CMOS compatible reconﬁgurable ﬁlter for high bandwidth non-blocking operation

: We design, fabricate and characterize a CMOS-compatible, Mach-Zehnder-coupled, second-order-microring-resonator ﬁlter with large Free Spectral Range and demonstrate non-blocking thermo-optical ﬁlter reconﬁguration. The device consists of 10- µ m radius silicon microring resonators, with an FSR equivalent to that of a structure consisting of 5- µ m radii microrings. The structure is reconﬁgurable over an 8.5 nm range without blocking other channels in the network.


Introduction
State-of-the-art multi-core microprocessor systems have already achieved astonishing performances, but the tradeoff between signal attenuation and bandwidth in metallic wires compromises further progress [1,2,3].A compelling alternative to decouple loss and bandwidth relies on Optical Networks-on-Chip (ONoC), which opens new possibilities to network architectures with unprecedented communication bandwidth [4,5].
Free Spectral Range (FSR) and reconfiguration dynamics of individual filters are two pivotal points which set boundaries to the overall capacity of an ONoC.Both are important for most metrics involving networks efficiency, being crucial factors on the overall aggregate bandwidth and network latency, respectively.The aggregate bandwidth of an ONoC is limited by the sum of the bandwidths of all channels comprising the network, which is ultimatelly limited by the FSR of individual channels.And a reconfigurable network might suffer unnecessary latency if single channel realocation requires disabling other channels.
Here, by the proper operation of a Mach-Zehder interferometer (MZI) enhanced secondorder microring-resonator filter, we demonstrate a non-blocking -or hitless [6] -reconfigurable filter with large FSR.The ability to efficiently increase the number of channels in a network has been demonstrated in passive non-reconfigurable structures, in a variety of ways, for example, by using small microring resonators [7,8,9], Vernier filters [10,11], and by merging MZI's with microring resonators (Fig. 1a) [11,12,13,14,15].The last approach is chosen for this work because it has the interesting features of doubling the FSR without imparting high radiation losses (intrinsic to tight bends) and without the typical insertion loss for misaligned resonances (intrinsic to Vernier filters).This paper expands our work presented in [16], presenting a detailed description of the synthesis procedure and non-blocking operation.

Description, synthesis and non-blocking operation
The device, shown in Fig. 1a, consists of a modified second-order microring-resonator filter, where the coupling between the microring and the waveguide is MZI assisted with a twopoint coupling topology instead of the usual single-point coupling (red inset in Fig. 1b).The MZI is composed of 2 arms with lengths L mz and L mzr , with equal field coupling κ for both coupling regions, as shown in Fig. 1a.The MZI provides a periodic wavelength dependency for the coupling between bus waveguides and resonators, with periodicity set by the arm length difference ΔL = L mz − L mzr .In Fig. 1b, the spectral responses of the ring and of the MZI are shown in red and green, respectively.For a given relation between the values of ΔL and κ one can achieve the removal of every other resonance of the microring leading to a doubled FSR filter with a box-like transfer function, as shown in Fig. 1c.In order to determine the required values of ΔL and κ, one needs to ensure that the minimum coupling κ e f f of the MZI overlaps with the resonance to be suppressed.The coupling (κ e f f ) and transmission (t e f f ) coefficients of an MZI are extracted from the input to output transfer function with where n e f f is the effective refractive index of the waveguides comprising the MZI, which is a function of wavelength λ and temperature T .and t e f f is the complex conjugate of t e f f .Therefore, the minimum coupling at the wavelength λ 0 is obtained when κ(λ 0 ) = 0, which leads to: where the wavelength λ m 1 is obtained from the resonance condition of a microring: Where R is the radius of the microring.Combining Eq. 2 and Eq. 5, the equation for the effective coupling at λ m 1 −1 : Therefore the coupling κ is given by: The geometry of the device is determined by choosing values for m 1 and m 2 that obey Eq. 8, which are then used to calculate ΔL and κ using Eqs. 4 and 7, while the bandwidth and passband ripple of the box-like filter are determined by the effective coupling κ e f f (λ m 1 −1 ) and ring to ring coupling κ rr , which are obtained from filter synthesis methods [17,18,19,20].For example, Fig. 2  In Fig. 2a, every other resonance is removed, while in Fig. 2b one out of every three resonances is removed, and in Fig. 2c one out of every five resonances is removed.We observe that the coupling, shown in green, has a sinusoidal behavior.Changing its periodicity and amplitude directly effects the sensitivity around the resonances λ m 1 and λ m 1 −1 .Consequently, the coupling is more (less) sensitive around the resonance λ m 1 −1 (λ m 1 ) for smaller m 2 values, which can be an important criteria when choosing the design parameters for specific applications.In order to obtain non-blocking operation of the filter, the following sequence of 3 events is implemented: the refractive index of the microring and of the MZI at the right is modified, which changes the box-like filter into an all-pass filter; the refractive index of the entire structure is modified altogether, moving the all-pass filter to a new wavelength; and finally the excess change in the refractive index of the microring and MZI at the right is removed, so that the allpass filter transitions back to a box-like filter at a new wavelength.We make use of the strong thermo-optical effect present in silicon to change the refractive index and achieve non-blocking tuning [21].
Figure 3 shows the transmission response of the structure and its non-blocking nature following the three steps of temperature tuning outlined above.The through port and drop port transmissions (E t and E d , respectively) where plotted using where t Le f t = t e f f (T Le f t ), κ Le f t = κ e f f (T Le f t ), t Le f t is the complex conjugate of t Le f t , t Right = t e f f (T Right ), and κ Right = κ e f f (T Right ), t Right is the complex conjugate of t Right , and α is the propagation loss.T Le f t is the temperature of the left microring and of the Mach-Zehnder arm connected to it, and T Right is the temperature of the right microring and of the Mach-Zehnder arm connected to it.Figure 3(i) shows the transmission when T Le f t = T Right = T 0 .Figure 3(ii) shows the transfer function when the temperature of right ring and MZI is increased to T Right = T 1 , obtaining an all-pass filter.Figure 3(iii) shows the transfer function when the temperature of the full device is increased by T F so that T Right = T 1 + T F and T Le f t = T F , shifting the all-pass filter to a new location.Finally, Figure 3(iv) shows the transfer function when temperature of the right side of the device is reduced to T F , reallocating the box-like transfer function at a new wavelength.Even though it is clear in Fig. 3 that the reconfiguration process does not block other channels, we observe that it imparts about 1 dB insertion loss to the intermediate wavelengths.
Optimization of design parameters can be used to reduce even more such reconfiguration insertion loss.

Fabrication, experiment and results
We fabricated the structure using a CMOS-compatible process.As shown in Fig. 4a, doped Si heaters were formed inside the microrings and in the surroundings of the external arms of the MZI's, with doping level of 1×10 20 cm −3 , using Ar − as a dopant.The cross section of the heaters is 215 nm high by 1000 nm wide, while the cross section of the crystalline silicon waveguides is 215 nm high by 450 nm wide.Heaters in inner part of bends are placed 1 µm from the waveguides, while heaters in outer part of bends are placed 2 µm from the waveguides, as can be seen in Fig. 4a.A thin 35 nm silicon slab is left underneath the structure to enhance the heat transfer from the heaters to the waveguides.The slab is removed elsewhere mainly to improve the coupling from the optical fiber to the inverse taper used as input of the device.Since Fig. 4a is slightly angled, scale and dimensions of the device are better verified in Fig. 4b.The overall structure is fabricated on an SOI wafer with a 3 µm buried oxide and is clad with (ii)  The transfer function of the fabricated device is measured as shown in Fig. 5a, where a doubled FSR of 19.2 nm can be observed for the 10 µm radius microrings, with its main resonance at 1594.6 nm.We observe less than 1 dB insertion loss for the drop port and 20 dB suppression for the removed resonance.The residual power dropped at the suppressed resonance (at 1604.2 nm) is about 16 dB below the signal level.This transfer function is equivalent to the one presented at Fig. 2c, with a small mismatch in the length of the MZI leading the box-like filter around 1613 nm to be slightly overcoupled.In Figs.5b and 5c we demonstrate the nonblocking tuning of the fabricated filter.For the first step of the non-blocking tuning, we apply 28 mW to the heater inside the microring connected to the drop port and to the Mach-Zehnder arm connected to it, which changes the box-like transfer function (Fig. 5a) to an all pass transfer function (Fig. 5b), as expected.In Fig. 5c we show the final step of the tuning, where a new central resonance wavelength, at 1603.1 nm, is observed under 115 mW of heat power applied for all heaters.The thermal response of the heaters was measured to be in the order of 10 µs.Nonblocking operation is clear from the experimental results, confirming that a doubled FSR filter can be reconfigured from a wavelength to another with negligible insertion loss for intermediate wavelengths.

Conclusion
We fabricate and characterize a CMOS-compatible, Mach-Zehnder-coupled, second-ordermicroring-resonator filter with doubled free spectral range and demonstrate non-blocking thermo-optical filter reconfiguration.We demonstrate that non-blocking tuning can be achieved for a doubled FSR filter, which translates to a higher throughput for NoC's.It is important to note that in the current configuration, when the device is reconfigured and the refractive index of part of the structure is modified to achieve the all-pass filter, an overcoupled resonance is obtained, which still has a small power penalty and imparts some loss (< 1 dB) on other channels allocated between the initial and final wavelength.Even though the procedure described does not block the communication of other channels, its power penalty must be considered in the network design, and may limit the number of channels that can be reconfigured simultaneously.

Fig. 1 .
Fig. 1.(a) Schematics of a second-order filter with MZ arms.(b) Transfer function of a microring resonator (red) and effective coupling κ e f f of a MZI (green).(c) Transfer function of through (red) and drop (blue) ports of the filter.

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151744 -$15.00USD Received 25 Jul 2011; revised 3 Sep 2011; accepted 6 Sep 2011; published 29 Sep 2011 (C) 2011 OSA In order to obtain real solutions, minimum and maximum boundaries are set for the possible values of m 2 : shows a few possibilities of transfer functions for different values of m 1 and m 2 and fixed values of κ e f f (λ m 1 −1 ) and κ rr .The examples shown in Figs.2a, b, and c are for m 2 = (m 1 − 1)/2, m 2 = (m 1 − 1)/3, and m 2 = (m 1 − 1)/5, which result in ΔL = 2πR/2, ΔL ≈ 2πR/3, and ΔL ≈ 2πR/5, respectively, all of them with 60 GHz flatband bandwidth and -20 dB passband ripple at resonance.All figures show a doubled FSR around the suppressed resonance at λ m 1 , with a box-like resonance at the next resonance at λ m 1 −1 and distinct behavior for further resonances, depending on the coupling provided by the MZI for each of them.

Fig. 3 .Fig. 4 .
Fig. 3. Non-blocking tuning.(i) Initial transfer function of the filter, with the whole structure at the same temperature T 0 .(ii) All-pass transfer function after the right side of the filter is at temperature T 1 .(iii) The all-pass transfer function is shifted completely by increasing the temperature of the whole structure by T F .(iv) Final transfer fuction, obtained by reducing the temperature of the right side down to T F .

Fig. 5 .
Fig. 5. (a) Original spectrum of the device, with through (red) and drop (blue) ports presenting the doubled FSR.(b) Spectrum after changing the effective index of the cavity coupled to the drop port.No resonances are observed.(c) New resonance of the filter after non-blocking tuning.
at Le f t t rr t Right φ Right − at rr φ Le f t + a 2 t Right φ Right φ Le f t 1 − a φ Le f t t Le f t + φ Right t Right t rr + a 2 φ Le f t t Le f t φ Right t Right φ Le f t κ rr κ Right φ Le f t φ Right 1 − a t Le f t φ Le f t + t Right φ Right t rr + a 2 t Le f t φ Le f t t Right φ Right φ 1 φ 2 E i