander was designed. A partial deflector was also demonstrated, yielding excellent agreement the simulation and measurement results. Furthermore, we demonstrated the feasibility of employing these nanophotonic deflector devices as transmitting and receiving on-chip antennas. We believe that these results open exciting prospects for free-space inspired optical beam manipulation in photonic chips.
Funding
Universidad de Málaga; Ministerio de Ciencia, Innovación y Universidades (FPU16/03401, TEC2016-80718-R).
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