Optics and Photonics Journal, 2012, 2, 255-259
http://dx.doi.org/10.4236/opj.2012.24030 Published Online December 2012 (http://www.SciRP.org/journal/opj)
Engineered Transitions in Photonic Cavities
Ali W. Elshaari1, Stefan F. Preble2
1Electrical and Electronic Engineering Department, University of Benghazi, Benghazi, Libya
2Microsystems Engineering Department, Rochester Institute of Technology, Rochester, USA
Received August 25, 2012; revised September 23, 2012; accepted October 15, 2012
ABSTRACT
We demonstrate for the first time, to best of our knowledge, that by engineering the states of a system of cavities it is
possible to control photon transitions using non-adiabatic refractive index tuning. This is used to realize a novel photon
transitions that are independent of the refractive index sign. In particular, we show through coupled mode theory and
FDTD simulations that red shifts are possible in silicon resonators using the free-carrier plasma dispersion refractive
index reduction.
Keywords: Integrated Optics; Resonators; Wavelength Shift
1. Introduction
The engineering and active control of resonant photonic
structures has enabled unique optical functionalities,
from isolators and delay elements [1-3] to 100% efficient
adiabatic wavelength conversion by trapping light while
tuning the state of a resonator [1-7]. However, these
functionalities have been limited by the mechanism used
to realize the refractive index change. This is particularly
the case for adiabatic wavelength conversion on the Sili-
con photonics platform where the free-carrier plasma
dispersion effect (PDE) is used to reduce the refractive
index of a cavity [8-10]. This always results in a wave-
length shift towards the blue, limiting the application of
the effect [7,11]. In contrast, it was shown in [4] that
when a resonator is non-adiabatically perturbed it is pos-
sible to transition photons to other resonant modes—even
towards the red, albeit with a low efficiency. The reason
for this is that the final state of the system couples to a
continuum of output modes—with a dominant excitation
of the adiabatic shift as seen in Figure 1 [7]. Here we
show that by carefully designing the states of a system
of cavities nearly all of the light can be non-adiabati-
cally transitioned to just one state—even towards the red.
This opens the possibility of using the PDE for both blue
and red shifts of light, which will enable rapidly recon-
figurable wavelength converters for use in future on-
chip wavelength-division-multiplexed systems. This is in
contrast to non-linear wavelength converters relying on
Raman scattering (RS) or four wave mixing (FWM)
where high powers are required and wavelength changes
are fixed by the wavelengths used in the system and can
only be reconfigured by slowly tuning an external laser
[12-14].
2. Designing System States
The proposed cavity system is shown in Figure 2. It
consists of one input and output cavity each with large
Free Spectral Range (FSR) and a transition cavity having
closely spaced states (small FSR). By initially aligning
one resonance of the input cavity and one resonance of
the transition cavity it is ensured that the system only has
one allowed state, which we call the input state, as shown
as a double solid line in the figure (the double lines indi-
cate that there is mode splitting). We note that although
there are many internal degrees of freedom for the transi-
tion cavity, they are not allowed because they will all be
off-resonance with respect to the input cavity. This is
ensured by the phase matching and the ortho-normality
of modes. So that only specific transition probabilities
don’t vanish. The probability of a transition between
modes a and b is dictated by the overlap between the
super-modes over the volume of the two rings in both
transverse and longitudinal directions (γ is the coupling
constant, φa,b are the initial and final modes).
volumeaba ab b
P   
Furthermore, light cannot couple to the output of the
system because the output cavities resonance is detuned
with respect to the input state (lower energy in Figure 2
[-Eg/2]). As will be shown, this red-shifted output cavity
determines the final state of the system, and consequently
the new wavelength of the light.
To transition the light efficiently to the red-shifted
ouput cavity we induce a non-adiabatic perturbation of t
C
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A. W. ELSHAARI, S. F. PREBLE 256
Figure 1. Light initially excites one state of the resonator (t < t0). When the resonator is switched at a fast rate, multiple
output states are excited (t > t0). Δω is the relative shift of all of the states due to the refractive index change.
Figure 2. Photonic transitions in system consisting of threecoupled-cavities. Initially (t < t0) the system only has one allowed
input state—formed by the alignment of the input and transition cavity resonance (m). The light cannot escape to the output
because the output cavity is in a forbidden state (-Eg/2). By non-adiabatically reducing the refractive index of the transition
cavity (t > t0) the states are shifted by Dw. Now the output cavity is in resonance with the (m–1) mode of the transition cavity.
This is the only allowed state of the system. The remaining transitions lie inside forbidden states in the energy diagram.
the transition resonator through a refractive index re-
ducetion. This will blue-shift all of the states of the tran-
sition resonator, including the initially excited input state.
However, now the output cavity will be on-resonance
with the (m–1) mode of the transition cavity—forming a
newly, and singly, allowed state for the system. Since
this state is at a lower energy than the original input state
the wavelength of the light is efficiently red-shifted.
In order to demonstrate this concept we use time do-
main coupled mode theory to simulate the different mode
dynamics [15-17]. The simulations takes into account
waveguide and carrier losses in the system [9] and has

A. W. ELSHAARI, S. F. PREBLE 257
been successfully applied to analysis of a multitude of
dynamically controlled cavity systems [2,11,17-19]. In
the model we consider realistic parameters—a typical
value of waveguide loss of 3 dB/cm is assumed, and ring
resonators are used as the cavities, with radii of Rinput/output
= 10 μm and Rtransition = 200 μm (FSRs of 8.8 nm and
0.437 nm, respectively). The resonator states are seen in
Figure 3 where we see that the input ring and the transi-
tion ring have the same resonance. The output ring is
placed at the midpoint of the gap between the (m) and
(m–1) mode of the transition resonator. It should be noted
that for clarity the individual ring resonances were cal-
culated separately in order to visualize the position of
different resonances with respect to each other, while in
the actual system they will be coupled—resulting in
mode splitting.
3. Red Transitions with Refractive Index
Reduction
The controlled transition of a pulse of light towards
lower energies (red) is demonstrated in Figure 4 by in-
jecting a carrier density of

3
4E16 cm%1%nn in
the transition resonator. The carriers are injected in a
time of 100 fs, which is significantly shorter than the
inter-mode coupling time

w
t1FSR

in order to en-
sure non-adiabatic transitions in the transition ring [4].
We note here that this fast switching speed in not a limi-
tation of the system and can be relaxed by using resona-
tors with a smaller FSR or by using resonant modulation
as discussed below in Section 3. In Figure 4 we see that
most of the light is red shifted to the new (m–1) mode of
the transition cavity and there is negligible excitation of
the other states. An important point to be emphasized
Figure 3. Transmission of different rings in the initial state
of the system. The input resonator and the transition
resonator have the same resonance condition, while the
output resonator is purposely shifted to a lower energy—
one-half FSR away.
Figure 4. States before the switching (blue) and after
switching (red) inside the transition ring. The conversion
efficiency is 96%.
here is the fact that this is a true mode coupling in the
transition ring, not a filtering effect—the spectrum shown
in Figure 4 is measured inside of the transition ring not
at the output port. Lastly, we should note that the posi-
tion of the converted light is not exactly at the half-FSR
point but is slightly blue-shifted by 0.06 nm because of
mode splitting of the coupled transition-output cavity
state. Here we have tuned the resonators coupling con-
stants in order to maximize coupling to only the blue-
shifted split mode. In order to verify the results from
coupled mode theory we numerically simulated the dy-
namic process by solving Maxwell’s equations using the
finite difference time-domain (FDTD) method [20]. The
system has the same configuration as the one described
earlier but with scaling differences in order to speed up
the computation process (Radii of Rtransition = 24 μm and
Rinput/output = 4 μm. These correspond to FSRs of ~4 nm
and ~26 nm, respectively). We see in Figure 5 that with
an index shift of


%9%nn the light is red-shifted
by 2 nm. The double peak in the figure results from the
interference of modes in the ring resonator which was
evident in our previous experimental work [15].
The behavior is qualitatively the same as the results
obtained with coupled mode theory. However, the con-
version efficiency is slightly lower (88%) since the non-
adiabatic transition is not as efficient with the large FSR
used in the FDTD simulation. This is not a fundamental
limitation provided the FSR of the transition ring is small
enough. It all depends on the strength of the wavelength
shift [7]. Provided a large enough refractive index, small
rings with large FSR can be used.
4. Efficiency and State Design
We have shown here that the placement of the cavity

A. W. ELSHAARI, S. F. PREBLE 258
Figure 5. Finite-difference-time-domain verification of red-
shifting results.
states will determine the new modes of the system. In
addition, the maximum conversion efficiency is deter-
mined by the state design. For example, we found that
this is achieved when the output cavities state is a half-
FSR away from the initial transition cavities state (i.e.
halfway between m and m–1). This can be understood
as follows. When this state is closer to the input state
there is unintended adiabatic coupling to original (m)
state. In addition, it would require a larger index change
to achieve red-shifting since the initial (m–1) mode would
be even farther away from the output state. On the other
hand, placing the out- put state closer to the initial (m–1)
state will also reduce the efficiency because the input and
output state are initially further apart, but the refractive
index change would be smaller—resulting in a weaker
non-adiabatic transition. This could be overcome, how-
ever, by using resonant transitions where the resonator is
switched at a rate corresponding to the difference in the
state [2] spacing. We should add that without resonant
transitions it is important to switch the transition cavity
on the order of less than ~30% of 1/FSR (where FSR has
units of frequency) in order to maximize the non-adia-
batic transition process, as simulated in Figure 6.
5. Concluding Remarks
In conclusion, we demonstrated that by engineering the
states of a system of cavities, and using non-adiabatic
transitions, it is possible to obtain wavelength changes
that are independent of the refractive index change sign.
This new phenomena will enable more robust recon-
figurable wavelength conversion systems where refrac-
tive index reductions can be used to both blue and red
shift the frequency of light. In addition, the scheme pro-
posed here for designing the states of a system of cavities
could lead to novel dynamically controlled cavity sys-
Figure 6. The efficiency decreases as switching speed is
slowed due to the enhancement of the adiabatic shift in the
resonator.
tems for optical signal processing.
6. Acknowledgements
We would like to thank Dr. Edwin Hach for helpful dis-
cussions. The authors would also like to thank Dr. Gernot
Pomrenke, of the Air Force Office of Scientific Research
for his support and we thank Joseph Lobozzo II for the
Lobozzo Optics Laboratory.
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