Designer spoof surface plasmon structures collimate terahertz laser beams

Journal name:
Nature Materials
Volume:
9,
Pages:
730–735
Year published:
DOI:
doi:10.1038/nmat2822
Received
Accepted
Published online

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.

At a glance

Figures

  1. Terahertz plasmonic collimator design.
    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, , 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=100 μm 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=2/4/8/7 μm; red dashed curve: b/t/p/h=2/4/8/8.5 μm; red dash–dotted curve: b/t/p/h=2.5/6.5/8/12 μm; red dash–double-dotted curve: b/t/p/h=2/7/8/16 μm. The horizontal dotted line indicates the lasing frequency. ko=2π/λo, where λo=100 μm. 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=2/4/8 μm.

  2. Simulations.
    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 65 μm. The grating period is 88 μm. The opening, bottom and depth of the second-order grating grooves are 19, 15 and 13.5 μm, respectively. e, The red, blue and black curves are line-scans of the near-field (|E|) along and 10 μm 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.

  3. Experimental results for a device fabricated according to the design in Fig. 1.
    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-mm-long, 150-μm-wide and 10-μm-thick waveguide and lases at λo=100 μm. The plasmon 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=3.0 A. 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.

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Author information

Affiliations

  1. School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

    • Nanfang Yu,
    • Qi Jie Wang,
    • Mikhail A. Kats,
    • Jonathan A. Fan &
    • Federico Capasso
  2. School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, UK

    • Suraj P. Khanna,
    • Lianhe Li,
    • A. Giles Davies &
    • Edmund H. Linfield
  3. Present address: School of Electrical and Electronic Engineering & School of Physical and Mathematical Sciences, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

    • Qi Jie Wang

Contributions

N.Y. designed the devices, in collaboration with J.A.F., and, with Q.J.W., fabricated them and carried out the experiments. M.A.K. participated in the device simulation and in the data analysis. S.P.K. and L.L. grew QCL material using molecular beam epitaxy. N.Y. and F.C. wrote the paper. F.C., A.G.D. and E.H.L. supervised the project.

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The authors declare no competing financial interests.

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