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b
Frequency
a
Frequency
addressed. When current is passed through
different electrodes, areas with different
lattice constants and therefore different
emission angles are excited. The researchers
were able to achieve discrete ~1o changes in
the emission angle over a total range of 30o.
Continuous, smooth shift of the emission
angle can also be achieved by changing the
ratio of the pumping currents for the two
adjacent electrodes.
Although the device performance looks
impressive, there are several possible areas
for further improvement. First of all, the
device emits two beams at angles of θ and
−θ with respect to the surface. This emission
characteristic is a consequence of the
symmetry of the dispersion curve. Although
this might be useful for certain applications,
it is usually desirable to have all of the laser
power concentrated into a single beam. Some
sort of asymmetry (for example, etching
the triangular holes such that they are not
perpendicular to the semiconductor surface)
could be introduced to favour one direction
over the other. Another issue is that the beam
can currently only be deflected by a single,
predetermined angle. An extension of this
approach to a two-angle beam deflection
scheme would greatly enhance the range of
possible applications. Solving these issues
may pave the way towards the realization of
very compact laser projectors (for example,
for use in mobile phones) or printing and
laser marking systems. As far as the further
Wavevector
Wavevector
Figure 2 | Flat dispersion points in the simplified dispersion relations of two photonic crystal lattices.
a, Dispersion relation of a square photonic crystal lattice with triangular air holes. The asymmetric nature
of the air holes gives two modes with zero group velocity at zero wavefactor (red ellipses), leading to
emission perpendicular to the surface. b, Dispersion relation of a composite photonic crystal lattice
comprising square and rectangular arrays of triangular air holes. The resulting additional branches in
the dispersion relation give two new flat regions of zero group velocity but at non-zero wavefactors (red
ellipses), resulting in angular emission.
development of photonic-crystal-based
devices is concerned, this study shows that a
perfect crystal is not always the best solution;
the engineered degrees of freedom are
greatly enhanced if combinations of different
crystals are used. There’s certainly a lot to be
discovered along this line of research.
❐
Martin Kamp is at Technische Physik,
Universtität Würzburg, Am Hubland,
D-97074 Würzburg, Germany.
e-mail: [email protected]
References
Kurosaka, Y. et al. Nature Photon. 4, 447–450 (2010).
Mukai, S. et al. Opt. Quant. Electron. 17, 431–434 (1985).
Painter, O. et al. Science 284, 1819–1821, (1999).
Noda, S., Yokoyama, M., Imada, M., Chutinan, A. &
Mohizuki, M. Science 293, 1123–1125 (2001).
5. Altug, H., Englund D. & Vuckovic, J. Nature Phys.
2, 484–488 (2006).
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OPTICAL GRATINGS
Nano-engineered lenses
High-performance, ultracompact lenses are needed in the quest to miniaturize optical systems. It now seems
that carefully engineered subwavelength gratings can function as almost perfect mirrors with custom-designed
focusing properties.
Lukas Chrostowski
C
onventional optical lenses, usually
made of thick glass, have excellent
optical properties but are heavy, bulky
and have limited functionality. In many
applications a thin lens is desirable to either
reduce weight or enable miniaturization.
These needs are currently addressed using
planar Fresnel lenses (also known as zone
plates), which can be found in the optical
systems of lighthouses, overhead projectors,
DVD players and cameras. In all cases, such
lenses use spatially selective phase shifts to
manipulate the wavefront of incident light
and bring it to a focus (Fig. 1a,b). These phase
shifts originate from the local thickness of the
optical element, which must therefore have its
shape and features precisely fabricated at the
scale of hundreds of nanometres1 in order to
operate correctly.
Now, in a striking study reported in
Nature Photonics, David Fattal and his coworkers2 have demonstrated a new method
of making ultrathin focusing elements. Their
approach relies on using optical resonances
in nanoscale, high-contrast, subwavelength
gratings (SWGs) to gain control over the
phase of the reflected light (Fig. 1c). First,
a resonator produces a phase shift that is a
function of the frequency of the incident
light. The response is determined by the
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signal’s spectral position with respect to the
natural resonant frequency of the resonator,
which in turn is dictated by the resonator’s
size. Thus, different sized resonators yield
different phase shifts. An array of these
resonators can be arranged in such a way that
allows almost any phase shift to be obtained,
enabling focusing as in conventional lenses
but in a much smaller size and based on a
physically different mechanism.
This concept is already used to direct
radiofrequency waves in phased-array
antennas; in fact, the approach of using
resonators to alter the phase of a reflected
radiofrequency electromagnetic wave has
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previously been demonstrated using tunable
inductor–capacitor resonators3.
The challenge of implementing this
concept at optical wavelengths is mostly one
of scaling; submicrometre-sized resonators
are required because optical wavelengths
are so much shorter than radiowaves. This
work demonstrates that carefully engineered
gratings can function as tiny mirror lenses
with almost perfect reflectivity, thus
potentially opening the way to new lowcost and compact optical assemblies such as
microlens arrays for CMOS image sensors
and lenses for digital cameras. By changing
the position, shape and index of refraction
of the grating mirror, dynamic focusing may
also be achievable in the future.
A remarkable property of SWGs is that
they can be designed to function as highly
reflective mirrors (>99%), but are much
thinner than multilayer films (hundreds of
nanometres versus several micrometres)4.
Such gratings are lithographically fabricated
on flat substrates using a binary process to
produce rectangular ‘fingers’. The grating’s
geometric parameters — thickness, period
and duty cycle — determine the amplitude
and phase of the reflection spectrum profile.
For example, phase control allows designers
to lithographically change the cavity
resonance wavelength in multiwavelength
laser arrays or optical filters.
So far, the most successful application of
these gratings has been their use as highly
efficient and compact replacements for
distributed Bragg reflectors in vertical-cavity
surface-emitting lasers (VCSELs). Because
SWGs are thin (~150 nm, for example)
and lightweight they can be moved quickly,
allowing rapid wavelength tuning, which is
useful in communications and spectroscopy 5.
For example, studies using electrostatically
actuated gratings have given wavelengthtunable VCSELs with tuning times of less
than 100 ns (refs 4,6).
The study of Fattal et al. extends the
usefulness of SWGs by adding the ability
to focus light — a critical function in most
laser applications. Stemming from this
work, SWGs could in principle be used for
fast dynamic focusing, beam steering and
collimation, for example to improve access
speeds in optical memory.
The operating principle behind SWGs
is similar to the guided-mode resonance
phenomenon7. The incident light is diffracted
by the grating and excites waveguide modes.
The light propagating in the waveguide
interacts with the grating and is re-coupled
back to radiative modes, resulting in high
optical reflectivity. SWGs are ‘subwavelength’
because the grating period is smaller than the
wavelength of light, and thus only the zeroorder mode is radiated. In a weak grating,
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a
b
c
Lens
Incoming wavefront
FZP
Transmitted/reflected wavefront
SWG
Focal point
Figure 1 | Comparison of different focusing concepts. a, Conventional lens. b, Diffractive optic such as a
Fresnel zone plate (FZP). c, Subwavelength grating reflector. In a and b, focusing originates from a phase
shift caused by the thickness of the material, but in c, the phase shift is due to the interaction of the light
with the high-contrast subwavelength grating, which locally acts as a resonator whose characteristics are
defined by its grating period and duty cycle.
light travels a long distance (as in fibre
Bragg gratings) and this gives a narrowband
resonance7. However, if the index contrast
in the grating is increased, the bandwidth
of the reflectivity spectrum increases (as in
the case of Bragg reflectors in VCSELs) and
the effective field penetration in the grating
direction decreases. Owing to the high
index contrast between the semiconductor
and the surrounding air, light only interacts
with a small number of grating periods
before being reflected8; for example, an
80% reflectivity can be obtained with only
five periods. Indeed, it was shown that four
grating fingers together with four distributed
Bragg reflector periods for the top mirror
are sufficient to make a VCSEL4. It is the
high contrast in these gratings that leads to
the strongly localized effect responsible and
necessary for the work of Fattal et al. For
this reason, these SWGs are also known as
high-contrast gratings4, as they offer much
larger reflectance bandwidths compared with
guided-mode resonant gratings.
The work of Fattal et al. demonstrates
that locally tuning the grating period (or
duty cycle) in SWGs can locally modify the
phase of the reflected (or transmitted) light.
This offers designers nearly full control over
the phase of the reflected wavefront. The
experiments and modelling were conducted
using gratings defined by e-beam lithography
on a 450-nm-thick layer of silicon on a
silicon dioxide (quartz) substrate. First, the
authors modelled the grating amplitude and
phase reflectivity for different geometries.
They then identified a range of parameters
such that a phase shift of almost 2π was
possible with nearly 100% reflectivity. The
relationship between the reflected phase
and the grating geometry was then used to
construct an optical element with a desired
phase response for focusing using a discrete
algorithm. The specific examples investigated
were cylindrical and spherical lenses, in
which the phase shift is a quadratic function
of the position. The authors showed that their
fabricated lens, with a diameter of 300 μm,
a focal length of 17.2 mm and for operation
with 1,550 nm light, successfully focused
light down to a 60 μm spot. This corresponds
to a numerical aperture (NA) of ~0.01.
Simulations of a larger-NA device were also
presented, in which the lens had a diameter
of 50 μm, a focal length of 50 μm and an NA
of 0.45.
An important consideration in the
application of these mirror reflectors is the
range of phase shifts required. For example,
the simulated design of Fattal et al. requires
a total phase shift of 8π, which, because of
phase wrapping over the period 0–2π, results
in sudden discontinuous jumps in phase. This
not only leads to imperfections in the phase
response at these points, but also reduces the
overall reflectivity. The degree of locality of
the resonance (that is, the number of fingers
required to achieve the strong resonance
effect) determines the amount of smoothing
of the phase response; this will limit the
maximum ‘curvature’ of the lens, particularly
for large-NA lenses that require phase shifts
of more than 2π. This approach therefore
yields the smoothest phase profiles for
applications that do not require any 2π phase
jumps, such as the low-NA experiments
presented here2.
Although SWG reflectivity profiles are
very broad (1,350–2,000 nm in this work),
the SWG mirror developed by Fattal et al.
is wavelength-dependent, and therefore
focusing will only be achieved in a narrow
wavelength range. Furthermore, SWGs are, in
general, polarization sensitive. For VCSELs,
this is advantageous because it can be used
to stabilize the laser’s polarization9. However,
for applications such as camera lenses, it is
desirable to have polarization insensitivity,
NATURE PHOTONICS | VOL 4 | JULY 2010 | www.nature.com/naturephotonics
© 2010 Macmillan Publishers Limited. All rights reserved
news & views
and it may be possible to fabricate similar
polarization-insensitive optical elements
using photonic crystals by varying the lattice
spacing and hole radius.
The fabrication of SWGs presents its own
challenges, as it requires the duty cycle and
period to be accurately patterned to obtain
the desired phase response. Roughness and
fabrication defects will also be a concern.
When used as VCSEL mirrors, SWGs have
a very large reflection bandwidth and hence
are extremely tolerant of roughness and
fabrication defects4. However, fabrication
tolerances for lenses will be more stringent
because wavefront phase is sensitive to
the lens geometry 2. It may therefore be
challenging to fabricate these elements
using low-cost mass-production techniques
such as nano-imprint lithography. Material
losses and roughness-induced scattering
will also degrade the performance of
such components.
This technique of using carefully
engineered SWGs to control phase has
interesting future potential. For laser
cavities, the high reflectivity of SWGs
together with their focusing ability could
provide a smaller optical mode profile,
which could be useful in low-thresholdcurrent quantum-dot VCSELs. Controlling
the transmission phase profile will be useful
for implementing collimators directly
onto VCSEL arrays or LEDs. Furthermore,
because lithography is used to define the
phase shift, any arbitrary wavefront can
be designed. Finally, this approach is an
alternative to diffractive optics1 that avoids
the requirement of multilevel lithography.
The fruition of future industrial applications
of these SWG-based focusing mirrors will
depend on whether they can be fabricated at
a low cost, and whether further performance
advantages over traditional technologies can
be demonstrated.
❐
Lukas Chrostowski is at the Department of Electrical
and Computer Engineering at the University of
British Columbia, Vancouver, British Columbia V6T
1Z4, Canada.
e-mail: [email protected]
References
1. Pitchumani, M., Hockel, H., Mohammed, W. & Johnson, E. G.
Appl. Opt. 41, 6176–6181 (2002).
2. Fattal, D., Li, J., Peng, Z., Fiorentino, M. & Beausoleil, R. G.
Nature Photon. 4, 466–470 (2010).
3. Sievenpiper, D. F., Schaffner, J. H., Song, J. H., Loo, R. Y. &
Tangonan, G. IEEE T. Antenn. Propag. 51,
2713–2722 (2003).
4. Chang-Hasnain, C. J., Zhou, Y., Huang, M. & Chase, C.
IEEE J. Sel. Top. Quant. Electron. 15, 869–878 (2009).
5. Buus, J., Amann, M.-C. & Blumenthal, D. J. Tunable Laser Diodes
and Related Sources (Wiley-Interscience, 2005).
6. Huang, M. C. Y., Zhou, Y. & Chang-Hasnain, C. J. Nature Photon.
2, 180–184 (2008).
7. Peters, D. W., Kemme, S. A. & Hadley, G. R. J. Opt. Soc. Am. A
21, 981–987 (2004).
8. Bisaillon, E. et al. Opt. Express 14, 2573–2582 (2006).
9. Gustavsson, J. et al. Opt. Express 13, 6626–6634 (2005).
TEMPORAL CAVITY SOLITONS
Buffering optical data
Packets of light persisting in a continuously driven nonlinear resonator in the time domain offer new possibilities
not only for applications in all-optical storage, pulse reshaping and wavelength conversion, but also for
fundamental experiments in nonlinear science.
William Firth
I
magine a device that can capture a 40 kbit
sequence from a 25 Gbit s–1 optical data
stream, store it for more than a second,
and provide continuously looped optical
read-out of the data at the original rate of
25 Gbit s–1. Such a device, here named the
“Kerrcam” for its use of the optical Kerr effect
to copy and sustain the optical bit sequence,
has been demonstrated by François Leo and
colleagues from Université Libre de Bruxelles
in Belgium and the University of Auckland in
New Zealand. Reporting in Nature Photonics,
the team analyse their prototype device,
which demonstrates the capability of alloptical buffering 1.
The essence of the Kerrcam can be
envisaged simply as an optical fibre coupled
to a fibre loop (Fig. 1a). A continuous-wave
field injected into the coupler sustains a
circulating field in the loop. The injection
of a short address pulse of sufficient power
into the coupler causes, through cross-phase
modulation, a local focusing (in time) of the
circulating field in the loop. Under the right
conditions, the resultant ‘bump’ in the field
can continue to grow, even after the address
pulse has passed through the system. The
field can self-organize, through self-phase
modulation, to form a stable large-amplitude
pulse that persists indefinitely in the loop as
a record of the address pulse. The width of
this copy pulse is determined by a balance
between the narrowing tendency of the
Kerr effect and the broadening effect of
anomalous dispersion.
Part of the copy pulse escapes as readout every time a roundtrip of the loop is
completed, but these and other losses are
compensated through interactions with the
continuous-wave background field. The copy
pulse can therefore persist indefinitely as long
as the continuous-wave input is maintained.
The pulse tails decay exponentially, making
them well localized in time. Thus it is easy
to see that whole sequences of pulses can be
written in the same way, and that they won’t
interact appreciably if they are more than a
few decay-lengths apart. The Kerrcam can
therefore function either as an all-optical
memory or, because of the roundtrip
read-out, as a delay line. Of course, the
real system is more complex than the ideal
Kerrcam; optical isolation is required to
prevent Brillouin back-scattering, and various
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control and diagnostic elements are also
essential (Fig. 1b).
As already mentioned, the width of
the copy pulse is determined by a balance
between the Kerr nonlinearity and
dispersion, which is familiar from solitons
in fibre optics. The stability and persistence
of the copy pulse, however, require a balance
between gain and loss. This double balance
is typical of a fundamental and universal
class of structures called dissipative solitons2,3
(DSs). In optics, as in many other fields, the
DS is the simplest possible structure that is
both self-organized and self-localized. More
complex structures can often be regarded
as combinations of DSs. Thus, the DS is
the natural ‘bit’ for the science of selforganizing systems.
The work of Leo et al. experimentally
demonstrates a type of optical DS predicted
in the early 1980s. It is the DS solution of
the Lugiato–Lefever Equation (LLE), which
was presented in 1987 in the context of
spontaneous optical pattern formation in an
optical resonator/cavity 4. The term ‘cavity
soliton’ (CS) is often used to describe DS
solutions to the LLE and analogous optical
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