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Adiabatic wavelength redshift by dynamic carrier depletion
using p-i-n-diode–loaded photonic crystal waveguides
K. Kondo and T. Baba
Phys. Rev. A 97, 033818 — Published 13 March 2018
DOI: 10.1103/PhysRevA.97.033818

Adiabatic Wavelength Redshift by Dynamic Carrier Depletion
using p-n Diode-Loaded Photonic Crystal Waveguides
K. Kondo1,2 and T. Baba1
Department of Electrical and Computer Engineering, Yokohama National University,
79-5 Tokiwadai, Hodogayaku, Yokohama 240-8501, Japan2
Photonics Integration System Research Center, Laboratory for Future Interdisciplinary Research of Science andTechnology, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midoriku, Yokohama 226-8503, Japan1

We demonstrate an adiabatic wavelength redshift using dynamic carrier depletion. Free carriers are
first induced through two-photon absorption of a control pulse and then extracted by a reverse-biased
p-i-n diode formed on a Si photonic crystal waveguide, resulting in rapid carrier depletion. A
co-propagating signal pulse is redshifted by the consequent increase in refractive index. We
experimentally evaluated the dynamics of the carrier depletion by the pump-probe method andexplored the suitable condition for adiabatic redshift. The signal’s redshift was observed, and wasconfirmed to originate in the dynamic carrier depletion. The redshift was experimentally determined
as 0.21 nm.
DOI:
I. INTRODUCTION
Wavelength conversion can be induced by dynamic
tuning of the refractive index. This phenomenon, called
adiabatic wavelength conversion, was suggested in atheoretical demonstration of the stop-light technique [1].
Since then, adiabatic wavelength conversion itself [2–8] andits advanced functions, such as Q-factor switching [9],ultrafast delay tuning [10,11], spectrum tuning [12], pulse
reflection in a moving index front and the consequent
Doppler shift [13–16], pulse compression [14,17], andon-demand pulse transfer [18], have been demonstrated bymany groups. However, to our knowledge, previous
experimental demonstrations have employed carrier
generation through photon absorption because it is a very
simple approach for changing the refractive index for an
optical pulse which passes at the speed of light. All of theseexperiments have reported a blueshift caused by the negativeindex change at the instant of carrier generation. An
adiabatic redshift would expand the flexibility of the tuning
and capability of the above applications. However, inducing
a redshift by positively changing the refractive index is adifficult task in integrated devices composed of common
materials. For example, the thermal-optic effect andelectrical control of the carrier-plasma effect cannot switch
at sufficient speed. The optical Kerr effect can change theindex at sufficient speed but induces not only the redshift at
pulse rise but also the blueshift at pulse fall simultaneously.
Furthermore, it is degraded by two-photon absorption (TPA)
and the subsequent free carrier absorption (FCA) in Si. In
this study, a redshift induced by a positive dynamic index
change is achieved by using free carrier generation by the
TPA and carrier extraction in a reverse-biased p-n diodeembedded on a photonic crystal waveguide (PCW). The
initial carriers for the following depletion are generated by ashort optical control pulse. These carriers are instantly
extracted by the depletion layer field, achieving thehigh-speed carrier depletion of shorter than several tens
picoseconds. Furthermore, we employ a lattice-shifted PCW(LSPCW) generating low-dispersion slow light pulses [8,19],
which enhances the TPA with the square of the group index,
and thereby improves the redshift. This process is carried out
in a co-propagating slow-light system in which we
previously demonstrated an adiabatic blueshift [8]. If aredshift can be demonstrated in the same system, we canrealize a bi-directional wavelength conversion in a single
system.
This paper describes our approach for inducing dynamic
redshift, and the device fabricated by a complementary
metal oxide semiconductor (CMOS) process. Next, weevaluate the carrier-depletion dynamics in the LSPCW by
the pump-probe method. Finally, we demonstrate theadiabatic redshift in the LSPCW and investigate its
dependence on the carrier dynamics.
II. PRINCIPLES AND DEVICE
Figure 1 schematizes the approach of generating theadiabatic redshift. First, the LSPCW loaded with aFIG. 1 (Color online) Schematic of the adiabatic redshift inthe LSPCW and the corresponding carrier density along the
waveguide.

reverse-biased p-n diode receives a high-power control pulse
and generates free carriers through the slow-light-enhanced
TPA. The index change of the order of 0.001 is induced by aseveral-tens-watts-level control pulse. The control pulse isadministered over a few picoseconds and the TPA occurs
with a sub-picosecond response time, meaning that thecarriers are generated within the pulse duration. The
generated carriers are instantly extracted by the reverse bias.
The lower panel of Fig.1 reveals a schematic of acarrier-density transition along the center line of the LSPCW.
The signal pulse propagating just behind the control pulse
encounters a positive index change Δn, and is consequently
redshifted. In such a co-propagating slow-light system, thewavelength shift Δλ is given by [8]λn g ξ

∂Δn( z , t ) dz
cn ∫ ∂t,∂λξ=Δn( z , t ) dt
n ∫ ∂t

Δλ =

C

(1)

C

where ng, c, z, and t denote the group index, the speed oflight in a vacuum, position in the LSPCW, and time,
respectively. ξ ≡ (n/ω)(∂ω/∂n) describes the dependence ofthe normalized photonic band frequency on the normalizedindex change, where ω and n are the frequency of the lightand the material index of the LSPCW, respectively. C is the
trajectory of the signal pulse, which satisfies t = (ng/c)z.
According to Equation 1, the redshift is enhanced byincreasing the index-change rate and elongating the overlap
duration of the signal pulse and dynamic carrier depletion.
Hence, a large redshift requires high-speed carrier depletionand group-velocity matching between the control and signal
pulses.
The LSPCW was fabricated on a silicon-on-insulator
wafer by the CMOS process. The Si layer was 210 nm thick.
The LSPCW was 400 μm long and cladded with SiO2.
Figure 2 is a magnified view of the center of the LSPCW
and its corresponding mode profile. To obtain the
low-dispersion band at an approximate wavelength of 1550

FIG. 2 (Color online) Structure and characteristics of the
LSPCW. (a) Shown is a top view of the fabricated LSPCW and(b) its corresponding optical intensity profile. The third-rows
holes (filled with SiO2) are shifted in the propagation direction by
s3. The intensity profile was calculated by a three-dimensional
finite-difference time-domain method, and was averaged over the
propagation band between the photonic band gap and light cone.

nm, we set the lattice constant a, hole diameter 2r, andthird-rows lattice shift s3 to 400, 215, and 110 nm,
respectively [20]. This device yielded ng ~ 24 in the
low-dispersion band. The optical pulse was sent from anexternal lensed fiber to the LSPCW through a spot-size
converter (SSC) [19] and a Si wire waveguide with a total
coupling loss of 3.5 dB. For high-speed carrier depletion, we
employed a p-i-n junction, adjusting the intrinsic-region
width until the depletion layer largely overlapped the opticalmode corresponding to the carrier- generation profile. The p
and n regions were formed by boron-ion (concentration:
10.5 × 1017 cm−3) and phosphorus-ion (6.2 × 1017 cm−3)
implantation, respectively. Furthermore, to contact the Al
electrodes, deeply doped p+ and n+ regions (1.9 × 1019cm−3) were formed on the outside of the p and n regions,
respectively. We set the distance between the p+ and n+regions to 3.8 μm.
III. CARRIER DEPLETION SPEEDAs described above, the large redshift is conferred byhigh-speed carrier depletion. We experimentally exploredthe conditions under which high-speed depletion occurs
under the signal pulse. The carrier-depletion dynamics wasevaluated by the pump-probe method. The control pulse(corresponding to the pump pulse) was first sent to the
LSPCW for free-carrier generation, followed by the signal
pulse (probe pulse) with a delay of Δt. The carrier density
under the signal pulse at Δt was estimated from the loss ofthe signal output, which here depended on the FCA.
Therefore, the temporal transition of the carrier density canbe obtained by acquiring the signal’s output power withchanging Δt [21]. The output power is exponentially
proportional to the FCA coefficient, which is itself
proportional to the carrier density [22]. Therefore, we
evaluated the signal loss by assessing the relative absorbance−log(P/P0), where P and P0 are the signal outputs with andwithout the control pulse, respectively. The optical setup for
generating the control and signal pulses is detailed in Ref.
[11]. After removing the control pulse by a band pass filter,
we measured the signal output by an optical power meter.
For maintaining the input Δt while the propagation in the
LSPCW, we set the control and signal pulses in the
low-dispersion band. However, the control and signal
wavelengths were separated for retaining only the signal
pulse in the LSPCW output. The lengths of the control andsignal pulses were set to 3.5 and 5.5 ps, respectively. By
setting the input power of the signal pulse to 0.8 W, we
suppressed the self-TPA of the signal and ensured asufficient signal-to-noise ratio at the output. Figure 3(a)plots the signal absorbance versus Δt under various bias
voltages Vbias and both low- and high-power control pulses(Pcon = 7.4 and 30 W, respectively). When Δt < 10 ps, thesignal pulse overlaps the control pulse and is excessively
decreased by the TPA generated between them. Therefore,
in the Δt ≥ 10 ps region, the absorbance originated by FCA
alone. For a clear comparison, each absorbance wasnormalized by its value at Δt = 10 ps. The carriers weredepleted by the reverse bias and the absorbance rapidly
decreased at early Δt. The initial decline was accelerated athigher reverse biases. At later times, the decrease slowed
under all bias voltages. This slow decrease might be sourced
from FCA in the 200-μm long SSC and the 30-μm long Si
wire waveguide. The initial rapid decline in carrier numbers
appeared to decelerate at higher powers of the control pulse,
possibly reflecting a space-charge effect [23,24]. When
excess carriers are generated, the free electrons andoppositely drifting holes create a space-charge field thatinternally cancels the depletion-layer field. Consequently,
the depletion speed reduces. Comparing the absorbances on
the same scale (Fig. 3(b)), increasing Pcon still improved thedepletion rate (i.e., the slope became large) when Δt ≥ 10 ps.
In the experiment, the carrier-depletion rate was raised atsmaller Δt, higher Vbias, and higher Pcon. Such a simple
feature enables easy tuning of the redshift. The excess loss

FIG. 3 (Color online) Measured results of the carrier-depletion
dynamics, evaluated by the absorbance at Δt for (a) different Vbias(distinguished by color) and Pcon (distinguished by panels) and (b)different Pcon. Gray region highlights the delay range in which thecontrol and signal pulses overlap in the LSPCW.

of the adiabatic-redshift tuning can also be estimated fromthese results. For Δt = 10 ps, Vbias = −25 V, and Pcon = 30 W,
the loss due to the tuning was approximately 5 dB.
IV. EXPERIMENT ON DYNAMIC REDSHIFTThe dynamic redshift was tested on the same setup as theabove-mentioned pump-probe measurement. Here weobserved the output spectrum of the signal pulse on an
optical spectrum analyzer. The lengths and peak powers
were set to 2.0 ps and 30 W respectively for the control
pulse, and to 7.0 ps and 0.8 W respectively for the signal
pulse. Figure 4 shows color maps of the signal output
spectra as functions of Δt at different Vbias values. The signal
spectra obtained with no control pulse are also exhibited forcomparison. Regardless of Vbias, the signal pulse wasredshifted when the control pulse was applied at Δt ≥ 10 ps.
Observing the spectral centers (white-solid and black-dottedlines), we confirm a larger redshift at higher voltage andsmaller Δt. Moreover, the redshift diminished withincreasing Δt. These trends confirm that the redshift
originates in the dynamic carrier depletion zone andincreases with increasing speed of the depletion process. A
feature arising from the carrier dynamics appeared also in
the length of Δt yielding the redshift. As the reverse bias
increased, the redshift was obtained in a comparatively short
Δt span because the carrier depletion was completed within ashort time. In contrast, at low reverse biases, the redshift was
small and long-lasting because the carriers were slowly
depleted.
As Δt approached zero, the two pulses overlapped and thesignal spectrum was expanded by the dynamic carrier
generation and the optical Kerr effect of the control pulse.
The spectral center of the signal then converted to blueshift.
Here, the signal spectrum was expanded because the signal
pulse was longer than the control pulse and was subjected(in part) to nonlinear effects [17]. However, a simple
blueshift sourced from carrier generation can be achieved byapplying a longer control pulse than the signal pulse [8].
Therefore, both the redshift and blueshift can be achieved
merely by changing the input timing of the control pulse,
thereby improving the flexibility of the adiabatic wavelength
conversion.
For Δt = 12 ps, Vbias = −25 V and Pcon = 30 W, the redshift(evaluated in the spectral center) reached 0.21 nm (see Fig.
5). The ripple in these spectra was caused not by dynamic
tuning, but by the transmission characteristics of the
LSPCW. The redshift was clearly obtained, but was an orderof magnitude smaller than the experimentally obtained
adiabatic blueshift [2,4–8]. The redshift may have been
diminished by slowdown of the carrier depletion under the
space-charge effect [23,24]. The space-charge effect clearly
appeared under a high-powered control pulse. Hence, theimprovement of the carrier depletion rate increasing thecontrol-pulse power and/or the ng of the LSPCW (i.e.,enhancing the slow light effect) is restricted. However, thespace-charge effect can be alleviated by optimizing the p-i-njunction structure. For example, it has been reported that the
space-charge effect can be suppressed by optimizing thewidth of the intrinsic region and offset of the intrinsic-

region center from the absorption region (corresponding to
the LSPCW’s center in this work) [24].
V. CONCLUSION
An adiabatic redshift was demonstrated in a
p-n-diode-loaded Si LSPCW and a co-propagatingslow-light system. Carriers were generated by photon
absorption and extracted in a reverse-biased p-n diode,enabling high-speed carrier depletion and effective redshift.
We explored the suitable conditions for the redshift using
the pump-probe method, and confirmed that a large redshift
can be simply induced by reducing the delay between thecontrol and signal pulses, increasing the bias voltage, andboosting the control-pulse power. Redshifts of up to 0.21 nm
were obtained in the experiments. At present, the redshift
performance might be limited by the space-charge effectcaused by excessive numbers of carriers, which degrades thecarrier depletion speed. We expect to resolve this problem
by optimizing the structure of the p-i-n junction. To date,adiabatic wavelength conversion has enabled many
advanced optical control techniques, as mentioned in thesection of the introduction, but has utilized only the blueshift.
The proposed redshift technique will improve and diversify
the applications of wavelength conversion, leading to novel
discoveries in physics and techniques such as a pulse
recovery and dynamic pulse acceleration and/or decelerate.
ACKNOWLEDGEMENTS
This paper is based on results obtained from a projectcommissioned by the New Energy and Industrial
Technology Development Organization (NEDO) and Japan
Science and Technology Agency ACCEL Project.
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FIG. 4 (Color online) Color maps of output signal spectra as afunction of Δt, obtained at different Vbias values. The white-solidand black-dotted lines indicate the spectral centers of the output
signals obtained with and without the control pulse, respectively.

FIG. 5 (Color online) Output signal spectra at the maximum
redshift (0.21 nm), which are normalized by (a) the peak in theabsence of the control pulse and (b) each peak.

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