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We experimentally demonstrate a tunable delay element that is inherently insensitive to free-carrier loss and achieves up to 300ps of delay. It is capable of arbitrarily storing and releasing a pulse of light through dynamic tuning of a system of microcavities. The inherent storage time is more than 32 times the duration of the stored pulse.
©2010 Optical Society of America
1. Introduction
Delay elements play an important role in quantum computing [1,2] and optical signal processing [3,4] which calls for the need of efficient controlled delay elements with large characteristic storage time. Passive optical delay lines have a fundamental tradeoff between the bandwidth they can accept and the amount of delay they can deliver [5–7]. In order to break this limit dynamic tuning from an initially large bandwidth state (small group index) to a narrow bandwidth state (large group index) is required [8–11]. Recently such systems were demonstrated on a silicon chip using an all-optical analogue of electromagnetically induced transparency (EIT) [11,12] and a coupled cavity-mirror system [10]. However, the amount of delay demonstrated was significantly limited to much less than one-hundred picoseconds [10,11]. This small amount of delay is due to the absorption of the stored light by the free-carriers that are inherently required to dynamically capture, store and release the pulse of light. Here we propose a novel solution to this problem by separating the primary functionalities (capture, storage and release of the light pulse) of the light storage system into separate cavities. By doing so we can ensure that the light only minimally interacts with free-carriers. As a result we experimentally demonstrate delay that can be continuously varied over ~300ps (with an intrinsic exponential decay time of ~160ps). The delay achieved in our system is four times larger than previously demonstrated active optical delays [11,12]. Our technique is only limited by the quality of the cavities used and can be easily extended to nanosecond delays with lower-loss cavities which inherently have a longer photon life time [13].
Our proposed scheme for achieving tunable delay is shown in Fig. 1 . It consists of three rows of resonators. The first and last rows are used to capture/release a pulse of light into/from the system. The middle row is the low loss storage unit where the light circulates until it is released and is equivalent to the EIT structure in [11]. The system works as follows: 1) Capture stage: Light is input into the large-bandwidth capture switch represented by the top cavity (Fig. 1-Step 1). The capture cavity initially has the same resonant wavelength as the storage unit so light automatically couples into the storage unit. 2) Storing stage: Once the light is completely in the storage unit the resonant wavelength of the capture switch is detuned by injecting free-carriers (cavity color changes from blue to green as seen in Steps 2 and 3). This effectively decouples the light from the input/output waveguides, which dramatically increases the group index of the system. In addition, the light is isolated from the free-carrier loss used to tune the system. This is the key for achieving the large and low loss delays demonstrated here. 3) Release: The signal can be released at any time by injecting carriers into the release switch (the ring in the third row). This aligns its resonance (color changes from red to blue in Fig. 1 Steps 4 and 5) with the storage unit resonance. The light automatically leaks out into the output cavity and then into the output waveguide.
Fig. 1 Schematic the system and its operation principle, (Step 1) shows the acceptance state of the system. Bits are stored as shown in (Steps 2 and 3) then released in (Steps 4 and 5)
In order to prove that our device is insensitive to free-carrier loss we used time domain coupled mode theory to compare our design with the previously demonstrated EIT delay element [11]. The following describe the equations used to model the time evolution of a field a inside a resonator that is evanescently coupled to two waveguides with fields Ethrough and Edrop, respectively [14]:
where ωo and κ1,2 are the resonance frequency of the cavity and the coupling coefficient from through/drop waveguides to the resonator, respectively. The times τint, τthrough, and τdrop represent the field decay constants through internal cavity loss, coupling to the through port, and coupling to the drop port, respectively. Equation (1), (2) and (3) were applied to each of the cavities in Fig. 1 and they were coupled to each other by appropriate waveguide amplitudes (Ethrough and Edrop). In addition, we assumed that there was no internal cavity loss in order to highlight the effect of free-carriers and also let κ1=κ2 for simplicity. To model the effects of the free-carriers during the capture/release steps we applied Eq. (4), (5) and (6) to the evolution of the field a in the resonator over one round trip: where ΔN cm−3 (electrons) and ΔP cm−3 (holes) are the injected carrier densities, and Δβ and Δα represent the changes in the propagation and attenuation constants in a waveguide with effective index neff and length l (which is the circumference of the resonator) [11,15].The results of the coupled mode simulations are seen in Fig. 2 . Light is captured in the storage unit at t~100ps and released at t=700ps. By comparing Fig. 2(a) (our design) and Fig. 2(b) (EIT) it is clear that our system stores the light signal in the system for a considerably longer time (potentially as long as 4.5ns in this example which is solely limited by the very small coupling to the capture switch in Step 3) than the comparable EIT system. This is even with the order of magnitude larger carrier density (5E18 cm−3) used in this example (and consequently order of magnitude larger absorption coefficient). And this free-carrier loss insensitivity applies for a very large range of carrier concentrations as plotted in Fig. 3 where the stored power is negligibly affected by the increase in the injected carrier density in our proposed scheme as compared to the fast decay with increasing the injected carrier density in the EIT structure [11]. Therefore, it is clear that by separating the capture/storage/release processes our system can be made insensitive to free-carrier loss. While the EIT structure could avoid the free-carrier loss by operating in the high free-carrier loss state initially and then switching to a low loss state for storage (by pulling carriers from the system) the carriers would need to removed from the system in a time less than one photon life time of the rings (with the high loss), which is not realizable with current electro-optic modulators [15]. One tradeoff of our approach is that the resonances need to be shifted farther than in the EIT structure. This will require more carriers and consequently more power. In addition, the injected carriers will broaden the capture switches resonance slightly however this effect is minimal (in this simulation the resonance is broadened to Δλ=0.8nm from Δλ=0.3nm with a 6.7nm shift in resonance). However, the higher carrier concentration is an acceptable tradeoff in order to obtain order of magnitude higher storage times.
Fig. 2 (a) Numerical simulations of storing a 20ps pulse in the proposed system with an injected carrier density of 5E18cm−3. (b) Same data is stored in the EIT device proposed in [11] with an injected carrier density of 5E17cm−3.
Fig. 3 Numerical simulations of the stored power after 100picoseconds in the storage unit with different carrier densities. Our proposed scheme is in blue while a comparable EIT system in red.
We see in Fig. 2(a) that approximately one-third of the input signal is released from the system. The first loss occurs in the initial storage of the pulse where we see ~53% of the input power is stored in the system. Approximately one-third of the initial pulse is lost in the input ring during the storage process (Steps 2 and 3) where it is changed to another wavelength via adiabatic wavelength conversion and also absorbed by free-carriers [19]. The remaining loss occurs because when the input ring and EIT mode are initially aligned in Step 1 the presence of the input ring actually disrupts the overall phase of the EIT mode, essentially opening it slightly, which allows some of the light to escape out of the other ports of the storage unit [11,18]. This disruption of the phase of the EIT mode also occurs during the release process when the resonance of the release ring is aligned with the storage unit resonance, which causes the final drop of power seen at t=700ps in Fig. 2(a). However, we believe the overall efficiency observed in these simulations is not a fundamental limit of our scheme and can be considerably improved by carefully selecting coupling coefficients and utilizing more cavities in the storage unit [16,17].
2. Passive device analysis
We fabricated our proposed delay element on an SOI platform as shown in Fig. 4 using E-beam lithography (JEOL 9300) with negative resist XR-1541 6%. However, instead of using a separate release cavity we removed it in order to simplify our experimental setup. This is because we found that the cavities have slight variations in the resonance positions from their predicted values due to fabrication imperfections, which can be corrected with thermal tuning. In order to reduce the number of cavities that need to be heated we only use three cavities in the fabricated structure, as opposed to four, which significantly simplifies our experimental setup. The top cavity still works as a capture switch, and the remaining two make up the storage unit. We can use one of the cavities in the storage unit as a release switch. While carriers need to be generated in this switch our simulations show that the light interacts with these carriers for only a short single photon lifetime of the cavity, which only induces a small power loss [19,20].
Fig. 4 Scanning electron microscope image of the fabricated device with three ring resonators with a schematic of the capture and release process of the three ring system similar to Fig. 1 .
The fabricated rings have a diameter of 42µm with a separation between the two storage rings of 132µm. The rings diameter and their separation were chosen to ensure constructive interference of the storage units supermode [11]. The waveguide dimensions are 250nm in height and 600nm in width in order to increase confinement of the mode and consequently minimize the loss from scattering along the rough etched sidewalls of the waveguides. In addition, the input ring and one of the storage unit rings (used as an output switch) were designed to have a slightly smaller diameter (ΔR=−3nm). This will deliberately locate the resonances at shorter wavelength to allow for subsequent red-tuning. In the switching process the applied heat from carrier recombination shifts the resonances to the correct position (all three rings in resonance).
In order to couple data from the input port into the storage unit all the cavities in the system should have the same resonance. The loaded Q of the rings were measured to be 5000 with an intrinsic Q of 200,000 (). To align them we applied heat [21] (supplied by the external laser used to switch the cavities as explained in Section 3) to the top input ring and one of the storage unit rings, both of which are designed to be initially blue-shifted. Figure 5 shows the transmission through the middle port of the device with different heating. The initial resonances with no heating are shown in Fig. 5(a). It consists of an “open” EIT mode of the storage unit superimposed on the input ring transmission dip to the left the EIT peak. In order to move to a closed EIT state for storing data, heating is applied to the blue shifted storage ring (ring with slightly smaller radius initially) as shown in Fig. 5(b). Consequently, the EIT peak will vanish creating a large photon life time state of 165ps for data storage [11]. There is still some leakage to the capture ring, however it is very minimal provided this ring resonance is shifted enough in the capture step. The final step is to align the input ring to the storage unit in order to couple light into the storage unit. The transmission after red shifting the input resonance is shown in Fig. 5(c). The small peak in the transmission spectrum in Fig. 5(c) at ~1555.2nm results from imperfect alignment of resonances. Unfortunately, the heat from the external laser was not enough to force all the resonance to align perfectly. The misalignment could be avoided in future designs by ensuring that the resonances are better-aligned initially.
Fig. 5 (a) Shows the transmission through the middle waveguide without heating (Open EIT), while (b) shows the transmission with heating of the blue storage ring (Closed EIT), finally (c) depicts the case when all the rings are approximately in resonance through heating of the input ring and the blue storage ring.
3. Experimental Setup
We can now store and release pulses of light now that the resonances are aligned by heat. The complete experimental setup is shown in Fig. 6 . It consists of a Ti:Sapphire laser generating 100fs pulses at a repetition rate of 80MHz. The pulses are centered at a wavelength of 830nm. The pulses are split using a 50/50 splitter. One half will be used to generate the bit to be stored at 1550nm telecom wavelength. The second half will generate the storage and release pulses at a wavelength of 415nm, which is efficiently absorbed by silicon micro-cavities The first half of the 830nm pulse is converted to 1550nm using an OPO (optical parametric oscillator). The resulting signal is very broadband (~22.5nm due to the short ~200fs pulses) so the bandwidth of the pulse is reduced to match that of the rings in the system using a 0.25nm Tunable Grating Filter (JDS Uniphase TB3). To compensate for the 20dB reduction in the power after the filter an EDFA (Erbium doped fiber amplifier) is used. To eliminate the spontaneous emission noise from the EDFA we use another filtering stage with a bandwidth of 0.5nm. A variable delay line is then used to synchronize the data with the storage and release pulses. Next the pulses polarization is rotated to the TM state (E-field perpendicular to the chip) using a polarization controller and launched into the chip where it couples into the storage unit through the input ring. When the pulse is released it is detected with a fast photodetector (impulse response of ~33ps) and then recorded on an oscilloscope.
Fig. 6 Experimental setup used .The stored pulses are generated in an OPO crystal from 830nm Ti-Sapphire laser, while SHG is used to generate 415nm storage and release signals.
The second part of the 830nm pulses is converted to high energy blue light in order to switch the silicon cavities through linear absorption (which generates free-carriers). First the 830nm pulses pass through an Isolator to prevent any back reflection to the laser. Then 415nm blue light pulses are generated through SHG (second harmonic generation) in a BBO (beta barium borate) crystal. The resulting 415nm pulses are split using a 50/50 beam splitter where one half (store pulse) is used to store the light in the system and the second half (release pulse) is used to release the 1550nm light from the system at any arbitrary time (the time is adjusted with a translation stage). Both 415nm pulses are coupled to equal length fibers with cleaved ends which are placed in close proximity to their respective input/storage ring. While the pulses are short (~100fs) they induce a steady-state amount of heat via phonons produced by carrier recombination which is also used to tune the resonance positions as discussed in the previous section.
4. Results
As discussed earlier the data is stored and released in the following manner: First the 1550nm pulse is coupled through the input ring to the storage unit in the closed EIT state. While the data is inside the storage unit the 415nm storage pulse switches the input ring decoupling it from the storage unit. The stored data is released from the system at any time by opening the EIT mode using a release pulse which switches one of the storage rings slightly off-resonance. The spot size of the switching pulses is 50µm in diameter with an overlap of 4% with each ring. Carriers of concentration 4E17cm−3 are generated in the waveguide through absorbing a pulse of energy of 0.73pJ from the 20pJ incident pulse (assuming 4% mode overlap with the ring). This causes a resonance shift of 0.8nm in the rings which is more than adequate to ensure that there is no coupling to the capture/storage rings in the experiment with a broadening in resonance from 0.3nm to 0.37nm (reduction in Q from 5000 to 4000). The total storage time is controlled by varying the delay between the store and release pulses. As seen in Fig. 7 we are able to achieve different storage times which can be continuously varied from zero up to ~300 picoseconds as seen in the specific examples in plots Fig. 7(a-d) (the smaller oscillations in the data come from the impulse response of the detector as independently verified by analyzing pulses of different powers outside the chip).
Fig. 7 Different delays are measured through changing the time between the store and the release top pumping pulses.
This large delay, as compared to previous dynamically tuned structures [10,11], is inherently due to the absence of free-carriers in the storage unit of our system. We expect that using an identical system a delay of several nanoseconds is possible provided the inherent waveguide/cavity loss is low enough. Here our waveguide loss was measured to be an exceedingly high 8dB/cm due to fabrication issues which introduced considerable sidewall roughness. This loss could be reduced to less than 3dB/cm with similar waveguide dimensions and could be further reduced by using etchless waveguides (loss of <0.5 dB/cm) [22].
The initial larger peak seen at t~100ps is due to power that leaks out from the system before the storage process takes place. As discussed earlier the initial alignment of the input ring with the EIT mode slightly disrupts the overall phase of the EIT mode, allowing some light to escape the storage unit [11]. This peak was not visible in Fig. 2(a) because the output ring (which is absent in the experiment) does not transmit this initial peak. In the experiment there is also an additional power leakage from the imperfect closing of the EIT resonance using heat as seen and discussed in Fig. 5(c) along with the low extinction ratios of the resonators. This initial peak can be minimized by utilizing a storage unit with multiple cavities and by tuning the coupling coefficients [16,17].
In order to compare the quality of the storing process against previously demonstrated systems the output power at different delays was measured as shown in Fig. 8 . The system shows the expected exponential relation between output power and storage time. The characteristic decay time of the system is measured to be 160ps which is four times larger than previous systems [10,11]. In addition, data is stored for more than 32-times the pulse duration as opposed to a fraction of the input pulse duration as demonstrated in a passive delay element [23]. This delay is achieved with a maximum efficiency of 24% (relative to the input pulse), which significantly breaks the time-bandwidth limit of a single cavity. We would expect that a ~5picosecond pulse that is coupled to a cavity with a photon lifetime of ~160 picoseconds would have an efficiency of at a maximum of 3%. However, here we show more than 9% of the initial pulse is stored after 160 picoseconds in the unit which is significantly larger than the time-bandwidth limit of a passive single cavity. And without the leakage of the light to the other ports of the storage unit during the storage/release process we would expect the efficiency could be further increased. We should note that in order to achieve 100% efficiency multiple cavities would need to be used in order to completely store the input pulse as proposed elsewhere [16,17,24].
5. Conclusion
We proposed, analyzed, and experimentally tested a novel design for an active delay element which has numerous applications ranging from optical signal processing to quantum computing. The dynamic nature of the system breaks the time bandwidth limitations imposed by static cavities, resulting in a storage time of approximately 300ps.The storage time is only limited by the quality of the cavities used and could be significantly increased to several nanoseconds by using low loss cavities and by optimizing the fabrication process [9,10,12,13,23]. One tradeoff of our approach is it does require more power to realize the system (in order to ensure complete isolation of the capture switch from the storage unit). However, this is an acceptable tradeoff in order to achieve the large delays shown here.
Acknowledgments
This research was partially supported by a DARPA Young Faculty Award (Award No. N66001-09-1-2113) and the National Science Foundation under awardECCS-0824103. This work was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765).
Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of DARPA.
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