The capture , hold and forward release of an optical pulse from a dynamic photonic crystal nanocavity

We develop a silicon photonic crystal nanocavity device capable of performing targeted optical pulse capture and release via distinct ports on demand, based on dynamic Q factor control. The capture of 4 ps pulses and their release up to 332 ps later is directly observed by time-resolved measurements of the energy behaviour in both the nanocavity and emitted from the release port. We also discuss how the behaviour of excited free carriers dictates the performance of such dynamic devices. ©2013 Optical Society of America OCIS codes: (230.5298) Photonic crystals; (230.5750) Resonators; (130.0130) Integrated optics. References and links 1. Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater. 6(11), 862–865 (2007). 2. E. J. Reed, M. Soljacić, and J. D. Joannopoulos, “Color of shock waves in photonic crystals,” Phys. Rev. Lett. 90(20), 203904 (2003). 3. Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007). 4. S. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Phys. 1, 293–296 (2007). 5. J. Upham, Y. Tanaka, T. Asano, and S. Noda, “On-the-fly wavelength conversion of photons by dynamic control of photonic waveguides,” Appl. Phys. Express 3(6), 062001 (2010). 6. T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett. 102(4), 043907 (2009). 7. D. M. Beggs, I. H. Rey, T. Kampfrath, N. Rotenberg, L. Kuipers, and T. F. Krauss, “Ultrafast tunable optical delay line based on indirect photonic transitions,” Phys. Rev. Lett. 108(21), 213901 (2012). 8. J. Upham, Y. Tanaka, T. Asano, and S. Noda, “Dynamic increase and decrease of photonic crystal nanocavity Q factors for optical pulse control,” Opt. Express 16(26), 21721–21730 (2008). 9. J. Upham, Y. Tanaka, Y. Kawamoto, Y. Sato, T. Nakamura, B. S. Song, T. Asano, and S. Noda, “Time-resolved catch and release of an optical pulse from a dynamic photonic crystal nanocavity,” Opt. Express 19(23), 23377–


Introduction
Nanophotonic devices, particularly photonic crystals (PC), provide precise spatial control of optical modes that in combination with temporal variations of their characteristics can lead to the dynamic manipulation of photons [1][2][3][4][5][6][7][8][9].We proposed that the dynamic control of a twodimensional (2D) PC nanocavity quality (Q) factor [10], which is proportional to its photon lifetime, could be achieved by manipulating the interference between two modes in a waveguide port connected to the nanocavity [1,8].Increasing the Q factor of a nanocavity from a low Q state to a high Q state just as light is coupling into the resonant mode can capture that energy in the resonant mode more effectively than a static system, and decreasing the Q factor later can release the captured energy on demand [3,9].This targeted capture of light in resonant modes with wavelength-order modal volumes for extended photon lifetimes (increased Q factors) could be applied to the slowing or stopping photons [11,12], the enhancement of light-matter interaction [13,14] and the manipulation of strong coupling behaviour [15,16].
We recently showed that direct, time-resolved measurements of the light amplitude inside the nanocavity during dynamic Q control provided a clear picture of the evolution of photon behaviour [9].However, such experiments did not measure the light released from the nanocavity.Furthermore, the investigated structure released the captured light back down the incident port, far less useful than releasing it out a different port, potentially to other devices.In this work we developed a PC nanocavity-based device with two independently controlled Q factors capable of dynamically capturing an optical pulse introduced via one port, then dynamically releasing it via a second port.By observing both the light amplitude in the nanocavity and at the output port, this process of dynamically delaying a pulse could be quantitatively appraised, including the influence of the initial conditions and the lifetime of photo-excited carriers.

Dynamic Q control
The device shown in Fig. 1(a) is a straightforward extension on our original dynamic Q system [1,8].A nanocavity is flanked by two equally spaced, identical waveguides, each of which is bound at one end by a hetero-interface.The total nanocavity Q factor is principally determined by three components: in-plane coupling to the lower (input) waveguide described by Q L , in-plane coupling to the upper (output) waveguide described by Q U , and coupling to free space modes out of the plane of the device according to Q V .The Q V term is determined by the nanocavity structure itself [17] with minor influence from imperfections introduced by the fabrication process [18].For a waveguide with open ends, the in-plane Q factor would be determined mainly by the nanocavity-waveguide separation (Q inO for either waveguide) but here the hetero-interface acts as a reflector [19], causing one optical path to double back and interfere with the other.Therefore both Q L and Q U can be individually manipulated by changing the refractive index of a portion of their waveguide, altering the phase difference between two optical paths.The total Q factor is then expressed as where θ L and θ U are the phase differences between the two optical paths of the lower and upper waveguides, respectively.In this system the nanocavity Q factor rises to its maximum Q V when both θ L and θ U = π.If one phase difference is lowered to 0 while the other is maintained at π, Q will lower to 1/(1/Q V + 2/Q in0 ), coupling to the one waveguide while remaining isolated from the other.When Q V is designed to be much larger than Q in0 , this tuning range can be approximated as between Q in0 /2 and Q V .The sequence we propose for dynamic capture and on-demand forward release of a light pulse in this two waveguide system is as follows: (a) Initially θ L is set to 0 while θ U is set to π. ) determined by the total Q factor of the system (τ = Q/ω o ).Without dynamic Q control, light coupled to the nanocavity in the low Q state would have a short cavity lifetime, but irradiating the lower waveguide with a control pulse changes the interference condition and catches energy in the nanocavity by suddenly increasing the cavity lifetime (Fig. 1(b)).(e) At some later time of our choosing, θ U is switched to 2π, lowering the Q factor again to Q in0 /2 by coupling the nanocavity to the upper waveguide while leaving it decoupled from the lower waveguide.The energy is released along the upper waveguide as a light pulse (Fig. 1(c)).The dynamic switching of the phase differences are executed by control pulses striking the waveguides, where they are partially absorbed, exciting free carriers and inducing a change to the refractive index [20].
In our previous work we used time-resolved measurements of the vertical emission from the nanocavity to observe the cavity field behaviour and confirmed pulse catch and release using a dynamic Q factor control [9].Irradiating the lower waveguide with a control pulse changes the interference condition and catches energy in the nanocavity by suddenly increasing the cavity lifetime.Introducing the second waveguide separates the input and output ports [21], which is of practical importance not only because light scattering at the sample input facet prevented the study of the released light in the previous one-waveguide configuration, but because releasing the pulse along an alternate path makes it possible to use this system as an on-chip, variable delay line.

Samples fabrication and measurement
Double waveguide PC patterns were made from silicon on insulator wafers by electron beam (EB) lithography and SF 6 -based inductively coupled plasma etching, followed by a wet etch to remove the insulator below and produce air-suspended devices with a lattice constant a 1 = 408 nm, hole radius r = 0.29a 1 and thickness t = 0.6a 1 .The nanocavities themselves consist of a line of three missing air holes (an L3 nanocavity), with the three holes at each edge shifted to provide experimental Q V of 80,000-100,000 [22] and resonant wavelengths near 1550 nm (Fig. 2(a)).Waveguides were formed near the nanocavity by line defects in the PC pattern and the hetero-interfaces acting as reflectors were placed about 110a away by writing PC regions with a smaller lattice constant a 2 = 393 nm [19].The waveguides were each separated from the nanocavity by a five rows to produce Q in0 of ~5000.To prevent evanescent coupling between the two waveguides running parallel for ~220a 1 , portions of each waveguide were given different widths.Each waveguide has a width equivalent to one row of missing air holes (W1) from its hetero-interface to 10a 1 past the nanocavity, but are made slightly wider (W1.05) along the rest of the device.The resulting difference between the waveguide dispersion curves is sufficient to inhibit cross-talk between the top and bottom waveguides where they have different widths, without being large enough to produce detectable reflection at the interfaces between the W1 and W1.05 regions in either waveguide.For a pulse coupling to the nanocavity, the group velocity in the W1 waveguide is ~0.06c, producing a round trip time between nanocavity and hetero-interface of about 5 ps.The initial phase differences are set to θ L ~0, and θ U ~π.The PC device was characterized by the timeresolved experimental set-up introduced in Ref. 9. A passively mode-locked laser produces 4 ps Gaussian pulses centered at the resonant wavelength (1550 nm), and the light beam is divided into four portions.A portion of the beam is amplified and introduced into the input facet of the lower waveguide from free space with TE-polarization as the signal pulse.Two other portions of the beam are amplified, independently delayed and frequency doubled to produce 4 ps control pulses at 775 nm that focus on the surface of the device with sufficient intensity to dynamically produce a π increase to θ L and θ U .Inducing a phase change π requires ~2 pJ from a control pulse be absorbed along ~10 µm of the waveguide between nanocavity and hetero-interface, exciting free carriers with an estimated mean density of 6 x 10 18 cm −3 to reduce the refractive index by ~0.3%.Light vertically emitted from the nanocavity or scattered from the upper waveguide's output facet is collected and made to interfere with a delayed and phase-modulated portion of the original beam that acts as a reference pulse.The cross-correlation interference between the device output and the reference as a function of delay produces time-resolved measurements of the amplitude of the signal light leaving the device via either of these ports with a resolution of ~4 ps.
Figures 2(b) and 2(c) show the log-scale, time-resolved field amplitude of light vertically emitted from the nanocavity and scattered from the upper waveguide output, respectively, measured for various dynamic control conditions of the interference phases.If the initial, low Q conditions are kept constant, there is a rapid increase and then decrease of the light amplitude in the nanocavity (black curve in Fig. 2(b)), which indicates that the time required for the coupling between the lower waveguide and the nanocavity is short (τ < 4ps, Q ~5000).The output from the upper waveguide in this case (black curve in Fig. 2(c)) also shows output over this brief time despite the initial coupling Q between the upper waveguide and the nanocavity being high.The reason for this is discussed later.Next we performed pulse capture by irradiating control pulse 1 as the signal pulse was introduced into the nanocavity, and 85 ps later performed pulse release the upper waveguide by irradiating control pulse 2. The nanocavity amplitude (Fig. 2(b) blue curve) shows a short coupling time (τ < 4ps Q ~5000) for the pulse injection, then a clear increase to τ = 40 ps (Q~48,600) starting at the moment of pulse capture, and finally a rapid decrease of the lifetime at the moment of release.The behaviour of the nanocavity field is consistent with pulse capture and release observed from a single waveguide dynamic Q system [9].The release port (Fig. 2(c) blue curve) again shows an initial peak when the signal pulse couples to the nanocavity, then some low level leakage during pulse holding, before emitting a clear pulse of light at the moment of release.The experimental results for longer delays between pulse capture and release (165ps) is also plotted in Figs.2(b) and 2(c) with green curves, showing the same behaviour.Therefore, the light observed from the upper waveguide can consistently be divided into these three components: initial peak, intermediate leakage and released pulse.

Performance analysis
These time-resolved results also provide an opportunity to examine the temporal characteristics of the released pulse itself.While the temporal resolution limit of the crosscorrelation measurement system is limited to 4 ps (the temporal width of the reference pulse in units of energy), with consideration of what the data represents, it is still possible to estimate the temporal profile of the released pulse.The inset of Fig. 2(c) shows the pulse released after 80 ps in a linear rather than logarithmic scale.The pulse can be reasonably fit by a Gaussian curve of the form (red dashed line in inset of Fig. 2), but this curve is a convolution of the field amplitude of the released pulse with that of the reference pulse and does not directly provide a temporal width for the released pulse in units of energy.As the reference pulse and the convolution of the two pulses appear Gaussian, we assume the released light can be estimated by a Gaussian as well and thus we use the known variances to determine the temporal full width half maximum (FWHM released ) of the released pulse in units of energy: ( ) where 3.4ps and 4ps in the right hand side are the measured FWHM of cross-correlation profile and FWHM of reference pulse profile in units of energy, respectively.Equation (2) suggests FWHM released is 4 ps.The resolution limit prevents a more detailed description of the pulse shape, but this does suggest that the released light has a temporal profile very similar to the original 4 ps signal pulse.This is reasonable considering that the low Q state was designed to match the temporal width of the incoming signal pulse in order to facilitate coupling to the resonant mode.When the system returns to the same low Q state at pulse release, the ~4 ps cavity lifetime will dictate the temporal width of the released pulse.Figure 3 shows the results of pulse catch hold and release experiments with various hold times of our choosing.The decay of the amplitude of the released pulse versus the holding time corresponds to the energy loss rate of the photons inside the nanocavity due to various sources (discussed later).In this particular device, our time-resolved measurement system can observe a clear release pulse with release timing up to 332 ps after capture.Thus the 4 ps pulse can be held for as long as 83 pulse widths and still be detectable upon release.To describe the other characteristics of the output we fit coupled mode theory simulations [9] to the experimental data, which can explain features of the upper waveguide output, such as the initial peak observed when the signal pulse couples to the nanocavity and the intermediate light leakage observed between catch and release.The initial peak visible from the output waveguide when pulse capture first occurs is caused by light escaping the nanocavity before the interference condition that determines the high Q condition in the upper waveguide (θ u = π) is established.In this particular sample it takes 5 ps for light to travel from the nanocavity to the hetero-interface and back again because the round trip length is 89 μm and the estimated group velocity of the light is 0.06c.In the intervening time some of the light in the nanocavity can escape to the output port because the coupling to the waveguide is determined by Q in0 only.This suggests that reducing the round trip time relative to the decay rate associated with Q in0 could significantly reduce this source of loss.The light leakage observed between the catch and release events can be attributed to a slight offset of the high Q condition from the ideal θ U = π, which can be attributed to variations the fabrication process producing small changes in the dispersion curve of the W1 waveguide between nanocavity and hetero-interface.Coupled mode simulations fit the experimental results when Q V = 100,000, Q in0 = 5000, θ L changes from 0.2π to π at pulse capture while θ U is initially 0.9π and increased to 2π at the moment of release (red curves).
These simulations can also evaluate the performance of our device design by evaluating how the energy coupled into the nanocavity will be distributed between the released pulse and the different sources of loss as a function how long the high Q state is maintained.The losses considered are: (1) Vertical emission from the nanocavity, which is determined by Q V .(2) Free carrier absorption that occurs because the free carriers photo-excited by the control pulses to induce the dynamic change of refractive index also attenuate a portion of the signal responsible for the high Q interference condition [9].(3) The initial loss of light out of the upper waveguide before the high Q interference condition is established.(4) The gradual leakage of light during pulse capture due to the θ U = π condition for decoupling the upper waveguide from the nanocavity not quite being met.Vertical emission and initial loss can be attributed to the device design and gradual leakage can be attributed to error at the fabrication level, while free carrier absorption is inherent to all silicon devices that use the excitation of free carriers for dynamic control.Figure 4 shows how the energy captured in the nanocavity is distributed between the release pulse and the different sources of loss as a function how long the light is held in the high Q state.The minimum hold time simulated here is 36 ps, because it is difficult to clearly distinguish the different outputs for shorter hold times.Using the parameters fitted to the experimental results of Fig. 3, the distribution of the captured energy showed that while the initial loss and gradual leakage out of the upper waveguide seen in experiment are noticeable factors, vertical emission and free carrier absorption were also significant sources of loss (Fig. 4(a)).Longer times between capture and release result in more of the light being lost to vertical emission, upper waveguide leakage and especially free carrier absorption, reducing the amount of light available to be released.At the design level, using nanocavities with inherently higher Q V could reduce vertical emission, while bringing that hetero-interface closer to the nanocavity in the upper waveguide would establish the high Q condition more quickly and could thus reduce initial losses.Interstitial leakage from the waveguide during pulse capture can be reduced post-fabrication by thermally tuning the interference condition [23].Next we consider how much such a system would be improved by optimization of the device design and fabrication process.Figure 4(b) simulates the performance of a device that is designed to minimize coupling losses and is perfectly fabricated, with a Q V of 3.87 million [24], the initial θ u is set to exactly π, and the time required to establish the dynamic high Q state is reduced to femtoseconds by shortening the distance between the nanocavity and the hetero-interface to 1a 1 .This ideal system reduces coupling of the captured light to external modes to negligible levels, however holding the light more effectively in the captured state makes it more susceptible to free carrier absorption.For this particular design the gains in how much light is captured and how long it can be held are significantly offset by the increased absorption.Limiting the impact of this absorption by reducing the amount of captured light exposed to the free carriers has been demonstrated for PC nanocavities [9] and similarly for coupled ring resonator devices [25], but improvements to how photons are held risk being offset by a corresponding reduction in the dynamic range of Q.Other possibilities for reducing the influence of the free carriers might include offsetting the balance of the interfering optical paths to compensate for absorption [26] or inducing the change in interference condition by making the dynamically changed region inaccessible to light [27].Even if the free carrier absorption losses described above could be neglected, the pulse capture state cannot be held indefinitely.To appraise the influence of carrier decay on dynamic Q factor control, we repeated the pulse capture experiment for another PC sample with the same design (a 1 = 410 nm, r = 0.29a 1 t = 0.53a 1 ) that showed clearer vertical emission and thus could be used to observe the cavity energy behaviour with a greater dynamic range.Figure 5 shows the vertical emission from the nanocavity during pulse capture, where the Q factor ranged from ~6000 to 40,000.Because a larger range of cavity energy behaviour is visible above the noise floor, we can now detect the decay of the capture state after several hundred picoseconds.Fitting the coupled mode theory simulations to the experimental results required incorporating a decay to the change of phase difference induced by dynamic control, suggesting that the density of photo-excited carriers in the waveguide (~6 x 10 18 cm −3 ) is declining exponentially with a lifetime of 1.6 ns.Because of the high surface to volume ratio in a thin PC slab, this lifetime is considered to be principally determined by carrier recombination at the silicon-air surfaces.The observed carrier lifetime suggests a surface recombination velocity of ~4000 cm/s, which is reasonable for thin, patterned silicon slabs [28].Because the surface conditions can vary between samples, devices measured to date have shown carrier lifetimes ranging between 1.4 and 1.8 ns.In order to overcome the limitations imposed by the finite carrier lifetime and free carrier absorption it would be desirable to design the device such that free carriers are only present during the short period when dynamic changes are being induced at the moment of catch and release event, rather than for the entire time that photons are held.This would necessitate creating devices with significantly shorter free carrier lifetimes (on the order of a few picoseconds) and still capable of dynamic control [29].

Conclusion
In summary, we developed a silicon PC device with two independently controllable Q factor components, demonstrating the capture and forward release of an optical pulse on demand.Time-resolved measurements of the field in the nanocavity and from the output port demonstrate that a 4 ps pulse can be dynamically captured, held for as long as 332 ps, then released again as a pulse of similar temporal width.This compact, all-optical yet dynamic system capable of delaying a pulse by 83 pulse widths demonstrates that such a device could lead to applications in signal processing and deeper investigations into the physics of lightmatter interaction.However, these results also suggest that gains made by further refinement of the device design will be limited by a commensurate increase in absorption losses and limited by the lifetime of the carriers.In the development of dynamic silicon nanophotonics employing free carriers [3-8, 16, 26], the carrier effects that make this dynamic photon control possible must themselves be controlled.

Fig. 1 .
Fig. 1.(a) Schematic of the waveguide dynamic Q control PC device design.The signal pulse can be captured in the nanocavity with an extended photon lifetime by control pulse 1 striking the lower waveguide and shifting the phase difference between the optical modes from 0 to π.At some later time the held light can be preferentially released along the upper waveguide by control pulse 2 shifting the phase difference of the upper waveguide from π to 2π.Sketch of (b) nanocavity emission and (c) upper waveguide output behaviour during pulse catch and release.

#Fig. 3 .
Fig.3.Time-resolved measurement of output from the upper waveguide for on-demand releases from 52 ps up to 332 ps after pulse capture.Coupled mode simulations are fit to the experimental data to determine the device parameters (red curves).

Fig. 4 .
Fig. 4. Simulations of how the energy in the nanocavity is distributed among the different outputs for hold times in the high Q state ranging from 36 to 450 ps.(a) Energy distribution for parameters fit to the experiment.(b) Energy distribution for an ideal structure with Q V = 3.87 million and optimal initial conditions limiting the undesired leakage to other modes.

Fig. 5 .
Fig. 5. Time-resolved measurement of nanocavity emission showing clear decay of the capture state with a lifetime of ~1.6 ns.