Lunch meetingPhilip ChimentoOctober 7, 2010

BRIEF NEWS

Explaining science to laymen

LETTERSPUBLISHED ONLINE: 8 AUGUST 2010 | DOI: 10.1038/NMAT2822

Designer spoof surface plasmon structurescollimate terahertz laser beamsNanfang Yu1*, Qi Jie Wang1†, Mikhail A. Kats1, Jonathan A. Fan1, Suraj P. Khanna2, Lianhe Li2,A. Giles Davies2, Edmund H. Linfield2 and Federico Capasso1*Surface plasmons have found a broad range of applications

in photonic devices at visible and near-infrared wavelengths.

In contrast, longer-wavelength surface electromagnetic waves,

known as Sommerfeld or Zenneck waves1,2, are characterized

by poor confinement to surfaces and are therefore difficult to

control using conventional metallo-dielectric plasmonic struc-

tures. However, patterning the surface with subwavelength

periodic features can markedly reduce the asymptotic surface

plasmon frequency, leading to ‘spoof’ surface plasmons3,4

with

subwavelength confinement at infrared wavelengths and be-

yond, which mimic surface plasmons at much shorter wave-

lengths. We demonstrate that by directly sculpting designer

spoof surface plasmon structures that tailor the dispersion

of terahertz surface plasmon polaritons on the highly doped

semiconductor facets of terahertz quantum cascade lasers,

the performance of the lasers can be markedly enhanced.

Using a simple one-dimensional grating design, the beam

divergence of the lasers was reduced from ∼180◦to ∼10

◦, the

directivity was improved by over 10 decibels and the power

collection efficiency was increased by a factor of about six

compared with the original unpatterned devices. We achieve

these improvements without compromising high-temperature

performance of the lasers.

Metamaterials and transformation optics offer major opportu-nities for the control of electromagnetic fields5–8. The underlyingparadigm is to design spatial variations of the magnitude and signof the effective refractive index; thus, the optical path, or moregenerally the ‘optical space’, can be engineered in a continuousand almost arbitrary way. One can extend the concept to surfaceplasmon (SP) optics where the dispersion properties of SPs aretailored by nanostructuringmetallic surfaceswith designer patterns.In this context ‘metasurfaces’ or ‘metafilms’ have found interestingapplications, such as subwavelength imaging9, waveguiding10,11 andthe localization10,11, confinement12 and slowing of light13.

Consider a structure composed of arrays of grooves withsubwavelength periodicities textured on the surface of a plasmonicmaterial (metals or highly doped semiconductors, which behaveas metals in the terahertz regime; see Fig. 1a). Such a structuresupports strongly confined surface waves with a dispersion relationω(β) similar to SPs on a planar metal surface in the visible regime,as calculated by Pendry, Martín-Moreno, and García-Vidal3,4 andobserved on structured metals at terahertz frequencies14. Theasymptotic frequency, ωspoof, is not solely determined by propertiesof the interface materials and can be designed over an extremelywide range by engineering the subwavelength pattern on theinterface3. If the metal can be treated as a perfect electric conductor,

1School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA, 2School of Electronic and Electrical Engineering,University of Leeds, Leeds LS2 9JT, UK. †Present address: School of Electrical and Electronic Engineering & School of Physical and Mathematical Sciences,Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore. *e-mail: nyu@fas.harvard.edu; capasso@seas.harvard.edu.

ωspoof = πc/2h, where h is the groove depth and c is the speedof light in vacuum4. Physically, this corresponds to first-orderstanding waves along the depth of the grooves. As ωspoof is primarilydetermined by surface texturing, one can engineer the spoof SPdispersion curve and obtain a sizeable deviation between the curveand the light line at terahertz frequencies; that is, β(ωTHz) >

ko(ωTHz) (refs 3,4,14; see Fig. 1b). Here β is the in-plane wave vectorof the SPs and ko is the free-space wave vector. As a result, theout-of-plane wave vector κ(ωTHz) = i

√β2(ωTHz)−k0

2(ωTHz) canbe considerable, corresponding to confined SPs with a 1/e decaydistance in the air normal to the interface equal to 1/|κ| (ref. 14).

In this Letter, we demonstrate the great design potential of spoofSP structures for active photonic devices by markedly improvingthe performance of terahertz quantum cascade lasers (QCLs).Terahertz QCLs have undergone rapid development recently andhave significant potential for applications in sensing, imaging andheterodyne detection of chemicals15–18. Terahertz QCLs with thehighest operating temperature and lowest threshold current so fartake advantage of the high optical confinement (near 100%) andheat removal properties of a double-metal waveguide design, inwhich the laser active region is located between a metal strip anda metal plane19–21. However, this leads to non-Fresnel reflectionat the subwavelength laser apertures (as small as one-tenth ofλo, the free-space wavelength), which gives rise to inefficientpower out-coupling (power reflectivity of laser modes at theaperture up to 90%) and poor beam quality (characterized bya divergence angle ∼180◦ perpendicular to the laser materiallayers)20,21. The last of these is a particularly serious problem forthe far-infrared heterodyne detection of chemicals because theoutput of terahertz QCLs (local oscillator) must be focused into asmall-area Schottky diode mixer15.

A number of schemes have been demonstrated to increase beamdirectionality and/or power out-coupling efficiency of terahertzQCLs (refs 22–27). One approach is to attach a silicon microlens22or a metallic horn antenna23 onto one of the facets of the laserwaveguide to reduce the mode impedance mismatch at the laseraperture, and thereby enhance the power output. However, thismethod requires meticulous manipulation and alignment of smalloptical components, which affects device yield and robustness.A monolithic approach would alleviate these problems. Anotherapproach relies on processing terahertz lasers into surface-emittingstructures with higher-order gratings24–26 or photonic crystals27;this approach relies on constructive interference between multiplesurface emissions or a large emission area to reduce beamdivergence. However, this results in devices with reduced modeconfinement and therefore increases the laser threshold current

730 NATUREMATERIALS | VOL 9 | SEPTEMBER 2010 | www.nature.com/naturematerials

TODAY’S FEATURED STORY

TEDGlobal 2010, Filmed Jul 2010; Posted Aug 2010

00:35 | 18:17

Subtitles Available in:

“...visualizing information, so that we can see the patterns and connections that matter and then designing that information so it makes more sense, or it tells a story, or allows us to focus only on the information that’s impor-tant. Failing that, visualized informa-tion can just look really cool.”

David McCandless, The Beauty of Information Visualization,

TED Global 2010

R esearch has shown that the rainbow color map israrely the optimal choice when displaying data

with a pseudocolor map. The rainbow color map con-fuses viewers through its lack of perceptual ordering,obscures data through its uncontrolled luminance vari-ation, and actively misleads interpretation through theintroduction of non-data-dependent gradients.

Despite much published research on its deficiencies,the rainbow color map is prevalent in the visualizationcommunity. We present survey results showing that therainbow color map continues to appear in more thanhalf of the relevant papers in IEEE VisualizationConference proceedings; for example, it appeared on61 pages in 2005. Its use is encouraged by its selectionas the default color map used in most visualizationtoolkits that we inspected. The visualization communi-ty must do better.

In this article, we reiterate the characteristics thatmake the rainbow color map a poor choice, provideexamples that clearly illustrate these deficiencies evenon simple data sets, and recommend better color mapsfor several categories of display.

The goal is to make the rainbow color map as rare invisualization as the goto statement is in program-ming—which complicates the task of analyzing and ver-ifying program correctness (see the classic “Go ToStatement Considered Harmful” paper by Dijkstra athttp://www.acm.org/classics/oct95/).

Problems with the rainbow color mapPseudocoloring is a visualization technique for dis-

playing scalar field data. Data values are mappedthrough a pseudocolor scale—or color map—to deter-mine the color representing each value. The mappingcan be arbitrary, but most color maps work by continu-ously varying some color property, such as hue or satu-ration, to represent higher and lower data values.

The rainbow color map varies hue to approximate theelectromagnetic spectrum’s visible wavelengths and isprobably the most common color map used in the visu-alization community. The reason for this popularitymight be due to inertia: users, especially physicists,adopted it early on, and others in many disciplines havesince followed. It might be due to the notion of “the morecolors, the better.” Or it might simply be that it’s thedefault option in many visualization toolkits and appli-cations. It’s used to display data in journals, conferenceproceedings, mouse pads, calendars, US Navy com-

mercials, weather forecasts, and even the IEEEVisualization Conference 2006 call for papers, just toname a few. The problem with this wide use of the rain-bow color map is that research shows that it is rarely, ifever, the optimal color map for a given visualization.1-6

Here we will discuss the rainbow color map’s charac-teristics of confusing the viewer, obscuring data, andactively misleading interpretation.

ConfusingFor all tasks that involve comparing relative values,

the color map used should exhibit perceptual ordering.A simple example of a perceptually ordered color map isthe gray-scale color map. Increasing luminance fromblack to white is a strong perceptual cue that indicatesvalues mapped to darker shades of gray are lower invalue than values mapped to lighter shades of gray. Thismapping is natural and intuitive.

The rainbow color map is certainly ordered—from ashorter to longer wavelength of light (or vice versa)—but it’s not perceptually ordered. If people are given aseries of gray paint chips and asked to put them in order,they will consistently place them in either a dark-to-lightor light-to-dark order. However, if people are given paintchips colored red, green, yellow, and blue and asked toput them in order, the results vary (see Figure 1).7 Someeven put them in alphabetical order. To put them in theso-called correct order, most people must remember RoyG. Biv (red, orange, yellow, green, blue, indigo, violet),or some other mnemonic representation of the order ofcolors in the rainbow.

When we use a color map that is not perceptuallyordered to present ordered data, confusion resultsbecause greater-than and less-than relationships arenot immediately evident, and we must infer themthrough remembering (an error-prone task) or con-sulting a legend (a needless distraction for determin-ing order, but good practice for conveying the data’sscale).

ObscuringThe visual system perceives high spatial frequencies

through changes in luminance.2,4 Thus, to see smalldetail and sharp features in a given data set, we shoulduse a luminance varying color map, such as the gray-scale color map. The rainbow color map is isoluminantfor large portions, with apparent changes only at colorboundaries. Therefore, the approach obscures small

David Borlandand Russell M.Taylor IIUniversity ofNorth Carolinaat Chapel Hill

Rainbow Color Map (Still) Considered Harmful ________

14 March/April 2007 Published by the IEEE Computer Society 0272-1716/07/$25.00 © 2007 IEEE

Visualization Viewpoints Editor: Theresa-Marie Rhyne

IEEE Computer Graphics & Applications, March/April 2007, pp. 14−17

R esearch has shown that the rainbow color map israrely the optimal choice when displaying data

with a pseudocolor map. The rainbow color map con-fuses viewers through its lack of perceptual ordering,obscures data through its uncontrolled luminance vari-ation, and actively misleads interpretation through theintroduction of non-data-dependent gradients.

Despite much published research on its deficiencies,the rainbow color map is prevalent in the visualizationcommunity. We present survey results showing that therainbow color map continues to appear in more thanhalf of the relevant papers in IEEE VisualizationConference proceedings; for example, it appeared on61 pages in 2005. Its use is encouraged by its selectionas the default color map used in most visualizationtoolkits that we inspected. The visualization communi-ty must do better.

In this article, we reiterate the characteristics thatmake the rainbow color map a poor choice, provideexamples that clearly illustrate these deficiencies evenon simple data sets, and recommend better color mapsfor several categories of display.

The goal is to make the rainbow color map as rare invisualization as the goto statement is in program-ming—which complicates the task of analyzing and ver-ifying program correctness (see the classic “Go ToStatement Considered Harmful” paper by Dijkstra athttp://www.acm.org/classics/oct95/).

Problems with the rainbow color mapPseudocoloring is a visualization technique for dis-

playing scalar field data. Data values are mappedthrough a pseudocolor scale—or color map—to deter-mine the color representing each value. The mappingcan be arbitrary, but most color maps work by continu-ously varying some color property, such as hue or satu-ration, to represent higher and lower data values.

The rainbow color map varies hue to approximate theelectromagnetic spectrum’s visible wavelengths and isprobably the most common color map used in the visu-alization community. The reason for this popularitymight be due to inertia: users, especially physicists,adopted it early on, and others in many disciplines havesince followed. It might be due to the notion of “the morecolors, the better.” Or it might simply be that it’s thedefault option in many visualization toolkits and appli-cations. It’s used to display data in journals, conferenceproceedings, mouse pads, calendars, US Navy com-

mercials, weather forecasts, and even the IEEEVisualization Conference 2006 call for papers, just toname a few. The problem with this wide use of the rain-bow color map is that research shows that it is rarely, ifever, the optimal color map for a given visualization.1-6

Here we will discuss the rainbow color map’s charac-teristics of confusing the viewer, obscuring data, andactively misleading interpretation.

ConfusingFor all tasks that involve comparing relative values,

the color map used should exhibit perceptual ordering.A simple example of a perceptually ordered color map isthe gray-scale color map. Increasing luminance fromblack to white is a strong perceptual cue that indicatesvalues mapped to darker shades of gray are lower invalue than values mapped to lighter shades of gray. Thismapping is natural and intuitive.

The rainbow color map is certainly ordered—from ashorter to longer wavelength of light (or vice versa)—but it’s not perceptually ordered. If people are given aseries of gray paint chips and asked to put them in order,they will consistently place them in either a dark-to-lightor light-to-dark order. However, if people are given paintchips colored red, green, yellow, and blue and asked toput them in order, the results vary (see Figure 1).7 Someeven put them in alphabetical order. To put them in theso-called correct order, most people must remember RoyG. Biv (red, orange, yellow, green, blue, indigo, violet),or some other mnemonic representation of the order ofcolors in the rainbow.

When we use a color map that is not perceptuallyordered to present ordered data, confusion resultsbecause greater-than and less-than relationships arenot immediately evident, and we must infer themthrough remembering (an error-prone task) or con-sulting a legend (a needless distraction for determin-ing order, but good practice for conveying the data’sscale).

ObscuringThe visual system perceives high spatial frequencies

through changes in luminance.2,4 Thus, to see smalldetail and sharp features in a given data set, we shoulduse a luminance varying color map, such as the gray-scale color map. The rainbow color map is isoluminantfor large portions, with apparent changes only at colorboundaries. Therefore, the approach obscures small

David Borlandand Russell M.Taylor IIUniversity ofNorth Carolinaat Chapel Hill

Rainbow Color Map (Still) Considered Harmful ________

14 March/April 2007 Published by the IEEE Computer Society 0272-1716/07/$25.00 © 2007 IEEE

Visualization Viewpoints Editor: Theresa-Marie Rhyne

IEEE Computer Graphics & Applications, March/April 2007, pp. 14−17

DANGER

R esearch has shown that the rainbow color map israrely the optimal choice when displaying data

with a pseudocolor map. The rainbow color map con-fuses viewers through its lack of perceptual ordering,obscures data through its uncontrolled luminance vari-ation, and actively misleads interpretation through theintroduction of non-data-dependent gradients.

Despite much published research on its deficiencies,the rainbow color map is prevalent in the visualizationcommunity. We present survey results showing that therainbow color map continues to appear in more thanhalf of the relevant papers in IEEE VisualizationConference proceedings; for example, it appeared on61 pages in 2005. Its use is encouraged by its selectionas the default color map used in most visualizationtoolkits that we inspected. The visualization communi-ty must do better.

In this article, we reiterate the characteristics thatmake the rainbow color map a poor choice, provideexamples that clearly illustrate these deficiencies evenon simple data sets, and recommend better color mapsfor several categories of display.

The goal is to make the rainbow color map as rare invisualization as the goto statement is in program-ming—which complicates the task of analyzing and ver-ifying program correctness (see the classic “Go ToStatement Considered Harmful” paper by Dijkstra athttp://www.acm.org/classics/oct95/).

Problems with the rainbow color mapPseudocoloring is a visualization technique for dis-

playing scalar field data. Data values are mappedthrough a pseudocolor scale—or color map—to deter-mine the color representing each value. The mappingcan be arbitrary, but most color maps work by continu-ously varying some color property, such as hue or satu-ration, to represent higher and lower data values.

The rainbow color map varies hue to approximate theelectromagnetic spectrum’s visible wavelengths and isprobably the most common color map used in the visu-alization community. The reason for this popularitymight be due to inertia: users, especially physicists,adopted it early on, and others in many disciplines havesince followed. It might be due to the notion of “the morecolors, the better.” Or it might simply be that it’s thedefault option in many visualization toolkits and appli-cations. It’s used to display data in journals, conferenceproceedings, mouse pads, calendars, US Navy com-

mercials, weather forecasts, and even the IEEEVisualization Conference 2006 call for papers, just toname a few. The problem with this wide use of the rain-bow color map is that research shows that it is rarely, ifever, the optimal color map for a given visualization.1-6

Here we will discuss the rainbow color map’s charac-teristics of confusing the viewer, obscuring data, andactively misleading interpretation.

ConfusingFor all tasks that involve comparing relative values,

the color map used should exhibit perceptual ordering.A simple example of a perceptually ordered color map isthe gray-scale color map. Increasing luminance fromblack to white is a strong perceptual cue that indicatesvalues mapped to darker shades of gray are lower invalue than values mapped to lighter shades of gray. Thismapping is natural and intuitive.

The rainbow color map is certainly ordered—from ashorter to longer wavelength of light (or vice versa)—but it’s not perceptually ordered. If people are given aseries of gray paint chips and asked to put them in order,they will consistently place them in either a dark-to-lightor light-to-dark order. However, if people are given paintchips colored red, green, yellow, and blue and asked toput them in order, the results vary (see Figure 1).7 Someeven put them in alphabetical order. To put them in theso-called correct order, most people must remember RoyG. Biv (red, orange, yellow, green, blue, indigo, violet),or some other mnemonic representation of the order ofcolors in the rainbow.

When we use a color map that is not perceptuallyordered to present ordered data, confusion resultsbecause greater-than and less-than relationships arenot immediately evident, and we must infer themthrough remembering (an error-prone task) or con-sulting a legend (a needless distraction for determin-ing order, but good practice for conveying the data’sscale).

ObscuringThe visual system perceives high spatial frequencies

through changes in luminance.2,4 Thus, to see smalldetail and sharp features in a given data set, we shoulduse a luminance varying color map, such as the gray-scale color map. The rainbow color map is isoluminantfor large portions, with apparent changes only at colorboundaries. Therefore, the approach obscures small

David Borlandand Russell M.Taylor IIUniversity ofNorth Carolinaat Chapel Hill

Rainbow Color Map (Still) Considered Harmful ________

14 March/April 2007 Published by the IEEE Computer Society 0272-1716/07/$25.00 © 2007 IEEE

Visualization Viewpoints Editor: Theresa-Marie Rhyne

IEEE Computer Graphics & Applications, March/April 2007, pp. 14−17

“Research has shown that the rain-bow color map is rarely the optimal choice when displaying data with a pseudocolor map. The rainbow color map confuses viewers through its lack of perceptual ordering, and actively misleads interpretation...”

R esearch has shown that the rainbow color map israrely the optimal choice when displaying data

with a pseudocolor map. The rainbow color map con-fuses viewers through its lack of perceptual ordering,obscures data through its uncontrolled luminance vari-ation, and actively misleads interpretation through theintroduction of non-data-dependent gradients.

Despite much published research on its deficiencies,the rainbow color map is prevalent in the visualizationcommunity. We present survey results showing that therainbow color map continues to appear in more thanhalf of the relevant papers in IEEE VisualizationConference proceedings; for example, it appeared on61 pages in 2005. Its use is encouraged by its selectionas the default color map used in most visualizationtoolkits that we inspected. The visualization communi-ty must do better.

In this article, we reiterate the characteristics thatmake the rainbow color map a poor choice, provideexamples that clearly illustrate these deficiencies evenon simple data sets, and recommend better color mapsfor several categories of display.

The goal is to make the rainbow color map as rare invisualization as the goto statement is in program-ming—which complicates the task of analyzing and ver-ifying program correctness (see the classic “Go ToStatement Considered Harmful” paper by Dijkstra athttp://www.acm.org/classics/oct95/).

Problems with the rainbow color mapPseudocoloring is a visualization technique for dis-

playing scalar field data. Data values are mappedthrough a pseudocolor scale—or color map—to deter-mine the color representing each value. The mappingcan be arbitrary, but most color maps work by continu-ously varying some color property, such as hue or satu-ration, to represent higher and lower data values.

The rainbow color map varies hue to approximate theelectromagnetic spectrum’s visible wavelengths and isprobably the most common color map used in the visu-alization community. The reason for this popularitymight be due to inertia: users, especially physicists,adopted it early on, and others in many disciplines havesince followed. It might be due to the notion of “the morecolors, the better.” Or it might simply be that it’s thedefault option in many visualization toolkits and appli-cations. It’s used to display data in journals, conferenceproceedings, mouse pads, calendars, US Navy com-

mercials, weather forecasts, and even the IEEEVisualization Conference 2006 call for papers, just toname a few. The problem with this wide use of the rain-bow color map is that research shows that it is rarely, ifever, the optimal color map for a given visualization.1-6

Here we will discuss the rainbow color map’s charac-teristics of confusing the viewer, obscuring data, andactively misleading interpretation.

ConfusingFor all tasks that involve comparing relative values,

the color map used should exhibit perceptual ordering.A simple example of a perceptually ordered color map isthe gray-scale color map. Increasing luminance fromblack to white is a strong perceptual cue that indicatesvalues mapped to darker shades of gray are lower invalue than values mapped to lighter shades of gray. Thismapping is natural and intuitive.

The rainbow color map is certainly ordered—from ashorter to longer wavelength of light (or vice versa)—but it’s not perceptually ordered. If people are given aseries of gray paint chips and asked to put them in order,they will consistently place them in either a dark-to-lightor light-to-dark order. However, if people are given paintchips colored red, green, yellow, and blue and asked toput them in order, the results vary (see Figure 1).7 Someeven put them in alphabetical order. To put them in theso-called correct order, most people must remember RoyG. Biv (red, orange, yellow, green, blue, indigo, violet),or some other mnemonic representation of the order ofcolors in the rainbow.

When we use a color map that is not perceptuallyordered to present ordered data, confusion resultsbecause greater-than and less-than relationships arenot immediately evident, and we must infer themthrough remembering (an error-prone task) or con-sulting a legend (a needless distraction for determin-ing order, but good practice for conveying the data’sscale).

ObscuringThe visual system perceives high spatial frequencies

through changes in luminance.2,4 Thus, to see smalldetail and sharp features in a given data set, we shoulduse a luminance varying color map, such as the gray-scale color map. The rainbow color map is isoluminantfor large portions, with apparent changes only at colorboundaries. Therefore, the approach obscures small

David Borlandand Russell M.Taylor IIUniversity ofNorth Carolinaat Chapel Hill

Rainbow Color Map (Still) Considered Harmful ________

14 March/April 2007 Published by the IEEE Computer Society 0272-1716/07/$25.00 © 2007 IEEE

Visualization Viewpoints Editor: Theresa-Marie Rhyne

IEEE Computer Graphics & Applications, March/April 2007, pp. 14−17

“The reason for this popularity might be due to inertia: users, especially physicists, adopted it early on, and others in many disciplines have since followed.”

Why so terrible?

No perceptual ordering

Why so terrible?

Obscures details due to isoluminance

Why so terrible?

Introduces artifacts due to sharp transitions between hues

OK, so what should we do instead?

Nominal data (no ordering)

© Cynthia Brewer, Mark Harrower and The Pennsylvania State UniversitySupportBack to ColorBrewer 1.0

Colorbrewer: Color Advice for Maps http://colorbrewer2.org/

1 of 1 20100928 17:16

Interval, ratio, or threshold data

http://www.research.ibm.com/people/l/lloydt/color/color.HTM

Ordinal data

“Black body” scale

Rainbow with increasing luminance

James McNames (2006). “An effective color scale for simultaneous color and gray-scale publications.” IEEE Signal Processing Magazine 23 (1), pp. 82−96.

Rainbow with increasing luminance

Rainbow with increasing luminance

Intensity and phase

Intensity and phase

Intensity and phase

Image creditsSlide Author/Copyright License Source1 zen CC-BY-NC-SA Flickr2 [BarZaN] Qtr [Boston] CC-BY-ND Flickr6 eschipul CC-BY-SA Flickr7 TED Fair Use Website14 juliaf Stock.xchng sxc.hu16 IBM Fair Use Website