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Arrayed waveguide gratings provide flexible spectral filtering functionality for integrated photonic applications. Achieving narrow channel spacing requires long optical path lengths which can greatly increase the footprint of devices. High index contrast waveguides, such as those fabricated in silicon-on-insulator wafers, allow tight waveguide bends which can be used to create much more compact designs. Both the long optical path lengths and the high index contrast contribute to significant optical phase error as light propagates through the device. Therefore, silicon photonic arrayed waveguide gratings require active or passive phase correction following fabrication. Here we present the design and fabrication of compact silicon photonic arrayed waveguide gratings with channel spacings of 50, 10 and 1 GHz. The largest device, with 11 channels of 1 GHz spacing, has a footprint of only 1.1 cm2. Using integrated thermo-optic phase shifters, the phase error is actively corrected. We present two methods of phase error correction and demonstrate state-of-the-art cross-talk performance for high index contrast arrayed waveguide gratings. As a demonstration of possible applications, we perform RF channelization with 1 GHz resolution. Additionally, we generate unique spectral filters by applying non-zero phase offsets calculated by the Gerchberg Saxton algorithm.
© 2017 Optical Society of America
1. Introduction
Filtering of narrowly spaced spectral lines is a critical operation in many optical signal processing applications, such as arbitrary waveform generation and RF signal channelization [1,2]. Both of these applications benefit from an increased optical resolution of filtering techniques. For the purpose of arbitrary optical waveform generation, the use of narrow filter resolution allows one to easily generate frequency combs through electro-optic means and produce waveforms with greater temporal length. In regards to RF channelization, optical methods benefit from very broadband operation, but are often limited in resolution. In order to compete with electrical methods, narrow spectral resolution filtering is a necessity.
Spectral filtering can be achieved in free space using high finesse Fabry-Pèrot cavities or large ruled gratings with long optical path lengths. The integrated photonic equivalent of a Fabry-Pèrot cavity is the micro-ring or micro-disk cavity and is routinely proposed for spectral filtering applications. While these cavities can provide high quality factors, as a result of the resonant nature of these structures, small input powers quickly build to a point where non-linear effects become an important consideration. For this reason resonant silicon photonic structures are limited to low optical powers on the order of a few hundred μW. On the other hand, ruled gratings provide spectral filtering through multi-path interference. The integrated photonic equivalent of the ruled grating is the arrayed waveguide grating (AWG). This device functions by splitting incoming light among a large number of waveguides. Each waveguide is incrementally longer than the previous. The light from each waveguide recombines at a star coupler, where it interferes in such a way that a different spectral slice is coupled into one of an array of output waveguides.
For many years AWG’s have been fabricated in silica on silicon platforms for wavelength division multiplexing [3]. This application requires a channel resolution of 25–100 GHz, or a wavelength resolution of 0.2–0.8 nm. Achieving resolutions higher than this requires an increase in the optical path lengths. Not only does this increase the footprint of the device, but also optical phase errors resulting from fabrication imperfections become a more significant issue [4]. Moving to a high index contrast platform, such as silicon, allows for more compact designs, however the unwanted phase errors become an even more substantial issue. For this reason, correction of waveguide phase error following fabrication is a necessity for high index contrast AWGs [5–7].
In this work we present the design, fabrication and optimization of a compact silicon photonic AWGs. By using active thermo-optic phase error correction we’re able to demonstrate low crosstalk AWGs with channel spacing as narrow as 1 GHz (8pm). Until now, 1 GHz channel spacing has only been demonstrated in silica on silicon platforms [8], while high index contrast AWGs have been limited to 10–25 GHz [9, 10]. Additionally, we demonstrate state-of-the-art cross-talk performance for high index contrast AWGs. Using this device, we are able to show analysis of RF signals as well as more complex functionality such as generating unique spectral shapes.
2. Design and fabrication
Figure 1(a) shows an example of one of the AWGs which has eleven input and output channels with a spacing of 1 GHz, 35 arrayed waveguides and footprint of approximately 9 mm × 12 mm. We also studied AWGs with 50 and 10 GHz channel spacing which had a similar design but footprints of 4 mm × 4 mm and 11 mm × 4 mm respectively. Light is edge coupled onto the chip using an inverse silicon taper. Eleven input tapers are combined at a star coupler as shown in Fig. 1(c). The star coupler consists of eleven input waveguides arranged along an arc, which couple to a silicon slab free propagation region (FPR). As light travels through the FPR it diverges. At the opposite end of the FPR, 35 output waveguides collect the light. The design of the star coupler is chosen so that approximately 80% of the light entering the center input waveguide is collected by the output waveguides, resulting in about −1 dB insertion loss in the ideal structure.
Fig. 1 (a) Image of an AWG with 1 GHz channel spacing mounted on a copper plate. Wirebonds for control of the integrated thermal phase shifters are visible at the top and bottom of the image, and optical fibers for coupling light in and out are visible at the left and right sides. (b) Optical microscope image of one of the integrated thermal phase shifters. (c) Dark field optical microscope image of one of the starcouplers with eleven input waveguides at the bottom coupling into 35 output waveguides at the top. (d) Close up of the shortest switchback section showing the 16 bends. (e) Detailed view of the bends, with the transition from 400 nm waveguide to 1 μm waveguide visible.
After being split among the 35 output waveguides of the star coupler, the light is directed along the left edge of the chip as it is pictured in Fig. 1(a). One by one, each waveguide turns to the right and travels across the chip. As the waveguide travels across the chip it goes through two sets of switchbacks which each contain 16 turns of 180°. The switchback type design was chosen due to its compact footprint. The length of the switchbacks is adjusted for each waveguide in order to accumulate the desired optical path length. The incremental increase in length of each waveguide is included in the straight section of the switchback. The number and radius of all waveguide bends is identical for each waveguide. These switchbacks appear as the two purple triangles seen in Fig. 1(a), and a close up of the shortest switchback is shown in Fig. 1(d) and (e). During straight sections, the waveguide is a fully etched ridge guide with a width of 1 μm. This provides low propagation loss, determined to be less than 1 dB/cm at a wavelength of 1550 nm by measuring waveguides of multiple lengths in a similar sample. At the same time this creates a multi-mode waveguide which is a potential problem due to mode mixing from surface roughness. To avoid this, at each 180° bend the waveguide tapers to a width of 400 nm, which is single mode. Light in higher order modes couples to radiative modes and is lost. The propagation loss of the 400 nm waveguide has been measured to be on the order of 3 dB/cm. This along with bending loss and the filtering of higher order modes contributes to insertion loss. Based on simulations, the bending loss and filtering loss is expected to be negligible compared to the 3 dB/cm propagation loss of the waveguide. Overall, each bend is estimated to contribute less than 0.03 dB of loss. With 32 bends in each waveguide, the extra insertion loss is less than 1 dB.
At the center of the chip, between the two switchbacks, the waveguide is tapered to a partially etched rib waveguide. This allows for the integration of a thermo-optic phase shifter. This phase shifter is pictured in Fig. 1(b). On either side of the rib waveguide is a region of n+ doped silicon slab. These two regions of doped silicon are connected in series and function as a resistive heater. When a current is applied to the doped silicon heat is generated in the waveguide which shifts the refractive index through the thermo-optic effect. This results in a phase shift which is approximately linear with the applied power. The doped regions are located 1.8 μm from the center of the waveguide on either side. Simulations reveal that the full width half maximum of the electric field in this waveguide is about 700 nm. By the time the field reaches the doped region it has decreased by a factor of 1000 and therefore we expect very little insertion loss from the phase shifter. Additionally, this short section of partially etched waveguide does not support TM modes. As a result this acts as a mode filter and only the TE mode is able to pass through the AWG. All measurements in this work are therefore done with TE polarization.
The device was fabricated using the silicon photonics platform at the Sandia Microsystems and Engineering Sciences Applications (MESA) silicon micro-fabrication facilies. The silicon photonics platform is a fully CMOS compatible process utilizing SOI wafers with a 250 nm silicon device layer and a 3 μm buried oxide layer. Following fabrication and dicing the device is mounted to a copper heatsink attached to a thermo-electric cooler and thermistor for accurate temeprature control. The 35 integrated thermo-optic phase shifters are connected through wirebonding to a breakout printed circuit board allowing control with three NI DAQ PXI-6704 analog output boards. Measurements of AWGs with 50 GHz and 10 GHz channel spacing were conducted in open atmospheric conditions, however, thermal fluctuations due to air flow above the sample proved to be a challenge for stable phase control of devices with 1 GHz channel spacing and therefore these samples were moved into an existing vacuum chamber. The system was kept under a vacuum of approximately 4×10−5 torr, however, measurements done inside the chamber at atmospheric pressure showed similar performance. Therefore, a hermetically sealed package would likely provide similar stable performance.
3. Source of optical phase errors
The use of silicon photonics as a platform for AWGs provides a significant advantage in device size. The high index contrast between the silicon waveguide and the silicon oxide cladding allows for sharp waveguide bends with relatively low optical losses. This allows for the switchback waveguide design which is presented here with a bend radius of only 6 μm. A device fabricated in silica on silicon with a 1 GHz channel spacing was demonstrated and had a foot-print of 44 cm2 [8], compared to the 1.1 cm2 footprint of our device. The main drawback to the use of high index contrast platforms is the significant increase in optical phase errors resulting from fabrication imperfections. The distribution of this random phase is given by eq. 1, where L is the waveguide length, Δ is the index contrast given by eq. 2, σ(δw) is the standard deviation in waveguide width, and σ(δn) is the standard deviation in waveguide index [4]. Variables A and B are proportionality constants determined by the waveguide geometry as explained in ref. [4]. From this we see that the standard deviation in the optical phase scales linearly with length and to the power of 3/2 with index contrast.
For the silicon photonic platform Δ is approximately 0.41, nearly 30 times greater than silica waveguide technology, introducing a factor of ∼160 increase in phase error standard deviation. The high group index of silicon waveguides allows the waveguides to be ∼2.5 times shorter than silica waveguides which cuts this factor in half, still resulting in phase errors ∼60 times greater in silicon photonics. Additionally, achieving 1 GHz channel spacing requires quite long optical path lengths. The longest path length on this chip is approximately 17.4 cm. For these reasons the optical phase error accumlated by light passing through each waveguide is significant and the transmission spectrum of each channel as fabricated is completely random. In order to operate the device as an AWG this phase error must be corrected following fabrication using either passive or active techniques [5–10].
4. Method for phase error correction
Applying the appropriate phase correction to each of the arrayed waveguides typically requires that the phase error first be measured. This is a challenging task and requires coherent phase-sensitive techniques which are described in more detail in section 5 and 6. First, we demonstrate an alternative technique which relies on a very simple experimental setup which may be suitable in less demanding applications. For this method a fixed wavelength laser is coupled into one of the AWG input waveguides, and the output power at a single channel is monitored. The intensity of the transmitted light can be pictured as the phasor addition of 35 individual components, one from each arrayed waveguide. Figure 2(a) shows an example of this for an AWG with seven waveguides, each with a random phase. Each waveguide is represented by a black arrow and the sum of the seven waveguides is represented by the red arrow. In Fig. 2(b) the ideal transmission spectrum is shown as a red dashed line, while the blue curve shows the transmission spectrum associated with these random phases. The arrows in Fig. 2(a) correspond to the wavelength associated with the peak transmission of the red dashed curve. With no phase error these arrows would be aligned and add up to a single phasor with a magnitude of one, however, the phase error causes a random walk which results in a magnitude much smaller than one, and therefore a transmission much less than 0dB.
Fig. 2 Simulated optimization of phase error in an AWG with seven waveguides. (a) Phasor addition at the expected peak of transmission. Randomly added phase error results in less than maximum transmission. (b) Simulated transmission spectrum of the ideal device(red dashed curve) and the device with random phase errors (blue curve). (c) Following the optimization procedure describe in the text, the phases have become aligned. (d) The simulated transmission of the optimized device (blue curve) compared to the ideal device(red dashed curve).
One can imagine applying a linearly varying phase to a single waveguide, which ramps the phase of the waveguide over a range greater than 2π. As this is done the phasor associated with the waveguide will rotate, and the assocated black arrow in Fig. 2(a) will trace out a circle in phase space. The point of the red arrow, representing the sum of all seven waveguides will trace out a similar circle. The distance of the point of the red arrow from the origin represents the transmission of the laser, so as the point moves around a circle in phase space the transmission of the laser will oscillate sinusoidally. If the phase of the waveguide is then chosen to be that which produces a maximum in the transmission, the phasor associated with this waveguide is rotated such that it, and the sum of all seven phasors (red arrow) point in the same direction. If this is then repeated sequentially for each of the waveguides, the result is that the phasors will be “straightened” to point in nearly the same direction as shown in Fig. 2(c). Since the red arrow shifts slightly after adjusting the phase of each waveguide, when the next waveguide phase is aligned to the red arrow, it has a slightly different phase than the previous waveguide. This is why the optimized phases are not perfectly straight in Fig. 2. In Fig. 2(d) the ideal transmission spectrum is shown once again as a dashed red line and the blue curve shows the transmission spectrum following one iteration of this method of sequentially varying each phase, revealing significant improvement in the insertion loss and cross-talk of the device. In theory this procedure could be repeated to further align each phasor and improve performance; however, in practice a single iteration produces the greatest improvement in performance and further improvement is limited by noise in the measurement of the laser intensity.
This method was successfully applied to AWG devices with 50 GHz and 10 GHz channel spacing. Figure 3(a) shows the transmission spectrum of a 50 GHz channel spacing AWG with random phase errors as fabricated (blue curve) and after optimization using the method described here. The optimization has resulted in an increase in transmission of 8.8 dB and an increase in peak to side-lobe contrast from nearly 0 dB to 19 dB. Figure 3(b) shows the transmission spectrum of each of the eleven channels, demonstrating that optimizing a single channel is sufficient to optimize all of them.
Fig. 3 Demonstration of phase error correction in an AWG with 50 GHz channel spacing, using the intensity measurement method described in the text. (a) Comparison of the device as fabricated (blue curve) and after optimization (red curve), showing improved transmission and a peak to side-lobe contrast of 19 dB. (b) Measured transmission of all eleven channels following optimization.
While this method proves simple to implement, there are two main limitations. The first is due to the magnitude of the intensity modulations. The intensity modulation can be no greater than twice the intensity of the light traveling through the waveguide which is having its phase modulated. Therefore, as the number of waveguides is increased, the intensity modulation decreases and becomes more difficult to detect, resulting in greater uncertainty in the phase selection. The second limitation is the result of thermal cross-talk when using thermal phase shifters. This method assumes that the phase of only a single waveguide is being changed at any time. In fact thermal cross-talk between waveguides causes small changes in the phases of nearby waveguides causing error in the chosen phase correction. Primarily due to thermal cross-talk this method became quite challenging to implement for the AWG with 1 GHz channel spacing, and as a result this device was optimized using direct phase measurement with a swept source interferometer.
5. Swept source interferometer
In order to directly measure the relative phase of each waveguide of the AWG a swept source interferometer was used, a technique commonly used for AWG optimization [10–13]. This technique is shown schematically in Fig. 4(a). The AWG is placed in one arm of a Mach-Zehnder interferometer (MZI). The two outputs of the MZI are coupled into an amplified balanced photo-detector. A tunable laser is passed through the MZI and the output interference pattern is recorded while the wavelength of the laser is swept. A second “clock” MZI provides a trigger for data acquisition. As the laser wavelength is swept the intensity from this second MZI oscillates, triggering data acquisition at equally spaced frequency intervals. By using a long spool of fiber in one arm of this MZI the frequency spacing of the data acquisition is set to approximately 1.4 MHz. Polarization controllers are placed at multiple locations in order to launch TE polarized light into the chip and in order to maximize interference at the MZI output.
Fig. 4 (a) Schematic of the swept-source interferometer used to measure the phase errors in fabricated AWGs. The interferometer consists of two Mach-Zehnder interferometers. One is used to accurately trigger data collection at equal frequency intervals, while the second produces an interferogram containing information on the phase errors. (b) Example of the fast Fourier transform of an interferogram collected by the swept-source interferometer. A peak is observed for each of the 35 waveguides, and the relative phase can be extracted from this.
In the device measurement MZI, light passes through each of the 35 waveguides of the AWG before interfering with light from the reference arm of the MZI. As the laser wavelength is swept, each of these 35 paths create an intensity oscillation with a slightly different frequency, related to the optical path length. This can be made very clear by taking the fast Fourier transform (FFT) of the interferogram as seen in Fig. 4(b), where 35 distinct peaks can be observed, each corresponding to one of the 35 waveguides within the AWG. The phase of each peak is relative to the reference arm of the MZI which is not stabilized. Therefore, the phase of one AWG waveguide is selected as a reference, and the relative phase of the other 34 waveguides is measured. The center waveguide (waveguide 18) was used as the reference waveguide for all measurements presented here.
6. Phase shifter calibration and phase error correction
Using the swept source interferometer each of the 35 integrated phase shifters was accurately calibrated, as well as the thermal cross-talk between each. The phase shift of each waveguide is expected to be nearly linear with applied power, however, the NI PXI-6704 board used to control the AWG provides accurate control of the current, but does not provide voltage information. Additionally, the resistance of the phase shifter depends on the temperature and therefore strongly varies with the applied power. For these reasons, accurate power measurement is not possible in our experimental setup. Instead, the phase shift was assumed to be linear with respect to power, and the non-linearity was removed by mapping the supplied current to a relative power scale which varied from 0% to 100%. This mapping is shown in Fig. 5, and was found to be consistent across all phase shifters. 100% power on this scale corresponds to 10mA of current. The maximum power available was limited by the voltage limit of 10V of the NI PXI-6704 board. At the voltage limite of 10V, approximately 11mA of current was supplied, or ∼110mW of power. Using this we can estimate that 100% power on our normalized scale corresponds to approximately 85mW of power. Due to slight variations in device resistance the current was limited to 10mA to avoid reaching the voltage limit of the board. Additionally, limiting the power range led to improved stability of the chip temperature. Figure 6 shows the calibration transfer matrix for both a 10 GHz channel spacing device and a 1 GHz channel spacing. In this matrix the diagonal terms represent the direct phase shift for each waveguide resulting from its respective phase shifter, and the off-diagonal terms represent the cross-talk from phase shifters in other waveguides. Since the phase is measured relative to waveguide number 18, the terms of the matrix corresponding to waveguide 18 are all zero. Additionally, power applied to phase shifter 18 appears as a negative phase shift in all of the other waveguides. The vertical scale in Fig. 6 is the slope of the phase shift with applied power. Since the power scale is in arbitrary units from 0 to 1, the slope is simply the maximum phase shift possible with the given setup. From this we can see that with the available power of ∼85mW we are not quite able to reach a full 2π phase shift. We also see that the thermal cross-talk is significantly larger in the device with 1 GHz channel spacing. This is a result of the greater waveguide lengths in this device which make the optical phase much more sensitive to temperature.
Fig. 5 Mapping used to linearize observed phase shift with applied power. The relative power scale is calculated using the square of a normalized current times an effective resistance. The resistance is assumed to vary linearly with power, so the effective resistance is also calculated in terms of the square of the normalized current. This mapping has been found to be extremely consistent between different phase shifters, both on the same chip as well as across different fabrication runs.
Fig. 6 Measured calibration matrix for a device with 10 GHz channel spacing (a) and 1 GHz channel spacing (b). This matrix connects the observed phase shift in each of the 35 waveguides to the power applied to each of the 35 integrated phase shifters. The diagonal terms correspond to the direct phase shift from a phase shifter, while the off-diagonal terms show thermal cross-talk. The 1 GHz device shows much greater thermal cross-talk due to the increased optical path lengths. The applied power has been normalized to a scale of 0 to 1, so the vertical scale represents the maximum phase shift possible with the available power. All phases are measured relative to waveguide 18. As a result all terms corresponding to waveguide 18 are zero, and applying power to phase shifter 18 appears to produce a negative phase shift in all of the other waveguides.
The off-diagonal terms of the calibration transfer matrix reveal important information about thermal cross-talk in the device. In an ideal device these terms would be zero, allowing one to change the phase of only the desired waveguide. The fact that these terms are non-zero results from heat transfer in the device, and the magnitude of these terms provides clues as to how heat is flowing within the device. It was noted that the thermal cross-talk could be separated into two distinct groups. When power was applied to any phase shifter in the range of 1 through 17, all of the waveguides in this range experience some phase shift. If power is applied to any phase shifter in the range of 18 to 35, the waveguides 1 through 17 experience less cross talk. The opposite is also true, waveguides in the range of 18 to 35 experience greater cross talk from phase shifters within this same range than they do from phase shifters in the range of 1 to 17. Since phase shifters 1 through 17 share a common metal ground trace, and phase shifters 18 through 35 share a separate common metal ground trace, this suggests that the most heat transfer is occuring through the metal traces. In fact, the length of metal trace separating two phase shifters has a stronger correlation with the thermal cross-talk than the direct distance between the two phase shifters. For this reason we expect the thermal cross-talk could be greatly reduced by maintaining separate ground traces for each phase shifter.
Finally, with this information it is possible to apply a phase correction to each of the phase shifters. In theory, the calibration transfer matrix could be used to directly solve for the power to each phase shifter by solving eq. 3, where H is the calibration transfer matrix, P⃗ is the power applied to each phase shifter and n⃗ is a vector of integer values.
In practice finding a solution for P⃗ and n⃗ which keeps the power within the bounds of 0 to 1 proves challenging. Instead, in order to optimize the AWG it is much simpler to implement an iterative method, in which the cross-talk terms are ignored. The power of each phase shifter is adjusted considering only the direct phase shift (diagonal) terms. The phases are then measured again and a new correction is calculated. After several iterations, the device begins to converge to an optimized solution. Additionally, more advanced optimization algorithms, such as PID type feedback, have been implemented with some improvement in performance.
Figure 7(a) compares the transmission spectrum of an AWG with 10GHz channel spacing which has been optimized by the intensity method described in section 4 (red curve) and the same device optimized using direct phase measurement with the swept-source interferometer (blue curve). The contrast of the main peak to first side-lobe is only improved by a few dB, however, the cross-talk observed further from the peak is improved by more than 15 dB. Figure 7(b) shows the transmission spectrum of all eleven channels, demonstrating greater than 20 dB of contrast for each and less than −25 dB of adjacent channel cross-talk. Light is coupled into the center input, and the transmission is measured at each of the eleven output waveguides. Transmission is normalized to 0 dB to remove variability in fiber to chip coupling and make comparison of cross-talk easier. Most channels had a peak transmission in the range of −7 to −8 dB, however, channels 10 and 11 were around −16.5 dB which is attributed to defects in the chip facet. The AWG itself is estimated to have less than 3 dB of loss, with the remaining 4 to 5 dB of loss coming from the fiber to chip coupling. The fiber to chip coupling can be improved to less than 1 dB by the use of index matching fluid and optimized mode matching between fiber and silicon inverse taper.
Fig. 7 (a) Comparison of optimizing an AWG with 10 GHz channel spacing using the intensity method described in section 4 (red curve) and using the interferometer method (blue curve). Using the interferometer improves cross-talk by more than 15 dB at channels far from the peak transmission. The ideal transmission spectrum is shown in light gray. (b) Measured transmission of each of the eleven channels of the 10 GHz channel spacing AWG following optimization with the interferometer. Each channel shows better than 20 dB of peak to side-lobe contrast and less than −25 dB of adjacent channel cross-talk.
7. Optimization of 1 GHz channel spacing AWG
As the channel spacing of the AWG becomes more narrow, thermal stability of the device becomes of greater importance. A variation in the temperature of the device creates a phase shift in each waveguide proportional to the length of the waveguide. This results in a linearly increasing phase across the 35 waveguides which has the effect of shifting the transmission spectrum. This shift was measured to be on the order of 11.2 GHz/°C. For an AWG with 10 GHz channel spacing the temperature must be stable to greater than ±1°C, and for an AWG with 1 GHz channel spacing the temperature must be stable to greater than ±0.1°C. For the initial optimization of the phase shifters it is actually necessary to have greater stability in order to accurately measure the waveguide phases. For this reason, the AWG device with 1GHz channel spacing required additional consideration. As previously mentioned, the device was mounted in a vacuum chamber in order to provide improved thermal stability. This allowed the temperature to be controlled to ±0.001°C. Additionally, an improved optimization algorithm was implemented which corrected the measured phases for any observed shift in the transmission spectrum. Using these techniques the 1 GHz channel spacing AWG was optimized as shown in Fig. 8(a). The remaining phase error is shown in Fig. 8(b). The phase has not been completely corrected, but the standard deviation of the remaining phase error was less than 0.1 radian. The remaining phase error is likely a result of the thermal cross-talk in the device as well as the fact that we can not achieve a full phase shift of 2π. Both of these issues can be corrected in future designs. Improved thermal isolation can be achieved between phase shifters by the use of independent metal traces for each. The design of the thermal phase shifter can also be modified in order to achieve a greater phase shift with a smaller applied power [14]. In Fig. 8(c) the peak transmission of each channel is plotted showing a channel spacing of 0.961 GHz. The transmission spectrum shows that, for this device, each channel is not identical. As a result the peak to side-lobe contrast varies from about −15 to −20 dB, and the adjacent channel cross-talk varies from −15 to −25 dB. Again, data is collected through the center input waveguide and normalized to 0 dB. Actual peak transmission ranged from −17 to −22 dB as expected due to the much greater waveguide lengths. Assuming the same 4 to 5 dB of fiber to chip coupling loss, the AWG shows around 12 to 18 dB of loss. This loss is largely a result of waveguide propagation loss and can be reduced either through changes in the waveguide geometry or improvement in the fabrication process. Increasing the waveguide width or moving to partially etched waveguide leads to lower propagation loss. Additionally, there is continual effort to reduce sidewall roughness which reduces propagation loss.
Fig. 8 (a) Transmission spectrum of each of the eleven channels of an AWG with 1 GHz channel spacing. The channels are not identical, and show peak to side-lobe contrast which ranges from 15 to 20 dB and adjacent channel cross-talk which ranges from −15 dB to −25 dB. (b) Remaining phase error measured using the interferometer. The standard deviation of the remaining phase is less than 0.1 radian. (c) Measured peak transmission of each channel, showing a channel spacing of 0.961 GHz.
8. Applications
In order to demonstrate the performance of the 1 GHz channel spacing AWG we used the device to create a RF channelizer. The idea of a photonic RF channelizer is that an RF signal is modulated on an optical carrier forming side-bands in the optical spectrum. These side-bands are then filtered and sent to different optical detectors using an AWG. Figure 9(a) shows a schematic of the setup used to implement this. A lithium niobate electro-optic modulator(EOM) is biased at its null point, allowing almost none of the carrier laser to pass. When an RF signal is applied to the modulator, light passes through, however, the frequency of the light is offset from the carrier frequency by the RF frequency. This light is then sent through the AWG, and the power at the output of each channel is recorded. Figure 9(b) and (c) show the output power measured at each channel with no modulation applied (blue curve) and with a 2GHz modulation (red curve). In Fig. 9(b) a pure sinusoidal modulation is applied, and optical power is detected at the channels corresponding to ±2 GHz. Due to cross-talk, optical power is detected at other channel outputs at a level approximately 20 dB lower than the peak signal. In Fig. 9(c) the modulation is changed to a triangular wave, demonstrating the detection of the fundamental frequency at ±2 GHz and the first harmonic at ±4 GHz.
Fig. 9 (a) Schematic of the experimental setup used to demonstrate a photonic RF channelizer. An RF signal is applied to a lithium niobate modulator biased at its null point. The RF signal is modulated onto a fixed wavelength carrier laser. The laser passes through the AWG and the power at each of the output channels is monitored. (b) The observed optical power at each output with(red curve) and without(blue curve) a 2 GHz sinusoidal modulation applied. The modulation appears as increased optical power detected at the channels corresponding to ±2 GHz. (c) The observed optical power at each output with(red curve) and without(blue curve) a 2 GHz triangular modulation applied. Similar to (b), optical power is detected at channels corresponding to ±2 GHz. Additionally, the first harmonic is observed at channels corresponding to ±4 GHz.
To demonstrate the flexibility of this AWG design, and also the advantages of dynamic phase error correction over static methods, we implemented spectral shaping in an AWG with 10 GHz channel spacing using the Gerchberg-Saxton algorithm [15]. This is an iterative algorithm, which was used to calculate a phase offset for each waveguide in order to approximate a desired target transmission spectrum. The space of achievable transmission spectrum shapes is limited by the number of arrayed waveguides, as well as by the fact that we are adjusting only the phase offset and not the amplitude. In Fig. 10(a) a phase offset was applied with the intended target of a transmission spectrum with eleven peaks with linearly increasing transmission amplitude. The blue curve shows the expected transmission spectrum calculated with the phases given by the Gerchberg Saxton algorithm, while the red curve shows the measured transmission. In Fig. 10(b), the target phase for each waveguide is shown in blue, while the measured phase of each waveguide is shown in red.
Fig. 10 (a) Target transmission spectrum calculated using phase offsets generated by the Gerchberg Saxton algorithm with a target shape of 11 peaks with linearly increasing transmission (blue curve) along with the measured transmission spectrum (red curve) after applying this phase offset to the AWG. (b) Phase offsets generated by the Gerchberg Saxton algorithm (blue circles) compared to the measured phase of the AWG.
As a final demonstration of the robustness of this device we measured the transmission spectrum of a single channel while increasing the optical power. Using an EDFA we were able to apply 85 mW of power to the device, measured just before the chip. We estimate the insertion loss of the inverse silicon taper to be −4 dB resulting in approximately 34 mW coupled onto the chip, just before the AWG. The shape of the transmission spectrum was not observed to change, however, the peak transmission shifted slightly as shown in Fig. 11(a). The peak shifted by approximately −70.4 MHz/mW. In Fig. 11(b), the peak shift with respect to temperature is shown for comparison. The shift resulting from increasing optical power could easily be compensated by a temperature change of only 0.006°C/mW.
Fig. 11 (a) Measured spectral shift of a single channel of the AWG as the optical power is increased. The shift was measured to be approximately −70.4 MHz/mW up to 34 mW of power. The maximum power just before the chip was measured to be 85mW with an estimated coupling loss of −4 dB). (b) For comparison, the spectral shift with temperature is observed to be about 11.2 GHz/°C.
9. Discussion
In conclusion we have have designed, fabricated and demonstrated operation of state-of-the-art silicon photonic integrated arrayed waveguide gratings. We have demonstrated a simple method of phase error correction which requires only a narrow linewidth laser and power meter. This method allows for up to 19dB of peak transmission contrast in AWG devices with 50 GHz and 10 GHz channel spacing. In order to optimze an AWG device with 1 GHz channel spacing we implement a swept-source interferometer in order to directly measure the phase error in each of the 35 waveguides. This technique allows for calibration of each of the 35 integrated phase shifters as well as calibration of thermal cross-talk between waveguides. With this information we are able to optimize the 1 GHz channel spacing AWG and demonstrate up to 20dB of peak to side-lobe contrast and up to −25 dB of adjacent channel cross-talk.
AWGs provide spectral filtering functionality which is useful for many applications. In order to demonstrate this we implement a photonic RF channelizer with 1 GHz resolution. The channelizer exhibits a background signal of less than −40 dB of optical power, and approximately −20 dB of cross-talk when detecting a 2 GHz sinusoidal signal. As a second demonstration, we show that we are able to apply arbitrary phase offsets to each of the 35 waveguides in order to shape the optical transmission spectrum. Finally, we show that device performance is not degraded by high optical intensities. While devices based on silicon micro-rings begin to show non-linear behavior at powers as low as 100 μW, the AWG is able to handle more than 30 mW of power with only a slight shift in peak transmission which can be easily corrected by thermal tuning.
This is the first demonstration of an AWG with a channel spacing of 1 GHz in a high index contrast platform. Additionally, the adjacent channel cross-talk observed in devices with 1, 10 and 50 GHz channel spacing is currently the best published result for high index contrast platforms with similar channel spacings [9, 10]. Thermal stability and thermal cross-talk between phase shifters remains the largest hurdle to further improvement of devices with 1 GHz channel spacing. Several routes exist for increasing thermal isolation between phase shifters such as the use of independent metal ground traces or the etching of trenches in the oxide between phase shifters. Another option is the use of electro-optic phase shifters which would entirely eliminate thermal cross-talk, although at the cost of a larger device footprint.
Acknowledgments
The authors would like to acknowledge funding from Georgia Tech Research Institute and the Office of Naval Research. Sandia is a multi-mission 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.
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