To realize a bandstop MPF, the DC should be set within the phase range (0,π/2). Under these conditions, as illustrated in Fig. 3a, the amplitude of the lower sideband is less than that of the upper sideband, a technique known as QSSB modulation. If the PS-WBG is configured to partially suppress the upper sideband at a frequency of the fc+fe, its amplitude can be made equal to that of the lower sideband at fc-fe. Due to the out-of-phase nature of the two sidebands, full cancellation occurs, resulting in a bandstop filter with theoretically infinite notch depth39. The rejection ratio can be fine-tuned and controlled by adjusting the bias voltage, offering more flexibility than the approach in34, where QSSB modulation was not utilized. To realize a bandpass MPF, as depicted in Fig. 3b, the DC should be set to zero. Under this condition, the DD-MZM functions similarly to a phase modulator, generating two sidebands with equal amplitudes but a phase difference of π. In the absence of the PS-WBG, beating between the optical carrier and each sideband leads to complete cancellation. However, when the PS-WBG is introduced, the spectral component at the notch frequency at fc+fe will not be canceled, thereby forming a bandpass filter. The frequency of both bandstop and bandpass filters can be adjusted by tuning the optical carrier wavelength.
To introduce the operating principle, we first describe the optical response of the PS-WBG. We analyzed the propagation properties of the proposed PS-WBG using an eigenmode expansion (EME) solver. Figure 4 vividly presents the simulated magnitude and phase of the reflection spectrum of PS-WBG. It shows a reflection spectrum with a flat band between 1546 and 1555 nm. Due to a phase shift being introduced in the middle of the grating, a narrow resonance appears in the reflection spectrum, corresponding to it; a phase shift occurs in the phase spectrum as expected. It is worth noting that the slight deviation of the notch from the center of the reflection spectrum originates from the mismatch between the effective refractive indices of the phase-shift section (n) and the grating (n), and the finite-length effects of the mirrors, including penetration depth causing a deviation from the ideal π phase shift. To align the notch precisely at the Bragg wavelength, further optimization of the phase-shift section and grating geometry would be needed.
The feasibility of realizing such spectral characteristics in fabricated devices has been confirmed by prior demonstrations of PS-WBGs exhibiting a narrow resonance within a broad flat-top reflection band. Also, to ensure realistic performance assessment, propagation loss was included in the simulations. Based on prior studies, sidewall roughness is recognized as the primary source of loss in WBGs, typically introducing attenuation in the range of 2-4 dB/cm. In our model, a loss of 3 dB/cm was applied. Nevertheless, the resulting insertion loss remained very low (less than 0.06 dB), indicating that the PS-WBG maintains excellent optical performance even under practical loss conditions.
Several fabrication techniques have been developed for implementing WBGs. Among them, electron beam (e-beam) lithography has been widely employed due to its capability to define nanoscale grating features with high precision. However, despite its excellent resolution, it is inherently slow and unsuitable for large-scale or commercial production. As a CMOS-compatible alternative, 193 nm deep ultraviolet lithography offers high pattern fidelity and scalability, making it a promising solution for mass fabrication. Furthermore, nanoimprint lithography has recently emerged as a cost-effective and high-throughput technique for fabricating Bragg gratings with sub-wavelength resolution, while remaining compatible with CMOS processes. A comprehensive review of the design and fabrication of WBGs, as well as their critical role in silicon photonics for optical and microwave signal processing, is provided in.
To assess the robustness of the proposed PS-WBG structure, we evaluated the impact of fabrication imperfections by introducing uniform deviations in both the grating depth (ΔW) and the grating period (Λ), which are among the most common sources of performance degradation. Specifically, spatial deviations of ± 5 nm and ± 10 nm were introduced in ΔW, and ± 1 nm and ± 2 nm in Λ. These variations effectively capture systematic fabrication errors such as etch bias and lithographic distortion.
A high refractive index contrast between the core (silicon) and the cladding (oxide or air) results in strong light confinement within the core. Due to the small waveguide dimensions and optical mode size, even minor sidewall perturbations can significantly influence the coupling coefficient. As shown in the equations presented in the Geometry of the PS-WBG section and in Fig. 5a, increasing the grating depth (Δw) enhances the refractive index modulation (Δn), thereby increasing the coupling coefficient (κ). A higher κ broadens the flat-band reflection bandwidth (Δλ) and exponentially improves the intrinsic quality factor (Q), resulting in a narrower resonance bandwidth (Δλ). Conversely, reducing Δw lowers Δn and κ, leading to a reduction in Δλ and a lower Q, which in turn broadens Δλ. Variations in Δw also alter the effective refractive index, which shifts the Bragg wavelength (λ). Therefore, analyzing the impact of Δw variations is essential to validate the tolerance and performance stability of the PS-WBG under realistic fabrication conditions.
The spectral position of the reflection response is highly sensitive to variations in the grating period (Λ), since the Bragg wavelength (λ = 2Λ·n) depends linearly on Λ according to Bragg's condition. As shown in Fig. 5b, even small deviations in Λ can noticeably shift the entire reflection spectrum, highlighting the need for precise control over the grating period during fabrication. Nonetheless, as discussed in, such variations can be mitigated through pre-fabrication calibration using experimental data, allowing for design-time compensation of systematic deviations.
Since experimental verification was not feasible, the operation and performance of the proposed MPF were evaluated through OptiSystem simulations, as illustrated in Fig. 6. The simulation setup follows the schematic representation of the proposed system shown in Fig. 2. A tunable laser source (TLS) with an output power of 9 dBm and a linewidth of 0.5 MHz was used to generate the optical carrier, which was then injected into a DD-MZM. The DD-MZM consists of two phase modulators, each having an RF half-wave voltage (Vπ) of 7 V. A microwave signal with a power of 5 dBm, used as the RF input, was applied to the DD-MZM through a hybrid coupler. The insertion loss of the DD-MZM was assumed to be 3.5 dB. To assess the overall insertion loss of the proposed MPF link, we considered the primary sources of optical loss in similar MWP systems. Although our current work did not include explicit simulation or measurement of coupling and routing losses, previous studies have reported a total fiber-to-fiber loss of approximately 21 dB in comparable configurations. Specifically, the fiber-to-chip coupling loss was estimated to be about 5 dB per facet, primarily due to the grating coupler (~ 4.5 dB) and residual misalignment (~ 0.5 dB). On-chip waveguide routing introduced an additional loss of approximately 2 dB, and the Y-junction in the reflection path contributed around 6.5 dB. To compensate for the insertion loss associated with the DD-MZM and the fiber-to-chip interface, we employed an EDFA with a noise figure of 8 dB. The EDFA was placed both before and after the chip to maintain sufficient optical power and signal quality during transmission and processing.
The optical response of the PS-WBG, obtained from the EME solver, was imported into the OptiSystem software by means of the 'measured optical filter' component. Finally, the optical signals were converted into the electrical domain using a 45-GHz photodetector with a responsivity of r = 0.75 A/W. The resulting electrical signals were analyzed by an RF spectrum analyzer, which recorded the output power spectrum as the RF input frequency was swept from 0.1 to 50 GHz. The collected data were subsequently post-processed in MATLAB to reconstruct and plot the frequency response of the proposed filter. To facilitate comprehension, Table 1 provides a concise summary of the simulation parameters for all key components.
The MPF is first demonstrated in the bandstop configuration. As shown in Fig. 3a, the optical carrier frequency was tuned slightly lower than the frequency of the PS-WBG's reflection notch, ensuring that the upper modulation sideband falls within the notch. We adjusted the bias voltage to ensure that the amplitude condition between the sidebands was satisfied.
According to the amplitude and phase responses of the PS-WBG shown in Fig. 4, the reflection notch was centered at 1550 nm, with an overall reflection bandwidth of approximately 1.12 THz. The 3-dB bandwidth of the notch was measured to be around 1.5 GHz, and the rejection ratio reached 25 dB. A nearly linear phase response was observed across a 916 GHz bandwidth, although it was slightly asymmetric with respect to the notch center. Theoretically, the microwave tuning range was approximately 245 GHz, corresponding to half of the 490 GHz linear phase response region on the right side of the reflection spectrum. However, considering the bandwidth limitations of system components such as the DD-MZM and photodetector, we limited the effective microwave tuning range to 50 GHz, covering half of the 100 GHz linear phase region within the operational bandwidth. This range could be extended using high-speed devices. To evaluate the frequency tunability of the system, we first set the optical carrier to 1550.04 nm, which corresponded to a detuning of Δλ = 0.04 nm (≈ 5 GHz) from the resonance wavelength of the PS-WBG. Here, the detected RF frequency (f) is defined as the spectral separation between the optical carrier and the modulation sideband. At this initial carrier wavelength, sweeping the RF input from 0.1 to 50 GHz produced a pronounced suppression notch at 5 GHz, which was consistent with the expected carrier-sideband alignment with the PS-WBG resonance. We subsequently tuned the carrier wavelength from 1550.04 to 1550.36 nm in discrete steps of 0.04 nm (≈ 5 GHz). For each carrier setting, the RF sweep revealed a distinct notch whenever the optically generated sideband coincided with the PS-WBG notch, i.e., at 10, 15, ..., up to 45 GHz. This systematic progression demonstrated the stable and predictable tunability of the RF notch frequency. As shown in Fig. 7, the simulated frequency response of the bandstop filter exhibits a deep notch with an ultra-high rejection ratio exceeding 55 dB across the entire tuning range.
The rejection ratio of the MPF is significantly higher than that of the PS-WBG alone (25 dB). This enhancement is attributed to the precise tuning of the power ratio between the two sidebands by adjusting the bias voltage, leading to full cancellation of the beating signals at the PD output. Subsequently, the MPF is configured as a bandpass filter. By setting to zero, an EPM condition is established, ensuring that the two sidebands have identical amplitudes with a π-phase difference. As shown in Fig. 3(b), the upper sideband is suppressed by the PS-WBG's reflection notch, converting the phase-modulated signal into a single-sideband intensity-modulated signal, thereby realizing bandpass filtering. Frequency tunability is also achieved by tuning the optical carrier wavelength, and the simulated frequency response is depicted in Fig. 8.
The peak-to-sidelobe ratio stays above 20 dB across most of the tuning range. However, at 5 GHz, a slight drop below this threshold is observed. This performance decline arises from the nonlinear phase behavior of the PS-WBG near the phase shift located at the center of the reflection band. In this region, the phase difference between the upper and lower sidebands cannot be preserved accurately, which leads to lower passband gain when operating as a bandpass MPF. To avoid such degradation, the tuning range is typically confined to the linear portion of the PS-WBG phase response, where the relative phase between sidebands is stable.
Furthermore, the rejection ratio of the MPF in bandstop mode is tunable by adjusting the bias voltage of the DD-MZM, which modifies the power ratio between the two sidebands. Incomplete cancellation of the sidebands leads to a reduced rejection ratio. Figure 9 illustrates the measured frequency response of the MPF operating as a bandstop filter with a tunable rejection ratio, with the bias voltage varied in steps of 0.5 V. This presents the correlation between the rejection ratio and bias voltage variations relative to the optimal bias setting for maximum rejection.
Finally, the transition of the MPF from bandstop to bandpass operation is demonstrated by further tuning the bias voltage. Figure 10 shows the corresponding frequency response, highlighting the MPF's capability to switch from a bandstop filter with a maximum rejection ratio of 60 dB to a bandpass filter with a peak-to-sidelobe ratio of 20 dB. Moreover, since PS-WBG has a notch with a 3-dB bandwidth of 1.5 GHz, the 3-dB bandwidth of the bandstop and passband MPF filter is around 1.5 GHz.
Table 2 presents a comprehensive comparison of the key performance characteristics of our proposed MPF with those from previous studies utilizing different techniques. The proposed MPF offers a significant improvement over existing technologies, particularly in terms of tunable range, which currently spans up to 50 GHz and has the potential for expansion to 245 GHz. This wide tunability, combined with the ability to operate in both bandpass and bandstop modes, makes the filter highly reconfigurable and suitable for various advanced microwave photonic applications. The proposed filter offers a 3-dB bandwidth of approximately 1.5 GHz and a peak-to-sidelobe ratio of 20 dB, providing a favorable balance between spectral resolution and selectivity. Its high rejection ratio, exceeding 55 dB, effectively suppresses undesired signals.
The monolithic integration of all components eliminates the need for optical amplification, while reducing footprint, power consumption, and insertion loss. It also enhances system stability by minimizing path-length fluctuations and improving overall link efficiency. Achieving full system integration on a chip relies on advancing key components, many of which have already reached high-performance levels. On-chip modulators that leverage diverse physical mechanisms, including plasmonics, P-N junctions, and electro-optic effects, have been successfully realized. Similarly, integrated PDs with bandwidths exceeding 100 GHz and high output power have been demonstrated. However, a challenge remains in integrating laser sources due to the indirect bandgap of silicon, which limits efficient light generation. To address this, significant progress has been made in developing III-V semiconductor lasers, which can be integrated with silicon platforms using bonding techniques like flip-chip bonding.