The capture, hold and forward release of an
optical pulse from a dynamic photonic crystal
nanocavity
Jeremy Upham,1,2,* Yuu Fujita,1 Yousuke Kawamoto,1 Yoshinori Tanaka,1
Bong Shik Song,1,3 Takashi Asano,1 and Susumu Noda1
1
Department of Electronic Science and Engineering, Kyoto University, Katsura, Nishikyo-ku, Kyoto 615-8510, Japan
2
Present address: the Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa Ontario K1N 6N5,
Canada
3
School of Electronic and Electrical Engineering, Sungkyunkwan University, Suwon Gyeonggi-do 440-746, Korea
*[email protected]
Abstract: 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
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1. 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 [1–9]. 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.
2. 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 QL, in-plane coupling to the upper (output) waveguide described by QU, and coupling to
free space modes out of the plane of the device according to QV. The QV term is determined
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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 (QinO 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 QL and QU 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
1 Q = 1 QV + (1 + cos θ L ) / Qin 0 + (1 + cos θU ) Qin 0 ,
(1)
where θL and θU 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
QV when both θL and θU = π. If one phase difference is lowered to 0 while the other is
maintained at π, Q will lower to 1/(1/QV + 2/Qin0), coupling to the one waveguide while
remaining isolated from the other. When QV is designed to be much larger than Qin0, this
tuning range can be approximated as between Qin0/2 and QV. 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 θL is set to 0 while θU is set to π. Thus the nanocavity can be
considered coupled to the lower waveguide while effectively decoupled from the upper
waveguide. (b) A signal light pulse with a bandwidth corresponding to Qin0/2 is injected from
the open end of the lower waveguide. (c) When the light energy in the nanocavity reaches
maximum, θL is switched to π. (d) The light energy is preserved in the nanocavity exhibiting
an exponential decay time ( e − t /τ ) determined by the total Q factor of the system (τ = Q/ωo).
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, θU is switched to 2π, lowering the
Q factor again to Qin0/2 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.
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Fig. 1. (a) Schematic of the double 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.
3. Samples fabrication and measurement
Double waveguide PC patterns were made from silicon on insulator wafers by electron beam
(EB) lithography and SF6-based inductively coupled plasma etching, followed by a wet etch
to remove the insulator below and produce air-suspended devices with a lattice constant
a1 = 408 nm, hole radius r = 0.29a1 and thickness t = 0.6a1. 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 QV 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 a2 = 393 nm [19]. The waveguides were
each separated from the nanocavity by a five rows to produce Qin0 of ~5000. To prevent
evanescent coupling between the two waveguides running parallel for ~220a1, 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 10a1 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 θL ~0, and θU ~π. The PC device was characterized by the timeresolved experimental set-up introduced in Ref. 9. A passively mode-locked laser produces
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4 ps Gaussian pulses centered at the nanocavity 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 θL and θU. 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
1018 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.
Fig. 2. (a) Composite SEM image of the PC device. (b) Time-resolved measurements of the
nanocavity field behaviour without dynamic capture or release (black), pulse capture then
release after 85 ps (blue) or 165 ps (green). (c) Upper waveguide output for each case. Inset:
linear scale view of released pulse is well matched to a Gaussian temporal profile (red dashed
line).
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,
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and 85 ps later performed pulse release via 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.
4. 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
2
2
by a Gaussian curve of the form e − t /2(3.4ps) (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 (FWHMreleased) of the released pulse in units
of energy:
2
2
2
 FWHM released 
 4ps 

 = ( 3.4ps ) − 
 ,
2
ln
2


 2 ln 2 
(2)
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 FWHMreleased 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.
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Log of upper waveguide output [a.u.]
-3
10
-4
10
-5
10
0
100
200
Time [ps]
300
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).
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 (θu = 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 Qin0 only. This suggests that reducing
the round trip time relative to the decay rate associated with Qin0 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 θU = 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 QV = 100,000, Qin0 = 5000, θL changes from
0.2π to π at pulse capture while θU 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 QV. (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 θU = 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
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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 QV 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 QV of 3.87 million [24], the initial θu 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 1a1. 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].
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 QV = 3.87
million and optimal initial conditions limiting the undesired leakage to other modes.
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 (a1 = 410 nm, r = 0.29a1 t = 0.53a1) 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.
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Fig. 5. Time-resolved measurement of nanocavity emission showing clear decay of the capture
state with a lifetime of ~1.6 ns.
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 1018 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].
5. 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.
Acknowledgments
This work was supported mainly by Grant-in-Aid for Scientific Research (S) and partially by
the Global COE Program of MEXT, Japan, and also partly by JSPS through the FIRST
Program initiated by CSTP. B. S. Song acknowledges the Human Resources Development
program (No. 20124010203280) of the KETEP grant funded by the Korean government,
Ministry of Knowledge Economy.
#179703 - $15.00 USD
(C) 2013 OSA
Received 12 Nov 2012; revised 31 Jan 2013; accepted 1 Feb 2013; published 7 Feb 2013
11 February 2013 / Vol. 21, No. 3 / OPTICS EXPRESS 3817