1. Introduction

In recent years, there has been intense research in ring resonators (RRs) as the building blocks for various photonic applications [1–10]. Wavelength division multiplexing and routing by add-drop filters [1-4], nonlinear optics, cascaded RRs as optical delay lines [5–7] and optical sensing [8] are some of the examples. Most of the previous work on optical resonators has focused on achieving very high quality factors (Q>50000) [10] to explore phenomena such as enhanced nonlinear effects and low threshold lasing. In these devices, only very weak coupling between the ring cavity and the access bus waveguide is required. Reducing the propagation loss and bending loss is the main challenge. On the other hand, a very high Q is undesirable for high speed signal processing and in optical delay lines, since it can significantly limit the operational bandwidth of the system. It is only recently that some research groups have began to address this issue [5–7]. When ring resonators are used for the processing of data signals (e.g. in add-drop filters), the bandwidth of the resonance must be sufficiently wide so that the signal can be transmitted through the ring with negligible distortion. For example, if a ring is used to transfer a signal with a bandwidth of Δv ∼ 10 GHz (e.g. a pulse train with ∼ 40 ps pulse width, which correspond to a spectral width of –λ ∼ 0.1 nm), it must have a resonance bandwidth several times of this value. At the same time, the coupling ratio and loss must be matched so that the ring operates near the critical coupling point to achieve a high extinction ratio. To obtain broad bandwidth, an obvious solution in ring resonators using a directional coupler (DC) is to increase the coupling between the ring and bus waveguides by reducing the gap between them. However, recent studies have shown that in ring resonators made of SOI photonic wires, the evanescent field in the coupler section is strongly coupled when a narrow gap (<0.1 μm) is used. Non-adiabatic mode transition between the ring and the coupler sections causes large excess mode conversion losses, limiting the flexibility of this approach [7].

Another type of coupler, namely the 2×2 multi-mode interference (MMI) coupler, has been employed in ring resonators. MMI couplers have been shown to have relaxed fabrication requirements, and are less sensitive to the wavelength or polarization variations. There have been experimental demonstrations of MMI-based ring resonators in III–V compound waveguides for e.g. ring lasers, where the MMI coupler lengths are on the order of a few hundreds of microns [11, 12]. We have proposed and theoretically shown that in SOI ridge waveguide RRs, using MMI couplers and cladding stress-induced birefringence is an effective approach to achieve polarization insensitive operation [13]. Experimental demonstration confirms the effectiveness of this approach [14]. In this contribution, we demonstrate for the first time ring resonators using MMI couplers in SOI photonic wire waveguides with sub-micron cross-sections. High bandwidth RRs with modest Q factors are readily achieved using very compact MMI couplers with length as small as 9 μm. Good reproducibility, uniform resonance bandwidth and extinction ratio over a large wavelength range are demonstrated in these devices. Since a strong coupling between the ring and bus waveguides can be easily achieved without the loss penalty observed in the directional coupler based ring resonators, we propose that MMI-coupled ring resonators are a suitable candidate for applications where high resonance bandwidth is preferred.

2. Theoretical analysis

A schematic of the MMI-coupled ring resonator is illustrated in Fig. 1(a). The power transmission in the bus waveguide can be express as [13, 15]:

where t² is the coupler power self-coupling coefficient, α² is the power loss factor which includes both the ring loss and the coupler loss, α² = α_MMI ² ∙ α_ring ² [13], and θ is the round trip phase accumulation. From Eq. (1), the quality factor Q of a ring resonator can be derived as:

where λ is the wavelength in vacuum, L is the ring cavity length, n_g is the ring waveguide group index, and αλ_FWHM is the resonance full-width-at-half-maximum which is also referred to as the resonance bandwidth. For a given loss factor α², the maximum (unloaded) Q_max occurs at t² = 1, while the largest resonance extinction occurs at α² = t² (critical coupling). Among these parameters, the ring waveguide loss factor is only weakly dependent on the wavelength λ. Another important parameter for resonators is the finesse F, which is defined and calculated as follows:

It is apparent that Q is a strong function of the cavity length L, and ring resonators with longer cavity length give larger Q. The finesse, on the other hand, is a better measure of the resonator figure-of-merit. It still depends on the cavity length implicitly through the loss factor a.

 

Fig. 1. (a). A ring resonator using an MMI coupler; (b) A close-up of the MMI section; (c) SEM image of an MMI-based ring resonator with a radius of 5 μm; (d) Close-up of the fabricated MMI section.

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Ring resonators based on DCs have been the most commonly used [1–10], since a directional coupler can be designed to give a coupling ratio ranging anywhere from zero to unity at a given wavelength. However, the coupling ratio naturally varies with the wavelength and is highly dependent on the waveguide dimensions in the DC section, particularly on the gap separating the coupler waveguides. The dependence of the coupling ratio on the wavelength increases with the strength of the coupling. The sensitivity to wavelength and fabrication tolerances can become severe for small silicon photonic wire waveguides, making it very difficult to control the coupling ratio and hence the Q at any given wavelength. For the directional couplers used in our experiment (dimensions specified below), a change of 10 nm in the gap size can cause a wavelength shift of 25 nm in the coupler transfer spectrum. This can be particularly important for devices with cascaded ring configuration, where the characteristics of the constituent rings must be precisely matched. Furthermore, directional couplers have long been thought as a low loss method for power transfer between waveguides, and it is only recognized recently that large mode conversion loss occurs when a narrow gap and a large curvature change is involved in these structures [7].

In MMI couplers, a 50:50 split is the most common, although designs with variable splitting ratios have been proposed and demonstrated [16]. Work on more weakly guided III–V compound waveguides have shown that for MMI couplers with a width of W_MMI = 2D or 3D, splitting ratios of 15:85 and 50:50 can be obtained, respectively [17, 18]. Here D is the separation between the two access waveguides as shown in Fig. 1(b). The advantages of MMI couplers are that the power coupling ratios t² and κ² are relatively insensitive to wavelength changes and fabrication inaccuracies, and the excess loss is low at the properly chosen imaging positions. In our first iteration, we have tested the separation of 1 μm and 1.5 μm, with the corresponding MMI width W_MMI = 3D = 3 μm, 4.5 μm, respectively, for a 50:50 split. The minimum gap between the waveguides is 0.55 μm, which can be achieved easily with electron beam lithography or even i-line steppers [9]. Due to the high index contrast in SOI, a large number of modes can be supported in a relatively small core area, making it possible to construct compact MMI couplers. For example, 18 horizontal modes were found in the 3 μm wide MMI section. The coupler lengths of 9 μm and 20 μm were determined using the 3D full-vectorial mode expansion software FIMMWAVE, for the 3 μm and 4.5 μm wide MMI couplers, respectively. Fig. 2(a) shows the simulated coupling coefficients for the 3 μm × 9 μm coupler, illustrating a close to 50:50 split within a ∼15 nm wavelength range even in this MMI coupler of very compact size.

 

Fig. 2. (a). Simulated and (b) Measured self (t²) and cross (κ²) power coupling ratios of a standalone 2×2 MMI coupler, with a 3 μm × 9 μm footprint.

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2. Fabrication and experimental results

Ring resonators with DC or MMI couplers, and stand-alone MMI couplers were fabricated on unibond SOI wafers with silicon core thickness of 0.26 μm and a buried oxide (BOX) of 2 μm. The ring and bus waveguide nominal width is 0.45 μm, and a 2 μm thick SU8 layer was used as the upper cladding. In the DC section, the nominal gap is 0.2 μm and the straight coupling length is 10 μm. The nominal dimensions of the MMI couplers are 3 μm × 9 μm or 4.5 μm ×9 20 μm as designed. SEM images of a fabricated resonator with a ring radius of 5 μm are shown in Figs. 1(c) and 1(d), with well defined features. To improve fiber to waveguide coupling efficiency, inversed taper mode size converters were integrated at each end of the bus waveguides, terminating with a nominal width of 0.15 μm at the facets [19]. The total device length is approximately 5 mm including the access waveguides. Waveguides were patterned using the electron beam lithography and transferred to Si using a cryogenic etch with an SF₆/O₂ chemistry in an inductively coupled plasma reactive ion etching (ICP-RIE) system. Devices with ring radii R ranging from 50 μm to 5 μm were tested and all were functional.

The optical testing was performed using a tunable laser, coupled to the waveguide via a polarization maintaining tapered fiber. The output light was collected and focused onto a photodetector using a 20× objective lens. The power splitting ratios measured on a standalone 3 μm × 9 μm MMI coupler are shown in Fig. 2(b). Over a 30 nm wavelength span from 1470 nm to 1500 nm, the splitting ratios are close to the 50:50 target, in close agreement with the simulation results shown in Fig. 2(a). There are obvious ripples, which is likely caused by back-reflections at the MMI end walls. In this first fabrication iteration, process bias in the coupler width and length has not yet been optimized. This also caused some excess loss. Although not straightforward to quantify, it was visible from the top-view IR images. Optimizing the layout feature size to compensate for the process bias is expected to reduce the excess loss. Tapering the access waveguides has been shown to be an effective method in reducing ripples [20, 21]. We have also fabricated MMI couplers with small length bias. For a coupler of 3 μm × 8.5 μm, the spectrum showed variations in the ripple amplitude as compared to the 3 μm × 9 μm coupler. However, the power splitting ratio variations are less than 15% in the 1470 nm to 1500 nm wavelength range, attesting to the more tolerant nature of MMI couplers to dimensional changes.

 

Fig. 3 Measured transmission spectrum of the (a) DC-based and (b) MMI-based resonator. The quality factor Q is shown in triangle symbols. The ring radius is 50 μm in both cases.

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Transmission spectra for ring resonators with a DC-coupler or a 3 μm × 9 μm MMI coupler and R= 50 μm are shown in Fig. 3 for the TM polarization, with the corresponding Q values shown as triangular symbols in the same figures. The envelop function in the DC-rings corresponds well to the sinusoidal dependence of the DC transfer function. Consequently, Q and extinction ratio vary strongly with the wavelength. Q reaches a maximum of ∼22,000 when t approaches unity at λ= 1570 nm, where the extinction diminishes. Near the critical coupling, the DC-ring shows a Q of ∼ 10,000 and a bandwidth of Δλ_FWHM ∼ 0.2 nm.

As expected from the transfer function of MMI couplers, the MMI-ring shows both uniform extinction (∼15 dB) and Q (∼6000) across a wavelength range of 30 nm. The envelop shows some undulation. We attribute this ripple to variations in t² of the MMI coupler, since the ripple periodicity in Fig. 2(b) and Fig. 3(b) are close to that expected for multiple reflection interference in a 9 μm cavity.

Figure 4(a) shows a close-up of the MMI-ring transmission spectrum as shown in Fig. 3(b) with the 3 μm × 9 μm coupler, while Fig. 4(b) show the spectrum for the ring with the same coupler design but with a radius of 5 μm. For the resonator shown in Fig. 4(a), the insertion loss is ∼ 11 dB, which includes the fiber to waveguide coupling loss, waveguide coupler loss and waveguide propagation loss. The resonance extinction is ∼ 12 dB. The free spectral range (FSR) increases with the wavelength, from 1.28 nm (λ = 1470 nm) to 1.60 nm (λ = 1570 nm) for the ring with R=50 μm, a result of the group index dispersion. At λ = 1470 nm, the bandwidth Δλ_FWHM measures approximately 0.25 nm and a Q of about 6,000. Keeping the same MMI design and reducing the ring radius from 50 μm to 20 and 5 μm, the bandwidths Δλ_FWHM increase from 0.25 to 0.4 and 0.8 nm, corresponding to Q values of ∼ 6000, 3500, and 2000 respectively. As shown in Fig. 4(b), the resonator with a radius of 5 μm also shows fairly uniform resonances.

Although the absolute Q values decreased with reducing radius, the finesse of the resonators increased from 5.4 to 7.5 and 9.8 respectively, for the corresponding radius of 50, 20 and 5 μm. By reducing the ring cavity length, the ring loss factor α decreases since the propagation length is shorter and the bend loss was found experimentally to be insignificant in these devices, similar to that reported in other publications [7]. Consulting Eq. (2) and Eq. (3), we observe that with decreasing cavity loss, the finesse increases while the increase in Δλ_FWHM is mainly a result of the decreasing L. For the resonator with a radius of 50 μm, the Δλ_FWHM is 0.25 nm for λ = 1470 nm and increased to 0.5 nm for λ = 1550 nm. This trend of increasing Δλ_FWHM with wavelength applies to the resonators with other radii as well. At the longer wavelength of 1550 nm, t² was observed to be smaller (over-coupling, see Fig. 2), leading to broader bandwidth. These dependencies are potential means to adjust the resonator bandwidths and Q values.

 

Fig. 4. Measured transmission spectrum of the MMI-coupled ring resonators with a 3 μm × 9 μm coupler, for (a) a ring radius of 50 μ m, and (b) a ring radius of 5 μm. The wavelength scan step was 5 pm. The loss includes the fiber to waveguide coupling loss and the waveguide coupling and propagation loss.

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The transmission spectrum for a resonator with a radius of 50 μm and the larger 4.5 μm × 20 MMI coupler is shown in Fig. 5. Here the resonance extinction ratio shows larger variation, which could be related to the imperfect imaging length of the MMI coupler. On the other hand, the resonance depth can be as large as 28 dB. The quality factors are ∼ 7000. These results indicate that further optimization of the device dimensions can improve the resonator performance.

For a ring with a 50:50 split coupler and a hypothetical lossless condition (α² = 1), the maximum Q is ∼10,000 for the resonators with a radius of 50 μm. Our measured Q values and extinction suggest that the fabricated resonators work near the critical coupling condition. By using MMI couplers with uneven splitting ratio (such as the 15:85 split design), higher Q is expected.

 

Fig. 5. (a). Measured transmission spectrum of the MMI-ring resonator with a radius of 50 μm and a 4.5 μm × 20 μm coupler. The wavelength scan step was 5 pm. (b) a close-up of the resonance at 1540.6 nm.

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3. Summary

We have demonstrated the novel implementation of SOI photonic wire microring resonators, using an MMI coupler between the ring and bus waveguides. The MMI coupler has compact sizes as small as 3×9 μm², and the minimum gap between the waveguides is ∼ 0.5 μm. The dimensional tolerances are largely relaxed compared to directional couplers commonly employed in ring resonators. A quality factor of 6,000–7,000, a high bandwidth of > 0.22 nm, and resonance extinction of 12 dB to 28 dB were achieved in these resonators. Unlike in DC-based RRs, MMI-based ring resonators can give high bandwidth and modest Q while maintaining ease of fabrication and robust performance, making these structures promising for high speed signal processing. The MMI coupler can be designed with low excess loss, with no known fundamental limit such as mode conversion loss as found in directional coupler based rings with small gaps. This is particularly important in applications requiring cascaded format such as optical delay lines. The resonance bandwidth and extinction are uniform over a large wavelength range, simplifying the design in optical multi-channel filtering and add-drop applications.