1. Introduction

Bragg gratings are a fundamental component of optical systems used in applications ranging from optical communications and sensing to lasers [1,2]. The motivation to explore on-chip integrated gratings stems from the rapid growth of silicon photonics where novel applications are enabled through compact circuits created using CMOS-compatible fabrication processes [3–6]. Gratings in both silicon (Si) and silicon nitride (SiN) have been demonstrated in a variety of geometries including corrugations and pillars on strip and ridge structures [7–12], where the diversity of approaches is driven by the need to tailor properties for each application. For example, the ability to spatially modulate gratings and apodize their response enables engineering single-mode distributed Bragg reflector (DBR) and distributed feedback (DFB) lasers [1]. For DFB lasers in particular, it has been shown that a $\lambda$/4 phase shift leads to increased mode stability at the center wavelength [13–16]. Here, we examine phase-shifted Bragg gratings in SiN produced on the AIM Photonics 300 mm silicon photonics line [6]. To date, SiN Bragg gratings for filters, reflectors, and lasers even at standard wavelengths near 1550 nm are not yet offered as standard Process Design Kit (PDK) components in foundries. Consequently, the drive for on-chip SiN Bragg gratings compatible with standard foundry lithography resolution and processes are of interest. We design the center wavelengths for operation near the 1550 nm telecommunications band and perform transmission measurements to extract key parameters such as the coupling coefficient $\kappa$ and bandwidth. The phase shift section has an important role in several device parameters detailed below. Typical extractions of these parameters involve gratings without a phase shift; below, we derive a new relationship for extracting these values for gratings with a $\lambda$/4 phase shift.

2. Phase-shifted Bragg gratings

The structure of the Bragg grating used here is composed of a waveguide of center width $W$ with corrugations of width $W\pm \Delta W$ on the sidewalls. Figure 1(a) shows a Bragg grating with square corrugations repeated with period $\Lambda$. Note that other geometries, such as triangular or trapezoidal, have been demonstrated [17]. The effective indices of the guided modes $n_{1, \textrm {eff}}$ and $n_{2, \textrm {eff}}$ correspond to the low and high indices, respectively, for light propagating along the $z$ direction through low and high index grating teeth.

 

Fig. 1. Phase-shifted Bragg gratings. (a) A quarter-wave phase shifted Bragg grating schematic with N 50% duty cycle square wave corrugations of period $\Lambda$ on each side of a phase shift facet of length $\Lambda$. The perturbations have a corrugation width $\Delta W$ in addition to the main width $W$. (b) TMM model transmission of a SiN grating with (solid) and without (dashed) the quarter-wave phase shift. (c) A phase-shifted Bragg grating response with the characteristic transmission peak at the center wavelength $\lambda$.

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In this work, the perfect periodicity of a regular Bragg grating is interrupted with the addition of an extra section of the high-index material. Using a length of a single period $\Lambda$ specifically creates a quarter-wave phase shift at the design wavelength. Alternative methods not shown here include leaving a gap of the low-index material or altering the lengths of these sections. The primary analytic equations governing the performance of Bragg gratings are:

The analytic equations used for pure gratings do not apply to the phase-shifted gratings. To build intuition for this phase effect, we used a Transfer Matrix Method (TMM) to model these structures [1]. Figure 1(b) compares a TMM model of gratings with (solid blue) and without (dashed orange) the quarter-wave phase shift $\lambda$/4 that are otherwise identical. Figure 1(c) shows a typical experimentally measured optical transmission spectrum of a phase-shifted device used in this work. The main impacts of the phase shift on the spectrum are the emergence of a transmission peak at the center of the transmission stopband and an evident increase in bandwidth $\Delta \lambda$ between the first nulls. As a result, one cannot extract $\kappa$ from Eq. (2) as was done in Ref. [17]. In lieu of Eq. (2), we derive a new equation for gratings with a $\lambda$/4 phase shift. The starting point is the analytic transmission equation for gratings with $\lambda$/4 phase shift (Eqn. 27) in Ref. [18]. To solve for the bandwidth $\Delta \lambda$, we set transmission to one for a detuning $\Delta \beta$>0 corresponding to the first nulls as is commonly done for gratings without a phase shift. After some algebra and trigonometric substitutions, we arrive at:

The main result is an additional term of $\left (\frac {2\pi }{L}\right )^2$. At small values of $\kappa$, this new term adds a significant bandwidth compared to a grating without a phase shift. The broader bandwidth of the $\lambda$/4 grating is apparent in Fig. 1(b). This result will now be used to directly characterize gratings with $\lambda$/4 phase shift sections.

3. Characterization of SiN gratings

3.1 SiN device fabrication and measurement

For the experiments, we designed quarter-wave shifted gratings in silicon nitride with square wave corrugations at a 50% duty cycle. The phase shift is introduced as shown above in Fig. 1 at the center of the grating. The devices were fabricated on the AIM Photonics 300 mm silicon photonics line using with 193 nm deep ultraviolet (DUV) photolithography with the standard multi-project wafer (MPW) device thickness [6]. Gratings of width 1.5 $\mu$m with periods $N$ (100, 200, and 300) at a pitch of $\Lambda$ = 520 nm were placed on either side of the center facet. We also measured three cases of corrugation half-widths $\Delta W$= 250, 350, and 450 nm, corresponding to three different $\kappa$ values.

For the measurements, we input and collected broadband incoherent light via on-chip edge couplers provided in the process design kit (PDK) and tapered lensed fibers. The polarization was set to transverse electric (TE) polarization in the plane of the device. After transmission, the light was sent to an optical spectrum analyzer (OSA) sampled at 0.1 nm intervals. First, we measured the transmission through on-chip waveguides without gratings to establish a baseline transmission and account for waveguide and coupling losses. Next, we passed the input light through the grating devices and took the difference to measure center wavelength, bandwidth, and center peak full-width at half-maximum (FWHM). The data are derived from three separate chips, showing the consistency of the foundry devices.

3.2 Analysis

We determined the properties of the gratings following the formalism developed above. Using the spectral measurements, we extracted the measured bandwidth $\Delta \lambda$ and the measured center wavelength $\lambda$ while the group index was determined numerically with Lumerical MODE. Figure 2(a) shows $\Delta \lambda$ as a function of the designed grating length $L$. With all of the other variables determined, we extract $\kappa _{\textrm {exp}}$ as the free parameter from a least-squares fit of Eq. (3). For $\phi = 2 \pi$ and $\Delta$W = 250 nm, we find $\kappa =$191 cm$^{-1}$. As a comparison, the pure grating equation using the same $\kappa$ is plotted as the dashed orange line; a significantly narrower transmission stopband would be expected. The two equations both reach an asymptote for long $L$, where the $\frac {1}{L}$ terms disappear and approaches a pure $\kappa$ limit. This method is much more accurate than extracting $\kappa$ from a single device, especially at shorter lengths. The rounded edges of the bandwidth (observable in Fig. 1(b)), which are asymmetric in real measurements of shorter devices, can cause a systematic deflation of bandwidth which often precludes the use of this method.

 

Fig. 2. Broadened bandwidth analysis methods. (a) Measured grating bandwidth of the phase-shifted gratings versus length with a least-squares fit of Eq. (3) to extract $\kappa _{\textrm {exp}}$. The equivalent bandwidth prediction for a grating without the phase shift is also shown. (b) Measured OSA trace with TMM model overlay of a typical grating transmission response. The design parameters are $\Lambda$ = 520 nm and $\Delta$W = 250 nm.

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In order to alternatively extract a value for $\kappa$, we used TMM models and compared them to the experimental transmission data. Figure 2(b) shows an example of solid agreement between the measurement and model. The slight differences in designed and simulation periods were on the order of 1 nm, which could occur due to fabrication variation. The central peak feature is impacted by both having a strong $\kappa$ relative to the length of the grating and loss in the device. The coupling coefficient $\kappa$ was determined by matching the bandwidth and spectral features. Table 1 displays the agreement between $\kappa _{\textrm {exp}}$, extracted from fits to experimental bandwidth data, and $\kappa _{\textrm {TMM}}$, validating the approach.

Table 1. Comparison of the experimental coupling coefficient $\kappa _{\textrm {exp}}$ to $\kappa _{\textrm {TMM}}$ extracted from the TMM model. $\kappa _{\textrm {exp}}$ was measured by fitting Eq. (3) to $\Delta \lambda$ versus $L$ data. $\kappa _{\textrm {TMM}}$ was extracted by aligning bandwidths of TMM simulations with measured spectra.

View Table

We also studied the effect of corrugation width on $\kappa$. Figure 3(a) uses the fit method outlined above for the three measured corrugation width cases. The results are shown in Table 1. Figure 3(b) shows three different spectra with identical period number and varying corrugation width. This figure illustrates that larger corrugation widths correspond to larger coupling coefficient, thus leading to wider bandwidths as predicted in Eq. (3). Another point of interest is the reduced transmission at the center wavelength, as seen in the 450 nm case (dash-dot). This is an example of the $\kappa$ term dominating the grating length term $\frac {\pi }{L}$, leading to the largest bandwidths in Fig. 3(b), but with the tradeoff of diminished center peak transmission. For the longest length devices, this led to the elimination of the center peak which is below the experimental polarization extinction. Figure 3(c) illustrates a typical extraction of the measured quality factor (Q) of the quarter-wave grating with a Lorentzian fit (solid line). The depicted device has a quality factor of $1.4~\times 10^4$. The inlaid plot shows the fit in the linear regime, where the agreement at the tails is more clear than in the logarithmic plot. The slight deviation of the peak from the center of the stop band is likely due to device-to-device fabrication differences inducing a small phase shift [19].

 

Fig. 3. Detailed analysis of the gratings. (a) Three transmission spectra are plotted with fixed characteristics $N = 100$ and $\Lambda$ = 520 nm and varying corrugation widths: 250 nm (solid), 350 nm (dashed), and 450 nm (dash-dot). Each are vertically offset for legibility. (b) Measured bandwidth data is fit as outlined above for three corrugation width cases with have the same labels as in panel (a). All devices have $\Lambda$ = 520 nm. (c) The transmission bandwidth (markers) of a device with $Q=1.4 \times 10^4$ from the overlaid Lorentzian fit of the center peak (solid). The inset plot shows the fit on linear scale. This device has N = 300, $\Lambda$ = 500 nm and $\Delta W$ = 250 nm.

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4. Conclusion

We have shown phase-shifted Bragg gratings in SiN fabricated with 193 nm DUV photolithography at AIM Photonics. We extracted $\kappa$ from two methods. First, we used experimentally measured center wavelengths and bandwidths and fitting bandwidth versus length curves. Second, we compared a TMM model to the measured spectra, which achieved consistent results. These phase shifts have an impact even when the grating strength $\kappa$ dominates the grating length term $\kappa >> \frac {\pi }{L}$. In particular, the phase shift broadens the bandwidth even if the center peak is strongly suppressed. By taking into account the role of the phase shift in the device bandwidth, these results enable researchers in the field to design more accurate on-chip gratings. Future work could include designing lower loss structures to reduce the impact on the central peak.