Dense dissimilar waveguide routing for highly efficient thermo-optic switches on silicon

Kyle Murray; Zeqin Lu; Hasitha Jayatilleka; Lukas Chrostowski

doi:10.1364/OE.23.019575

1. Introduction

Phase shifters find fundamental applications in many silicon photonic devices including switches [1, 2], modulators [3, 4], and tunable filters [5]. Two common ways of implementing a phase shifter rely on the plasma dispersion effect [6], in which a change in the density of charge carriers effects the refractive index of silicon, and the thermo-optic effect [7], in which a temperature change effects the refractive index. Plasma dispersion-based phase shifters, while having fast operation, often require large footprints or high operating voltages and have an optical loss modulation associated with the phase shift [6]. Thermo-optic phase shifters can achieve large phase shifts in small footprints with low operating voltages and without introducing optical loss modulation. However, they have slower response times and typically require more power for switching [8,9]. A review of recent progress in SOI switches in the context of optical interconnects can be found in [10].

A number of methods for increasing the efficiency of thermal phase shifters have been proposed. These methods include improving thermal isolation by removing the material surrounding the phase shifters [11], or folding a waveguide many times under a heater to increase the optical interaction length with the heated region [12,13]. This paper consists of the analysis and demonstration of a proposed improvement on the latter method.

When folding a waveguide under a heater, the waveguide spacing between each fold is limited by the evanescent coupling of light between adjacent waveguides. When adjacent waveguides are identical, the coupling of power between them is resonant, and a complete transfer of power can be achieved over a characteristic coupling length [14]. The coupling length is strongly dependent on the waveguide spacing, and so the spacing must be chosen such that the power coupling over the length of the device is sufficiently small for the desired application. This need for a sufficiently large spacing limits the achievable density of waveguide routing and therefore, limits the number of times a waveguide can be folded under a heater and its power efficiency.

In this paper we propose utilizing different waveguide widths in each fold of the phase shifter to overcome this limit. The evanescent coupling between dissimilar waveguides does not achieve phase matching. Therefore, the power coupling between waveguides is not complete [15]. For a given waveguide spacing, if the mismatch between adjacent waveguide widths is sufficiently large, then the power coupling can be made negligibly small over any coupling length. Without the need to have a large spacing, the density of waveguide folding under a heating element can be increased dramatically, and the efficiency of thermal heaters can be correspondingly improved. We model cross coupling in Mach Zehnder interferometers utilizing folded waveguides and show that the ripple in the through spectrum of the switch is an appropriate metric for measuring the degree of crosstalk present. We have recently demonstrated a Michelson interferometer using dissimilar waveguide routing, showing that the technique suggested herein can be extended to other switching architectures to achieve extremely low switching power [16]. Additionally, we have proposed utilizing dissimilar waveguides to increase waveguide routing density in photonic circuits [17, 18], and a thorough analysis has been performed [19]. Dissimilar waveguide routing has also been proposed for dense mode division multiplexing with gaps between adjacent waveguides as small as 100 nm [20]. After the submission of this paper, Mrejen et al. demonstrated control of the coupling between two waveguides by controlling the refractive index of an intermediate dissimilar waveguide [21].

This paper is organized as follows. In section 2, we provide a review of the coupled mode theory of dissimilar waveguides to specify notation and describe the method of calculation used herein. We then introduce a tight-binding coupled mode model of folded waveguides to demonstrate the need for dissimilar waveguides for dense routing, and to provide a metric for evaluating the success of our designs. In section 3 the design of the fabricated switches is described. In section 4 the experimental procedure for characterizing the switches is discussed. The results of the experiments are discussed in section 5, before concluding in section 6.

2. Theoretical device model

2.1. Coupled mode theory of dissimilar waveguides

In this section we compute the crosstalk between a pair of dissimilar waveguides. To achieve this, we define a notion of the power in a waveguide by projecting the optical field of the two-waveguide system onto the field of a single waveguide mode. We perform a change of basis from the two-waveguide eigenmode basis, in which the propagation is simple to describe, to a basis in which the power in each waveguide is simple to compute. In this basis the propagation is more complicated due to the appearance of coupling between modes.

Consider two parallel waveguides, denoted as waveguides A and B, of thickness t and widths w_A and w_B separated by a gap, g, as shown in Fig. 1. The two waveguide system has transverse electric (TE) eigenmodes |1⟩ and |2⟩, each normalized to unit power, with propagation constants k₁ and k₂ respectively. Waveguides A and B considered in isolation have eigenmodes |A₀⟩ and |B₀⟩, respectively. With the inner product [15]:

〈 ψ_{1} | ψ_{2} 〉 = \frac{1}{4} [\int E_{1} \times H_{2}^{*} \cdot d S + \int E_{2}^{*} \times H_{1} \cdot d S],

where E_i and H_i, i = 1,2, are the transverse electric and magnetic field profiles of two modes |ψ_i⟩ and S is the plane normal to the propagation direction, we can decompose the single waveguide state |A₀⟩ in terms of the two-waveguide eigenmodes:

| A 〉 = 〈 1 | A_{0} 〉 | 1 〉 + 〈 2 | A_{0} 〉 | 2 〉 .

Fig. 1 Dissimilar waveguide structure and horizontal electric field profile of its modes. Modes |1⟩ and |2⟩ are the modes of the two-waveguide structure. Modes |A₀⟩ and |B₀⟩ are the modes when only waveguide A or waveguide B are present, respectively.

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The difference between |A⟩ and |A₀⟩ is due to not including the complete set of radiation modes in the mode decomposition. Define the power normalized state

| \bar{A} 〉 = \frac{| A 〉}{\sqrt{〈 A | A 〉}},

and define

| \bar{B} 〉

similarly. A general superposition in the |1⟩, |2⟩ basis is then denoted as a vector with components a and b:

V = [\begin{matrix} a \\ b \end{matrix}] = a | 1 〉 + b | 2 〉 .

Evolution along the propagation direction, z, is trivial:

\frac{d V}{d z} = i [\begin{matrix} k_{1} & 0 \\ 0 & k_{2} \end{matrix}] V \equiv i P V .

Performing a change to the $| \bar{A} 〉$ , $| \bar{B} 〉$ basis with components c and d,

\bar{V} = [\begin{matrix} c \\ d \end{matrix}] = c | \bar{A} 〉 + d | \bar{B} 〉

V = [\begin{matrix} \frac{〈 1 | A_{0} 〉}{\sqrt{〈 A | A 〉}} & \frac{〈 1 | B_{0} 〉}{\sqrt{〈 B | B 〉}} \\ \frac{〈 2 | A_{0} 〉}{\sqrt{〈 A | A 〉}} & \frac{〈 2 | B_{0} 〉}{\sqrt{〈 B | B 〉}} \end{matrix}] \bar{V} \equiv M \bar{V},

the new evolution follows:

\frac{d \bar{V}}{d z} = i M^{- 1} P M \bar{V} \equiv i \bar{P} \bar{V} .

It should be noted that since in general M is not unitary the inner product is

V^{†} V = {\bar{V}}^{†} M^{†} M \bar{V} \neq {\bar{V}}^{†} \bar{V},

so the sum of the squares of the norms of the components of

\bar{V}

is not in general a conserved quantity. Nevertheless, we will identify the squares of the norms of the components of

\bar{V}

with the informal notion of the power contained in each waveguide. More precisely, the square of the norm of the first component of

\bar{V}

is the power that would be transmitted in to waveguide A if waveguide B were abruptly terminated and the squared norm of the second component has a similar interpretation.

If we consider a situation where at z=0 the waveguide system is excited in the state $| \bar{A} 〉$ , then one can consider the power coupled to waveguide B over some length L as the squared norm of the amplitude of $| \bar{B} 〉$ at z = L. In the special case where waveguides A and B are identical the power is transferred completely from waveguide A to waveguide B over a characteristic length, L_c = π/(k₁ − k₂), depending on the dimensions of the waveguides and their separation [15]. Thus, if one wishes to limit the crosstalk between the waveguides over their length then the separation between the waveguides must be made large enough such that L_c >> L.

If the two waveguides are not identical, then the power is still periodically coupled between the waveguides, but the transfer of power is incomplete [15]. The maximum crosstalk, CT, can then be computed as the maximum value of the squared norm of the second component of $\bar{V}$ in the solution to Eq. (8):

\bar{V} (z) = M^{- 1} e^{i P z} M \bar{V} (0) = M^{- 1} e^{i P z} M [\begin{matrix} 1 \\ 0 \end{matrix}]

\begin{matrix} CT = \max_{z} ({| [0 1] \bar{V} (z) |}^{2}) = \max_{z} ({| [0 1] M^{- 1} e^{i P z} M [\begin{matrix} 1 \\ 0 \end{matrix}] |}^{2}) \\ = 4 \cdot \frac{〈 B | B 〉}{〈 A | A 〉} \cdot \frac{{| 〈 1 | A_{0} 〉 〈 2 | A_{0} 〉 |}^{2}}{{| 〈 1 | A_{0} 〉 〈 2 | B_{0} 〉 - 〈 1 | B_{0} 〉 〈 2 | A_{0} 〉 |}^{2}} \end{matrix}

Figure 2 shows the computed maximum crosstalk for waveguides with a fixed center to center separation of 1 µm and thickness 220 nm as the widths of the waveguides are varied for a wavelength of 1550 nm [18]. The modes and propagation constants were computed using a numerical mode solver. It can be seen that by making the waveguide widths sufficiently different the crosstalk can be limited for small separations regardless of the length of the coupler. The asymmetry of the crosstalk under interchange of waveguide A and B is due the difference between first exciting state |A⟩, then later measuring state |B⟩, and first exciting state |B⟩, then later measuring state |A⟩. This difference is due to the non-orthogonality of |A⟩ and |B⟩ for dissimilar waveguides.

Fig. 2 Maximum crosstalk between 220 nm thick waveguides with 1 µm pitch.

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2.2. Folded waveguide structures

Figure 3 shows a schematic of the folded waveguide structure consisting of a waveguide folded N times, with widths w_m, m = 1,2,..N. Light is injected into waveguide 1 and the transmitted light is measured at waveguide N. We consider an odd number of waveguides so that the input and transmitted light are travelling in the same direction. To model the propagation, we utilize a tight-binding coupled mode model where we consider coupling only between nearest neighbour waveguides. The propagation is described by the differential equations:

\frac{d {\bar{V}}_{m}^{+}}{d z} = a_{m} {\bar{V}}_{m}^{+} + b_{m} {\bar{V}}_{m - 1}^{+} + c_{m} {\bar{V}}_{m + 1}^{+}

\frac{d {\bar{V}}_{m}^{-}}{d z} = - a_{m} {\bar{V}}_{m}^{-} - b_{m} {\bar{V}}_{m - 1}^{-} - c_{m} {\bar{V}}_{m + 1}^{-},

where

{\bar{V}}_{m}^{+}

and

{\bar{V}}_{m}^{-}

, m = 1,2,…N, are the amplitudes of the modes in waveguide m travelling in the positive and negative z directions. Here a_m, b_m, and c_m are the pairwise self and cross coupling coefficients computed as described in Eq. (8). Specifically, a_m are the self coupling coefficients found as the diagonal elements of,

i \bar{P}

and b_m and c_m are the cross-coupling coefficients found as the off-diagonal elements of

i \bar{P}

. Further, the system adheres to the boundary conditions:

{\bar{V}}_{0}^{+} (0) = 1

{\bar{V}}_{N}^{-} (L) = 0

\begin{matrix} {\bar{V}}_{m}^{-} (L) = {\bar{V}}_{i - 1}^{+} (L) e^{i ϕ_{m - 1}} \\ {\bar{V}}_{m}^{+} (L) = {\bar{V}}_{m - 1}^{-} (L) e^{- i ϕ_{m - 1}} \end{matrix}} for m evan

\begin{matrix} {\bar{V}}_{m}^{-} (0) = {\bar{V}}_{m - 1}^{+} (0) e^{i ϕ_{m - 1}} \\ {\bar{V}}_{m}^{+} (0) = {\bar{V}}_{m - 1}^{-} (0) e^{- i ϕ_{m - 1}} \end{matrix}} for m odd, m > 1,

where ϕ_m is the phase associated with the bend connecting waveguide m with waveguide m + 1. The system of Eqs. (12, 13), obeying the boundary conditions given by Eqs. (14–17) was numerically solved for N = 9, L = 90 µm, and identical waveguides of thickness 220 nm and width 500 nm for gaps, g = 500 nm, 750 nm, and 1 µm, as well as for a system consisting of alternating waveguides of widths 500 nm and 600 nm with a gap of 500 nm. The phases ϕ_m were all set to zero for simplicity. The results as a function of wavelength are presented in Fig. 4(a). It is clear that in the case of identical waveguides there is already significant ripple in the spectrum for a gap of 750 nm and a stop band appears for a gap of 500 nm. With the dissimilar waveguides, however, the ripple in the spectrum for a gap of 500 nm is less than that for the identical waveguides at a gap of 1 µm. The shape of the spectrum depends strongly on the phases ϕ_m, however, the degree of ripple in the spectrum does not. The degree of ripple was characterized by computing the minimum transmission of the folded waveguide structure as the gap between the waveguides was varied. The results are presented in Fig. 4(b). It can be seen that for the identical waveguides, the ripple in the spectrum causes the transmission to rapidly fall off for waveguide separations less than 1 µm. On the other hand, the reduction in crosstalk between the dissimilar waveguides effectively keeps the spectrum from developing significant ripple until the waveguide separation is less than 500 nm.

Fig. 3 Schematic diagram of folded waveguide structure.

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Fig. 4 (a) Calculated spectra of the folded waveguide structure for 9 identical waveguides with gaps g_I = 500 nm, 750 nm, and 1000 nm, and alternating dissimilar waveguides with widths of 500 nm and 600 nm with gap g_D = 500 nm, (b) Minimum transmission of the folded waveguide structure.

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3. Device design

Figure 5(a) shows a schematic diagram of the fabricated devices. Input light is split by a 50–50 adiabatic splitter [22] and the light traveling along one of the Mach-Zehnder interferometer (MZI) arms passes N times through the thermal phase shifter before recombining with the light from the other arm at the device output. Figures 5(c) and 5(d) show the cross-section of the phase shifter region for unetched and underetched devices respectively. Each of the N waveguides has a thickness of 220 nm, a width, w_i, i = 1,2,…,N, and all waveguides are separated by a common gap, g. A 10 µm wide heater of length L is used to apply a temperature change to the waveguides to induce a thermo-optic phase shift. In the case of the underetched devices, the silicon substrate has been removed to form a 12 µm wide suspended bridge to increase thermal isolation. The devices were fabricated using 248 nm optical lithography at the Institute of Microelectronics (IME), Singapore. The unetched and underetched versions of the device were measured from different wafers. Figure 5(b) shows an optical image of a fabricated device.

Fig. 5 (a) Schematic of thermally tunable MZI switch. Black traces: WGs, Red: Oxide openings define underetched region, Purple: Routing metal, and Green: Heater metal. Inset: Waveguide taper region. (b) An optical micrograph of a fabricated device. (c) Thermal phase shifter cross-section before underetching. (d) Thermal phase shifter cross-section after underetching. In (c) and (d), silicon dioxide is blue, silicon is tan, the metal heater is grey, and air is white.

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Five different devices were fabricated to study the effect of dense dissimilar waveguide routing on the tuning efficiency of MZI switches. Device 1 was used as a baseline device using identical waveguides and a gap of 3 µm to ensure no degradation of the spectrum due to crosstalk. Devices 2 and 3 used dissimilar waveguide routing with a gap of 1 µm, and devices 4 and 5 used dissimilar waveguides with a gap of 0.5 µm for the most dense routing. Table 1 summarizes the parameters of each device. The widths of the waveguides were picked such that adjacent waveguides have a width difference of at least 100 nm and next-to-adjacent waveguides have a width difference of at least 50 nm to protect against any effect of non-nearest neighbour coupling that was not considered in the theoretical analysis [19]. Device 1 was fabricated only in an unetched configuration while devices 2–5 were fabricated in both unetched and underetched configurations. The footprints of device 1, devices 2 and 4, and devices 3 and 4 were approximately 650 µm × 180 µm, 600 µm × 180 µm, and 800 µm × 180 µm, respectively.

Table 1. Device Parameters

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4. Experimental procedure

A Keysight 81682A tunable laser source was used to inject 0 dBm of light through an optical fiber into the chip through TE grating couplers [23]. After passing through a device the light exited the chip through a second fiber grating coupler and the transmitted light was passed to a Keysight 81635A photodetector. The wavelength of the input light was swept from 1530 nm to 1580 nm in 0.1 nm steps and the transmission spectrum of the device was recorded. This procedure was repeated while applying several different current levels to the phase shifter heaters and recording the power supplied.

5. Results and discussion

In all cases the extinction ratio of the switch was measured to be greater than 20 dB. Figures 6(a) and 6(b) show example optical spectra of the underetched versions of devices 3 and 5, respectively, in the on and off state. It can be seen that even for the longest devices tested the more aggressive waveguide routing density of device 5 compared to device 3 has not had a negative effect on either the extinction ratio of the switch or the ripple in the transmission spectrum, which is maintained at below 0.1 dB peak to peak. This suggests that the dissimilar waveguides have successfully prevented cross-coupling of power in the dense routing regions of the switch. The insertion losses of the switches were estimated to be −0.9 dB, −1 dB, −2.5 dB, −1.2 dB, and −2.9 dB for devices 1–5, respectively. The difference in insertion loss is due to the difference in propagation loss for the different arm path lengths. The insertion loss was found not to depend on whether or not the device was underetched. The envelope of the transmission spectrum in the on state is due to the wavelength-dependent coupling efficiency of the grating couplers used [22]. The wavelength dependence of the extinction ratio is due to an optical length mismatch between the two arms, which is likely due to variations in the thickness of the silicon layer across the wafer [24]. Though for any operating wavelength the 20 dB extinction ratio bandwidth was only approximately 5 nm in all cases, the device could be used with greater than 20 dB extinction at every wavelength we measured. This indicates that the range of possible operating wavelengths is at least 50 nm wide. The period of the variations in extinction ratio could be extended to create a more broadband device by designing a switch such that the average distance between its arms is smaller, at the expense of an increased thermal crosstalk between the arms.

Fig. 6 Measured spectra of the underetched versions of (a) device 3 and (b) device 5.

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Table 2. Tuning Efficiency of MZI Switches

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Figure 7 shows the normalized transmission functions of the unetched and underetched versions of devices 2–5 as functions of the power applied to the thermal phase shifter, along with sinusoidal fits to the data. The wavelength of operation was 1550 nm. It can be seen that in all cases the devices with more dense waveguide routing give higher phase shifter efficiency. The measured efficiencies are given in Table 2. It can be seen that the relative improvement in phase shifter efficiency when increasing waveguide routing density is greater for short devices than for long devices, and that the ratio of efficiencies approaches the ratio of waveguide densities for the long devices. Further, the relative change in efficiency when increasing waveguide routing density is similar for both the unetched and underetched devices. Thermal simulations of phase shifters with similar designs, and a discussion of thermal optimization of the design are performed in [16]. The highest efficiency achieved, 95 µW/π, is to the best of our knowledge the highest efficiency reported to date for thermally actuated MZI switches.

Fig. 7 Normalized transmission functions of the (a) short (devices 2 and 4) unetched, (b) long (devices 3 and 5) unetched, (c) short underetched, and (d) long underetched MZI switches.

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Figure 8 shows the temporal response of the MZI switches when the heaters were driven with a square pulse. The temporal response was found not to depend significantly on the waveguide routing density, but only on the heater length and whether or not the device was underetched. This suggests that the increase in device efficiency with increasing waveguide density does not come at the expense of a slower response time. The measured response times are summarized in Table 3. The greater fluctuations in the transmitted power for devices 3 and 5 compared to devices 2 and 4 are due to the lower signal to noise ratio for these devices as results of their larger insertion loss. The spikes in transmission at the beginning and end of the pulse for device 2 are a result of spikes that appear in the output of the voltage source when supplying voltages large enough to switch the unetched version of device 2. It is clear that the increases in efficiency when underetching devices or increasing device length come with an increase in the response time due to the improved thermal isolation of the heated region from its environment.

Fig. 8 Temporal response of (a) unetched, and (b) underetched MZI switches.

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Table 3. Response Times of MZI Switches

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6. Conclusions

It was shown that the increase in waveguide routing density near a heating element achievable by using dissimilar waveguides can be an effective way to improve the efficiency of thermal phase shifters. Utilizing highly dense routing of 9 waveguides under a 10 µm wide heater allowed us to fabricate an MZI switch with ultra-low switching power of 95 µW while maintaining an extinction ratio greater than 20 dB and ripple in the through response of less than 0.1 dB. The waveguide routing density was found to not impact the switch response time. The device footprint was less than 800 µm × 180 µm.

Acknowledgments

The authors would like to thank CMC Microsystems, Huawei, and the Natural Sciences and Engineering Research Council of Canada, in particular the Si-EPIC program, for financial support. Zeqin Lu would like to acknowledge the China Scholarship Council (CSC) for financial support. The authors thank Miguel Guillén-Torres for assistance with the optical micrographs.

References and links

1. T. Chu, H. Yamada, S. Ishida, and Y. Arakawa, “Compact 1 × N thermo-optic switches based on silicon photonic wire waveguides,” Opt. Express 13, 10109–10114 (2005). [CrossRef] [PubMed]

2. L. Sanchez, A. Griol, S. Lechago, A. Brimont, and P. Sanchis, “Low-Power Operation in a Silicon Switch Based on an Asymmetric Mach-Zehnder Interferometer,” IEEE Photon. J. 7, 1–8 (2015). [CrossRef]

3. P. Dong, L. Chen, and Y. kai Chen, “High-speed low-voltage single-drive push-pull silicon Mach-Zehnder modulators,” Opt. Express 20, 6163–6169 (2012). [CrossRef] [PubMed]

4. G. Kim, I. G. Kim, S. Kim, J. Joo, K.-S. Jang, S. A. Kim, J. H. Oh, J. W. Park, M.-J. Kwack, J. Park, H. Park, G. S. Park, and S. Kim, “Silicon photonic devices based on SOI/bulk-silicon platforms for chip-level optical interconnects,” Proc. SPIE 9368, 93680Z (2015). [CrossRef]

5. P. Dong, W. Qian, H. Liang, R. Shafiiha, D. Feng, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Thermally tunable silicon racetrack resonators with ultralow tuning power,” Opt. Express 18, 20298–20304 (2010). [CrossRef] [PubMed]

6. R. A. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987). [CrossRef]

7. G. Cocorullo, F. G. Della Corte, and I. Rendina, “Temperature dependence of the thermo-optic coefficient in crystalline silicon between room temperature and 550 K at the wavelength of 1523 nm,” Appl. Phys. Lett. 74, 3338–3340 (1999). [CrossRef]

8. Y. Shoji, K. Kintaka, S. Suda, H. Kawashima, T. Hasama, and H. Ishikawa, “Low-crosstalk 2 × 2 thermo-optic switch with silicon wire waveguides,” Opt. Express 18, 9071–9075 (2010). [CrossRef] [PubMed]

9. M. R. Watts, J. Sun, C. DeRose, D. C. Trotter, R. W. Young, and G. N. Nielson, “Adiabatic thermo-optic Mach-Zehnder switch,” Opt. Lett. 38, 733–735 (2013). [CrossRef] [PubMed]

10. H. Subbaraman, X. Xu, A. Hosseini, X. Zhang, Y. Zhang, D. Kwong, and R. T. Chen, “Recent advances in silicon-based passive and active optical interconnects,” Opt. Express 23, 2487–2511 (2015). [CrossRef] [PubMed]

11. Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M. B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon. Technol. Lett. 23, 525–527 (2011). [CrossRef]

12. Y. Hashizume, S. Katayose, T. Tsuchizawa, T. Watanabe, and M. Itoh, “Low-power silicon thermo-optic switch with folded waveguide arms and suspended ridge structures,” Electron. Lett. 48, 1234–1235 (2012). [CrossRef]

13. A. Densmore, S. Janz, R. Ma, J. H. Schmid, D.-X. Xu, A. Delâge, J. Lapointe, M. Vachon, and P. Cheben, “Compact and low power thermo-optic switch using folded silicon waveguides,” Opt. Express 17, 10457–10465 (2009). [CrossRef] [PubMed]

14. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973). [CrossRef]

15. W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11, 963–983 (1994). [CrossRef]

16. Z. Lu, K. Murray, H. Jayatilleka, and L. Chrostowski, University of British Columbia, 2332 Main Mall, Vancouver, BC V6T 1Z4, are preparing a manuscript to be called “Michelson interferometer thermo-optic switch on SOI with a 50 microwatt power consumption,”.

17. V. Donzella, S. Talebi Fard, and L. Chrostowski, “Study of waveguide crosstalk in silicon photonics integrated circuits,” Proc. SPIE 8915, 89150Z (2013). [CrossRef]

18. L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems (Cambridge University, 2015). Chap. 4.1.

19. W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y.-C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6, 7027 (2015). [CrossRef] [PubMed]

20. L. Liu, “Densely packed waveguide array (dpwa) on a silicon chip for mode division multiplexing,” Opt. Express 23, 12135–12143 (2015). [CrossRef] [PubMed]

21. M. Mrejen, H. Suchowski, H. Taiki, W. Chihhui, F. Liang, O. Kevin, Y. Wang, and X. Zhang, “Adiabatic elimination-based coupling control in densely packed subwavelength waveguides,” Nat. Commun. 6, 7565 (2015). [CrossRef] [PubMed]

22. H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-db coupler on silicon-on-insulator rib waveguides,” Proc. SPIE , 8915, 89150V (2013). [CrossRef]

23. Y. Wang, J. Flueckiger, C. Lin, and L. Chrostowski, “Universal grating coupler design,” Proc. SPIE 8915, 89150Y (2013). [CrossRef]

24. L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. T. Fard, “Impact of fabrication non-uniformity on chip-scale silicon photonic integrated circuits,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2014), p. Th2A.37.

	Device 1	Device 2	Device 3	Device 4	Device 5
N	3	5	5	9	9
w_i (nm)	500, 500 500	500, 400 550, 650 500	500, 400 550, 650 500	500, 600, 400 550, 650, 450 600, 400, 500	500, 600, 400 550, 650, 450 600, 400, 500
g (µm)	3.0	1.0	1.0	0.5	0.5
L (µm)	120	90	290	90	290

	Device 1	Device 2	Device 3	Device 4	Device 5
Unetched	14 mW/π	8.7 mW/π	5.9 mW/π	3.8 mW/π	4.2 mW/π
Underetched	N/A	0.68 mW/π	0.16 mW/π	0.20 mW/π	0.095 mW/π

	Device 1	Device 2	Device 3	Device 4	Device 5
N	3	5	5	9	9
w_i (nm)	500, 500 500	500, 400 550, 650 500	500, 400 550, 650 500	500, 600, 400 550, 650, 450 600, 400, 500	500, 600, 400 550, 650, 450 600, 400, 500
g (µm)	3.0	1.0	1.0	0.5	0.5
L (µm)	120	90	290	90	290

	Device 1	Device 2	Device 3	Device 4	Device 5
Unetched	14 mW/π	8.7 mW/π	5.9 mW/π	3.8 mW/π	4.2 mW/π
Underetched	N/A	0.68 mW/π	0.16 mW/π	0.20 mW/π	0.095 mW/π

Dense dissimilar waveguide routing for highly efficient thermo-optic switches on silicon

Abstract

1. Introduction

2. Theoretical device model

2.1. Coupled mode theory of dissimilar waveguides

2.2. Folded waveguide structures

3. Device design

4. Experimental procedure

5. Results and discussion

6. Conclusions

Acknowledgments

References and links

Cited By

Figures (8)

Tables (3)

Equations (17)

Optics Express

	Unetched Short	Unetched Long	Underetched Short	Underetched Long
Rise Time (µs)	40	60	550	750
Fall Time (µs)	45	65	550	1200

	Unetched Short	Unetched Long	Underetched Short	Underetched Long
Rise Time (µs)	40	60	550	750
Fall Time (µs)	45	65	550	1200