Integrated waveguides and nanowires for optical spectral shaping by using Sagnac loop reflectors

doi:10.21203/rs.3.rs-1308584/v1

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Integrated waveguides and nanowires for optical spectral shaping by using Sagnac loop reflectors

https://doi.org/10.21203/rs.3.rs-1308584/v1

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We propose and theoretically investigate integrated photonic filters based on two coupled Sagnac loop reflectors (SLRs) formed by a self-coupled optical waveguide. Recently we investigated integrated photonic filters based on cascaded SLRs and coupled SLRs. Here, we advance this field by presenting a unique approach of using coupled SLRs formed by a self-coupled optical waveguide. This enables us to achieve high performance filter functions including Fano-like resonances and wavelength interleaving with a simpler design and a higher fabrication tolerance by tailoring coherent mode interference in the device. Our design takes into account the device fabrication issues as well as the requirements for practical applications. As a guide for practical device fabrication, an analysis of the impact of the structural parameters and fabrication tolerance on each filter function is also provided. The Fano-like resonances show a low insertion loss (IL) of 1.1 dB, a high extinction ratio of 30.2 dB, and a high slope rate (SR) of 747.64 dB/nm. The combination of low IL and high SR promises this device for Fano resonance applications. Our device also can achieve wavelength de-interleaving function with high fabrication tolerance which is attractive for optical interleavers that need a flat-top symmetric filter shape. Optical interleavers and de-interleavers are core elements for signal multiplexing and demultiplexing in wavelength division multiplexing optical communication systems. Versatile spectral responses with a simple design, compact device footprint, and high fabrication tolerance make this approach highly promising for flexible response shaping in a wide variety of applications.

Nanoscience

Integrated photonic resonators

Sagnac loop reflectors

Fano resonance

interleavers

Integrated photonic resonators (IPRs) have allowed a variety of functional optical devices, including filters, modulators, sensors, switches, and logic gates, thanks to their compact footprint, flexible topology, and great scalability [1-4]. Compared to the IPRS formed by photonic crystal structures [5] and gratings [6] that have sub-wavelength cavity lengths, the IPRs formed by directional-coupled wire waveguides with longer cavity lengths have smaller free spectral ranges (FSRs) that match the spectral grids of state-of-the-art wavelength division multiplexing (WDM) optical communication systems, thus making them more widely applicable to these systems. In addition, sub-wavelength dimensions of photonic crystal cavity and Bragg grating structures are more prone to fabrication tolerances as compared with directional-coupled wire waveguides. Ring resonators (RRs), and Sagnac loop reflectors (SLRs), which are essential building blocks for IPRs, are made up of directional couplers. Unlike RRs, which only allow for unidirectional light propagation, SLRs allow for bidirectional light propagation as well as mutual coupling between light travelling in opposing directions, resulting in a more versatile coherent mode interference and spectral response. Furthermore, a standing-wave (SW) resonator made up of cascaded SLRs has a cavity length about half that of a traveling wave (TW) resonator made up of a ring resonator with the same FSR, allowing for a more compact device footprint.

We investigated integrated photonic filters based on cascaded SLRs [7, 8] and coupled SLRs [9, 10] in our previous work. Here, we advance this field by presenting the novel approach of using two coupled SLRs with a feedback loop formed by a self-coupled wire waveguide that yield different response shapes including Fano-like resonances and wavelength de-interleaving [11].

In our design, we take into account the device fabrication issues experienced in Refs. [7, 8] as well as the needs for practical applications. As a guide for practical device fabrication, an analysis of the influence of structural parameters and fabrication tolerance is also provided.

The proposed structure is illustrated schematically in Fig. 1, which consists of two inverse-coupled SLRs with a feedback loop formed by a single self-coupled wire waveguide. Table 1 details the device's structural parameters. To simplify the discussion, we assume that L_SLR1 = L_SLR2 = L_SLR. The spectral response of the device is calculated using the scattering matrix method [7, 9]. In the device model, we use waveguide group index of n_g = 4.3350 (transverse electric (TE) mode) and propagation loss of α = 55 m⁻¹ (i.e., 2.4 dB/cm), which are in line with our previously fabricated silicon-on-insulator (SOI) devices [7, 8, 12]. The device is designed based on, but not limited to, the SOI platform.

Table 1

Definitions of device structural parameters
Waveguides	Length	Transmission factor ^a		Phase shift ^b
Feedback loop between SLRs (i = 1, 2)	L_FL	a_f		φ_f
Sagnac loop in SLR_i (i = 1, 2)	L_SLRi	a_si		φ_si
Directional couplers	Field transmission coefficient ^c		Field cross-coupling coefficient ^c
Coupler in SLRs (i = 1, 2)	t_i		κ_i
Coupler between SLR_s	t₂		κ₂
^a a_f = exp(-αL_FL / 2), a_si = exp(-αL_SLRi / 2), α is the power propagation loss factor.
^b φ_f = 2πn_gL_FL / λ, φ_si = 2πn_gL_SLRi / λ, n_g is the group index and λ is the wavelength.
^c t_i² + κ_i² = 1 for lossless coupling are assumed for all the directional couplers

In the following sections, mode interference in the device is tailored to achieve high-performance filtering functions, including Fano-like resonances and wavelength de-interleaving.

Fano resonances are a fundamental physical phenomenon demonstrating an asymmetric spectral lineshape arising from quantum interference between discrete and continuum states [13, 14]. They have underpinned many applications such as optical switching, data storage, sensing, and topological optics, due to their unique physics and capability of providing ultra-narrow spectral linewidths [13-15]. In this section, the spectral response of the device in Fig. 1 is tailored to realize Fano-like resonances with high slope rates (SRs) and low insertion loss (IL). The power transmission and reflection spectra is depicted in Fig. 2(a). The device structural parameters are L_SLR = 100 µm, L_FL = 300 µm, t₁ = t₃ = 0.82, and t₂ = 0.92. Clearly, there are periodical Fano resonances with identical asymmetric resonant lineshape in each period at output port. The high uniformity of the response shape of the resonator could be suitable for applications in WDM systems. A zoom-in view of Fig. 2(a) is shown in Fig. 2(b), together with another curve showing the corresponding result for another device with the same structural parameters except for a different t₂ = 1. As can be seen, when t₂ = 1, there is no Fano resonance, distinguishing between the device in Fig. 1 and the two cascaded SLRs in Ref. [16]. The Fano resonances in Fig. 2(a) show a high extinction ratio (ER) of 30.2 dB and a high SR (defined as the ratio of the ER to the wavelength difference between the resonance peak and notch) of 747.64 dB/nm.

The performance of the Fano-like resonances generated by the coupled SLRs in our prior work [9, 10] and the device in Fig. 1 are compared in Table 2. For comparison, the device structural parameters (L_SLRi, n_g, and α) of all the three structures were kept the same except for the transmission coefficients (t_i) that were tuned to obtain the highest SR for each structure. As compared with previous devices, the device presented here has a much lower IL of 1.1 dB, along with a slightly improved SR. The combination of high SR and low IL promises this device for Fano resonance applications. We note that a low IL of 1.1 dB is outstanding among the reported Fano-resonance devices on the SOI platform [17, 18], which makes the device here more attractive for practical applications.

Table 2

Performance comparison of Fano-like resonances generated by different SLR-based devices.
Device structure	IL (dB)	ER (dB)	SR (dB/nm)	FSR (GHz)	Ref.
Two parallel WC-SLRs ^a	6.3	13.9	389	692.02	[9]
Three zig-zag WC-SLRs ^b	3.7	63.4	721.28	230.68	[10]
Device in Fig. 1	1.1	30.2	747.64	173	This work
^a WC-SLRs: waveguide coupled SLRs.
^b For comparison, the length of the SLRs (L_SLRi, i = 1–3) and the connecting waveguide (L_i, i = 1–4) is slightly changed from 115 µm in [10] to 100 µm.

In Figs. 3(a)–(c), we further investigate the impact of the device structural parameters including t_i(i = 1–3) andlength variations of feedback loop (∆L_FL) on the performance of the Fano resonance. In each figure, we changed only one structural parameter, keeping the others the same as those in Fig. 2 (a). In Figs. 3(a)–(c), (i) shows power transmission spectra and (ii) shows the corresponding IL and SR for different t_i(i = 1–3), and ∆L_FL, respectively. The SR decreases with t_i (i = 1, 3), while the IL first decreases with t_i (i = 1, 3) and then remains almost unchanged. The SR decreases with t₂, while the IL shows an opposite trend, reflecting that both of the two parameters can be improved by enhancing the coupling strength between SLR₁and SLR₂. As shown in Fig. 3(c), the filter shape remains unchanged while the Fano-like resonance peak redshifts as ∆L_FL increases. This indicates that the resonance wavelengths can be tuned by introducing thermo-optic micro-heaters [18] or carrier-injection electrodes [19] along feedback loop to tune the phase shift.

Optical interleavers and de-interleavers are core elements for signal multiplexing/demultiplexing in wavelength division multiplexing (WDM) optical communication systems [20, 21]. In this section, we engineer the spectral response of the device in Fig. 1 to achieve wavelength de-interleaving function. Flat-top spectral response of de-interleavers minimize the filtering distortions and group delay variation and high ER minimize signal crosstalk between adjacent channels [22]. Fig. 4(a) shows the power transmission and reflection spectra when the device structural parameters are L_SLR = 100 µm, L_FL = 300 µm, t₁ = 0.992, and t₂ = t₃ = 0.95. The IL, ER, and 3-dB bandwidth for the passband at output port are 0.36 dB, 12.7 dB, and 83.65 GHz, respectively. The IL, ER, and 3-dB bandwidth for the reflection spectrum at input port are 0.33 dB, 12 dB, and 91.9 GHz, respectively. As compared with flat-top filters based on cascaded ring resonators [23], ring-assisted Mach-Zehnder interferometers [24], and cascaded SLRs [7], our device can achieve the same level of filtering flatness with fewer subunits.

We further investigate the impact of varied t_i (i = 1–3) in Figs. 4(b)–(d), respectively. For simplification, we only show the spectral response at output port. In Fig. 4(b), as t₁ increases, the ER of the passband decreases while the top flatness improves, reflecting the trade-off between them. In Figs. 4(c)–(d), the bandwidth of the passband increases with t₂, t₃, respectively, while the ER shows an opposite trend.

We also investigate the impact of varied ∆L_SLRi (i = 1, 2) and ΔL_FL in Figs. 5(a)–(c), respectively. In Figs. 5(a)–(c), as ∆L_SLRi (i = 1, 2) or ΔL_FL increases, the filter shape remains unchanged while the resonance redshifts. Since the resonant cavity of the device is formed by a single self-coupled wire waveguide, random length fabrication errors in different parts (i.e., SLR₁ in Fig. 5(a), SLR₂ in Fig. 5(b), and feedback loop in Fig. 5(c),) will not induce any asymmetry in the filter shape. This yields a higher fabrication tolerance as compared with the coupled SLRs in Refs. [9, 10], which is particularly attractive for optical interleavers that require a flat-top symmetric filter shape.From Figs. 4(b)–(c) and Fig. 5, it can be seen that the slight changes in the structural parameters induced by fabrication disorders have no major impact on device performance.

We have theoretically investigated integrated photonic filters based on two coupled SLRs with a feedback loop formed by a self-coupled optical waveguide. High performance filter functions including Fano-like resonances and wavelength de-interleaving are achieved by tailoring coherent mode interference in the device. Our design takes into account the device fabrication experience as well as the requirements for practical applications. The impact of device structural parameters on each filter function is analyzed to facilitate optimized performance. Versatile spectral responses, compact device footprint, and high fabrication tolerance make this approach highly promising for flexible response shaping in a wide variety of applications including potentially optical microcombs for advanced dispersion design for many applications. [25-145]

Competing interests:

The authors declare no competing interests.

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Moss, David, “Microcombs for Ultrahigh Bandwidth Optical Data Transmission and Neural Networks.” OSF Preprints. March 8. (2021). DOI:10.31219/osf.io/ne9wx.

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Integrated waveguides and nanowires for optical spectral shaping by using Sagnac loop reflectors

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1. Introduction

2. Device Configuration

3. Fano-like Resonances

4. Wavelength De-interleaving Function

5. Conclusions

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