Grating Coupler Design for Low-Cost Fabrication in Amorphous Silicon Photonic Integrated Circuits

1. Introduction

Photonic devices and circuits find applications in various fields of science, including communications [1,2], quantum computing [3,4,5], neural networks [6,7,8,9] and sensing: biosensors [10,11,12,13,14], temperature sensors [15] and gas detectors [16,17,18]. Amorphous silicon in its hydrogenated form (a-Si:H) and hydrogenated amorphous silicon nitride (a-SiN:H) are suitable materials for photonic components, the former is usually preferred for applications in the near infrared (NIR) [19] and the latter is used for near infrared [20,21,22] and visible light [22,23,24,25]. Hydrogenated amorphous silicon compounds have the advantage of being compatible with CMOS manufacturing technology [23] and with low temperature deposition methods, such as Plasma-Enhanced Chemical Vapor Deposition (PECVD) [26,27] and Hot Wire Chemical Vapor Deposition (HWCVD) [28], contributing to a significant reduction in manufacturing costs. The relatively low extinction coefficient of hydrogenated amorphous silicon in the optical C-band (1530-1565), makes it a suitable material for near infrared photonics. Waveguides, having a-Si:H as core material, can achieve remarkably low propagation losses, of 1 dB/cm [29] or less [30,31].

There are several methods to couple light from optical fibers to photonic waveguides and vice-versa, the more common are based on [32,33]: end fire-coupling, grating couplers or adiabatic coupling. Grating couplers are attractive due to their off-plane coupling capability, which increases integration with other photonic devices, such as photodetectors and optical fibers. When used in conjunction with high efficiency compact broadband tapers [34], coupling schemes featuring grating couplers, can theoretically achieve efficiencies over -3 dB. Light couplers based on diffraction gratings offer some advantages over other coupling methods, such as waveguide tapers and adiabatic couplers, in the sense that the former do not require application specific fiber terminations [35] or anisotropic etching [36]. The avoidance of complex and tailor-made processes increases repeatability and lowers fabrication complexity.

In this study, we compare different a-Si:H grating coupler (GC) designs, for this purpose bi-dimensional finite-difference time-domain (2D-FDTD) analysis were performed. Simulations were performed with the RSoft software package (Synopsys, Inc.), via University Donation Program [37]. Grating couplers featuring apodization (variation of the period and fill-factor along the coupler’s length) are compared with GCs without apodization. Several approaches are taken to optimize coupling efficiency, such as: quadratic and linear variation of the effective refractive index over GCs’ length on apodized designs, lithography mask superimposition with offset and fill-factor greater than 50 % on non-apodized GCs. Due to the fact that the diffracted field decays in an exponential-like fashion in non-apodized gratings (over length), these have lower efficiencies (under -4 dB), in comparison, the diffracted field of apodized grating couplers has a distribution closer to a gaussian, resulting in higher efficiencies (over -3.2 dB). Even for designs (such as those presented in this work), which do not feature any kind of buried layer acting as a reflector.

Hydrogenated amorphous silicon (a-Si:H), the material employed in the proposed devices can be deposited by Plasma-Enhanced Chemical Vapor Deposition (PECVD) at low temperatures (≤ 250 °C), contributing to a production cost reduction. The a-Si:H layer can be deposited over a substrate of silica, or in alternative, above a glass surface, not requiring a silicon wafer. The grating couplers presented in this study can be fabricated with one or two lithographic masks, lowering the probability of imperfections caused by misalignment. Photolithography can be used to pattern the designs, employing either deep or extreme ultraviolet (UV) technology, thus avoiding the expensive and time-consuming electron beam (E-beam) process.

This article is an extended version of the paper published in the Proceedings of the SPIE 12880, Physics and Simulation of Optoelectronic Devices XXXII (11 March 2024) [38].

2. Materials and Methods

2.1. Single-Mode Optical Fiber

Considering a design operating wavelength of 1550 nm for the waveguide and light coupler, it is necessary to take into account the effects of the coupling optical fiber. The fiber of choice is the SMF-28, due to its ultra-low propagation loss in the optical C-band (1530-1565 nm) and also for its ubiquity, being a very common type of optical fiber employed in optical communications, Figure 1.

A summary of the optical fiber typical parameters at a wavelength of 1550 nm is presented in Table 1. Since the refractive index of the optical fiber’s core and refractive index difference are known, it is possible to determine the average cladding refractive index, which is about 1.4629. The refractive index values are similar to the figures presented by Saktioto et al. for a SMF28e optical fiber [39].

2.2. Single-Mode Waveguide

A 220 nm thick hydrogenated amorphous silicon (a-Si:H) strip waveguide is used to couple light into the diffraction grating coupler. The model of the photonic waveguide material is the GUTL (Gauss-Urbach-Tauc-Lorentz) [41], which is based on the optical characteristics of a-Si:H. The complex refractive index at the operating wavelength (1550 nm) is approximately $3.4824+3.023i\times {10}^{-8}$.

The 220 nm a-Si:H layer is deposited over silica, environment is air, Figure 2. Attenuation was not calculated as it depends on the width of the waveguide, and simulations were performed using a 2D model.

2.3. Light Coupler Design

Size mismatch between the optical fiber (i. e. SMF-28) and photonic waveguide is significant, Figure 3. In our specific setup, the former have a core diameter of 8.2 µm and the later a core height (thickness) of 0.22 µm. The optical fiber mode field diameter is approximately 10.4 µm.

Several coupling schemes can be employed to overcome this issue, we highlight [33]:

• Adiabatic couplers [33,35];
• Grating couplers [42,43,44,45];
• Lensed fibers [46];
• Spot size converters [33,47,48,49,50].

The 1st and 3rd methods, Figure 4(a) and (c), require tailor-made optical fiber terminations which demand fiber manipulation techniques, needing expensive equipment that are not commonly found in most optical laboratory setups. The 1st, 4th and 5th schemes, Figure 4(a), (d) and (e) typically require a very good matching between the optical fiber termination and the waveguide’s coupling region(s). These designs require very high precision lithographic equipment (e. g. based on Electron Beam), which is very expensive and not compatible with CMOS technology. Some spot size converters also rely on vertical structures which can be very complex and expensive to manufacture, like for example 3D tapers [48,49,50], Figure 4(d) and vertical couplers [46]. Unlike its crystalline counterparts, amorphous silicon cannot be subjected to anisotropic wet etching [36], making the development of 3D structures more complex. Some grating couplers can have minimum feature sizes on the orders of dozens of nanometers or even a few hundred nanometers, making these devices feasible by photolithographic processes, such as deep UV (DUV) lithography [42,51], employing excimer lasers.

There are several variations of grating couplers [52,53], specifically designed to improve coupling efficiency [42,43,54,55,56] and bandwidth [56,57,58], such as:

• Dual-level grating couplers [43];
• Gratings featuring stacked layers [53,59];
• Grating couplers with distributed Bragg reflectors (DBR) [57,58,60];
• Grating couplers based on metamaterials [44];
• Gratings with bottom metal reflector [44,61,62,63];
• Grating couplers with bottom grating reflector [56].

Designs presented in Figure 5(a), (b), (c), (e) and (f) can achieve remarkable performance, however, some of these (b), (c), (e) and (f) require multiple deposition steps, increasing fabrication complexity and cost. Gratings based on metamaterials, Figure 5(d) typically require a specific set of equipment that is not found in most typical semiconductor laboratory setups.

To simplify the etching process, we designed a fully etched grating coupler (i.e., the silicon layer is etched to the substrate/under cladding) in alternative to the more common partially etched designs, which require two lithographic processes/masks [42,58,65] or even more [43,51,56]. With the increased number of lithographic masks, misalignment impacts must be studied, since these can have an impact on the grating coupler’s performance [43].

The main design parameters of a grating coupler are: period ($\mathsf{\Lambda }$), coupling angle ($\theta$) and fill-factor ($F$). A grating coupler can have a constant effective refractive index (fill-factor and period) throughout its length, in a non-apodized design, or have a variation of the effective refractive index (fill-factor, period or both) over its span in an apodized variant.

Figure 6. Simplified representation of an optical fiber to silicon waveguide light coupling scheme, showing some of the grating coupler design parameters, coupling angle (θ), grating period ($\mathsf{\Lambda }$), etched length ($L_E$) and unetched length ($L_U$). This figure does not represent a functional coupling scheme and is not up to scale (e. g. the size mismatch between the optical fiber and the grating coupler is significantly greater).

Figure 6. Simplified representation of an optical fiber to silicon waveguide light coupling scheme, showing some of the grating coupler design parameters, coupling angle (θ), grating period ($\mathsf{\Lambda }$), etched length ($L_E$) and unetched length ($L_U$). This figure does not represent a functional coupling scheme and is not up to scale (e. g. the size mismatch between the optical fiber and the grating coupler is significantly greater).

The fill factor corresponds to the ratio between the unetched length ($L_U$) and the grating period ($\mathsf{\Lambda }$), which can be expressed as a percentage (1):

$$F=\frac{L_U}{\mathsf{\Lambda }}.$$

(1)

The effective refractive index of a diffraction grating coupler ($n_{eff}$) can be obtained from its fill-factor ($F$), the refractive index of the etched ($n_E$) and unetched segments ($n_U$) of the grating, as described in expression (2) [54]:

$$n_{eff}=F\times n_U+\left(1-F\right)\times n_E,$$

(2)

in this case, $n_E$ and $n_U$, correspond to the refractive indexes of air and of the waveguide’s fundamental mode of propagation, the transverse electric (TE) mode. Having the effective refractive index, $n_{eff}$, it is possible to calculate the required grating coupler period ($\mathsf{\Lambda }$), for a given coupling angle (θ), typically represented in degrees and free space wavelength (${\lambda }_0$) as described in equation (3) [66]:

$$\mathsf{\Lambda }=\frac{{\lambda }_0}{n_{eff}-\sin \theta },$$

(3)

the resulting grating period has the same units as the free space wavelength, typically both are represented in units of nanometer (nm).

Having the main design expressions, it is possible to begin the design of a grating coupler in its simplest form. Defining the fill-factor ($F$) has 0.5 (50%), while trying to keep the value of the denominator of expression (3) as low as possible, to achieve a higher period and consequently a large feature size. These measures can significantly decrease production costs if successfully implemented. The grating’s refractive index, $n_{eff}$, cannot be varied without changing the materials composing the grating coupler, waveguide’s height or width, fill-factor or etch depth, so this value is regarded as a constant. The coupling angle, $\theta$, was set to a very high value of 22.5°. Operating wavelength is 1550 nm, a typical value used in optical fiber communications, situated close to the middle of the optical C-band. Since the grating is fully etched, without upper cladding and simulated in an environment filled with air, $n_E$ can be assumed as 1, $n_U$ was obtained using the Finite Element Method (FEM), having a value of approximately 2.8372. The effective refractive index of the grating coupler can now be obtained from (2), having a value of about 1.9186. In the presence of all variables it is now possible to calculate the grating’s period ($\mathsf{\Lambda }$), equation (3), which is approximately 1009.2 nm (1.0092 µm), resulting in a feature size of about 505 nm, a value close to the required width of a silicon single-mode strip waveguide operating at 1550 nm [30,31]. A grating coupler with these characteristics has a relatively narrow diffracted field. The grating coupler was simulated using the 2D-FDTD method and the coupling efficiency (SMF-28 optical fiber) was average, measuring under -9 dB. There was some discrepancy in the value of the coupling angle which was found (in simulation) to be about 16.5° for optimum coupling.

2.4. Grating Coupler Optimization

Without apodization grating couplers exhibit an exponential decay of the diffracted field over its length [59], Figure 7(a), due to this fact most authors tend to prefer designs employing some form of apodization [42,43,55]. With this technique, the diffracted field distribution becomes more like a gaussian throughout the grating coupler’s length [59], the field distribution commonly found in optical fibers, Figure 7(b), resulting in more efficient coupling.

In the most common approach, gratings feature linear apodization (i.e., the fill-factor varies linearly throughout the grating’s length), equation (4) [54].

$$F\left(z\right)=F_0-R\times z,$$

(4)

where $F_0$ corresponds to the grating’s initial fill-factor, refer to expression (1), $R$ is the linear apodization factor, typically expressed in units of µm^-1 or nm^-1, $z$ corresponds to the distance from the beginning of the grating, usually in units of µm (if R is represented in µm^-1) or nm (when R is represented in nm^-1), respectively.

2.5. Linear Refractive Index Variation

A linear variation of the grating’s refractive index can be achieved by varying both the period and fill-factor over the grating coupler’s length, Figure 8, while maintaining the coupling angle constant.

The expression for the linear variation of the effective refractive index over a grating’s length can be written as (5):

$$n_{eff}\left(z\right)=n_{eff}\left(0\right)+m\times z,$$

(5)

where $n_{eff}\left(0\right)$ is the effective refractive index at the start of the grating coupler (the effective refractive index of the first grating period), $m$ corresponds to the slope of the refractive index variation, in µm^-1 and $z$ is the position measured from the start of the grating.

Following optimization in 2D-FDTD software, expression (6), was obtained, for a 220 nm thick fully etched grating coupler of hydrogenated amorphous silicon (a-Si:H), operating at a wavelength of 1550 nm:

$$n_{eff}\left(z\right)=2.65348-0.0288z.$$

(6)

The value of $n_{eff}\left(0\right)$, 2.65348, was obtained considering a maximum fill-factor of 0.9 (90%), an etched section refractive index, $n_E$, of 1 and an unetched section effective refractive index, $n_U$, of 2.8372, refer to expression (2). The slope was adjusted considering a correlation which was observed between the length of the diffracted field distribution (gaussian like function) and the total variation of the refractive index over the grating coupler’s length. It was found on 2D-FDTD simulation, that for maximum coupling efficiency, the variation of the refractive index, $∆n_{eff}$, over a length of one optical fiber MFD (10.4 µm), $∆z$, had to be of about -0.3, resulting in a slope, $m$, of approximately -0.0288 µm^-1. Refer to expression (7) and plot of Figure 9.

$$m=\frac{∆n_{eff}}{∆\mathrm{z}}\left[{\mu m}^{-1}\right].$$

(7)

The plot of function (6) is represented in Figure 9, for a 20 µm grating coupler.

Figure 9. Proposed linear variation of the refractive index over the grating coupler’s length (represented in red).

Figure 9. Proposed linear variation of the refractive index over the grating coupler’s length (represented in red).

Accounting for the variation of the refractive index over the length of the grating coupler it is possible to rearrange (2), to obtain the fill-factor for each grating position (8):

$$F\left(z\right)=\frac{n_{eff}\left(z\right)-n_E}{n_U-n_E}.$$

(8)

The expression which gives the grating period (3) can also be rewritten to account for the variation of the effective refractive index over the grating’s length (9):

$$\Lambda \left(z\right)=\frac{{\lambda }_0\left[\mu m\right]}{n_{eff}\left(z\right)-\sin \theta }[\mu m].$$

(9)

A computational algorithm, implemented in MATLAB (The MathWorks, Inc.), obtains the effective refractive index values at the begin of each grating period, using expression (6) and calculates the fill factor, F from function (8), and period, Λ, using expression (9) at each iteration, until the end of the grating coupler. The diffraction angle was defined as 15°. The pseudo-code algorithm is presented in Appendix A. The resulting grating coupler is presented in Figure 10. The length can overshoot the predefined value, in this case, for example, it is approximately 20.6 µm, instead of 20 µm, it was decided that it is preferable to have a slightly longer grating coupler than the opposite.

The fill-factor (F) and period (Λ) for each grating segment, numbered from the beginning to the end of the grating coupler (or from left to right in Figure 10), considering a total of 28 segments. are presented in Table 2.

2.6. Quadratic Refractive Index Variation

The refractive index of the grating coupler can also have a quadratic variation, in this case the function which gives the refractive index over the grating’s length is defined as follows (10):

$$n_{eff}\left(z\right)=n_{eff}\left(0\right)+a\times z^2+b\times z,$$

(10)

following the same approach as in the previous subchapter, the initial fill-factor if defined as 0.9, resulting in an $n_{eff}\left(0\right)$ of 2.65348, $z$ corresponds to the grating position relative to its starting point, $a$ and $b$ are the coefficients of the quadratic polynomial, with units µm^-2 and µm^-1, respectively. Like in the linear function, a $∆n_{eff}$ of -0.3 is pretended for a ∆z of 10.4 µm (measured from the grating’s starting point, z = 0). The vertex of the parabola is set to occur at or near the end of the grating coupler, at $z_{max}$, 20 µm. With known values for $∆n_{eff}$ (-0.3), ∆z (10.4 µm) and $z_{max}$ (20 µm), it is possible to calculate the values of the coefficients $a$ and $b$, recurring to a system of linear equations (11):

$$\left\{\begin{array}{c}∆n_{eff}=n_{eff}\left(∆\mathrm{z}\right)-n_{eff}\left(0\right)\\ -\frac{b}{2a}=z_{max}\end{array}\right.,$$

(11)

which can be rearranged as (12):

$$\left\{\begin{array}{c}∆n_{eff}=a\times {∆z}^2+b\times ∆z\\ -\frac{b}{2a}=z_{max}\end{array}\right..$$

(12)

By solving the linear system, the values obtained for $a$ and $b$, are of approximately $9.745\times {10}^{-4}{\mu m}^{-2}$ and $-3.898\times {10}^{-2}{\mu m}^{-1}$, respectively. Equation (10) can now be rewritten with the approximated values of the quadratic function coefficients, which were round to the 3rd decimal place (13):

$$n_{eff}\left(z\right)=2.65348+0.001z^2-0.039z.$$

(13)

The plot of the quadratic function which gives the effective refractive index for each position along the grating’s length is represented in Figure 11.

Like in the linear variation of the refractive index, a computational algorithm was written in MATLAB (The MathWorks, Inc.), to calculate the fill-factor and period for each segment of the grating coupler, using expressions (8), (9) and (13). The pseudo-code is presented in Appendix B. The grating coupler of Figure 12 was obtained after running the algorithm. As in the case of the grating coupler designed for linear refractive index variation, the length of the grating slightly overshoots the preset value of 20 µm, achieving a length of about 20.25 µm over 28 periods (segments).

The period (Λ) and fill-factor (F) of the quadratic refractive index variation grating coupler is presented in Table 3, for a total of 28 segments.

2.7. Fill-Factor Greater than 50 %

An alternative to apodization is to use a fill-factor different than 0.5 (50%), the fill-factor was increased over ½ in an attempt to decrease the decay rate of the diffracted field intensity over the grating coupler’s length. In our observations of simulations using the 2D-FDTD method, there was evidence that a correlation exists between the fill-factor and the exponential decay of the diffracted field. The higher the fill-factor, the slower the field decreases over the grating’s length, however, there is also a drawback since the field intensity (per unit area) decreases as the fill-factor increases. The best result of our optimization process was obtained for a grating coupler with a period of 690 nm and a fill-factor of approximately 82.6%, having a coupling angle (θ) of about 13.3°, Figure 13.

2.8. Overlapped Grating Design

Another interesting method consists in the superposition (overlap) of two grating couplers with a fill-factor of 0.5 (50%), using this method it is possible to fabricate gratings using two lithography processes (and/or masks). This method enables the fabrication of grating couplers with fill-factors different from ½ from designs with periods over 1000 nm, allowing the usage of masks with larger feature sizes and consequently lowering production costs. A modest efficiency results from this technique, with values typically over -10 or -9 dB.

During optimization process, the highest coupling efficiency (considering an SMF-28 optical fiber), was obtained for the overlap of two 1500 nm period diffraction gratings, with a -400 nm z axis offset, Figure 14, resulting in a fill-factor of 0.7(6) and an optimum coupling angle of 22°. Minimum feature size is 750 nm. The same grating coupler if fabricated using a single lithography procedure would have a feature size of 350 nm, requiring higher precision in mask fabrication.

2.9. Random Distribution Overlapped Grating Design

Following a similar approach as in the previous subchapter overlapped grating couplers with chaotic (random) distributions were also simulated. To decrease production costs, the period of the gratings was set between 1 µm and 1.5 µm and varied at a step of 0.1 µm. The combination which results in the highest efficiency consists in the overlap of a 1.3 µm over a 1.5 µm grating, with a z-axis offset of -0.3 µm applied to the grating with the smallest feature size, Figure 15. For simplification purposes both gratings have a fill factor of 0.5 (50%). The optimized coupling angle is about 20.9°.

3. Results

3.1. Fundamental Mode of the Waveguide

All grating couplers covered in this work are optimized for the fundamental quasi-transverse electric mode (quasi-TE₀₀). The fundamental mode of the 220 nm strip waveguide was analyzed using the 2D-FEM (two-dimensional finite element method). The effective refractive index of the TE₀₀ mode of the waveguide is approximately $2.8372$, with an extinction coefficient of $3.037\times {10}^{-8}$ for a 1550 nm operating wavelength. The intensity of the electric (E_y) and magnetic (H_x) major fields along the x axis is represented in Figure 16a and b, respectively.

3.2. Simulated Single-Mode Fiber Fundamental Mode

To estimate the coupling efficiency, it is necessary to obtain the field distribution for the typical parameters of the single-mode optical fiber (SMF-28) of the coupling setup, refer to Table 1. The optical fiber was simulated using 2D-FDTD like the single-mode waveguide. The CAD design is identical to Figure 1b, for simplicity and algorithm efficiency reasons, the effects of the coating layer were not considered. Results of the simulation of the fiber model are presented in Figure 17, showing the electric, E_y (a) and magnetic, H_x (b) field distributions along the x axis, for the TE₀₀ mode at a wavelength of 1550 nm.

3.3. Non-optimized Grating Coupler Performance

As previously mentioned, without apodization and with a fill-factor of 0.5 (50 %), the coupling efficiency is typically modest. In the simulation that we performed a value slightly above -10 dB, was obtained for this parameter. It is thought of imperative importance that some additional measures are taken to improve grating coupler performance.

Two monitors were used in the calculation of coupling efficiency, one centered at position (x, z) = (0, 8), measuring the power near the output of the waveguide and another centered at position (x, z) = (5, 11.4), to measure the overlap between the diffracted field and the fundamental mode of the optical fiber. This second monitor is placed at an angle of 16.5° (optimized coupling angle), its center is at a distance of 5 µm from the grating center axis and at a distance of 2.4 µm from the grating coupler’s starting point, measured in the vertical z axis. The access waveguide is 9 µm long.

In Figure 18, it is noticeable that the diffracted electric field intensity decays at a very high rate (exponentially), following the two first periods of the grating coupler, due to this fact, coupling efficiency, Figure 19, is relatively low.

Looking at the results presented in Figure 19, it is possible to assert that the waveguide monitor overlap (with the launch field, or fundamental quasi-TE₀₀ mode), remains nearly constant throughout the integration time. The coupling efficiency value achieved at the time of convergence is slightly over -9.7 dB (~ 10.8 %). The overlap with the diffracted field (i.e., the percentage of power of the diffracted field passing through the monitor which is converted to the SMF-28 fundamental mode) is about 36.4%. The ratio between diffracted power reaching the monitor and waveguide’s power is slightly over -5.3 dB (~ 29.7%).

3.4. Constant Refractive Index and Fill-factor Greater Than 50 %

The results of the grating coupler featuring an 82% fill-factor and a period of 690 nm are presented herein. In Figure 20, the contour map of the diffracted electric field is presented. Two monitors are included, one centered at position (x, z) = (0, 5), measuring the power near the output of the waveguide and another centered at position (x, z)=(4, 11.2), which measures the overlap between the diffracted field and the fundamental mode of the optical fiber. This second monitor is placed at an angle of 13.3° (optimized coupling angle), its center is at a distance of 4 µm from the grating center axis and at a distance of 5.2 µm measured from the grating coupler’s starting point. The access waveguide is 6 µm long.

In Figure 20, it is possible to notice that the diffracted field intensity decays (exponentially) along the coupler’s length, a characteristic of non-apodized grating couplers. By optimizing the fill-factor, monitor angle and position, it was possible to maximize the coupling efficiency.

Efficiency test results are shown in Figure 21, it is possible to verify that the waveguide monitor overlap (with the launch field, or fundamental quasi-TE₀₀ mode), remains nearly constant throughout the integration time. The coupling efficiency value achieved at the time of convergence is slightly under -4.3 dB (~ 36.9%). The overlap with the diffracted field (i.e., the percentage of power of the diffracted field passing through the monitor which is used to excite the SMF-28 fundamental mode) is about 85.6%. The ratio between diffracted power reaching the monitor and waveguide’ power is slightly over -3.7 dB (~ 43.1%).

Coupling efficiency was measured for wavelengths in vacuum between 1520 nm and 1580 nm, Figure 22. The -1 dB bandwidth is of about 25 nm and the -3 dB bandwidth is 44 nm. The center wavelength (peak efficiency) occurs at 1549 nm. The optical C-band (1530-1565 nm) is covered with a maximum 2 dB penalty.

3.5. Linear Effective Refractive Index Variation

The results of the apodized grating coupler with linear variation of the effective refractive index are presented herein. In Figure 23, the distribution of the diffracted electric field is shown. Two monitors are included, one centered at position (x, z) = (0, 6), measuring the power near the output of the waveguide and another centered at position (x, z) = (4, 13.3), measuring the overlap between the diffracted field and the fundamental mode of the optical fiber. The second monitor is positioned at an angle of 10.8° (optimized coupling angle), its central position is at a distance of 4 µm from the grating center axis relative the x axis and at a distance of 6.3 µm measured from the grating coupler’s starting point in the z axis. The access waveguide is 7 µm long.

In Figure 23, it can be noticed that the diffracted field intensity has a distribution closer to a gaussian, having a higher intensity near the center of the monitor, a characteristic of apodized designs. By optimizing apodization, monitor angle and position, it was possible to maximize coupling efficiency. The values of period and fill-factor presented in Table 2, where limited to two decimal points in simulations, since most optical lithography systems do not have precisions greater than 10 nm. The impact of this loss of precision was minimal.

In Figure 24, efficiency results are presented, it is possible to confirm that the waveguide monitor overlap (with the launch field, or fundamental quasi-TE₀₀ mode), remains nearly constant throughout the integration time. The coupling efficiency achieved at the time of convergence is slightly under -3.1 dB (~ 48.4%). The overlap with the diffracted field (i.e., the percentage of power of the diffracted field passing through the monitor which is used to excite the SMF-28 fundamental mode) is approximately 96.1%. The ratio between the diffracted power reaching the monitor and waveguide’s power is slightly over -3 dB (~ 50.4%).

Coupling efficiency was measured for wavelengths in vacuum between 1520 nm and 1580 nm, Figure 25. The -1 dB bandwidth is approximately 26 nm, and the -3 dB bandwidth is 47 nm. Peak efficiency (center wavelength) occurs at 1550 nm. The optical C-band (1530-1565 nm) is covered with a maximum 2.1 dB penalty.

3.6. Quadratic Effective Refractive Index Variation

The performance results of the apodized grating coupler with quadratic (polynomial) variation of the effective refractive index are presented in this subchapter. In Figure 26, the distribution of the diffracted electric field is shown. Two monitors are included, one centered at position (x, z) = (0, 6), measuring the power near the output of the waveguide, and another centered at position (x, z) = (4, 12.9), measuring the overlap between the diffracted field and the fundamental mode of the optical fiber. The second monitor is positioned at an angle of 10.5° (optimized coupling angle), its center is at a distance of 4 µm from the grating center axis, relative to the x axis, and at a distance of 5.9 µm measured from the grating coupler’s starting point, in the z axis. The waveguide has a length of 7 µm.

After carefully looking at Figure 26, it can be noticed that the diffracted field intensity has a gaussian like distribution, like in the previous apodized grating coupler, exhibiting higher intensity near the center of the monitor, a characteristic of apodized designs. By optimizing apodization, monitor angle and position, it was possible to maximize the coupling efficiency. The values of period and fill-factor presented in Table 3, where limited to two decimal points in simulations, due to the fact most optical lithography systems do not have precisions greater than 10 nm. The impact of this loss of precision was verified as having a negligible impact on the results.

In Figure 27, coupling efficiency results are depicted, it is possible to verify that the waveguide monitor overlap (with the launch field, or fundamental quasi-TE₀₀ mode), remains nearly constant throughout the integration time. Coupling efficiency achieved at the time of convergence is slightly under -2.8 dB (~ 52.2%). The overlap with the diffracted field (i.e., the percentage of power of the diffracted field passing through the monitor which is used to excite the SMF-28 fundamental mode) is around 97.4%. The ratio between the diffracted power reaching the monitor and waveguide’s power is slightly under -2.7 dB (~ 53.6%).

Coupling efficiency was measured for wavelengths in vacuum between 1520 nm and 1580 nm, Figure 28. The -1 dB bandwidth is approximately 25 nm and the -3 dB bandwidth is 46 nm. Peak efficiency (center wavelength) occurs at 1551 nm. The optical C-band (1530-1565 nm) is covered with a maximum 2.4 dB penalty.

3.7. Overlapped Micrometric Design

The coupling efficiency results for the overlapped micrometric period gratings (1500 nm) are presented herein. The two superimposed gratings with an offset of -400 nm form a grating coupler with a period of 1500 nm and a fill-factor of 0.7(6) (76.(6) %). In Figure 29, the contour map of the diffracted electric field is presented.

Two monitors are included, one centered at position (x, z) = (0, 5), measuring the power near the output of the waveguide and another centered at position (x, z) = (6, 11.9), which measures the overlap between the diffracted field and the fundamental mode of the optical fiber. This second monitor is placed at an angle of 22° (optimized coupling angle), its center is at a distance of 6 µm from the grating center axis (due to the higher coupling angle) and at a distance of 5.9 µm measured from the grating coupler’s starting point. The access waveguide is 6 µm long.

Figure 29. Representation on the XZ plane of the diffracted electric field, the green (transparent filled) horizontal bar is the waveguide’s monitor and the slanted green (transparent filled) slanted bar is the diffracted field monitor. Image obtained from 2D-FDTD.

Figure 29. Representation on the XZ plane of the diffracted electric field, the green (transparent filled) horizontal bar is the waveguide’s monitor and the slanted green (transparent filled) slanted bar is the diffracted field monitor. Image obtained from 2D-FDTD.

In Figure 29, it is possible to notice that the diffracted field intensity (exponentially) decays along the coupler’s length, a characteristic of non-apodized gratting couplers. By optimizing the fill-factor, monitor angle and position, it was possible to maximize the coupling efficiency.

In Figure 30, coupling efficiency results are shown, it is possible to attest that the waveguide monitor overlap (with the launch field, or fundamental quasi-TE₀₀ mode), remains nearly constant throughout the integration time. Coupling efficiency achieved at the time of convergence is slightly over -7.5 dB (~ 20.0%). The overlap with the diffracted field (i.e., the percentage of power of the diffracted field passing through the monitor which is used to excite the SMF-28 fundamental mode) is approximately 80.8%. The ratio between the diffracted power reaching the monitor and waveguide’ power is slightly under -6.5 dB (~ 22.3%).

Coupling efficiency was measured for wavelengths in vacuum between 1530 nm and 1565 nm, Figure 31. The -1 dB bandwidth is approximately 22 nm. Peak efficiency (center wavelength) occurs at 1549 nm. The optical C-band (1530-1565 nm) is covered with a maximum 6.3 dB penalty.

3.8. Random Distribution

Results obtained for the random (chaotic) distribution grating coupler are presented in this subchapter. Two gratings with periods of 1500 and 1300 nm where overlapped, with the second grating having a z axis offset of -300 nm. This was the combination which held the best results for a grating coupler featuring a random distribution, achieved by the superposition of two gratings with periods over 1000 nm.

Two monitors are included, one centered at position (x, z) = (0, 6), measuring the power near the output of the waveguide and another centered at position (x, z) = (6, 11.4), which measures the overlap between the diffracted field and the fundamental mode of the optical fiber. This second monitor is placed at an angle of 20.9° (optimized coupling angle), its center is at a distance of 6 µm from the grating center axis (due to the higher coupling angle) and at a distance of 4.4 µm measured from the grating coupler’s starting point. The waveguide is 7 µm long.

In Figure 32, it is noticeable that the diffracted electric field shows several diffraction angles, resulting in a poor coupling efficiency, Figure 33.

Looking at the results presented in Figure 33, it is possible to assert that the waveguide monitor overlap (with the launch field, or fundamental quasi-TE₀₀ mode), remains nearly constant throughout the integration time. The coupling efficiency value achieved at the time of convergence is slightly under -12.8 dB (~ 5.2 %). The overlap with the diffracted field (i.e., the percentage of power of the diffracted field passing through the monitor which is converted into the SMF-28 fundamental mode) is about 33.3 %. The ratio between diffracted power reaching the monitor and waveguide’ power is slightly over 8.1 dB (~ 15.7%).

4. Discussion

To summarize, all results obtained in this work are presented and compared with State-of-the-Art (SoA) and high efficiency grating coupler designs, Table 4. All grating couplers presented herein were projected to operate in the optical C-band (1530-1565 nm). In Table 4, GC stands for grating coupler, N/A means information is not available, BW corresponds to bandwidth and DBR is distributed Bragg reflector.

Despite having inferior performance when compared to the state-of-the-art in grating coupler designs, the devices have the possibility of being manufactured at a lower cost. The devices, made of a-Si:H, can be deposited at low temperature by Plasma Enhanced Chemical Vapor Deposition (PECVD), over a substrate of silica. Since silica is one of the main constituents of glass, there is also the possibility of adapting the devices to be fabricated over a substrate of this material.

Due to the fully etched grating design, all devices can be fabricated using one or two lithographic masks, making misalignment less of an issue. Designs requiring 3 lithographic processes are more affected by misalignment issues, a study about its impact must be conducted [43]. Using the method covered in this work no silicon wafers are required, the devices work without any bottom silicon layer(s) or upper cladding and do not rely on any sort of bottom reflector for efficiency enhancement. All presented designs can be patterned by photolithography [68], requiring either deep-UV (DUV) or extreme UV (EUV) lithographic processes.

Regarding the performance of the presented devices, it is clear that apodization plays a significative role in performance enhancement, at the cost of requiring more expensive lithographic procedures, such as DUV, EUV or E-beam. The results suggest that quadratic refractive index variation might present a small improvement in coupling efficiency when compared with linear variation. By optimizing the fill-factor or opting for a grating made from the overlap of two lithographic masks it is possible to make a compromise between performance and manufacturing costs. The chaotic (random) distribution, overlapped mask grating designs that we tested failed to achieve acceptable performance, suggesting that more complex AI-based optimization algorithms are required for achieving better performance. In addition, it might be necessary to decrease the feature size of such grating designs to improve efficiency.

5. Conclusions

Five different grating couplers were successfully designed and simulated, achieving coupling efficiencies between -12.8 dB and -2.8 dB. These results were obtained considering a hydrogenated amorphous silicon (a-Si:H) over silica platform, without any silicon bottom layer or bottom reflector. The technology is compatible with low temperature PECVD significantly reducing production costs.

Since the designs are fully etched only one or two lithographic masks are required, reducing the dependency on mask alignment.

The simulations were conducted using the Finite-Difference Time-Domain (FDTD) analysis and Finite Element Method (FEM). The optical fiber model was based on a commercial type (SMF-28), typically used in near infrared communications, being characterized by typical design parameters.

The grating coupler featuring quadratic variation of the effective refractive index achieved the highest efficiency of the devices studied in this work. Opening the way for studies of different arithmetic functions or combination of functions (e. g. polynomial, exponential, logarithmic, hyperbolic) in the variation of the refractive index through the gratings’ length.

The superposition of two masks to produce a different grating coupler from two gratings is also a possible method, which allows a more complex design, with smaller feature sizes to be fabricated using photolithography techniques, thus avoiding electron beam (e-Beam).

6. Future Work and Improvement

In our perspective this work contributes to open ways to future research in the optoelectronics and photonic fields, undeniably several paths still need to be explored. Since the analysis performed in this work was performed using a bidimensional model, further analysis should be conducted using a tridimensional (3D) model. With one more dimension, simulation of adiabatic tapers for grating coupler (GC) connection and focusing grating designs can be studied and its geometry optimized. Following the tridimensional analysis, it is the time to proceed to the production of real-world prototypes, followed by characterization and testing.

Despite the increase in costs and complexity, the inclusion of one or more bottom layers of silicon (arranged as a DBR stack) and under-cladding thickness adjustment, could be possibilities for further improvements in performance, as well as performing a performance comparison analysis of such designs with the same GC devices featuring metal bottom reflectors.

It is also important to study the impacts of the arithmetic functions, used in the apodization of the grating couplers to tailor the shape, distribution and length of the diffracted field, and analyze its importance in matching the optical fiber’s field profile and mean field diameter (MFD). In addition, it is relevant to study the effects on the diffracted field, of the slope and initial fill-factor in linear apodization and of the coefficients of polynomial functions, like the quadratic distribution (where concavity can play a significant role).

Of course, there is also space for the utilization of machine learning (e.g., neural networks) and other artificial intelligence techniques for the optimization of apodization parameters. The study of arithmetic functions alone or combined, opens an interesting perspective in the optimization of diffraction grating couplers.