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Abstract
We propose a class of wavelength-division multiplexing (WDM) demultiplexers having a novel monitor and control scheme enabling dense WDM on Si nano-waveguide (NW) photonic integrated circuits (PICs), which had been impossible due to the critically small fabrication tolerance of the extremely miniaturized waveguide structure. With a computer simulation, we show our proposed demultiplexers enable crosstalk in the range of -50 to -40 dB, flat-topped spectrum for high spectral efficiency, and channel counts as large as 64. We have experimentally evaluated the validity of this type of demultiplexers by using a 4-ch WDM demultiplexer, which has shown total crosstalk of < -49 dB as a result of fully automatic control of heaters. This technology is expected to drastically shrink the size of dense WDM transceivers, paving the way for future sustainable scalability in the capacity of optical transceiver systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The recent trend of increase in single-carrier bitrate has successfully reduced size and cost per bandwidth of transceivers, which has contributed to keeping the trend of capacity increase of WDM transceiver systems. As the symbol rate exceeds 100 Gbd, however, this trend is approaching its limit due to saturated performance of digital signal processors by slowdown of complementary metal-oxide-semiconductor (CMOS) advancement [1], and limitations in component bandwidths [2]. In order to keep the trend of capacity increase under this circumstance, large-scale integration of transceivers by shrinking the sizes is required. For this purpose, integrating transceiver optics on Si NW PICs is highly effective.
In order to reduce the number of costly fiber coupling, the WDM (de)multiplexer must be implemented on the same Si NW PIC as the other transceiver components. Thus, maximum achievable number of demultiplexer channels is a key to attain scalability in transceiver capacity. However, channel counts of > 10 have not been practical so far on Si NW PICs having a waveguide dimension of hundreds of nanometers. This is due to an exceptional nature of Si NW PICs explained in the following. By using Si NW PICs, the sizes of optical components have been drastically reduced because the light can be strongly confined in the waveguide core by exceptionally high refractive index contrast between Si core and SiO2 cladding as shown in Fig. 1(a). As a drawback, however, this makes effective refractive index determining optical length of waveguides very sensitive to core size as shown in Fig. 1(b). Demultiplexers are interferometric devices, the characteristics of which are very sensitive to optical length of waveguides, thus requiring an impractically high precision control of core size [3]. As reported in Ref. [3] for example, only 1-nm fluctuation in the waveguide thickness causes 1-nm shift of a ring resonance wavelength. This has been a critical problem in implementing WDM functions on Si NW PICs.
Fig. 1. Comparison between SiO2 + α (doped silica), Si3N4, and Si waveguides regarding (a) minimum bend radius determining circuit size, and (b) sensitivity of effective refractive index to waveguide core size. High index contrast of Si waveguide helps downscaling. However, as schematically depicted in (b), it also enhances errors in effective refractive index thus enhancing optical length errors of waveguides.
Excellent works have pioneered the field of very compact WDM demultiplexers with Si NW PICs [3–15]. These consists of various types of demultiplexer, such as cascaded asymmetric Mach-Zehnder (AMZ) interferometer [4–6], arrayed waveguide grating (AWG) [7–10], rings [11,12], and grating [13–15]. Despite the superiority in compactness, there is a difficulty in increasing channels with suppressed crosstalk as seen in the previous reports [4–15], where the values of total crosstalk lies on the range of -24 to -12 dB, which are much larger than those required for most of WDM systems.
In each type of demultiplexers, the errors in optical lengths of waveguides cause crosstalk as depicted in Fig. 2. To overcome this, exploiting tunability of rings has been proposed [12]. The idea of correcting errors through refractive index changes by heaters can also be applied to other types of demultiplexers as illustrated in Fig. 3. Table 1 shows a comparison of suitability of 4 demultiplexer types for error corrections by heaters. The heating of waveguides on Si NW PICs is very power efficient, because it can be localized to the vicinity of waveguides due to high thermal isolation of SiO2 cladding. As shown in Fig. 3, this power efficient heating can be applied to all types but grating. Rings are attractive because they have a radius of several microns, thus occupying a very small area. However, large temperature changes on the order of hundreds of °C are required to fully cover the required tuning range. This drastically degrades durability of heaters, making rings impractical. As for grating, heating the entire area covering optical paths would be a practical way to tune. Although the control algorithm is simple, it only shifts the spectrum and does not have degree of freedom to fully correct the errors. In contrast, other types have degree of freedom sufficient to completely correct the errors. Considering these aspects, cascaded AMZ and AWG are most suitable for error correction by heaters, but only provided that the control algorithm is established, which has been a challenge for both types [16,17].
Table 1. Comparison of Suitability of 4 Demultiplexer Types for Error Correction by Heaters
Based on the principle of cascaded AMZ, we have proposed cascaded AMZ triplet (CAT), a demultiplexer having a novel monitor and control scheme to completely correct errors, and have shown both theoretically [18] and experimentally [19] that this has an ability to completely correct errors, and enables an unprecedentedly low crosstalk of ∼ -50 dB. In this paper, we will show the details of the operation principle as well as introduce a variation of CAT enabling WDM with higher spectral efficiency. This paper is organized as follows. Sec. 2 explains a fundamental mechanism of an AMZ triplet as an element of CAT. Sec. 3 shows structure and characteristics of CAT as an aggregate of AMZ triplets. Sec. 4 shows experimental results and compares with other existing demultiplexer. Finally, Sec. 5 introduces a variation of CAT having flat-topped spectra as a demultiplexer for high spectral efficiency WDM systems.
2. Asymmetric Mach-Zehnder (AMZ) triplet
Cascaded AMZ is composed of AMZ interferometers shown in Fig. 4(a), where 2 waveguides unequal in the optical length are placed between two 3-dB couplers [4–6]. The transmissivity spectrum has a shape of raised cosine function [20]. Defining L as LU - LL, where LU and LL are optical lengths of upper and lower arms, respectively, the wavelengths of peaks are expressed by L/m (m is an integer). The spacing between peaks can be expressed by λ2/L. Due to the periodic nature of peaks (pass bands) and valleys (reject bands) in the transmissivity spectrum, AMZ functions as a WDM de-interleaver for signals having a spacing of Δλ = λ2/2L.
Fig. 4. Changes in the monitor values with a heater power. (a) An AMZ with tap monitors (b) An AMZ triplet.
Denoting a fabrication error by ΔL, L can be expressed by Ldesg + ΔL, where Ldesg is a design value at which transmissivity peaks and valleys match the WDM channel wavelengths. Defining P as the power difference between the upper and lower heaters, PU - PL, and L0 as the value of L without turning on heaters, L becomes L0 + CP, where L0 = Ldesg + ΔL, and C is a coefficient of heater efficiency. This indicates that L can be corrected to Ldesg by changing P with heaters. Increasing or decreasing P shifts the transmissivity spectrum toward longer or shorter wavelengths, respectively, which can be used for error correction to match the transmissivity peaks and valleys with WDM channel wavelengths. To perform this automatically, we must somehow detect the deviation of the peaks and valleys from WDM signals. Although one might think that power monitors at output ports shown in Fig. 4(a) can detect this, it is impossible because the values of power monitors do not change with P if all channels are launched. Because this is the case in the actual network operation, it is impossible to detect and correct errors occurring during network operation.
AMZ triplet shown in Fig. 4(b) is our solution to solve this problem [18,19]. This structure functions as a de-interleaver with an automatic error correction capability. An AMZ triplet has 3 identically designed AMZs (AMZs 1, 2, and 3 in Fig. 4(b)) connected in a binary tree structure, where we assume that all of the 3 AMZs have phase errors which are not necessarily correlated to each other. We denote P, L, L0, and ΔL for AMZ n (n = 1, 2, 3) by Pn, Ln, Ln0, and ΔLn, respectively. Monitors 1A and 1B detect optical powers at 2 output ports and monitors 2 and 3 detect those at the opposite ports. In contrast to AMZ in Fig. 4(a), the monitors change sinusoidally with P1 and P2. In Fig. 4(b), value of monitor 1A is shown as functions of P1 and P2, where the best conditions are located at the peaks in sinusoidal curves. This indicates that we can automatically correct the errors by simply tuning P1 and P2 to increase the value of monitor 1A.
Figures 5(b)-(d) give details of how the value of monitor 1A in Fig. 5(a) changes with P1 and P2 through changes in the transmissivity spectrum from input port to monitor 1A. The values of transmissivity in Fig. 5(b) are those normalized by the maximum value. In the 5×5 matrix of transmissivity spectra in Fig. 5(b), horizontal (rightward) and vertical (upward) directions correspond to increases in P1 and P2, respectively.
Fig. 5. (a) Structure of an AMZ triplet and definitions of heater powers, P1 and P2. (b) Changes in transmissivity spectra to monitor 1A with P1 and P2. (c) 2D space (P1, P2) where transmissivity spectrum in (b) was obtained (d) Changes in the values of monitors 1A and 2 with P1 and P2. Left graphs are values obtained with an incidence of λ1 and λ3 only. Center graphs are those for λ2 and λ4 only. Right graphs are those with an incidence of all channels, which are equivalent to summations of left and center ones. Monitor values are normalized by the maximum value.
λ1−4 are the center wavelengths of WDM channels 1 to 4 as shown in Fig. 5(a). Solid circles in Fig. 5(b) are the values of transmissivity at λ1−4, summation of which is proportional to the value of monitor 1A. In Fig. 5(c), the crossings of 5×5 grid lines represent positions in 2-dimensional (2D) space (P1, P2) at each of which, transmissivity spectrum at the corresponding position of the 5×5 graph matrix in Fig. 5(b) was obtained. At the point depicted by a solid circle, transmissivity peaks match λ2 and λ4, and valleys match λ1 and λ3, indicating this point is the best to pass λ2 and λ4 and reject λ1 and λ3. At the points depicted by open circles, the transmissivity peaks match λ1 and λ3 and valleys match λ2 and λ4, indicating those are the best to pass λ1 and λ3 and reject λ2 and λ4. The shape of transmissivity spectrum changes periodically with P1 and P2 and the periods are equal to the full horizontal and vertical spans of 5×5 grid, respectively. Therefore, defining Pπ as π-shift heater power, these spans can be expressed by 2Pπ. Figure 5(d) shows values of monitors 1A and 2 in 2D space (P1, P2) having the same definition as in Fig. 5(c). Right graphs are those obtained with the presence of all channels. The left and center graphs are those obtained with only odd or even channels, respectively. When all channels are present, all peaks in monitor 1A are located at either a solid or an open circle. This indicates simply changing P1 and P2 to increase monitor 1A results in reaching the nearest solid or open circle, one of the best conditions to pass even or odd channels. To exclude uncertainty of which even or odd channels are passed, such an initialization procedure is effective that increasing monitor 1A with the presence of only odd or even channels depending on whether odd or even channels we want to pass. As shown in the upper left graph in Fig. 5(d), with only odd channels, all peaks in monitor 1A are located at open circles. Therefore, simply increasing monitor 1A leads to the nearest open circle, which is best condition to pass odd channels. The upper middle graph in Fig. 5(d) indicates similar initialization can be done for even channels. Even if the monitor value is initially zero and undetectable like the solid circle in the left upper graph or the open circles in the upper middle graph in Fig. 5(d), the dithering of a heater causes an offset from these points. This increases the monitor value, enabling to decide in which direction to move. Once this initialization procedure is performed, simply increasing monitor 1A with an incidence of all channels can correct the deviation from the points depicted by the open and solid circles. Because this procedure is with an incidence of all channels, it can be performed during network operation, which enables correction of the deviation occurring in the long lifetime of network operation. As shown by the right lower graph in Fig. 5(d), the positions of peaks and valleys are exchanged in the plot for monitor 2. This indicates that decreasing monitor 2 can be an alternative to control P1 and/or P2.
Figure 6 shows an example of configuration for monitors and controllers. Parts labeled Inc or Dec controls heaters to increase or decrease the total value of connected monitors, respectively. To detect the slope of monitor value with regard to heater power, dither signal is added to heater power. An example of control sequence for Inc controller is shown in Fig. 7. In Step 1, the controller adds dither ±Δ to current heater power, Pi. We denote heater powers with added dither by $P_i^ + $ and $P_i^ - $, for positive and negative dither, respectively. In Step 2, the controller measures monitor currents $I_i^ + $ and $I_i^ - $ under heater powers of $P_i^ + $ and $P_i^ - $, respectively, and compares $I_i^ + $ and $I_i^ - $. Finally, in Step 3, if $I_i^ + $ is > $I_i^ - $ as depicted by blue line, heater power at next cycle, Pi+1 is set to be $P_i^ + $. In the opposite case depicted by red line, Pi+1 is set to be $P_i^ - $. Sequence for Dec controller can be obtained by changing the condition $I_i^ + > $ $I_i^ - $ to $I_i^ + < $ $I_i^ - $. The control cycle consisting of 3 steps above is performed sequentially for all the AMZs and repeated until monitor currents no longer change in the initialization process before starting communications. This cycle is also repeated even during communications to compensate the changes with time.
Fig. 6. Structure of an AMZ triplet. An AMZ triplet has 3 identically designed AMZs having the same arm length difference, ΔL in the design. This functions as a WDM de-interleaver. Inc and Dec are heater controllers, control sequences of which are depicted in Fig. 7.
Fig. 7. Control sequence of Inc controller. Exchanging “$I_i^ + > I_i^ - $” and “$I_i^ + < I_i^ - $” gives that of Dec controller.
We have conducted a computer simulation of control sequence explained above for AMZ triplet shown in Fig. 6 with an incidence of WDM channels λ1 and λ2. In the simulation, we have calculated the intensity of each channel at each monitor by calculating the transmissivity of all AMZs lying between the input and the monitor port. This was performed whenever the intensity has been updated with changes in heater powers. Figure 8(a) shows transients of heater powers and monitor values starting with zero heater powers. The unit of time is the control cycle. It can be seen that monitors 1A and 1B are increased and monitors 2 and 3 are decreased by Inc and Dec controllers connected to them through changes in heater powers P1−3. After 350 control cycles, all monitor values became steady indicating heater powers P1−3 have reached to one of the points depicted by circles in Fig. 5(d). Transmissivity spectra at times 0 and 350 are shown in Fig. 8(b). At time 0, the spectra have irregular shapes and the peaks are apart from λ1 and λ2. At time 350, transmissivity spectra have peaks exactly at λ1 and λ2. As this result indicates, the errors in an AMZ triplet can be completely corrected with the control sequence in Fig. 7.
Fig. 8. (a) Transients of heater powers (normalized by 2π-shift power, P2π) and monitor values. (b) Transmissivity spectra at times 0 and 350.
3. Cascaded AMZ Triplet (CAT)
As explained in Sec. 2, an AMZ triplet functions as a WDM de-interleaver having a capability of automatic error correction. This indicates that by cascading AMZ triplets in a N-stage tree structure as shown in Fig. 9, you can obtain a 2N-channel WDM demultiplexer with automatic error correction capability [18,19].
As shown in Fig. 6, each square in Fig. 9 represents an AMZ triplet, and the symbol in each square indicates its arm length difference. The arm length difference of an AMZ triplet is set to be half of that in the preceding stage to set the spacing of transmissivity peak to be double of that in the preceding stage.
By performing the control sequence for each AMZ triplets in Fig. 9, we can correct all the optical length errors existing in the CAT demultiplexers. Figure 10 shows transmissivity spectra at the start (uppermost row), after error corrections (lowermost row), and intermediate conditions (second and third rows) for each configuration shown in Fig. 9. This result clearly shows that CAT has a capability to completely correct errors in optical lengths automatically regardless of the number of stages. This indicates that CAT is highly scalable in number of channels, and the scaling is done by simply increasing the number of stages.
Fig. 10. Transmissivity spectra at the start (uppermost rows), after error corrections (lowermost rows), and intermediate conditions (two rows in the middle) for 4-, 8-, 16-, 32-, and 64-channel CAT demultiplexers shown in Fig. 9.
We can expect a remarkable suppression of crosstalk with CAT. Figure 11 shows values of crosstalk for various numbers of channels. For each trial of the simulation, the errors in the arm length difference were randomly selected with a Gaussian probability distribution, and the mean values and standard deviations were derived from hundreds of trials. The standard deviations of the Gaussian distribution were obtained as a function of the total waveguide length of the two AMZ arms [18]. These were large enough that the errors in the phase difference between the two AMZ arms can be considered to have a constant probability distribution if wrapped into an interval of 0 to 2π. The result clearly indicates that CAT has a strong capability to suppress crosstalk and can achieve a value of as small as < -50 dB for a wide range of channel counts.
Fig. 11. Crosstalk of CAT for various numbers of channels with a spacing of 100 GHz. Each circle and error bar indicate the mean value and standard deviation, respectively.
4. Experiments
We have experimentally confirmed the powerful error correction capability and extremely small crosstalk by using our fabricated 4-channel CAT. The structure was folded to reduce the footprint as shown in Fig. 12(a). A Si NW PIC die having 2 CATs was fabricated in a multi-project wafer (MPW) with a standard CMOS PIC process. The dimension of Si waveguide is 450×220 nm. The monitors are lateral PIN Germanium photodiodes (PDs) having a dimension of 140×20 µm. N-doped Si region on each side of the waveguide was used as a heater. The total heater length for one AMZ arm was 400 µm in AMZ triplet 1 and 200 µm in AMZ triplets 2 & 3, whose values of resistivity were 2.2 kΩ and 1.1 kΩ, respectively. The 2π-shift heater power, P2π was evaluated to be 50.7 mW, regardless of the lengths. The arm length difference was 25 µm for AMZs in AMZ triplet 1, and 50 µm for those in AMZ triplets 2 and 3. Multi-mode interferometers (MMIs) having a dimension of 160×20 µm were used as the couplers.
Fig. 12. (a) Layout of fabricated 4-channel CAT demultiplexer. (b) A photo of Si NW PIC die having 2 CAT demultiplexers.
The die was mounted on an organic substrate, and electric connections from monitors and heaters to external controllers were made by die-to-substrate bonding wires and signal lines on the substrate (Fig. 12(b)). External controller consisted of a laptop computer, 18 digital-to-analog converters (DACs) as heater drivers, and 12 analog-to-digital converters (ADCs) as current monitors. The 18 DACs consist of 5 instruments, each of which has 4 channels of DACs and a general purpose interface bus (GPIB) interface for connections to the computer. The 12 ADCs consists of 12 instruments, each of which functions as a single-channel current monitor having a GPIB interface. 18 DACs and 12 ADCs were connected to the 18 heaters and 12 monitor PDs in the CAT one-to-one, respectively. Connections to DACs and ADCs enabled the computer to control the heater powers and acquire the values of photocurrents. With these functions, the computer was enabled to perform the control sequence shown in Fig. 7. In practical implementations requiring higher space efficiency and scalability, an application-specific integrated circuit (ASIC) die accommodating the controllers is supposed to be attached directly on the CAT in PIC die, where bump matrix can make connections with a much higher density. The footprint of the CAT is 900×500 µm, which is still large but can be potentially reduced by an order of magnitude, because it is currently dominated by the size of components such as monitor PDs, couplers, and heaters still having much room for improvement: lateral PIN Germanium PDs having a dimension of 20×3 µm [21], and an MMI coupler having a size of 13×3 µm [22] are available, and the heaters can be shortened to be ∼ 100 µm without causing a durability problem due to high temperature, and can be further reduced by folding. Shorter heaters are also effective in reducing the required heater voltage.
Input and output ports were connected to grating fiber couplers, on which fiber assembly was attached. 4-channel WDM light was launched to input port and control sequence shown in Fig. 7 was performed. Limited by the response times of the instruments, duration of each cycle was a few seconds. Without this limitation, it can be reduced to be on the order of a few tens of msec: because the heater response time is ∼ 100 µs, the duration of the cycle can be on the order of a few msec for each AMZ and 9 times of this for all the 9 AMZs if performed serially. Figure 13 shows transients of heater powers and monitor currents for AMZ triplets 1–3. The monitor currents were successfully increased or decreased as shown in the lower graphs. The upper graphs show changes in heater powers during this process.
Fig. 13. Transients of heater powers and monitor currents for AMZ triplet 1, 2, and 3 in Fig. 12(a). 1, 2, and 3 in the upper graphs are AMZ numbers. 1A, 1B, 2, and 3 in the lower graphs are monitor numbers. The unit of the time is a control cycle, which consists of 3 steps shown in Fig. 7 sequentially performed for all the AMZs. In this experiment, one cycle was on the order of a few seconds.
Left graphs in Figs. 14(a) and (b) show the transmissivity spectra measured at times 0 and 160, respectively. These transmissivity spectra were measured by using an amplified spontaneous emission light source. Fiber coupler losses were excluded. As shown in left graph in Fig. 14(b), the transmissivity peaks were successfully corrected to be equally spaced. At the peaks, transmissivity to other ports, which is the origin of crosstalk, is significantly suppressed. This very much contrasts to the initial state shown in the left graph of Fig. 14(a), where peak positions were irregular due to fabrication errors. The remarkable contrast between Fig. 14(a) and (b) demonstrates the powerfulness of error correction in CAT.
Fig. 14. Transmissivity spectra from input to output ports (left figures) and signal spectra obtained from 4 output ports with an incidence of 4-channel WDM signal (right figures) at (a) initial state and (b) after error correction. The numbers, 1–4 in the figures correspond to output ports 1–4 in Fig. 12(a), respectively.
Right graphs in Figs. 14(a) and (b) show spectra of demultiplexed signal before and after error correction, respectively. In Fig. 14(b), only one prominent peak exists in each spectrum, indicating significantly suppressed crosstalk. The values of total crosstalk, defined as a ratio of the total power of crosstalk from a port to the signal power, were measured to be as low as -57.6, -52.1, -54.5, and -49.3 dB for output ports 1–4, respectively. The measured loss was 5.0 dB for the worst port and 2.9 dB in average. With the values for the worst port, the performance of this CAT demultiplexer was plotted by a black solid circle in Fig. 15(a) for comparison with other demultiplexers on Si NW PIC. Total crosstalk represented in y-axis of Fig. 15(a) can be regarded as a measure for waveform degradation. On the other hand, per-channel crosstalk, defined as the total crosstalk divided by Nch – 1 (Nch is the number of channels) was represented in y-axis of Fig. 15(b), which provides a fair comparison among demultiplexers with different Nch. In both cases, the values of crosstalk for CAT demultiplexer are unprecedented among those fabricated on Si NW PIC platforms. This advantage comes from the capability of automatic error correction of CAT, which none of the other demultiplexers in Fig. 15 possess. As for power consumption, that for CAT was evaluated to be 76 mW, while other demultiplexers without heaters consume no power. Although this is apparently a disadvantage of CAT, it has only a limited impact on the total power consumption of transceivers as explained in Sec. 5. The loss of 5.0 dB for the worst channel is still larger compared to Refs. [5,8–10] having Nch of 6–12. This large loss is attributed to both losses at tap couplers having coupling efficiency η of 15%, and the large loss of 0.45 dB for each MMI coupler at the channel distant from its transmissivity peak. η of 15% selected to secure a sufficient margin of signal-to-noise ratio in monitors has much room for reduction. As for MMI couplers, those having a loss of < 0.1 dB over entire C-band were reported [23], indicating that the current loss of 0.45 dB also has much room for reduction. As depicted by green open circles in Figs. 15(a) and (b), loss of 4-channel CAT can be reduced to be 1.87 dB if η becomes 5% and the coupling loss of each MMI coupler is reduced to be 0.1 dB. The footprint scales with Nch - 1, because the number of AMZ triplets is equal to Nch - 1. Supposing that the footprint can be reduced from the current value of 0.45 mm2 to 0.045 mm2 through the size reductions of PDs, couplers, and heaters as discussed above, that for a channel count of Nch becomes equal to 0.045 mm2 × (Nch – 1)/3. By increasing the core size of Si waveguide, a 40-ch demultiplexer on Si has achieved well suppressed crosstalk of < -30 dB in expense of compactness [24]. Compared to the footprint of 100 mm2 of this demultiplexer, that for 40-ch CAT which can be estimated to be 0.585 mm2 is smaller by more than two orders of magnitude.
Fig. 15. Comparison of CAT demultiplexers with other demultiplexers on Si NW PIC. (a) Total crosstalk vs. loss for the worst ports (b) Per-channel crosstalk vs. loss for the worst ports
5. Flat-topped CAT for WDM with high spectral efficiency
In order to increase spectral efficiency, the channel spacing in recent WDM systems is set to be close to the spectral width of Nyquist-filtered modulated signal. For these applications, flat-topped transmissivity spectrum is required for demultiplexers. As reported in [25], transmissivity spectra of AMZs can be flattened by increasing the number of arm pairs. This method can also be applied to AMZ triplets with the error correction capability preserved. The configurations are shown in Fig. 16. Figure 16(a) is an AMZ triplet identical to Fig. 6, and thus not flat-topped. We call this 1st-order AMZ triplet. Figure 16(b) has 2 pairs of arms for each AMZ, which we call 2nd-order AMZ triplet. As a generalized form, we call those having N pairs of arms shown in Fig. 16(c), Nth-order AMZ triplet.
Figures 17(b)–(m) show how the values of monitors 1A and 2 in the 4th-order AMZ triplet shown in Fig. 17(a) change with the heater powers. P1-1, P1-2, P1-3, P1-4, P2-1, P2-2, P2-3, P2-4, P3-1, P3-2, P3-3, and P3-4, are defined as the difference between the upper and lower heater powers for the corresponding heater pairs shown in Fig. 17(a). In each of Figs. 17(b)–(m), the values of two heaters selected from P1-1, P1-2, P1-3, P1-4, P2-1, P2-2, P2-3, and P2-4, were changed, each of which was taken in x- or y-axis. The ranges of x- and y-axes are equal to 2Pπ as in Figs. 5(c) and (d), and the open and solid circles are the best points to pass odd or even channels, respectively. The heater powers other than those taken in x- or y-axis were fixed at the point equivalent to the solid circles, i. e. the best point to pass even channels. In Figs. 17(b)(c), the left and center graphs are those obtained with only odd or even channels, respectively. Right graphs in Figs. 17(b) and (c) and those in Figs. 17(d)–(m) were obtained with the presence of all channels. Figure 17(b) is the case that heater powers in the first arm pairs, P1-1 and P2-1 were changed. The color patterns are quite similar to those in Fig. 5(d), where the locations of peaks and valleys are exactly the same. Figure 17(c) is the case that heater powers in the second arm pairs, P1-2 and P2-2, were changed. The patterns for this case are also similar to those in Fig. 5(d) except for the weaker contrast. As seen in Figs. 17(d) and (e), the contrast becomes even weaker for the third and fourth arm pairs, while the positions of peaks and valleys are the same as in Fig. 5(d). The color patterns for various other combinations of heaters were depicted in Figs. 17(f)–(m). In every case, monitor 1A has only one peak and monitor 2 has only one valley within the range, which are all located at the center, indicating that we can correct the phase errors simply by increasing monitor 1A or decreasing monitor 2 with an incidence of all the channels. These results indicate that high-order AMZ triplets can also be controlled by controller configurations and algorithms similar to those of 1st-order AMZ triplets as shown in Fig. 16. The only difference is that each controller controls plural numbers of heater pairs and performs 3 steps shown in Fig. 7 for each heater pair sequentially.
Fig. 17. (a) Structure of a 4th-order AMZ triplet, and heater powers, P1-1, P1-2, P1-3, P1-4, P2-1, P2-2, P2-3, P2-4, P3-1, P3-2, P3-3, and P3-4, each defined as the difference between the upper and lower heater powers for the corresponding heater pairs. The color scale in the lower left is for Figs. (b)–(m). The graph in the upper left is the spectra of input signal used for calculation of Figs. (b)–(m). (b)–(m) Changes in the values of monitors 1A and 2 with changes in the values of two heaters selected from P1-1, P1-2, P1-3, P1-4, P2-1, P2-2, P2-3, and P2-4, where monitor values are normalized by the maximum value. In Figs. (b) and (c), left graphs are values obtained with an incidence of λ1 and λ3 only. Center graphs are those for λ2 and λ4 only. Right graphs in Figs. (b) and (c), and graphs in Figs. (d)–(m) are those with an incidence of all channels.
High-order AMZ triplets also have a capability to correct errors automatically. Each graph in the lower row of Fig. 18(b) shows spectra obtained after performing error corrections for each AMZ triplet initially having spectra shown in the upper row. The sequence of error corrections was performed with an incidence of WDM light shown in Fig. 18(a), assuming 66 Gbd QAM 16 modulation, having channel spacing of 75 GHz. This result indicates that by increasing the number of orders, the spectrum of an AMZ triplet can be more flat-topped, and more adaptable to WDM signals having higher spectral efficiency. Table 2 summarizes the coupling coefficients, κ of 2×2 couplers used in the simulation.
Fig. 18. (a) Spectrum of input signal. (b) Transmissivity spectra of 1st-, 2nd-, 3rd-, and 4th-order AMZ triplets before and after error correction.
Table 2. Coupling Coefficients Used for 1st- and High-Order AMZ Triplets
By replacing 1st-order AMZ triplets shown in Fig. 9 with high-order ones, we can flatten the transmissivity peaks of CAT demultiplexers. An example is shown in Fig. 19, where 4th- and 2nd-order AMZ triplets are placed in the first and second stages, respectively. For the succeeding stages, 1st-order is sufficient because the flatness in the transmissivity of these stages does not affect that of the entire demultiplexer.
Even with the use of high-order AMZ triplets, we can preserve the capability of automatic error correction of CAT. Figure 20 shows transmissivity spectra before and after error corrections (top and bottom rows, respectively), and intermediate conditions (two rows in the middle). It is clearly seen that high-order CATs are effective in flattening the transmissivity peak without deteriorating the capability of automatic correction.
Fig. 20. Transmissivity spectra from input to output ports before and after error corrections (top and bottom rows, respectively), and intermediate conditions (two rows in the middle) for 4, 8, 16, 32, and 64 channel CATs shown in Fig. 19.
CAT consumes power for heaters, which is an obvious disadvantage in comparison with other demultiplexers. We discuss the impact of this aspect in the following. Figure 21(a) shows total heater power consumed by round-top and flat-topped CAT demultiplexers. Here, we assumed 2π-shift heater power, P2π of 20 mW, which is typical for standard Si NW PIC. Defining Nch as the number of channels as in Sec. 4, the number of AMZ triplets can be expressed by Nch - 1. Therefore, round-top CATs have 3(Nch - 1) heater pairs. On the other hand, flat-top CATs shown in Fig. 19 have 12 heater pairs for Nch = 2, and 3(Nch + 4) of those for Nch ≥ 4. The total power consumption shown in Fig. 21(a) obtained with a simulation is approximately proportional to these numbers of heater pairs. It should be noted that the difference in the number of heater pairs between round- and flat-top CATs is constant at 15 regardless of the value of Nch for Nch ≥ 4, because flat-top CATs have high-order AMZ triplets only in the first and second stages. Therefore, per-channel heater powers for round- and flat-top CATs get closer with an increase with Nch as shown in Fig. 21(b) and converges at ∼ 12 mW. On the other hand, the per-channel power consumption of transceivers including modulator drivers, transimpedance amplifiers, and digital signal processors in some cases, is on the order of a few hundreds of mW to a few tens of Watts, depending on the modulation format and the transmission distance, indicating that CAT demultiplexers have only a limited impact on the power consumption of transceivers.
Combined with the flat-top structure, the strong error correction capability demonstrated in Sec. 4 enables the integration of high performance WDM demultiplexers on Si NW PICs with negligible cost of power consumption. The automatic error correction is also effective in drastically improving production yields and in realizing temperature insensitivity. This technology is expected to drastically shrink the size of dense WDM transceivers, paving the way for future sustainable scalability in the capacity of optical transceiver systems.
6. Conclusion
We have proposed cascaded AMZ triplets (CATs), a class of WDM demultiplexers having a novel monitor and control scheme enabling extremely low-crosstalk, flat-topped spectrum for high spectral efficiency WDM, high channel count, which had been impossible to achieve on Si NW PIC platforms. We have experimentally demonstrated fully automatic optical length error correction of 4-channel CAT with a simple algorithm and obtained total crosstalk of as small as -49 dB. The loss for the worst channel was 5.0 dB, which is still larger compared to other demultiplexers. This is attributed to both loss at tap couplers and MMI couplers, having room for reduction. Total power consumption of heaters was evaluated to be 76 mW. Although the power consumption is apparently a disadvantage of CAT, it has only a limited impact on the total power consumption of transceivers. This technology is also expected to drastically increase production yields and to realize temperature insensitivity. We believe these features of this technology will strongly lead the capacity increase in transceiver systems.
Funding
New Energy and Industrial Technology Development Organization (JPNP13004).
Disclosures
The authors declare no conflicts of interest.
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