Optonanomechanical self-adaptive photonic devices
based on light forces: A path to robust high-indexcontrast nanophotonic circuits
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Citation
Popovic, Milos A., and Peter T. Rakich. “Optonanomechanical
self-adaptive photonic devices based on light forces: a path to
robust high-index-contrast nanophotonic circuits.” Optoelectronic
Integrated Circuits XI. Ed. Louay A. Eldada & El-Hang Lee. San
Jose, CA, USA: SPIE, 2009. 72190A-11. © 2009 SPIE
As Published
http://dx.doi.org/10.1117/12.813591
Publisher
Society of Photo-Optical Instrumentation Engineers
Version
Final published version
Accessed
Wed May 25 21:54:37 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/52628
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Detailed Terms
Invited Paper
Optonanomechanical self-adaptive photonic devices based on light
forces: a path to robust high-index-contrast nanophotonic circuits
Miloš A. Popovi *a and Peter T. Rakich †b
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, USA 02139
b
Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM, USA 87185-1082
a
ABSTRACT
We describe a proposed new class of optonanomechanical integrated photonic devices that can have self-adaptive
behavior and self-adaptive optical frequency response, through the use of optical forces to manipulate their movable
parts. We propose applications for this technology, and show how such devices can address the enormous dimensional
and thermal sensitivity present in nanophotonic structures. Through synthesis of the optomechanical potential, we
propose to design and control either the effective optical, or the mechanical, properties of the nanostructure, such as a
giant effective optical nonlinear response, nonlinear dynamics and memory. We show device designs that can trap
desired states at picometer resolution. We also describe the design of a novel, self-tuning microcavity design whose
moving parts adjust in response to light forces alone to always place the resonance at the wavelength of the incident light
over a wide wavelength range. This device concept provides an athermal resonator design (temperature-independent
resonance frequency), without use of materials with negative thermooptic coefficients. It could also address a major
challenge with conventional strong-confinement (high-index-contrast) integrated photonics – their extreme sensitivities –
through a self-locking filter bank and optical cross-connect proposal, that in principle can use arbitrarily low power to
trim resonant filter passbands to a wavelength channel grid.
Keywords: Optomechanics, light forces, self-adaptive, self-tuning cavity, nanophotonics, nanomechanics, potential
synthesis, athermal resonators, nanophotonic cross-connect, robustness.
1. INTRODUCTION
Light forces have a long history [8-11]. Optical forces resulting from interacting modes and cavities can scale to large
values as optical modes shrink to nanometer-scale dimensions [1-7]. Such forces can be harnessed in fundamentally new
ways when optical elements are free to move and adapt to them through exchange of optical and mechanical energy. In
0 Position (motion) depends on light forces 0 Optical response
0 Resonantly-enhanced light forces
depends on position
of nanomechanical
system
I,'
Output
0 Optical response
[0 Position (motion) j
H(o)
o Light forces
depend on
optical response
(resonant enhancement)
(a)
Input
(b)
Fig. 1. Proposed self-adaptive nanophotonic devices based on light forces [1] – the idea is that optical forces dominate
the behavior: (a) the interplay of a resonant optical response generating enhanced optical forces, their causation in turn
of motion, and the effect of the motion on the optical response produce novel physics: an artificially engineered (and
very large) effective nonlinear optical response, self-adaptive behavior and all-optical feedback, memory; (b) concrete
illustration using microring resonators [1].
*
†
E-mail: mpopovic@alum.mit.edu, Telephone: +1 (617) 253-2585, Webpage: http://www.mit.edu/~milos
E-mail: ptrakic@sandia.gov, Telephone: +1 (505) 284-6501, Webpage: http://sites.google.com/site/pubsrakich/
Optoelectronic Integrated Circuits XI, edited by Louay A. Eldada, El-Hang Lee,
Proc. of SPIE Vol. 7219, 72190A · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.813591
Proc. of SPIE Vol. 7219 72190A-1
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Dielectric
namb
flpert> namb
flpert> namb
'I,
q
namb
out
__________
q
f
+
TM excitation
(b)
(a)
(c)
npert < namb
namb
pert < namb
Iii
namb
(d)
(a)
/
V
Dielectric
q
+
'I,
.-..
I-I
q
TE excitation
(e)
(f)
(b)
(c)
Fig. 2. Basic geometries for attractive and repulsive resonantly-enhanced optical forces. An attractive optical force is
present when bringing a perturbing object closer to a resonator causes a red-shift in resonance frequency: which can be
realized by (a-b) a dielectric perturbing body with index larger than ambient, npert > namb; or by (c) a perfect electric
conductor (PEC) for a TM polarized excitation (motion assumed vertical). For repulsive forces, a blue shift is needed,
calling for either (d-e) a dielectric perturbing body with smaller index than ambient (e.g. air), or (f) a PEC over a TE
polarized mode. Since three of these four idealized sitations aren’t practical in optics (c-f), we propose using a
geometry based on dual coupled cavities, which by the image principle provide behavior equivalent to (c,f).
recent work [1], we proposed the use of opto-mechanically coupled resonators as a general means of tailoring optomechanical potentials through the action of optical forces. We show that attractive and repulsive forces arising from
opto-mechanically coupled cavity resonances can give rise to strong and highly localized opto-mechanical potential
wells whose widths approach picometer scales. These potentials enable all-optical, self-adaptive behaviors such as the
trapping and corralling (or dynamic-capture) of microcavity resonances with light [1]. Fig. 1 illustrates the basic device
physics we propose to harness in the service of device design. The idea is that an optical driving signal, enhanced by the
resonant optical response, gives rise to resonantly-enhanced optical forces; these forces act on movable nanomechanical
parts of the photonic device; and the motion leads to a change in optical coupling between cavities, in the optical
resonant frequencies of the system, and thus in turn to a change in the forces generated. The result is a form of feedback
(Fig. 1a), or engineered nonlinear response. We approach engineering novel devices and functionality based on such
physics through design of the optomechanical potential. Two important elements in design of such devices will be: (1)
trapping the nanomechanical structure, through light forces, into a stable state; and (2) design allowing the optical input
or device dynamics to manipulate the state of the device. These steps require the synthesis of trapping optomechanical
potential wells, and their dynamical control.
In the first part of this paper (Sec. 2), we show [1] how practical devices realizing these capabilities may be designed,
and explain the physics of their operation. As one example, we apply these concepts to the design of a novel, first-of-itskind resonator which dynamically self-aligns (or spectrally bonds) its resonance to an incident laser line all-optically
(“passively”). Such “smart” resonators can adaptively track the wavelength of a laser-line through minimization of
optomechanical energy [1]. Though these concepts are illustrated through dual-microring-cavity designs, broad
extension to other photonic topologies is straightforward. In the second part of this paper (Sec. 3-4), we propose some
applications of this technology, and describe two already promising applications based on the self-tuning cavity concept.
The first is an athermal (temperature-independent resonance frequency) optical resonator. The second is a nanophotonic
Proc. of SPIE Vol. 7219 72190A-2
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Mobile ring
Lc)
0.10
CD
-o
200
e
0.09
0
0.08
0
0) 0.07
C
a)
UEM
Static ring
(I)
0.06
0)
0.05
0
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0.03
C 0.04
b
t
q
0
0.02
+
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a)
0
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0.01
cj
U)
0)
300 c
0)
C
400 1
500
700
0.00 1
196
E
198
200
202
204
Frequency (THz)
Fig. 3. Synthesis of an optomechanical potential well using attractive and repulsive forces designed into the same
resonant structure [1]: (a) dual-ring cavity geometry with movable top ring (weakly suspended in practice); (b) crosssection and the cross-sectional field distributions of the (c) symmetric (attractive) and (d) antisymmetric (repulsive)
resonant supermodes; (e) optical force amplitude vs. wavelength and coupling strength (distance q) between the rings.
filter bank that, through intrinsic optonanomechanical feedback, can lock to an optical frequency reference signal, and
eliminate sensitivity to dimensional variations, a major problem for scaling nanophotonic devices and circuits.
2. DUAL-MICROCAVITY UNIT CELL FOR OPTOMECHANICAL POTENTIAL SYNTHESIS
We explore these novel physical behaviors through coupled cavity systems such as the dual-microring resonator design
shown in Fig. 1(a). This design results from a desire to obtain large resonantly-enhanced optical forces of either sign
(attractive or repulsive), at practical optical driving signal powers. The rationale is explained in the following.
Some basic geometries allowing resonantly-enhanced optical forces are shown in Fig. 2. A perturbing structure,
dielectric or metallic, that is moved within the evanescent field of a resonant cavity can greatly shift the resonant
frequency [12]. A large shift in resonance frequency per unit distance of the motion corresponds to a large change in
optical energy, and leads to a large force. If the perturbing structure is dielectric and has an index higher than the
ambient (e.g. air) index (Fig. 2a,b), there is a red shift of the resonance when moving the structure closer to the
resonator, so the force is attractive (no motion). On the other hand, it is not straightforward to extend this to obtain a
repulsive force because the perturbing structure requires an index below that of air (Fig. 2d,e). However, a metallic
perturbing structure (sheet) can produce both attractive and repulsive forces (Fig. 2c,f), using different polarizations with
a perfect electric conductor (PEC). Both signs of force could in theory be obtained also in the same polarization, using
alternately perfect electric and magnetic conductors (PEC and PMC). Since PMCs do not have a physical realization,
and metals (that approximate PECs at low frequency) are highly absorptive at optical frequencies, the conductor
approach does promise high-Q resonances needed to develop large optical forces. For this reason, we turn to theory of
image charges: a perfect conductor is an electromagnetic “mirror”. Hence we use a dual-cavity geometry that is
equivalent to having one cavity, with a perfect conductor at the half-way point between the two cavities. Symmetric and
anti-symmetric supermodes correspond to the PEC and PMC cases, and provide attractive and repulsive forces.
Coupled microcavities were previously shown by Povinelli et al. [2] to allow both signs of force, but the geometry we
propose is uniquely suited to developing very strong optical forces. In this design, the lower ring and bus waveguide are
assumed to be fixed (e.g. on a silicon chip) while the upper ring is assumed to move unimpeded in the vertical direction
in response to optically induced forces generated by the guided light. Close approximations of this arrangement can be
realized using membrane or cantilever structures to suspend the upper ring, and could be achieved using available
fabrication techniques [13]. This geometry (of two co-propagating rings, Fig. 3a) enables strong coupling between
nominally degenerate ring modes creating symmetric and antisymmetric supermodes [Fig. 3(b)-(d)] whose frequencies
are remarkably sensitive to device geometry (and hence which allow large optical forces). Fig. 3(e) shows that as the
waveguide coupling strength, (q), is increased (or distance q in Fig. 3b decreased) a resonance frequency splitting that
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-----
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(b)
(c)
Fig. 4. Optonanomechanical device with a trapping and corralling potential well [1]: the width of the potential well
varies with wavelength of the driving laser (see illustrated cases 1 to 3), while the equilibrium state (position of the
potential minimum) is independent of wavelength. (a) the optomechanical potential is defined for the displacement of
the top resonator relative to the bottom one; (b) the potential surface (shown over the top central part of Fig. 3) with the
potential for three optical excitation frequencies highlighted (black line), and shown in Fig. 3(e); (c) potentials.
is linear in (q) (or exponential in q) results between the symmetric (blue) and antisymmetric (red) modes. Fig. 3(e),
which shows the resonant optical force, also reveals that strong coupling results in crossings between adjacent
longitudinal resonance orders. These crossings give rise to fundamentally new means of manipulating optical
resonances and mechanical structures when optomechanical forces and energy are considered, as illustrated in the
following subsections.
2.1 Picometer-Scale Positional Control via Trapping Optomechanical Potentials
Through open and closed system analyses of optomechanical energy [1], we can show that the resonant excitation of the
symmetric ring system supermode results in attractive forces between the rings [shown in Fig. 4(a)], while excitation of
the antisymmetric mode results in repulsive forces [1-3]. If the system is excited (via the bus waveguide) by a
monochromatic laser-line both the symmetric and anti-symmetric microring supermodes can be excited as the separation
between the rings (q) is varied (due to the large frequency splitting afforded by this geometry, as shown in Fig. 3(e)).
We first show how practical optonanomechanical trapping can be designed using a realistic example based on siliconcore microring resonators with 5-micron diameter. If the system, shown in Fig. 3(a), is excited by a fixed laser-line at
200 THz, or 1500nm wavelength [represented by a vertical dotted line in Fig. 3(e)], resonant excitation of a cavity
supermode will be achieved at various coupling strengths, (q), corresponding to different positions, q. Since both
attractive and repulsive forces are generated (respectively) by the excitation of symmetric and antisymmetric resonances
along this trajectory of motion, nontrivial optomechanical potentials are created. In particular, when attractive and
repulsive resonant forces alternate as ring-ring distance is decreased, as in Fig. 3(e), a series of trapping optomechanical
potential wells is created. Fig. 4(b) shows the rigorously computed normalized effective potential corresponding to the
coupling strengths shown in the top half of Fig. 3(e), for three laser frequencies including 200 THz [1]. The potential for
each of the three laser frequencies is a two-dimensional cut of the surface map in Fig. 4(b), shown as a thick, solid-line
trace projected onto the surface plot. Along the shown trajectory, a minimum of optomechanical potential is seen, which
results from resonant excitation of cavity modes of differing symmetries. These minima of potential indicate that the
system can be trapped, effectively pinning the optomechanical system at a position, q, corresponding to the placement of
symmetric and antisymmetric mode resonances at positions q±q on either side of being resonant with the laser-line.
This design allows corralling or dynamic capture of the optomechanical system. That is, if a single laser-line is
continuously swept toward the resonance crossing [over the trajectory shown by laser-lines indicated by the solid lines
labeled (1)-(3) in Fig. 4(b)] one can adiabatically narrow the potential from a wide square-well to a near -function,
effectively allowing us to corral the system to one of several localized positions in space. The evolution of the potential
for laser-lines (1)-(3) can be seen in Fig. 4(c) for a realistic guided power of about 1 mW within the bus waveguide
(photon flux of = 1016 photons/sec). For these modest powers the depth of the potential well (~30 eV) is far greater
than kBT, and the optically induced forces corresponding to this potential are 1 to 10μN in magnitude, which are
sufficient to dominate in experimentally realistic situations [1,4].
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40
>
20
(1)
-20
(2)
g
0)
)I)
0
)I)
Cs
0
0
(3)
0
005
40
0
(a)
0.01
0.03
0.02
Coupling strength
(b)
0.04
0.05
(K)
(c)
Fig. 5. Optonanomechanical device with a tunable-position trapping potential well [1]. Excitation at two wavelengths
simultaneously allows the width and the position of the potential well to be optically controlled (by choice of the two
wavelengths). (a) The same structure excited at two wavelengths, (b) the optomechanical potential surface, showing
the potentials at two exemplary excitation wavelengths, and (c) the total potential due to the sum of the two potentials
generated by each wavelength of excitation,, showing a single trapping potential well. The asymmetric total potential
is due to wavelength dependence in the ring-to-ring coupling coefficient.
2.2 Optically Tunable Position: Control of Equilibrium State of Optomechanical Potentials
In this section we show designs that allow the optical input signal to control and determine the position of the
nanomechanical system, i.e. to tune the equilibrium state or optomechanical potential minimum. In the previous section
we showed that the potential could be tuned from wide to narrow, to capture the mechanical system, by tuning the single
excitation wavelength. But, the equilibrium position was fixed by the design (the cavity FSR, and spatial dependence of
coupling). We show that using multiple wavelengths to excite the system allows a tunable-position potential well.
Fig. 5 shows the same system, excited simultaneously by two laser wavelengths. The total optomechanical potential (3),
relevant for the mechanics, is the sum of the potentials [(1) and (2)] due to each wavelength shown in Fig. 5(b) in thick,
solid line. If the two laser wavelengths [(1) and (2) in Fig. 5(b)] are detuned to the left and right of the crossing, and
excited with equal intensity, one creates a potential well (2) and one a potential “hill” (1). If the wavelengths are equally
detuned from the crossing, the potentials will add in cancellation to a nearly featureless, flat potential. However, if
wavelength (1) is detuned less than wavelength (2), producing a narrower potential, their sum will produce two potential
wells, at positions above and below the crossing. If, furthermore, wavelength dependence of the coupling coefficient is
accounted, only one potential well may be favored, as shown in Fig. 5(c). The position of this potential may be varied
by simultaneously tuning both excitation wavelengths (in opposite directions) away from the crossing wavelength.
2.3 Bound Optomechanical States and Self-Aligning “Smart” Microcavities [1]
In this section, we describe the more complex design of a novel device we refer to as a self-tuning cavity, shown in Fig.
4J
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Separation(s)
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(a)
0065
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0.055
Normalized cooplirrg strength (0)
0.2
007
0.061
0.062
0.063
0.064
0.065
0.066
0.067
Normalized coupling strength (0)
(b)
(c)
Fig. 6. (a) Proposed optonanomechanical self-tuning resonator [1]. Engineering a device that adjusts to always be
resonant with the incident laser wavelength requires a combination of a resonant and a broadband optomechanical
potential (e.g. due to coupled waveguides). (b) The potential map shows that the total (sum) potential has the same
shape and simply translates the minimum (equilibrium state) position for different wavelengths (3 examples shown as
black lines). (c) The antisymmetric resonance is at the right potential wall, so the cavity always moves to be resonant.
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0
Ultrasensitivity of Silicon Resonators
Wafer SQl Core Thickness
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104
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(b)
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101
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(c)
Fig. 7. Major challenges in strong-confinement (high-index-contrast) nanophotonics circuits are strong dimensional and
thermal sensitivity: (a) 1 angstrom error in the width or height of a waveguide cross-section that forms part of a
microring resonator leads to tens of GHz shift in the resonance frequency; (b) standard thick-BOX SOI wafers used for
silicon nanophotonics show several nanometers of thickness variation across the wafer; (c) silicon microring resonators
shift as much as 10 GHz for a 1°C change in temperature (figures (a,c) from [14,15], (b) courtesy of T. Barwicz).
6(a). It achieves a tunable potential (mechanical position) using only a single laser wavelength excitation, giving rise to
a unique “wavelength-to-position” converter. But, it also places the potential exactly at the location that makes it
resonant with the incident line, producing a form of “spectral bonding” between the continuous-wave (CW) input light
and the resonance frequency of the optomechanical system. The nanomechanical system adjusts to change in the optical
input wavelength, resulting in all-optically (optomechanically) controlled ultra-wide tuning of the cavity resonance,
potentially over 10’s and 100’s of nanometers, with extraordinary precision (subject to the width of the trapping
potential well, and the stability and linewidth of the driving laser).
This device can be designed by combining a resonant and a broadband optomechanical potential. This is accomplished
by starting with the dual cavity of the previous examples providing a resonant repulsive potential in this case, and adding
a coupled waveguide pair that adds a broadband attractive potential. The waveguide pair is optically isolated from the
cavities, but is mechanically coupled such that there is only one mechanical degree of freedom in the system [Fig. 5(a)].
The optomechanical potential is the sum of the resonant and the broadband potential as illustrated in Fig. 5(a). This
leads to a total potential with a mostly monotonic slope and a local potential minimum introduced by the resonant
potential of the cavity pair. This potential step always occurs at ring-ring displacement and wavelength combinations at
which the antisymmetric resonance in resonantly excited, i.e. resonant at the driving wavelength. A consequence of this
fact is that the system will modify position in response to optical forces until it is trapped in the potential minimum, and
when it is at the potential minimum it is resonant (with a slight detuning) with the antisymmetric cavity supermode.
Thus, the system adapts to make the antisymmetric mode’s resonance frequency coincide with the laser wavelength.
Fig. 5(b) shows a potential surface showing the optomechanical potential at three different excitation wavelengths. Thus
the potential simply shifts to have its minimum at a different position for each wavelength. Fig. 5(c) compares the
intracavity power and the optomechanical potential vs. displacement (i.e. coupling) showing that the supermode
resonance is indeed near the potential minimum. Self-adaptive devices such as this self-tuning cavity design, that
leverage optical forces to produce useful function and feedback, have the potential for major impact in nanophotonics.
3. APPLICATIONS: LIGHT-POWERED NANOMACHINES AND ALL-OPTICAL FEEDBACK
Optonanomechanical devices based on light forces can be used to produce optically-controlled optical properties, as
illustrated in the previous examples, or optically-controlled mechanical properties. These and similar self-adaptive,
“smart” optonanomechanical systems have the potential for far reaching impact in integrated photonic systems in part
due to their ability to eliminate complex electronic feedback controls necessary to implement numerous optical
functions.
Strong-confinement nanophotonic circuits [16,17], due to their unique properties such as support for wavelength-scale,
high-Q resonators, enable chip-scale solutions and unique functionalities for next-generation communication and
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computation technologies, including reconfigurable/tunable optical add-drop multiplexers for wavelength-routing optical
networks, and scalable integrated photonic crossconnects for energy efficient manycore processor to memory
communication for future supercomputers. Telecom-grade switchable and tunable filters [16], modulators [18] and other
components have been demonstrated in this technology. However, strong-confinement (high-index-contrast)
nanophotonic waveguides and resonators have been shown to have extreme intrinsic sensitivities (Fig. 7) – including
subatomic dimensional tolerances [14,15,19] and sensitivity to temperature and waveguide wall roughness (optical
losses). One of the principal challenges to unleashing the promise of strong-confinement photonics lies in taming these
extreme sensitivities. For example, Fig. 7(a) shows that a 1nm error in the width or height of a conventional (e.g.
450x200nm cross-section) silicon microring resonator will lead to a 100-200GHz shift in resonance frequency. While
relative dimensional control can be excellent in lithography thus allowing adjacent resonators to be at least resonant at
the same wavelength, typical wafer-level thickness variations [Fig. 7(b)] would require thickness mapping to maintain
device operation over larger areas. Even then absolute dimensional errors lead to absolute frequency errors that cannot
be easily compensated in design.
One approach to solving this problem has been to introduce tuning capability (e.g. thermooptic) and feedback control
electronics for each photonic element. However, such solutions become increasingly power hungry and complex with
scaling of nanophotonic circuits to higher complexities where their greatest potential for impact lies.
Optonanomechanics could address some of these problems by enabling a new family of nanophotonic device designs
with physics-based, built-in feedback, such as the self-tuning cavity. Such designs may in principle approach no power
consumption for tuning and stabilization.
In this section, we propose optonanomechanics based solutions two important problems in nanophotonics: athermal
resonators, and resonant filter banks and cross-connects impervious to dimensional errors. Solving these problems will
have important implications for scalable nanophotonic integration, and its impact on applications from multicore
computing, through photonic signal processing, to communication networks.
3.1 Athermal Optical Resonators
In this section, we describe how the self-tuning cavity design described can be used to achieve athermal resonator
operation. An athermal resonator design refers to one whose resonance frequency is insensitive to temperature over a
substantial range. This is an important problem, for example, in the future integration of nanophotonics with multicore
processors, since on-chip temperature varies substantially (by 10’s of degrees) in space and in time. Thermooptic tuning
would introduce substantial power use and require active electronic control to track dynamical temperature changes.
The self-tuning cavity provides a conceptually simple, highly scalable approach, in principle free of power consumption,
at the expense of inclusion of nanomechanical parts.
Fig. 8 illustrates the basic concept, based on the self-tuning cavity of Fig. 6. The basic idea is that an optical frequency
reference is provided to drive the resonator at the wavelength desired to be the resonant wavelength of the cavity. The
nanomechanical system will adjust in response to optical forces to become resonant with the driving optical signal. If a
resonant
light force
light-force-induced motion
Thon-resonant
laser input light force
(a)
light-force induced
nanomechanical shift
.
r
thermal
s h if t
(b)
Fig. 8. (a) Proposed athermal resonator concept: the self-tuning cavity concept (exemplified by the implementation in
Fig. 7) provides inherently a temperature-insensitive resonance frequency without the need to use materials with
negative thermooptic coefficients, such as polymers, which often are not CMOS integrable. (b) If the temperature
increases, the resonance frequencies shift (potential surface in Fig. 7(b) shifts toward lower frequency). The new
potential is of the same shape, but the minimum is at a smaller coupling strength, i.e. larger ring spacing. The optical
forces push the rings further apart, but the resonance is still always at the right potential wall, and thus still resonant.
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temperature change is introduced, this will result in a shift of the nominal resonance frequencies of the individual ring
cavities. This means that for the ring cavity pair alone, the diagonal resonance contours in Fig. 3(e) will simply shift to
laterally on that plot (e.g. left to lower frequency, if the temperature increases and the thermooptic coefficient of the
waveguides is positive). However, the potential of the entire system in Fig. 8 is shown in Fig. 6(b). Its lateral shift
along the frequency axis will retain the same shape of potential, with the potential minimum position shifted (e.g. to a
larger displacement, consistent with the example given here). Thus, the nanomechanical system will readjust in response
to generated optical forces, but after settling into the new potential minimum, the system will still be resonant with the
incident laser wavelength which remains unchanged. This behavior can remain valid over a large range of motion, and
hence over large temperature ranges of several hundred degrees Celsius. Furthermore, energy is used from the optical
driving signal during motion of the nanomechanical parts (since power = force*velocity), but when equilibrium is
reached and the system is static, no optical power is used. Thus, as optical waveguides approaching low propagation
losses, this approach approaches no power consumption for the stabilization.
3.2 Self-locking, Robust Nanophotonic Filter Banks and Cross-connects, Impervious to Dimensional Variations
In this section, we describe a new architecture for nanophotonic resonator-based filter banks for demultiplexers and
cross-connects (Fig. 10). The architecture is based on a filter that is a more complex variant of the self-tuning cavity.
Each filter comprises a narrowband self-tuning cavity and a wide bandwidth filter cavity. The self-tuning cavity will
lock the device to a reference laser input signal, and the filter cavity will be used to form the passband for optical signal
processing. A bank of such filters would be impervious to dimensional variations.
The problem of dimensional sensitivity in conventional nanophotonic filter banks is illustrated in Fig. 9. An example
optical cross-connect/demultiplexer, shown in Fig. 9(a), is formed of an array of nodes each comprising an add-drop
filter, for example based on microring resonators [Fig. 9(b)]. Dimensional variations, such as wafer-level thickness
variations [Fig. 7(b)] will make the designed regular filter passband spacing in general irregular and not lined up with the
grid of wavelength channels [Fig. 7(c)]. Furthermore, even without wafer variations, absolute dimensional control in
lithography and etching is not good enough to line up the passband array with the channel grid (in an absolute
wavelength sense) without external tuning. Power consuming tuning mechanisms and complex control are needed.
In the architecture we propose in Fig. 10, a reference laser is used to lock all filters to an absolute wavelength, or in
accurate relation to it. The building block filter here is shown in Fig. 10(b). It uses a “master-slave” design, consisting
of two, mechanically coupled parts: a self-tuning locking cavity (right) and a filter cavity (left). The self-tuning cavity
(“master”) is the design of Fig. 6, and is designed to be as high-Q as possible (limited by intrinsic loss), to develop large
forces and adjust to be resonant with the reference laser, that is guided to all filters in the array [Fig. 10(a)]. Such a
linewidth cavity would be too narrow to operate on optical signals so the functions are separated by introducing the filter
cavity pair (“slave”), that are designed to have a wide bandwidth (low Q) of 10’s of GHz to support modulated optical
signals in the wavelength channels. The mechanical coupling means that the locking cavity (“master”) adjusts the
mechanical degree of freedom to become resonant with the reference laser, and the filter cavity (“slave”) follows. The
filter cavity can be accurately spaced in frequency from the locking cavity because they are fabricated next to each other,
and because relative dimensional control in nanofabrication is excellent. For example, the filters can be spaced from the
locking cavities respectively by 100, 200, 300, 400… GHz, thus creating a filter bank with 100-GHz channel spacing.
One way to produce the detuning in electron-beam lithography is by dose control [20].
The proposed architecture promises a major advance in filters because feedback is intrinsic to the device design, power
consumption for the stabilization can approach very low values as waveguide loss is reduced through improvements in
fabrication, and in addition locking in absolute wavelength is possible. This approach is highly scalable.
4. CONCLUSIONS
We have proposed a new class of light-powered nanomachines and all-optical self-adaptive optomechanical circuits that
rely on the interplay between optically-induced forces and mechanical-motion-induced change in optical properties of a
system. By synthesizing optomechanical potentials through the action of optical forces, unique designs result enabling
all-optical operations on light that would be difficult to achieve by any other means. As first examples of how this
concept could be applied, we have shown how all-optical self-adaptive photonic devices can be made to effectively
corral and trap microcavity resonances and achieve dynamic self-alignment of a microcavity resonance to a single laser
line over very large wavelength ranges. Such devices have the potential to provide many new and unique kinds of alloptical (optomechanical) functionality.
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Conventional Nanophotonic Crossconnect/Demux based on Microring-Resonator Add-Drop Filters
DRAM Memory Banks
xA2
Al
A3
I
ec
Add-drop filter
A2
A1
through
I
o
drop
in
A1
B2
B1
B3
0
L)
A2
A3
A3
Filters
C3
WDM Channels
(a)
II
+
+
Fig. 9. Conventional filter bank suffers from enormous dimensional sensitivity in nanophotonic structures. (a) Onchip all-to-all wavelength routing network relevant for telecom and supercomputer applications; (b) each node may
comprise a microring-resonator add-drop filter; (c) due to dimensional sensitivity, waveguide-layer thickness nonuniformity and lithographic variations the filter array is misaligned with respect to the evenly spaced multi-channel
spectrum it is intended to operate on. Extreme sensitivities (Fig. 8) mean that in realistic silicon nanophotonic
implementations the misalignment can be on the order of 500GHz.
Passively X-Locked Crossconnect/Demux based Optonanomechanical Add-Drop Filters
Add-drop filter (low-Q slave)
tFirough
DRAM Memory Banks
REF
Laser
!
B3
Al
?
A2
2
A3
X1
0
L)
B2 XB3
2'Cl 2'C2
I
A
_________
I
t
in
2'Al
o
motion
-
AI:A2 >
.---D
Locking resonator (hgh-Q master)
A2
LXREFi
(b)
A3
A3
Filters
NO X
XRE F
CS
I
+
WDM Channels
(a)
+
+
(c)
II
(d)
Fig. 10. Proposed self-locking filter bank circumventing enormous dimensional sensitivity in nanophotonic
structures: (a) the proposed self-locked on-chip optical cross-connect comprises a filter array, where each element (b)
is an optonanomechanical photonic device comprising a self-tuning cavity to lock onto a reference wavelength, and a
mechanically coupled add-drop filter that tracks wavelength with it. The filter is fabricated with a resonance frequency
offset relative to the locking cavity, which can be very well controlled, because they are adjacent. (c) Without the
reference laser excitation, dimensional sensitivity gives an unevenly spaced, misaligned filter bank spectrum, but with
the reference laser excitation present, the filters lock to that wavelength. For low waveguide losses, the power
consumed in the steady state, for this type of “trimming” approaches zero.
The new physics allows for new concepts of device design and control, and may provide an approach to eliminate the
extreme dimensional and thermal sensitivities of strong-confinement photonic devices.
The potential of
optonanomechanics to lead to novel device concepts and applications has yet to be fully explored. Furthermore, the
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unique functionality available through optomechanical energy coupling, the highly nonlinear behavior and possibilities
available through the potential synthesis viewpoint make it desirable to develop a comprehensive design approach (a
“circuit theory”) for the systematic design of all-optical optomechanical systems with prescribed desired properties. We
have made initial steps in this direction [21].
ACKNOWLEDGMENTS
We acknowledge helpful technical discussion with Gregory N. Nielson and Zheng Wang, and thank Profs. E.P. Ippen,
M. Soljacic and Y. Fink for generous support and encouragement. This work was supported in part by the office of the
Director of Defense Research and Engineering under Air Force contract FA8721-05-C-0002. Interpretations, opinions,
and conclusions are those of the authors and do not reflect the official position of the United States government. Sandia
is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States
Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
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