Designer spoof surface plasmon structures collimate terahertz laser beams

Designer spoof surface plasmon structures collimate terahertz laser beams

(Parte 1 de 2)

Designer spoof surface plasmon structures collimate terahertz laser beams

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 structures. 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 beyond, which mimic surface plasmons at much shorter wavelengths. 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 opportunities for the control of electromagnetic fields5–8. The underlying paradigm is to design spatial variations of the magnitude and sign of the effective refractive index; thus, the optical path, or more generally the ‘optical space’, can be engineered in a continuous and almost arbitrary way. One can extend the concept to surface plasmon (SP) optics where the dispersion properties of SPs are tailoredbynanostructuringmetallicsurfaceswithdesignerpatterns. In this context ‘metasurfaces’ or ‘metafilms’ have found interesting applications, such as subwavelength imaging9, waveguiding10,1 and the localization10,1, confinement12 and slowing of light13.

Consider a structure composed of arrays of grooves with subwavelength periodicities textured on the surface of a plasmonic material (metals or highly doped semiconductors, which behave as metals in the terahertz regime; see Fig. 1a). Such a structure supports strongly confined surface waves with a dispersion relation ω(β) similar to SPs on a planar metal surface in the visible regime, as calculated by Pendry, Martín-Moreno, and García-Vidal3,4 and observed on structured metals at terahertz frequencies14. The asymptotic frequency, ωspoof, is not solely determined by properties of the interface materials and can be designed over an extremely wide range by engineering the subwavelength pattern on the interface3. 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 = pic/2h, where h is the groove depth and c is the speed of light in vacuum4. Physically, this corresponds to first-order standing waves along the depth of the grooves. As ωspoof is primarily determined by surface texturing, one can engineer the spoof SP dispersion curve and obtain a sizeable deviation between the curve and 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 vector of the SPs and ko is the free-space wave vector. As a result, the be considerable, corresponding to confined SPs with a 1/e decay distanceintheairnormaltotheinterfaceequalto1/|κ|(ref.14).

In this Letter, we demonstrate the great design potential of spoof

SP structures for active photonic devices by markedly improving the performance of terahertz quantum cascade lasers (QCLs). Terahertz QCLs have undergone rapid development recently and have significant potential for applications in sensing, imaging and heterodyne detection of chemicals15–18. Terahertz QCLs with the highest operating temperature and lowest threshold current so far take advantage of the high optical confinement (near 100%) and heat removal properties of a double-metal waveguide design, in which the laser active region is located between a metal strip and a metal plane19–21. However, this leads to non-Fresnel reflection at the subwavelength laser apertures (as small as one-tenth of λo, the free-space wavelength), which gives rise to inefficient power out-coupling (power reflectivity of laser modes at the aperture up to 90%) and poor beam quality (characterized by a divergence angle ∼180◦ perpendicular to the laser material layers)20,21. The last of these is a particularly serious problem for the far-infrared heterodyne detection of chemicals because the output of terahertz QCLs (local oscillator) must be focused into a small-area Schottky diode mixer15.

A number of schemes have been demonstrated to increase beam directionality and/or power out-coupling efficiency of terahertz QCLs (refs 2–27). One approach is to attach a silicon microlens2 or a metallic horn antenna23 onto one of the facets of the laser waveguide to reduce the mode impedance mismatch at the laser aperture, and thereby enhance the power output. However, this method requires meticulous manipulation and alignment of small optical components, which affects device yield and robustness. A monolithic approach would alleviate these problems. Another approach relies on processing terahertz lasers into surface-emitting structures with higher-order gratings24–26 or photonic crystals27; this approach relies on constructive interference between multiple surface emissions or a large emission area to reduce beam divergence. However, this results in devices with reduced mode confinement and therefore increases the laser threshold current

730 NATURE MATERIALS | VOL 9 | SEPTEMBER 2010 | w.nature.com/naturematerials

NATUREMATERIALSDOI:10.1038/NMAT2822 LETTERS Light line πc/2h=spoof THz a h

1ωβ()2ωωβ() 3β()

μ m)

Frequency (THz)

) (cm β βω (THz)ω cd e f μ m) (μ m)

Laser waveguide oλ Laser aperture

Laser substrate

Figure 1 | Terahertz plasmonic collimator design. a, By texturing a metal or a metallic semiconductor surface with subwavelength structures of various geometries, one can engineer the dispersion of SPs. In this way, complex designer plasmonic structures can be constructed to greatly improve device performance or to realize new functionalities. b, Schematic dispersion curve for terahertz spoof SPs on a perfect metal. The asymptote of the curve, ωspoof, the in-plane wave vector, β, and the out-of-plane wave vector, κ =i√ β2−k20, can be tailored by changing the geometry of the subwavelength grooves.

c, Schematic of a terahertz QCL patterned with a spoof SP collimator. The plasmonic patterns are directly sculpted on the highly doped GaAs facet of the device. Artificial colouring in the figure indicates deep and shallow spoof SP grooves. The ‘blue’ grooves adjacent to the laser aperture increase device power throughput by coupling more laser output into spoof SPs on the facet; the deep ‘pink’ grooves modulate the dispersion properties of SPs on the facet, creating a second-order grating for power out-coupling; the shallow ‘blue’ grooves contribute to SP confinement. d, Cross-section of the design for a λo =100µm device. All of the grooves have trapezoidal cross-sections to resemble structures fabricated by FIB milling. The bottom and top of the grooves, their period and depth are labelled as b, t, p and h, respectively. e, The black curve is the dispersion diagram of surface waves on the planar semiconductor/air interface. In this frequency range, it is essentially linear with a slope extremely close to the speed of light in vacuum, a manifestation of the poor confinement of surface waves at terahertz frequencies. The red curves are the dispersion diagrams corresponding to the different sections of the collimator. Red solid curve: b/t/p/h=2/4/8/7µm; red dashed curve: b/t/p/h=2/4/8/8.5µm; red dash–dotted curve: b/t/p/h=2.5/6.5/8/12µm; red dash–double-dotted curve: b/t/p/h=2/7/8/16µm. The horizontal dotted line indicates the lasing frequency. ko =2pi/λo, where λo =100µm. f, Black open circles: the 1/e decay length of the spoof SP electric field (|E|) normal to the interface into the air as a function of h. Red open triangles: imaginary part of the in-plane wave vector as a function of h, which characterizes propagation loss of spoof SPs. Other groove dimensions are fixed: b/t/p=2/4/8µm.

density, which usually leads to reduced maximum operating temperatures in continuous-wave operation.

Conventional metallo-dielectric plasmonic structures defined on laser facets have been used to shape the wavefront of midinfrared semiconductor lasers28–31. Unfortunately this methodology is not scalable to far-infrared wavelengths, because those structures do not significantly modify the SP dispersion properties and in particular the asymptotic SP frequency, thus providing limited control of terahertz surface waves.

A schematic of our design for a 3THz frequency (λo =100µm) laser and its cross-section are shown in Fig. 1c and d, respectively.

The double-metal waveguide of the laser is defined on a 450-µmthickhighlydopedGaAssubstrate.TwocoloursareusedinFig. 1c,d to identify shallow and deep spoof SP grooves. All of the grooves are defined directly on the GaAs substrate without any metal coating. We take advantage of the fact that in the terahertz regime the carrier concentration in highly doped semiconductors is sufficiently large that the semiconductor is ‘metallic’ with the real part of its dielectric permittivity being largely negative (see the Methods section for more details).

At the aperture of the double-metal waveguide, the laser emits both directly into the far-field and also into surface waves on the device facet. In the original unpatterned device, both components have a wave vector close to ko. The wave vector of the laser mode in the waveguide is several times larger, ∼neffko (neff ≈ 3.5 is the effective mode index). Therefore, there is a wave vector mismatch of the modes at the aperture. In our collimator, the spoof SP grooves adjacent to the aperture increase the effective in-plane wave vector of the SPs, reducing the wave vector mismatch. More light is therefore coupled out from the laser cavity and a larger percentage of it is channelled into the spoof SP modes instead of being directly emitted into the far-field. In addition, the deep grooves(pinkinFig. 1d)periodicallymodulatethedispersionofthe SPs on the device facet, creating an effective second-order grating that scatters the energy of the SPs into the far-field. Constructive interference between these scattered waves and the direct emission

NATURE MATERIALS | VOL 9 | SEPTEMBER 2010 | w.nature.com/naturematerials 731

LETTERS NATUREMATERIALSDOI:10.1038/NMAT2822

|E| (a.u.) Intensity (a.u.)

z (μm)

= 90°

200 μm θ

50 μm 200 μm 200 μm a ef bc d

Figure 2 | Simulations. a, Simulated distribution of the electric field (|E|) of the device shown in Fig. 1. The simulation plane is perpendicular to the laser facet and along the plane of symmetry of the laser waveguide. b, Zoom-in view of a showing the region around the device facet. c,d, Simulated electric-field distribution (|E|) of a device with a conventional second-order grating (c) and of the original device (d). The conventional second-order grating was optimized to give the highest directivity, although it is still less effective than the spoof SP collimator. The centre-to-centre distance between the aperture and the closest groove of the second-order grating is 65µm. The grating period is 88µm. The opening, bottom and depth of the second-order grating grooves are 19, 15 and 13.5µm, respectively. e, The red, blue and black curves are line-scans of the near-field (|E|) along and 10µm above the facet for the devices in a, c and d, respectively. f, The red, blue and black curves are calculated vertical far-field intensity profiles (|E|2) for a, c and d, respectively. Gaussian fits to the central lobes of the blue and red curves are plotted and the area under the fits is shaded light blue and light red, respectively. The shaded area is a measure of the percentage of total optical power in the main lobe. The main lobe of the device with the terahertz spoof SP collimator contains 70% of the output power, whereas it contains only 45% for the device with the second-order grating.

from the laser aperture gives rise to a low-divergence beam normal to the facet in the far-field28,29. Most importantly, the shallow grooves (blue in Fig. 1d) greatly increase the confinement of SPs, thusimprovingthescatteringefficiencyofthesecond-ordergrating. We use the concept of directivity D, borrowed from antenna theory, to characterize collimation for our devices. Directivity is defined as D = 10log10(2piIpeak/Itotal) (ref. 32), where Ipeak is the far-field peak intensity and Itotal is the total intensity under the beam profile. In summary, the spoof SP structures are multifunctional; by engineering the dispersion of SPs, they form a collimator that improvesdevicepowerthroughputandincreasesdirectivity.

To better understand the effect of the spoof SP grooves, we calculated the dispersion curves, the confinement and propagation losses of spoof SPs for different groove geometries (Fig. 1e,f). The in-plane wave vector increases by ∼25% for the grooves adjacent to the laser aperture (red dash–dotted curve in Fig. 1e), which reduces mode impedance mismatch, thus increasing optical power throughput owing to improved coupling into spoof SP modes, as discussed previously. The depth of the shallow grooves (blue in Fig. 1d) was chosen to be in the range 7–12µm to provide sufficient confinement without introducing large optical losses, which are mainly due to ohmic absorption and rise sharply as the groove depth increases33. Figure 1f shows that the confinement of SPs is improved to a few tens of micrometres, representing a reduction by approximately one order of magnitude compared with Zenneck waves on a planar interface (∼300µm). The depth of the shallow grooves (blue in Fig. 1d) decreases away from the laser aperture to reduce absorption losses. This leads to a non-constant SP phase velocity, which is smaller in the regions closer to the aperture. To make sure that all of the scattered waves are in phase to maximize constructive interference, the periods of the second-order grating are chosen to be shorter in the vicinity of the aperture.

The simulated electric-field distribution of the device is presented in Fig. 2a. Waves scattered from the laser facet by the spoof SP collimator are clearly observed in the near- and mesofield, and on closer inspection (Fig. 2b), confined spoof SPs can be seen on the facet. As a comparison, the simulated electricfield distributions for a device with a conventional second-order grating and for the original device without any facet patterning are presented in Fig. 2c and d, respectively. Figure 2e shows linescans of the near-fields of three devices. Note that the near-fields on the facet are the strongest for the device with the spoof SP collimator. This is due to the improved confinement of SPs, as well as the increased device power throughput and a more efficient coupling into the spoof SP modes. Indeed, simulations indicate that compared with the original unpatterned device, the power throughput of the device with the spoof SP collimator is increased by approximately 25%. On the basis of the simulation results in

732 NATURE MATERIALS | VOL 9 | SEPTEMBER 2010 | w.nature.com/naturematerials

NATUREMATERIALSDOI:10.1038/NMAT2822 LETTERS

Intensity (normallized) 0.2

Intensity (normallized) 0.2

15 Voltage (V)

Intensity (a.u.) Wavelength (μm)

Peak power (mW) de f cb Intensity (normalized)

Figure 3 | Experimental results for a device fabricated according to the design in Fig. 1. a, Scanning electron microscope image of the device facet. The device has a 1.2-m-long, 150-µm-wide and 10-µm-thick waveguide and lases at λo =100µm. The plasmonic pattern is wider at the bottom part to further expand the wavefront of SPs. b,c, Measured (b) and simulated (c) 2D far-field intensity profiles of the device. d, Line-scans of b (red circles) and c (black curve) along ϕ =0◦. The far-field measurement range is from θ =−40◦ to θ =+45◦ in the vertical direction, limited by the window of the cryostat. e, The black triangles and black dotted curve are, respectively, measured and simulated laser intensity profiles along ϕ =0◦ for the original unpatterned device. The blue circles and black solid curve are, respectively, measured and simulated laser intensity profiles along ϕ =0◦ for the device after defining the second-order grating (pink in Fig. 1d). f, Power output and voltage as a function of pump current for the device. The black, blue and red curves are for the unpatterned device, the device with only the second-order grating and the device with the spoof SP collimator, respectively. Inset: Spectrum of the device with the spoof SP collimator measured at I=3.0A. The 2D far-field map shown in b was taken at this current. The spectrum shows one comb of longitudinal modes belonging to the fundamental TM00 transverse mode of the waveguide.

Fig. 2a, it is estimated that 45% of the laser output is coupled into the spoof SP modes on the facet and the remaining 5% is emitted directly into the far-field. In contrast, the simulation with only the second-order grating (Fig. 2c) shows that the power coupled into surface waves is merely 15%, and the remaining 85% is radiated directly into the far-field. As a result of a more uniform intensity distribution in the near-field, the device with the spoof SP collimator shows increased directivity, from ∼10dB for the device with the second-order grating to ∼16dB (see Fig. 2f).

The experimental realization of the collimator is shown in Fig. 3.

Figure 3a is a scanning electron microscope image of the facet of a device fabricated using focused ion beam (FIB) milling according to the design in Fig. 1d. The collimator occupies a small footprint with dimensions ∼4λo × 4.5λo. The measured two-dimensional (2D) far-field intensity profile of the device and its vertical line-scan are presented in Fig. 3b and d, respectively. The central beam has vertical and lateral divergence angles of ∼1.7◦ and ∼16◦, respectively (full-width at half-maximum); the optical background has an average intensity that is below 10% of the central lobe peak intensity. Both are in good agreement with the 3D full-wave simulation results in Fig. 3c,d. The emission of the original device is highly divergent (see Fig. 3e for its vertical far-field profile). The measured beam directivity is increased from ∼5dB for the original unpatterned laser, to ∼11dB for the device with only the second-order grating (pink in Fig. 1d) and to ∼16dB for the device with the spoof SP collimator, representing a major performance improvement. The directivity of our collimated device is better than or comparable to those obtained in terahertz QCLs with higher-order gratings, photonic crystals or mounted micro optical elements22–27. The small-divergence beam emitted from our terahertz device is compatible with the receiver front end of modern submillimetre heterodyne detection systems34,35.

Reduction of beam divergence occurs in both the vertical and lateral directions. In the vertical direction, the collimation is essentially an antenna array effect28,29,31. In the lateral direction, it is due to an increased emission area: the spoof SP patterns were intentionally chosen to be wider than the laser waveguide (Fig. 3a), which helps spread SPs laterally by using a transmission line effect (see Supplementary Information for more details). As such, 2D collimation was realized using a 1D structure composed of straight grooves; this is different from ring-shaped 2D plasmonic collimators for mid-infrared QCLs (ref. 28).

The collected power of the device with the terahertz spoof SP collimator increases by a factor of ∼6 compared with the original unpatterned device under the same measurement conditions (see Fig. 3f). The enhancement factor is ∼5 for the device with

NATURE MATERIALS | VOL 9 | SEPTEMBER 2010 | w.nature.com/naturematerials 733

LETTERS NATUREMATERIALSDOI:10.1038/NMAT2822 only the second-order grating (pink in Fig. 1d). This difference in measured power is primarily a result of the increased total power throughput originating from the reduced wave vector mismatch in the spoof SP collimator. Our power measurement apparatus with a collection cone of ∼50◦ captures the main lobe as well as a significant portion of the background light. Eventually, what matters most for applications is the power carried in the main lobe of a laser beam, because the optical background outside the main lobe is often lost during propagation in optical systems. On the basis of the far-field measurements, the power in the main lobe of the device with the spoof SP collimator is about two times larger than that of the device with only the second-order grating.

The maximum operating temperature of the patterned device is 135K, the same as that of the original device. Figure 3f shows that the lasing threshold was not changed after defining the collimator.

(Parte 1 de 2)

Comentários