Abstract

Using a compact (0.03 mm2) silicon-photonic bias-free thermo-optic cross-bar switch, we demonstrate microsecond-scale switching of twenty wavelength channels of a C-band wavelength-division multiplexed optical ring network, each carrying 10 Gbit/second data concurrently, with 15 mW electrical power consumption (no temperature control required). A convenient pulsed driving scheme is demonstrated and eye patterns and bit-error rate measurements are shown. An algorithm is developed to measure the power-division ratio between the two output ports, the insertion and switching losses, and non-ideal phase deviations.

© 2014 Optical Society of America

1. Introduction

Data-center networks with optical interconnects [1, 2] may lower energy consumption, and scale more efficiently if silicon photonic components can replace some of the conventional offthe-shelf components used today. MORDIA (Microsecond Optical Reconfigurable Datacenter Interconnect Architecture), shown in Fig. 1, is a multi-wavelength, multi-port optical circuit-switched network, designed to support a wide variety of all-to-all communication workloads, e.g., MapReduce, TritonSort, and data sorting and searching [3]. It may benefit scalability, reconfigurability and maintenance of networks if optical switching can be incorporated within the ring. Such switches have to be capable of supporting the full optical bandwidth in the ring (here, more than 30 nm) and be reconfigurable in a few microseconds (currently about 12 μs in the MEMS-based implementation [3]). It is also necessary that such a switch be energy-efficient, and can be driven in a manner that is compliant with digital controllers.

 

Fig. 1 A) Hardware for the optical circuit-switched multi-wavelength MORDIA ring network at UC San Diego, including data servers, optical amplifiers (EDFAs), optical spectrum analyzer (OSA) for power monitoring, and hardware for wideband wavelength-selective switching (WSS). There are six nodes and four host stations per node. B) Schematic of the ring network topology, in which any of the nodes can access the full bandwidth of the ring (about 30-nm wavelength span). C) Optical spectrum of 20 data channels, each carrying 10-Gbit/s data, used in the switching demonstration (some extraneous channels, not carrying data, or at long wavelengths that lie outside the range of the tunable filters used to measure the individual eye patterns, also propagate through the chip but were not measured here).

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While thermo-optic silica and polymer switches are mature technologies, and have shown excellent output-port contrast [4], their large footprints, large power consumptions, and relatively slow switching times suggest areas for improvement. Silicon can be used to make a broadband, yet energy-efficient, microsecond-scale switch that is highly integrable and can operate on many wavelength channels. One method is to use a microring resonator, designed with a free-spectral range (FSR) equal to the inter-channel spacing. All-optical switching of 20 CW wavelengths (and one data channel) in this configuration has been demonstrated, albeit with a significant power penalty and change-of-slope in the bit-error-rate sensitivity curve [5]. In principle, the microring could be thermo-optically switched: energy-efficient thermo-optic tuning of a microring has been demonstrated with a power consumption of only 0.5 mW per nanometer of wavelength shift, and a 10%–90% switching time of about 1 μs [6]. However, this resonant structure may be subject to crosstalk between the optical channels, and the alignment of the resonances to the ITU-T wavelength grid may depend on temperature. Also, the coupling coefficient of a compact directional coupler, as typically used between a microring and a waveguide, tends to vary widely with wavelength [7], and longer (adiabatic) couplers which overcome this limitation may not allow the microring resonator to achieve the requisite free-spectral range.

A second approach is to use a Mach-Zehnder interferometer (MZI) [8], here implemented with wideband 3-dB couplers, and an energy-efficient thermo-optic phase-shift mechanism in one arm. Compared to carrier injection in silicon MZIs, the thermo-optic MZI should have smaller insertion loss and greater scalability to larger switching fabrics, because the device is much smaller as a result of the larger magnitude of the thermo-optic effect compared to the free carrier plasma dispersion effect. Here, the 3-dB couplers attempt to achieve wavelength-insensitive power splitting by lithographic design [9]. However, the thermo-optic phase shift should also be wavelength-insensitve, which can be fundamentally difficult. While care has been taken to investigate the nonlinearity of the thermo-optic phase shift with temperature [10], the wavelength variation of this effect remains relatively unexplored.

The differential phase shift accumulated in an incremental distance dx of optical path length is not only proportional to the change in the refractive index Δn induced by the temperature rise ΔT, but is also inversely proportional to the optical wavelength λ, i.e., = (2π/λndx. Thus, to minimize the variation of the cumulative phase with wavelength, we need to increase the magnitude of Δn, so that integration over a long optical path length is not required to achieve π phase shift. This requires increasing the temperature range ΔT introduced by the heating source, and also minimizing the spread of the temperature away from the heating source along the optical path, so that the range of integration is minimized. Efficient and fast heating can be achieved by directly heating the silicon waveguide in close proximity to the optical mode [6, 9, 11, 12]. Reducing the heat spreading along the silicon waveguide can be achieved by varying the driving waveform at sub-microsecond time-scales, as discussed in Section 3.1.

Here, we demonstrate and characterize microsecond time-scale cross-bar digital switching of twenty 10 Gbit/s wavelength channels spanning the wavelength range from 1531.12 nm (ITU Channel 58) to 1563.05 nm (ITU Channel 18), using a thermo-optically driven wideband Mach-Zehnder interferometer, with an electrical power consumption of 15 mW and a 10%–90% switching time of 11 μs. In this report, we investigate the 2 × 2 switch as a building block of a larger switching fabric; therefore, optical coupling to and from the chip was not optimized and we incurred large losses (about 10 dB per coupler) when using lensed tapered fibers and multi-access nano-positioning stages. Electrical contacts to the chip were made using a multi-contact wedge. There was no need to stabilize the chip temperature in our demonstration (i.e., no power consumption for thermo-electric cooling).

2. Cascaded phase-shift thermo-optic switch

Our switch is based on the Mach-Zehnder interferometer (MZI), with adiabatic wide-band 3-dB splitters [9]. The switch was operated by heating one arm of the MZI shown in the Fig. 2, which, in general, causes an amplitude and phase change in that arm. When no DC voltage was applied to the contact pads labeled Vmod in Fig. 2, all the wavelengths exited the device in the “cross” port, i.e. the device is, to a good approximation, bias-voltage free. Upon applying a voltage to the contact pads shown in Fig. 2, all the wavelengths are switched over to emerge from the “bar” port. Unlike conventional thermo-optic MZIs, in which a metallic heater is fabricated at some distance from the silicon waveguide, and separated from it by a certain thickness of insulating oxide [13], current was driven through a dopant-implanted region of the waveguide itself, in close proximity to the optical mode. The waveguide was widened in certain regions from about 0.4 μm to about 1.0 μm, N-doped, and contacted with narrow N-doped silicon tethers connected to metal, through which an electrical current was directly injected in close proximity to the optical mode. The device was fabricated, using a fully CMOS-compatible process with 248-nm lithography at Sandia National Laboratories, on a 150-mm silicon-on-insulator wafer (250-nm active layer, 3-μm buried oxide). The waveguides were fully etched with nominal width × height dimensions of 400 × 230 nm2. Additional details are described elsewhere [9].

 

Fig. 2 A) Mach-Zehnder interferometer thermo-optic silicon-photonic cross-bar switch with bias voltage (Vbias, unused) and switching voltage (Vmod = 0 V or Vmod = 4.25 V) indicated. The region highlighted in yellow contains a bank of five phase shifters, as shown schematically in B. The optical field experiences a thermo-optic phase-shift in each of the widened arcs, the inside of which is doped to create a resistor. These resistive heaters are electrically wired in parallel, so as to reduce the switching voltage compared to a single heater. (The axial co-ordinate x is referred to in Section 3.1.)

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An earlier version of the device with a single phase-shift element in each arm has been previously reported [9, 12]. The MZI used here comprises a sequence of five thermo-optic phase shifters in each arm. As shown schematically in Fig. 2, the five resistors were electrically driven in parallel (Rtotal = 1.17 kΩ), thus reducing the drive voltage needed to achieve π phase shift from Vπ = 20 V for a single-element phase shifter to about Vπ = 4.25 V. Characterization measurements showed that heaters could withstand no more than about 40 mW of electrical power before damage, and that the five-element parallel-heater structure was noticeably more robust than the single-element heater. However, there is a concern regarding the increased insertion loss, since each of the five phase-shifting elements imparts some loss to the optical transmission in the “hot” state, when an electrical current passes in close proximity to the optical mode. This issue is investigated in the following section.

2.1. Device modeling and parameter extraction

The switch structure shown in Fig. 2(a) was modeled using transfer matrices. We label the optical field amplitude cross-coupling and through-coupling coefficients by κ and t, respectively [14]. The transfer function of the device can be calculated as a cascade of coupling (ℂ) and propagation (ℙ) matrices:

(barcross)=(tκ*κt*)(aeiϕ001)(tκ*κt*)(10)=(at2eiϕ+|κ|2aκteiϕt*κ)
where ϕ is a function of the thermally-induced phase shift, and hence, of the applied voltage. The parameter a in matrix ℙ represents the loss introduced by heating portions of one of the MZI arms, by driving an electrical current in close proximity to the optical mode, as shown in Fig. 2(b). We take a = 1 when no voltage is applied, and also assume that the lower-right term of ℙ (i.e., the unheated arm) has no thermally-induced amplitude attenuation. A common multiplicative factor (amplitude or phase) affecting all the terms of the ℙ matrix has no bearing on our parameter extraction algorithm described below, which is based on ratios of measured bar and cross transmissions.

The measured quantities were 10 · log10 |bar|2 and 10 · log10 |cross|2, as functions of wavelength, and for different voltages as shown in Fig. 3. As with all MZI devices, at certain voltages, the bar transmission was minimized and the cross transmission was maximized; in our device, this occured, to a good approximation, with no voltage applied, i.e., exp() was approximately −1, based on the algebraic form of Eq. (1). More precisely, we write exp()V=0 = −exp(0) where the small parameter δ0, a function of wavelength, represents a phase variation because it is generally impossible for lithography to achieve exact phase equality over a wide range of wavelengths (here, exceeding 30 nm). The bar transmission was maximized, and the cross transmission was minimized, when a voltage of Vπ ≡ 4.25 V was applied. In this case, exp() was approximately +1, and we write exp()V=Vπ = +exp(V).

 

Fig. 3 A) Transmission in the cross and bar output ports, at 0 V (crossoff and baroff), and Vπ = 4.25 V (crosson and baron) applied to the switching arm. Using the algorithm described in Section 2.1, the wavelength variation of the main device parameters were measured. There are two mathematical solutions, shown in black and green, and the physically meaningful ones are plotted in black. B) The coupling coefficient for the adiabatic 3-dB couplers (nominally 0.5). C) The loss induced in the “hot” state by the cascade of five phase shifters (a = 0.5 dB for five heaters implies 0.1 dB loss per heater section). D) The wavelength variations of the phase parameters which describe the phase slip from 0 or π phase. As shown by the flat lines for δ0, there is no wavelength variation of the phase slip when no voltage is applied; however, there is significant variation with wavelength in δV. Note that both branches of the |κ|2 solution result in the similar phase estimations for |δV|.

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From Eq. (1), the algebraic expressions for these quantities are:

baron=20log10|at2eiδV+|κ|2|;crossoff=20log10|κteiδ0t*κ|;baroff=20log10|t2eiδ0+|κ|2|;crosson=20log10|aκteiδVt*κ|.
To each of the expressions in Eq. (2) must be added the fiber-to-chip coupling losses at each interface. To factor out the latter, we defined four ratios: baron/baroff, crossoff/crosson, crossoff/baroff, and baron/crosson. In Fig. 3, we assumed |κ|2 + |t|2 = 1, i.e., the coupler sections were lossless, and relax this assumption in Fig. 4. We calculated the remaining four parameters (|κ|2, a, δ0, and δV) based on a Levenberg-Marquardt nonlinear fitting algorithm. We are interested in quantifying the wavelength variations of |κ|2, a, and the “phase slip” parameters δ0 and δV.

 

Fig. 4 A) Similar spectral variations were extracted for the coupling coefficient under the three separate assumptions: no coupler loss (|κ|2 + |t|2 = 1, shown in black), or increasing amounts of loss, (|κ|2 + |t|2 = 0.95, shown in blue, and |κ|2 + |t|2 = 0.90, shown in red). B) For these three assumptions, the differences in the loss induced in the “hot” state were not significant. C) The three assumptions also gave essentially the same estimate regarding the variation of the phase slip with wavelength in the “hot” state, |δV|. There is not much significance to the numerical value of the phase slip in the “cold state” |δ0| since a spectrally-flat phase slip can be easily compensated for by heating the bias arm; however, the wavelength-dependent variations in |δV| cannot be compensated by a bias voltage simultaneously at all wavelengths and pose a fundamental limitation to the extinction ratio of the switch.

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Figure 3 shows the extracted parameters for the measured device. There are two possible mathematical solutions at each wavelength for |κ|2 and for a, which are indicated by black and green colors [15]. The former was seen to be the physically-correct solution by performing an additional experiment: we measured the baron transmission (i.e., when voltage was applied to the heater) when the heater in the cross arm was heated, instead of in the bar arm. In this new configuration, the bar arm was left unheated. (With reference to Fig. 2(a), we switched the role of the Vbias and the Vmod electrical contacts, while leaving the optical input, bar and cross pathways as indicated.) The baron transmission was seen to increase (by 0.5 dB) at all wavelengths. The two measurements are represented by

baron|(barheat)=20log10|at2eiδV+|κ|2|baron|(crossheat)=20log10|t2+a|κ|2eiδV|.
Assuming that the heaters are identical (and 0 < a < 1), the observation that baron|(cross heat) was greater than baron|(bar heat) implies that |κ|2 < 0.5. (On the other hand, |κ|2 > 0.5 would result in the baron transmission decreasing when the cross arm was heated instead of the bar arm.)

As shown in Fig. 3(b), the nominally 3-dB couplers were, in fact, slightly imbalanced as a function of wavelength. However, even a 60-40 splitting imbalance has only a minor effect on crossoff, and mainly impacts baroff, i.e., reduces the contrast between baron and baroff. The ability to trim the splitting ratio may be useful in order to achieve higher contrast throughout a wide range of wavelengths.

Figure 3(c) quantifies the attenuation in the “hot” arm of the MZI with 20 · log10(a) ≈ −0.5 dB resulting from the cascade of five heaters in series. The loss of a single heater section is therefore about −0.1 dB, which is consistent with finite-element simulations [12]. This low loss suggests that a significant number of thermo-optic 2 × 2 switching elements can be cascaded, in order to build up a larger switching fabric.

A non-zero value of δ0 limits the amount of interferometric cancellation between −t2 and |κ|2 in the expression for baroff in Eq. (2), and also affects crossoff. Going beyond this, we are interested in the difference between δV and δ0, since ideally, the wavelength variation of both these quantities should be identical, if the heating-induced phase shift had no spectral dependency. However, Fig. 3(d) shows that the relative phase slip, i.e., the difference between |δV| and |δ0|, is not spectrally flat. This is not unexpected, because the voltage-induced phase shift is both a function of the change of the effective index change due to temperature and the wavelength (Δϕ ∝ Δneff/λ).

In Fig. 4, we investigate the assumption made earlier that |κ|2 + |t|2 = 1. Specifically, we made alternate assumptions that |κ|2 + |t|2 = 0.95 or |κ|2 + |t|2 = 0.90 (the latter implies nearly −0.5 dB loss per coupler, which is rather high for this fabrication technology). There was no observable difference in our estimate of a (heating induced loss), or of the wavelength variations of the phase-slip parameters (from 0 or π, respectively, when voltages of 0 and Vπ volts were applied). Similar to previous investigations of coupler loss [7], under the assumptions of increased coupler loss, there were corresponding small reductions in the estimated |κ|2 values, preserving the wavelength trends observed in Fig. 3. These results show that relaxing our earlier assumption that the couplers are lossless to practically-relevant coupler-loss numbers does not significantly change our conclusions regarding the wavelength variation of the switch parameters, or the approximate magnitude of the heating-induced loss.

Taken together, the results shown in Figs. 3(b)–3(d) suggest that the most significant reason for limited on-off contrast in Fig. 3(a) was the heating-induced spectral slip. Although |δ0| was flat over all wavelengths (since the couplers are adiabatic and the two arms of the MZI were fabricated with nearly exactly equal lengths), the wavelength variation of |δV| was clearly evident. For example, a phase imbalance of about 0.4 radians limits the on-off contrast to about 14 dB even if we were to take a = 1 and |κ|2 = |t|2. Referring back to Eq. (1), the bandwidth of this switch was limited by the properties of the matrix ℙ (the phase shifter) rather than the matrix ℂ (the couplers).

2.2. Device modeling of other silicon photonic carrier-injection switches

The algorithm we have developed in Section 2.1 can be used to study the performance of any silicon photonic 2 × 2 switch. To demonstrate this utility, we have taken the data for two other broadband, energy-efficient, silicon, electro-optic switches from the literature [16, 17]. In both these cases, current was driven through the silicon waveguide cross-section in close proximity to the optical mode; however, both relied on the refractive index shift due to the plasma dispersion of injected free carriers [18]. The design goals are the same as those of our thermo-optic switch: to minimize the on-state insertion loss and to achieve wideband operation with low crosstalk.

Figure 5 shows the results of running the extraction algorithm on the present, as well as on the literature, devices. Subsequent reconstruction of the experimentally measured transmission spectra, which makes use of the extracted device parameters, are also shown; this confirms the validity of the extracted parameters. In the case of the literature devices, a similar procedure, as discussed in the foregoing section, was performed to ascertain the correct solution branch. In the respective reports, data is also included for the on-state bar transmission when the input port is switched to the originally “unused” port (e.g. switching the input port to the unlabeled port in Fig. 2(a)). The correct solution branch is then identified by comparing the relative magnitudes of this second bar transmission to the on-state bar transmission in Fig. 5.

 

Fig. 5 Comparison of transmission spectra, intensity coupling coefficients |κ|2, on-state losss a, and phase slips δ0 and δV for three different devices. First column: data for the present device. Middle column: transmission data from Ref. [16]. Last column: transmission data from Ref. [17]. The parameters in each column; |κ|2, a, δ0, and δV; were extracted from the respective transmission spectra in the first row. For the sake of device-to-device comparison, each set of transmission spectra is normalized to the maximum of its respective crossoff response. Note that the abscissas are different column-to-column since the devices are optimized for different spectral regions.

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Several observations can be made by comparing the columns of Fig. 5. The slightly improved transmission contrast of the literature devices occurs as a result of values of |κ|2 closer to 0.5 as well as more favorable phase slips. In the present device, the improved tracking of the crosson response to the baroff response occurs because of less on-state loss. In all three devices, the presence of loss limits the attainable transmission contrast as per Eq. 2.

The measured insertion loss a (in units of decibels) for a single 2 × 2 switch element can be used to estimate scalability. For example, the overall insertion loss L (in units of decibels, excluding waveguide crossing loss) in an N × N Cantor-type switch architecture scales with the number of ports N as

L=2(log2(N1)+log2(log2N))a.
For N = 64, the foregoing yields 8.5 dB of insertion loss for the current-driven thermo-optic switch reported here, and 17 dB [16] and 29 dB [17] for the carrier-injection switches.

3. Switching time constant and digital driving using voltage pulses

Large scale switching fabrics constructed out of 2 × 2 building blocks will require many electrical control signals. It will be more convenient if these signals can be obtained from digital ports of an FPGA or microcontroller, e.g., via pulse width modulation, rather than analog output ports. However, a digital driving waveform potentially causes a concern with ringing, e.g., as is seen in the current MEMS implementation of switching in MORDIA [3]. In this section, we discuss how to avoid ringing when driving the heater control using on-off voltage pulses. Experimental measurements include eye patterns and bit-error-rate sensitivity measurements of switching with both analog and digital drives.

3.1. Digital heating: analytic formulation

The goal of this analysis is to obtain insight into the physical mechanisms governing a compact heater driven by a time-varying waveform. For reasons discussed in Section 2.1, the length of the heated section should be kept short. The silicon waveguide itself is narrow, and the surrounding oxide is a relatively poor conductor of heat. For these reasons, it is reasonable to approximate each heated section of the waveguide by a one-dimensional model, with x being the spatial coordinate along the light path, and x = 0 defining the location of the heat source (see Fig. 2(b)). Light propagating past the hot spot picks up a phase around x = 0 over a length scale that is defined by the temperature profile. We will show this length varies inversely with the square root of the driving frequency.

Because of the symmetry of the x coordinate, we can solve for the heat distribution u(x, t) in the semi-infinite region x > 0 only, and extend the solution to negative x. We seek the solution to the homogeneous diffusion equation,

ut=k2ux2,withu(0,t)=g(t),u(x,0)=0.
where k is the thermal diffusivity of silicon (the thermal conductivity divided by the product of the mass density and the specific heat capacity) and g(t) is the driving waveform, which is proportional to the product of the square of the electrical current and the electrical resistance, at x = 0. We expand g(t) in a Fourier series,
g(t)=nAneiΩnt,
where, since g(t) is a digital (e.g., pulse-width modulated) waveform with period T, An ∝ 1/n and Ωn = n2π/T.

We can solve Eq. (5) by expanding u(x, t) in normal modes, paralleling Eq. (6), and taking the Fourier sine transform of each term, defined as u˜n(ω,t)=(2/π)0un(x,t)sinωxdx, resulting in

du˜ndt+kω2u˜n=2πkωAneiΩnt.
Multiplying both sides by exp(2t) and integrating, we obtain,
u˜n(ω,t)=[u˜n(ω,0)+i2πkωAnπΩnikω2]ekω2t+2πωAnω2+iΩn/keiΩnt.
Since the first term on the right-hand side quickly decays to zero, we inverse-transform the second term, resulting in
un(x,t)Anexp(Ωn2kx)cos(ΩntΩn2kx).
Thus, for each harmonic mode of the driving waveform, the heat spreads out to a distance of about Ln2k/Ωn on either side of the origin. Based on k (silicon) = 0.8 cm2/s, 2L1 = 2.6 μm for the n = 1 Fourier component for an alternating current at 15 MHz, as used in the experiment described in Section 3.2. In general, the effective heater length (and hence the thermally-induced phase shift picked up by the light as it propagates past the hot spot) can be controlled not only by amplitude but also by frequency, and by shaping the waveform, i.e., the amplitude coefficients in the harmonic mode expansion.

In this paper, to achieve error-free switching of 10 Gbps data, we are only interested in the DC term and inhibition of ringing. For higher Fourier components, Lnn−1/2, and further, Ann−1, and only odd integers contribute in the case of a pulse-width modulated square wave i.e., the effective length and amplitude of the heater for the higher harmonic components is too small to affect light propagation. As such, we may expect that for AC frequencies that are high enough, there is no Gibbs phenomenon associated with a digital current drive, whereas some ripples may be seen if the frequency is reduced. In the latter case, the heat waves can spread out over a longer distance, and thus, interact with the optical field over a longer length, imparting a harmonic oscillation to the optical field. This is indeed seen in the experimental traces shown in Fig. 6, where some ringing was observed at 5 MHz, but not at 15 MHz.

 

Fig. 6 Pulse-width modulation of a digital heater drive (10 V amplitude), with different duty cycles as indicated by the percentages. A) Using a slow (10 kHz) drive, the rise and fall time constants were measured to be 11.1 μs and 11.3 μs, respectively, at 50% duty cycle. B, C) Here, both the drive frequencies were greater than the inverse of the time constants. The vertical axis shows the cross-state transmission when a heating voltage was applied, i.e., the desirable transmission was as close to 0 as possible with minimum ripple. The results show that at the lower frequency (B, 5 MHz), the residual ripple at the frequency of the drive signal was greater than at a higher frequency (C, 15 MHz), in accordance with the discussion in Section 3.1.

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3.2. Experimental verification

Figure 7(a) shows a typical eye pattern of a single 10 Gbit/s channel, demonstrating that the same bar switching behavior was achieved by driving the heaters with a 10 V, 42% duty cycle, rectangular waveform at 15 MHz, thus mimicking Vπ = 4.2 V. In Fig. 7(b), bit-error-rate sensitivity curves versus power are shown in the three cases, at a representative wavelength of 1550 nm, using a 231 − 1 pseudo-random bit sequence. There was no observable penalty difference between the DC drive and pulsed-drive bar states. The bar states show slightly better sensitivity curves than the cross state. The cause for this difference is still under investigation; one possible factor is that the switching voltage Vπ to enable bar transmission was fine-tuned to its optimum value, whereas no voltage was applied to the MZI in the cross state, resulting in a small phase-slip in the latter case at the measured wavelength.

 

Fig. 7 A) 10 Gbit/s eye patterns of cross and bar states (analog and digital drives) for a selected channel at 1558 nm. B) Bit-error-rate (BER) power sensitivity curves, showing no penalty between analog and digital voltages for switching. The optical power labeled on the horizontal axis was measured at the detector.

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4. Performance in the network

The device was tested during live operation of the 20-wavelength network, i.e., all wavelengths “loading” the device simultaneously. The network’s wavelength channels all lie within the highest transmission-contrast region of Fig. 3(a). The transmitters were commercial DWDM SFP+ form-factor modules transmitting 10 Gbit/s data, fed from computer servers, in 9000-bit-length TCP packets over single-mode fiber at a power level between 1–3 dBm. Since no line-by-line equalization of power levels in the ring is performed under normal operating conditions, this results in non-uniform channel powers, as shown in Fig. 1(c). Figure 8 shows open eyes for all indicated channels (20 × 10 Gbps) in both the cross and bar states. As there was no difference between the bar (Fig. 8(a)) and cross (Fig. 8(b)) eyes for all channels, the channel-to-channel variations can be attributed to the normal differences in circulating power in the network itself.

 

Fig. 8 10 Gbit eye patterns (labeled by ITU-T G.694.1 DWDM channel number) in the bar (A) and cross (B) states for server-driven data. Channel-to-channel differences correspond to normal variations in the ring (see Fig. 1(c)). C) For a single channel at 1558 nm, Q-factor versus received power curves for the cross and bar states are nearly identical. Horizontal red dashed lines ‘A’ and ‘B’ refer to estimated packet loss rate of 10−4 and estimated BER of 10−12. D) The histogram of Q-factors, with all channels above the A threshold.

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Further evidence of the satisfactory performance of the silicon switch was obtained from the Q versus received power measurements, where Q is the signal-to-noise ratio measured from each eye pattern. In these measurements, a linear PIN detector was used with 15 GHz bandwidth, 300 V/W responsivity, and noise equivalent power NEP = 30 pW/Hz1/2, with optical pre-amplification using an erbium-doped fiber amplifier and ASE filtering. As shown in Fig. 8(c), both sensitivity lines have very similar slopes. The dashed red line labeled B in Fig. 8(c) represents a bit-error-rate (BER) of 10−12, assuming Gaussian statistics, and the line labeled A represents a packet loss probability p = 1 − (1 − BER)L = 10−4, where L = 9000 is the number of bits in a packet. All the eyes measured in Fig. 8(a) and Fig. 8(b) were above this threshold, an order-of-magnitude lower (better) than the typical packet error rate under normal software operating conditions or due to congestion, buffer overflows, TCP incast, etc.

5. Conclusion

This paper summarized our testing and component-level modeling of an energy-efficient wideband silicon photonic switching element used in a wavelength-division multiplexed ring network, whose good performance imposes no penalty on the normal operating error threshold of the network. Our parameter-extraction method shows how to relate transmission measurements of switches (which are commonly reported) to the intrinsic device parameters (which are less commonly reported). The extracted parameters of this thermo-optic switch were compared to those of two recently-published electro-optic switches. In all these cases, an electrical current is driven in close proximity to the optical mode, in order to increase the efficiency and reduce the switching speed of the underlying physical phenomena. Minimizing wavelength variations of the passive couplers (e.g. by improving the adiabatic coupler design or by using MZI splitters [16], multi-mode interference couplers [17], or three-waveguide couplers [19, 20]), as well as of the phase-shifting mechanism itself, will be important to achieve truly wideband crossbar switching and fully exploit the spectral transparency advantage that optical switching has over electronic switching.

In our demonstration, twenty server-driven 10 Gbit/s wavelengths between 1531 nm and 1563 nm with TCP packets were loaded onto the device and simultaneously switched between cross and bar ports in a footprint of 0.6 mm × 0.05 mm. Although five heating elements were cascaded and driven in parallel to reduce the required voltage, the cascaded losses in the thermo-optic “hot” arm were only about 0.5 dB. The power consumption of this “fat pipe” switch is about 15 mW, and no thermo-optic cooling or temperature stabilization was required. The measured on-off switching time constant of the chip-based switch was 11 μs, which is about the same as the loss-of-light time in the current bulk-optics implementation of the MORDIA network architecture [3]. Possible improvements in the device performance may be made by reducing the contact resistance [21], or by implementing a dual-drive operation [22, 23]. In summary, we believe this compact, broadband, microsecond-scale switch can be a low insertion-loss building block for scalable switching fabrics using silicon photonics.

Acknowledgments

The authors acknowledge funding support from the NSF CIAN ERC EEC-0812072 and NSF MRI ECCS 1229677. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

References and links

1. A. Vahdat, H. Liu, X. Zhao, and C. Johnson, “The emerging optical data center,” in Proc. Optical Fiber Communication Conf. (2011), paper OTuH2. [CrossRef]  

2. G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338. [CrossRef]  

3. N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012). [CrossRef]  

4. Y. O. Noh, H. J. Lee, Y. H. Won, and M. C Oh, “Polymer waveguide thermo-optic switches with −70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006). [CrossRef]  

5. B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photonics Technol. Lett. 20, 767–769 (2008). [CrossRef]  

6. M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Proc. Conf. Lasers and Electro-Optics (2009), paper CPDB10. [CrossRef]  

7. R. Aguinaldo, Y. Shen, and S. Mookherjea, “Large dispersion of silicon directional couplers obtained via wideband microring parametric characterization,” IEEE Photonics Technol. Lett. , 24, 1242–1244 (2012). [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. C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3. [CrossRef]  

10. G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advances in thermo-optical switches: principles, materials, design, and device structure,” Opt. Eng. 50, 071112 (2011). [CrossRef]  

11. M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2514–2516 (2004). [CrossRef]  

12. 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]  

13. R. L. Espinola, M. C. Tsai, J. Yardley, and R. M. Osgood Jr., “Fast and low power thermo-optic switch on thin silicon-on-insulator,” IEEE Photonics Technol. Lett. 15, 1366–1368 (2003). [CrossRef]  

14. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6 (Oxford University, 2007), Chap. 4.

15. For example, by examining the expression for ‘baroff’ in Eq. (2) in the simple case when δ0= 0, we see that −t2+ |κ|2(for |κ| > 0.5 and t < 0.5) and +t2 − |κ|2 (for |κ| < 0.5 and t > 0.5) give the same numerical value.

16. J. Van Campenhout, W. M. J. Green, S. Assefa, and Y. A. Vlasov, “Low-power, 2×2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks,” Opt. Express 17, 24020–24029 (2009). [CrossRef]  

17. P. Dong, S. Liao, H. Liang, R. Shafiiha, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Submilliwatt, ultrafast and broadband electro-optic silicon switches,” Opt. Express 18, 25225–25231 (2010). [CrossRef]   [PubMed]  

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

19. P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. 168, 349–354 (1999). [CrossRef]  

20. G. Calò, A. D’Orazio, and V. Petruzzelli, “Broadband Mach-Zehnder switch for photonic networks on chip,” J. Lightwave Technol. 30, 944–952 (2012). [CrossRef]  

21. W. Zortman, A. Lentine, D. Trotter, and M. Watts, “Integrated CMOS comaptible low power 10Gbps silicon photonic heater modulator,” in Proc. Optical Fiber Communication Conf. (2012), paper OW4I.5. [CrossRef]  

22. M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2039–2041 (2004). [CrossRef]  

23. Y. Li, J. Yu, S. Chen, Y. Li, and Y. Chen, “Submicrosecond rearrangeable nonblocking silicon-on-insulator thermo-optic 4X4 switch matrix,” Opt. Lett. 32, 603–604 (2007). [CrossRef]   [PubMed]  

References

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  1. A. Vahdat, H. Liu, X. Zhao, and C. Johnson, “The emerging optical data center,” in Proc. Optical Fiber Communication Conf. (2011), paper OTuH2.
    [Crossref]
  2. G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338.
    [Crossref]
  3. N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
    [Crossref]
  4. Y. O. Noh, H. J. Lee, Y. H. Won, and M. C Oh, “Polymer waveguide thermo-optic switches with −70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006).
    [Crossref]
  5. B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photonics Technol. Lett. 20, 767–769 (2008).
    [Crossref]
  6. M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Proc. Conf. Lasers and Electro-Optics (2009), paper CPDB10.
    [Crossref]
  7. R. Aguinaldo, Y. Shen, and S. Mookherjea, “Large dispersion of silicon directional couplers obtained via wideband microring parametric characterization,” IEEE Photonics Technol. Lett.,  24, 1242–1244 (2012).
    [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. C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3.
    [Crossref]
  10. G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advances in thermo-optical switches: principles, materials, design, and device structure,” Opt. Eng. 50, 071112 (2011).
    [Crossref]
  11. M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2514–2516 (2004).
    [Crossref]
  12. 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]
  13. R. L. Espinola, M. C. Tsai, J. Yardley, and R. M. Osgood, “Fast and low power thermo-optic switch on thin silicon-on-insulator,” IEEE Photonics Technol. Lett. 15, 1366–1368 (2003).
    [Crossref]
  14. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6 (Oxford University, 2007), Chap. 4.
  15. For example, by examining the expression for ‘baroff’ in Eq. (2) in the simple case when δ0= 0, we see that −t2+ |κ|2(for |κ| > 0.5 and t < 0.5) and +t2 − |κ|2 (for |κ| < 0.5 and t > 0.5) give the same numerical value.
  16. J. Van Campenhout, W. M. J. Green, S. Assefa, and Y. A. Vlasov, “Low-power, 2×2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks,” Opt. Express 17, 24020–24029 (2009).
    [Crossref]
  17. P. Dong, S. Liao, H. Liang, R. Shafiiha, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Submilliwatt, ultrafast and broadband electro-optic silicon switches,” Opt. Express 18, 25225–25231 (2010).
    [Crossref] [PubMed]
  18. R. Soref and B. Bennett, “Electrooptilcal effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
    [Crossref]
  19. P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. 168, 349–354 (1999).
    [Crossref]
  20. G. Calò, A. D’Orazio, and V. Petruzzelli, “Broadband Mach-Zehnder switch for photonic networks on chip,” J. Lightwave Technol. 30, 944–952 (2012).
    [Crossref]
  21. W. Zortman, A. Lentine, D. Trotter, and M. Watts, “Integrated CMOS comaptible low power 10Gbps silicon photonic heater modulator,” in Proc. Optical Fiber Communication Conf. (2012), paper OW4I.5.
    [Crossref]
  22. M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2039–2041 (2004).
    [Crossref]
  23. Y. Li, J. Yu, S. Chen, Y. Li, and Y. Chen, “Submicrosecond rearrangeable nonblocking silicon-on-insulator thermo-optic 4X4 switch matrix,” Opt. Lett. 32, 603–604 (2007).
    [Crossref] [PubMed]

2013 (1)

2012 (3)

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

R. Aguinaldo, Y. Shen, and S. Mookherjea, “Large dispersion of silicon directional couplers obtained via wideband microring parametric characterization,” IEEE Photonics Technol. Lett.,  24, 1242–1244 (2012).
[Crossref]

G. Calò, A. D’Orazio, and V. Petruzzelli, “Broadband Mach-Zehnder switch for photonic networks on chip,” J. Lightwave Technol. 30, 944–952 (2012).
[Crossref]

2011 (1)

G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advances in thermo-optical switches: principles, materials, design, and device structure,” Opt. Eng. 50, 071112 (2011).
[Crossref]

2010 (2)

2009 (1)

2008 (1)

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photonics Technol. Lett. 20, 767–769 (2008).
[Crossref]

2007 (1)

2006 (1)

Y. O. Noh, H. J. Lee, Y. H. Won, and M. C Oh, “Polymer waveguide thermo-optic switches with −70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006).
[Crossref]

2004 (2)

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2514–2516 (2004).
[Crossref]

M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2039–2041 (2004).
[Crossref]

2003 (1)

R. L. Espinola, M. C. Tsai, J. Yardley, and R. M. Osgood, “Fast and low power thermo-optic switch on thin silicon-on-insulator,” IEEE Photonics Technol. Lett. 15, 1366–1368 (2003).
[Crossref]

1999 (1)

P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. 168, 349–354 (1999).
[Crossref]

1987 (1)

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

Aalto, T.

M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2039–2041 (2004).
[Crossref]

Aguinaldo, R.

R. Aguinaldo, Y. Shen, and S. Mookherjea, “Large dispersion of silicon directional couplers obtained via wideband microring parametric characterization,” IEEE Photonics Technol. Lett.,  24, 1242–1244 (2012).
[Crossref]

Andersen, D. G.

G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338.
[Crossref]

Asghari, M.

Assefa, S.

Bennett, B.

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

Bergman, K.

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photonics Technol. Lett. 20, 767–769 (2008).
[Crossref]

Biberman, A.

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photonics Technol. Lett. 20, 767–769 (2008).
[Crossref]

Biswas, J. C.

P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. 168, 349–354 (1999).
[Crossref]

Calò, G.

Chen, S.

Chen, Y.

Coppola, G.

G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advances in thermo-optical switches: principles, materials, design, and device structure,” Opt. Eng. 50, 071112 (2011).
[Crossref]

D’Orazio, A.

Das, S.

P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. 168, 349–354 (1999).
[Crossref]

DeRose, C.

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]

C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3.
[Crossref]

Dong, P.

P. Dong, S. Liao, H. Liang, R. Shafiiha, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Submilliwatt, ultrafast and broadband electro-optic silicon switches,” Opt. Express 18, 25225–25231 (2010).
[Crossref] [PubMed]

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photonics Technol. Lett. 20, 767–769 (2008).
[Crossref]

Espinola, R. L.

R. L. Espinola, M. C. Tsai, J. Yardley, and R. M. Osgood, “Fast and low power thermo-optic switch on thin silicon-on-insulator,” IEEE Photonics Technol. Lett. 15, 1366–1368 (2003).
[Crossref]

Fainman, Y.

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

Farrington, N.

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

Feng, D.

Ford, J.

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

Forencich, A.

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

Ganguly, P.

P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. 168, 349–354 (1999).
[Crossref]

Geis, M. W.

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2514–2516 (2004).
[Crossref]

Green, W. M. J.

Harjanne, M.

M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2039–2041 (2004).
[Crossref]

Hasama, T.

Heimala, P.

M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2039–2041 (2004).
[Crossref]

Iodice, M.

G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advances in thermo-optical switches: principles, materials, design, and device structure,” Opt. Eng. 50, 071112 (2011).
[Crossref]

Ishikawa, H.

Johnson, C.

A. Vahdat, H. Liu, X. Zhao, and C. Johnson, “The emerging optical data center,” in Proc. Optical Fiber Communication Conf. (2011), paper OTuH2.
[Crossref]

Kaminsky, M.

G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338.
[Crossref]

Kapulainen, M.

M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2039–2041 (2004).
[Crossref]

Kawashima, H.

Kekatpure, R.

C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3.
[Crossref]

Kintaka, K.

Kozuch, M.

G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338.
[Crossref]

Krishnamoorthy, A. V.

Lahiri, S. K.

P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. 168, 349–354 (1999).
[Crossref]

Lee, B. G.

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photonics Technol. Lett. 20, 767–769 (2008).
[Crossref]

Lee, H. J.

Y. O. Noh, H. J. Lee, Y. H. Won, and M. C Oh, “Polymer waveguide thermo-optic switches with −70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006).
[Crossref]

Lentine, A.

W. Zortman, A. Lentine, D. Trotter, and M. Watts, “Integrated CMOS comaptible low power 10Gbps silicon photonic heater modulator,” in Proc. Optical Fiber Communication Conf. (2012), paper OW4I.5.
[Crossref]

Li, G.

Li, Y.

Liang, H.

Liao, S.

Lipson, M.

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photonics Technol. Lett. 20, 767–769 (2008).
[Crossref]

Liu, H.

A. Vahdat, H. Liu, X. Zhao, and C. Johnson, “The emerging optical data center,” in Proc. Optical Fiber Communication Conf. (2011), paper OTuH2.
[Crossref]

Luck, D. L.

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Proc. Conf. Lasers and Electro-Optics (2009), paper CPDB10.
[Crossref]

Lyszczarz, T. M.

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2514–2516 (2004).
[Crossref]

Mookherjea, S.

R. Aguinaldo, Y. Shen, and S. Mookherjea, “Large dispersion of silicon directional couplers obtained via wideband microring parametric characterization,” IEEE Photonics Technol. Lett.,  24, 1242–1244 (2012).
[Crossref]

Ng, T. S. E.

G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338.
[Crossref]

Nielson, G.

C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3.
[Crossref]

Nielson, G. N.

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]

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Proc. Conf. Lasers and Electro-Optics (2009), paper CPDB10.
[Crossref]

Noh, Y. O.

Y. O. Noh, H. J. Lee, Y. H. Won, and M. C Oh, “Polymer waveguide thermo-optic switches with −70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006).
[Crossref]

Oh, M. C

Y. O. Noh, H. J. Lee, Y. H. Won, and M. C Oh, “Polymer waveguide thermo-optic switches with −70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006).
[Crossref]

Osgood, R. M.

R. L. Espinola, M. C. Tsai, J. Yardley, and R. M. Osgood, “Fast and low power thermo-optic switch on thin silicon-on-insulator,” IEEE Photonics Technol. Lett. 15, 1366–1368 (2003).
[Crossref]

Papagiannaki, K.

G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338.
[Crossref]

Papen, G.

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

Petruzzelli, V.

Porter, G.

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

Rendina, I.

G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advances in thermo-optical switches: principles, materials, design, and device structure,” Opt. Eng. 50, 071112 (2011).
[Crossref]

Ryan, M.

G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338.
[Crossref]

Shafiiha, R.

Shen, Y.

R. Aguinaldo, Y. Shen, and S. Mookherjea, “Large dispersion of silicon directional couplers obtained via wideband microring parametric characterization,” IEEE Photonics Technol. Lett.,  24, 1242–1244 (2012).
[Crossref]

Shoji, Y.

Sirleto, L.

G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advances in thermo-optical switches: principles, materials, design, and device structure,” Opt. Eng. 50, 071112 (2011).
[Crossref]

Soref, R.

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

Spector, S. J.

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2514–2516 (2004).
[Crossref]

Suda, S.

Sun, J.

Sun, P.-C.

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

Trotter, D.

C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3.
[Crossref]

W. Zortman, A. Lentine, D. Trotter, and M. Watts, “Integrated CMOS comaptible low power 10Gbps silicon photonic heater modulator,” in Proc. Optical Fiber Communication Conf. (2012), paper OW4I.5.
[Crossref]

Trotter, D. C.

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]

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Proc. Conf. Lasers and Electro-Optics (2009), paper CPDB10.
[Crossref]

Tsai, M. C.

R. L. Espinola, M. C. Tsai, J. Yardley, and R. M. Osgood, “Fast and low power thermo-optic switch on thin silicon-on-insulator,” IEEE Photonics Technol. Lett. 15, 1366–1368 (2003).
[Crossref]

Vahdat, A.

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

A. Vahdat, H. Liu, X. Zhao, and C. Johnson, “The emerging optical data center,” in Proc. Optical Fiber Communication Conf. (2011), paper OTuH2.
[Crossref]

Van Campenhout, J.

Vlasov, Y. A.

Wang, G.

G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338.
[Crossref]

Watts, M.

C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3.
[Crossref]

W. Zortman, A. Lentine, D. Trotter, and M. Watts, “Integrated CMOS comaptible low power 10Gbps silicon photonic heater modulator,” in Proc. Optical Fiber Communication Conf. (2012), paper OW4I.5.
[Crossref]

Watts, M. R.

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]

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Proc. Conf. Lasers and Electro-Optics (2009), paper CPDB10.
[Crossref]

Williamson, R. C.

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2514–2516 (2004).
[Crossref]

Won, Y. H.

Y. O. Noh, H. J. Lee, Y. H. Won, and M. C Oh, “Polymer waveguide thermo-optic switches with −70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006).
[Crossref]

Yardley, J.

R. L. Espinola, M. C. Tsai, J. Yardley, and R. M. Osgood, “Fast and low power thermo-optic switch on thin silicon-on-insulator,” IEEE Photonics Technol. Lett. 15, 1366–1368 (2003).
[Crossref]

Yariv, A.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6 (Oxford University, 2007), Chap. 4.

Yeh, P.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6 (Oxford University, 2007), Chap. 4.

Young, R.

C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3.
[Crossref]

Young, R. W.

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]

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Proc. Conf. Lasers and Electro-Optics (2009), paper CPDB10.
[Crossref]

Yu, J.

Zhao, X.

A. Vahdat, H. Liu, X. Zhao, and C. Johnson, “The emerging optical data center,” in Proc. Optical Fiber Communication Conf. (2011), paper OTuH2.
[Crossref]

Zheng, X.

Zortman, W.

W. Zortman, A. Lentine, D. Trotter, and M. Watts, “Integrated CMOS comaptible low power 10Gbps silicon photonic heater modulator,” in Proc. Optical Fiber Communication Conf. (2012), paper OW4I.5.
[Crossref]

C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3.
[Crossref]

Zortman, W. A.

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Proc. Conf. Lasers and Electro-Optics (2009), paper CPDB10.
[Crossref]

ACM SIGCOMM Computer Commun. Rev. (1)

N. Farrington, G. Porter, P.-C. Sun, A. Forencich, J. Ford, Y. Fainman, G. Papen, and A. Vahdat, “A demonstration of ultra-low-latency data center optical circuit switching,” ACM SIGCOMM Computer Commun. Rev. 42, 95–96 (2012).
[Crossref]

IEEE J. Quantum Electron. (1)

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

IEEE Photonics Technol. Lett. (5)

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2514–2516 (2004).
[Crossref]

R. L. Espinola, M. C. Tsai, J. Yardley, and R. M. Osgood, “Fast and low power thermo-optic switch on thin silicon-on-insulator,” IEEE Photonics Technol. Lett. 15, 1366–1368 (2003).
[Crossref]

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photonics Technol. Lett. 20, 767–769 (2008).
[Crossref]

R. Aguinaldo, Y. Shen, and S. Mookherjea, “Large dispersion of silicon directional couplers obtained via wideband microring parametric characterization,” IEEE Photonics Technol. Lett.,  24, 1242–1244 (2012).
[Crossref]

M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermooptic switch,” IEEE Photonics Technol. Lett. 16, 2039–2041 (2004).
[Crossref]

J. Lightwave Technol. (1)

Opt. Commun. (2)

Y. O. Noh, H. J. Lee, Y. H. Won, and M. C Oh, “Polymer waveguide thermo-optic switches with −70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006).
[Crossref]

P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. 168, 349–354 (1999).
[Crossref]

Opt. Eng. (1)

G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advances in thermo-optical switches: principles, materials, design, and device structure,” Opt. Eng. 50, 071112 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Other (7)

W. Zortman, A. Lentine, D. Trotter, and M. Watts, “Integrated CMOS comaptible low power 10Gbps silicon photonic heater modulator,” in Proc. Optical Fiber Communication Conf. (2012), paper OW4I.5.
[Crossref]

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6 (Oxford University, 2007), Chap. 4.

For example, by examining the expression for ‘baroff’ in Eq. (2) in the simple case when δ0= 0, we see that −t2+ |κ|2(for |κ| > 0.5 and t < 0.5) and +t2 − |κ|2 (for |κ| < 0.5 and t > 0.5) give the same numerical value.

C. DeRose, M. Watts, R. Young, D. Trotter, G. Nielson, W. Zortman, and R. Kekatpure, “Low power and broadband 2 X 2 silicon thermo-optic switch,” in Proc. Optical Fiber Communication Conf. (2011), paper OThM3.
[Crossref]

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Proc. Conf. Lasers and Electro-Optics (2009), paper CPDB10.
[Crossref]

A. Vahdat, H. Liu, X. Zhao, and C. Johnson, “The emerging optical data center,” in Proc. Optical Fiber Communication Conf. (2011), paper OTuH2.
[Crossref]

G. Wang, D. G. Andersen, M. Kaminsky, K. Papagiannaki, T. S. E. Ng, M. Kozuch, and M. Ryan, “c-Through: Part-time optics in data centers,” in Proc. ACM SIGCOMM ‘10(2010), pp. 327–338.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

A) Hardware for the optical circuit-switched multi-wavelength MORDIA ring network at UC San Diego, including data servers, optical amplifiers (EDFAs), optical spectrum analyzer (OSA) for power monitoring, and hardware for wideband wavelength-selective switching (WSS). There are six nodes and four host stations per node. B) Schematic of the ring network topology, in which any of the nodes can access the full bandwidth of the ring (about 30-nm wavelength span). C) Optical spectrum of 20 data channels, each carrying 10-Gbit/s data, used in the switching demonstration (some extraneous channels, not carrying data, or at long wavelengths that lie outside the range of the tunable filters used to measure the individual eye patterns, also propagate through the chip but were not measured here).

Fig. 2
Fig. 2

A) Mach-Zehnder interferometer thermo-optic silicon-photonic cross-bar switch with bias voltage (Vbias, unused) and switching voltage (Vmod = 0 V or Vmod = 4.25 V) indicated. The region highlighted in yellow contains a bank of five phase shifters, as shown schematically in B. The optical field experiences a thermo-optic phase-shift in each of the widened arcs, the inside of which is doped to create a resistor. These resistive heaters are electrically wired in parallel, so as to reduce the switching voltage compared to a single heater. (The axial co-ordinate x is referred to in Section 3.1.)

Fig. 3
Fig. 3

A) Transmission in the cross and bar output ports, at 0 V (crossoff and baroff), and Vπ = 4.25 V (crosson and baron) applied to the switching arm. Using the algorithm described in Section 2.1, the wavelength variation of the main device parameters were measured. There are two mathematical solutions, shown in black and green, and the physically meaningful ones are plotted in black. B) The coupling coefficient for the adiabatic 3-dB couplers (nominally 0.5). C) The loss induced in the “hot” state by the cascade of five phase shifters (a = 0.5 dB for five heaters implies 0.1 dB loss per heater section). D) The wavelength variations of the phase parameters which describe the phase slip from 0 or π phase. As shown by the flat lines for δ0, there is no wavelength variation of the phase slip when no voltage is applied; however, there is significant variation with wavelength in δV. Note that both branches of the |κ|2 solution result in the similar phase estimations for |δV|.

Fig. 4
Fig. 4

A) Similar spectral variations were extracted for the coupling coefficient under the three separate assumptions: no coupler loss (|κ|2 + |t|2 = 1, shown in black), or increasing amounts of loss, (|κ|2 + |t|2 = 0.95, shown in blue, and |κ|2 + |t|2 = 0.90, shown in red). B) For these three assumptions, the differences in the loss induced in the “hot” state were not significant. C) The three assumptions also gave essentially the same estimate regarding the variation of the phase slip with wavelength in the “hot” state, |δV|. There is not much significance to the numerical value of the phase slip in the “cold state” |δ0| since a spectrally-flat phase slip can be easily compensated for by heating the bias arm; however, the wavelength-dependent variations in |δV| cannot be compensated by a bias voltage simultaneously at all wavelengths and pose a fundamental limitation to the extinction ratio of the switch.

Fig. 5
Fig. 5

Comparison of transmission spectra, intensity coupling coefficients |κ|2, on-state losss a, and phase slips δ0 and δV for three different devices. First column: data for the present device. Middle column: transmission data from Ref. [16]. Last column: transmission data from Ref. [17]. The parameters in each column; |κ|2, a, δ0, and δV; were extracted from the respective transmission spectra in the first row. For the sake of device-to-device comparison, each set of transmission spectra is normalized to the maximum of its respective crossoff response. Note that the abscissas are different column-to-column since the devices are optimized for different spectral regions.

Fig. 6
Fig. 6

Pulse-width modulation of a digital heater drive (10 V amplitude), with different duty cycles as indicated by the percentages. A) Using a slow (10 kHz) drive, the rise and fall time constants were measured to be 11.1 μs and 11.3 μs, respectively, at 50% duty cycle. B, C) Here, both the drive frequencies were greater than the inverse of the time constants. The vertical axis shows the cross-state transmission when a heating voltage was applied, i.e., the desirable transmission was as close to 0 as possible with minimum ripple. The results show that at the lower frequency (B, 5 MHz), the residual ripple at the frequency of the drive signal was greater than at a higher frequency (C, 15 MHz), in accordance with the discussion in Section 3.1.

Fig. 7
Fig. 7

A) 10 Gbit/s eye patterns of cross and bar states (analog and digital drives) for a selected channel at 1558 nm. B) Bit-error-rate (BER) power sensitivity curves, showing no penalty between analog and digital voltages for switching. The optical power labeled on the horizontal axis was measured at the detector.

Fig. 8
Fig. 8

10 Gbit eye patterns (labeled by ITU-T G.694.1 DWDM channel number) in the bar (A) and cross (B) states for server-driven data. Channel-to-channel differences correspond to normal variations in the ring (see Fig. 1(c)). C) For a single channel at 1558 nm, Q-factor versus received power curves for the cross and bar states are nearly identical. Horizontal red dashed lines ‘A’ and ‘B’ refer to estimated packet loss rate of 10−4 and estimated BER of 10−12. D) The histogram of Q-factors, with all channels above the A threshold.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

( bar cross ) = ( t κ * κ t * ) ( a e i ϕ 0 0 1 ) ( t κ * κ t * ) ( 1 0 ) = ( a t 2 e i ϕ + | κ | 2 a κ t e i ϕ t * κ )
bar on = 20 log 10 | a t 2 e i δ V + | κ | 2 | ; cross off = 20 log 10 | κ t e i δ 0 t * κ | ; bar off = 20 log 10 | t 2 e i δ 0 + | κ | 2 | ; cross on = 20 log 10 | a κ t e i δ V t * κ | .
bar on | ( bar heat ) = 20 log 10 | a t 2 e i δ V + | κ | 2 | bar on | ( cross heat ) = 20 log 10 | t 2 + a | κ | 2 e i δ V | .
L = 2 ( log 2 ( N 1 ) + log 2 ( log 2 N ) ) a .
u t = k 2 u x 2 , with u ( 0 , t ) = g ( t ) , u ( x , 0 ) = 0 .
g ( t ) = n A n e i Ω n t ,
d u ˜ n d t + k ω 2 u ˜ n = 2 π k ω A n e i Ω n t .
u ˜ n ( ω , t ) = [ u ˜ n ( ω , 0 ) + i 2 π k ω A n π Ω n i k ω 2 ] e k ω 2 t + 2 π ω A n ω 2 + i Ω n / k e i Ω n t .
u n ( x , t ) A n exp ( Ω n 2 k x ) cos ( Ω n t Ω n 2 k x ) .

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