of 8
Efficient dielectric metasurface
collimating lenses for mid-infrared
quantum cascade lasers
Amir Arbabi,
1
Ryan M. Briggs,
2
Yu Horie,
1
Mahmood Bagheri,
2
Andrei Faraon
1
,
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, 1200 E.
California Blvd., Pasadena, CA 91125, USA
2
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
faraon@caltech.edu
Abstract:
Light emitted from single-mode semiconductor lasers generally
has large divergence angles, and high numerical aperture lenses are required
for beam collimation. Visible and near infrared lasers are collimated
using aspheric glass or plastic lenses, yet collimation of mid-infrared
quantum cascade lasers typically requires more costly aspheric lenses made
of germanium, chalcogenide compounds, or other infrared-transparent
materials. Here we report mid-infrared dielectric metasurface flat lenses
that efficiently collimate the output beam of single-mode quantum cascade
lasers. The metasurface lenses are composed of amorphous silicon posts
on a flat sapphire substrate and can be fabricated at low cost using a single
step conventional UV binary lithography. Mid-infrared radiation from a
4.8
μ
m distributed-feedback quantum cascade laser is collimated using a
polarization insensitive metasurface lens with 0.86 numerical aperture and
79% transmission efficiency. The collimated beam has a half divergence
angle of 0.36
and beam quality factor of
M
2
=1.02.
© 2015 Optical Society of America
OCIS codes:
(050.6624) Subwavelength structures; (140.5965) Semiconductor lasers, quan-
tum cascade; (160.3918) Metamaterials; (050.0050) Diffraction and gratings.
References and links
1. A. Kosterev and F. Tittel, “Chemical sensors based on quantum cascade lasers,” IEEE J. Quantum Electron.
38
,
582–591 (2002).
2. Y. Bakhirkin, A. Kosterev, R. Curl, F. Tittel, D. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, “Sub-ppbv
nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based inte-
grated cavity output spectroscopy,” Appl. Phys. B
82
, 149–154 (2005).
3. A. Kosterev, G. Wysocki, Y. Bakhirkin, S. So, R. Lewicki, M. Fraser, F. Tittel, and R. Curl, “Application of
quantum cascade lasers to trace gas analysis,” Appl. Phys. B
90
, 165–176 (2007).
4. R. M. Briggs, C. Frez, C. E. Borgentum, M. Bagheri, S. Forouhar, and R. D. May, “Five-channel infrared laser
absorption spectrometer for combustion product monitoring aboard manned spacecraft,” (44th International Con-
ference on Environmental Systems, 2014).
5. P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y.-C. Chang, L. Hvozdara, H. P. Herzig, P. Wagli, A. Homsy,
N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and
liquids based on quantum cascade technologies,” Analyst
139
, 2039–2046 (2014).
6. M. Amanti, M. Fischer, C. Walther, G. Scalari, and J. Faist, “Horn antennas for terahertz quantum cascade lasers,”
Electron. Lett.
43
, 573 (2007).
7. A. A. Danylov, J. Waldman, T. M. Goyette, A. J. Gatesman, R. H. Giles, K. J. Linden, W. R. Neal, W. E. Nixon,
M. C. Wanke, and J. L. Reno, “Transformation of the multimode terahertz quantum cascade laser beam into a
Gaussian, using a hollow dielectric waveguide,” Appl. Opt.
46
, 5051 (2007).
#248830
Received 31 Aug 2015; accepted 11 Dec 2015; published 17 Dec 2015
(C)
2015
OSA
28
Dec
2015
| Vol.
23,
No.
26
| DOI:10.1364/OE.23.033310
| OPTICS
EXPRESS
33310
8. R. Degl’Innocenti, Y. D. Shah, D. S. Jessop, Y. Ren, O. Mitrofanov, H. E. Beere, and D. A. Ritchie, “Hollow
metallic waveguides integrated with terahertz quantum cascade lasers,” Opt. Express
22
, 24439–49 (2014).
9. N. Yu, E. Cubukcu, L. Diehl, D. Bour, S. Corzine, J. Zhu, K. B. Crozier, F. Capasso
et al.
, “Bowtie plasmonic
quantum cascade laser antenna,” Opt. Express
15
, 13272–13281 (2007).
10. N. Yu, R. Blanchard, J. Fan, Q. J. Wang, C. Pfl
̈
ugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso,
“Quantum cascade lasers with integrated plasmonic antenna-array collimators,” Opt. Express
16
, 19447 (2008).
11. N. Yu, J. Fan, Q. J. Wang, C. Pfl
̈
ugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-
divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics
2
, 564–570 (2008).
12. M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum
cascade laser,” Nat. Photonics
3
, 586–590 (2009).
13. J. Fonollosa, R. Rubio, S. Hartwig, S. Marco, J. Santander, L. Fonseca, J. Wollenstein, and M. Moreno, “Design
and fabrication of silicon-based mid infrared multi-lenses for gas sensing applications,” Sens. Actuator B-Chem.
132
, 498–507 (2008).
14. E. Logean, L. Hvozdara, J. Di-Francesco, H. P. Herzig, R. Voelkel, M. Eisner, P.-Y. Baroni, M. Rochat, and
A. M
̈
uller, “High numerical aperture silicon collimating lens for mid-infrared quantum cascade lasers manufac-
tured using wafer-level techniques,” in “SPIE Optical Systems Design,” L. Mazuray, R. Wartmann, A. P. Wood,
M. C. de la Fuente, J.-L. M. Tissot, J. M. Raynor, T. E. Kidger, S. David, P. Ben
́
ıtez, D. G. Smith, F. Wyrowski,
and A. Erdmann, eds. (International Society for Optics and Photonics, 2012), p. 85500Q.
15. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science,
339
, 1232009
(2013).
16. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater.
13
, 139–50 (2014).
17. D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing
abilities,” Nat. Photonics
4
, 466–470 (2010).
18. F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture
low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express
18
, 12606–14
(2010).
19. A. B. Klemm, D. Stellinga, E. R. Martins, L. Lewis, G. Huyet, L. O’Faolain, T. F. Krauss, and L. O. Faolain,
“Experimental high numerical aperture focusing with high contrast gratings,” Opt. Lett.
38
, 3410–3 (2013).
20. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science
345
, 298–302 (2014).
21. A. Arbabi, M. Bagheri, A. J. Ball, Y. Horie, D. Fattal, and A. Faraon, “Controlling the Phase Front of Optical
Fiber Beams using High Contrast Metastructures - OSA Technical Digest (online),” in “CLEO: 2014,” (Optical
Society of America, San Jose, California, 2014), p. STu3M.4.
22. S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, R. G. Beausoleil, and M. Fiorentino, “Sub-wavelength Grating
Lenses with a Twist,” IEEE Photon. Technol. Lett.
26
, 1375–1378 (2014).
23. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical
apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun.
6
, 7069 (2015).
24. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Efficient high NA flat micro-lenses realized using
high contrast transmitarrays,” in “SPIE OPTO,” , C. J. Chang-Hasnain, D. Fattal, F. Koyama, and W. Zhou, eds.
(International Society for Optics and Photonics, 2015), p. 93720P.
25. E. D. Palik,
Handbook of Optical Constants of Solids
(Academic press, 1998).
26. R. M. Briggs, C. Frez, C. E. Borgentun, and S. Forouhar, “Regrowth-free single-mode quantum cascade lasers
with power consumption below 1 W,” Appl. Phys. Lett.
105
, 141117 (2014).
27. V. Liu and S. Fan, “S4 : A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun.
183
, 2233–2244 (2012).
28. F. T. Chen and H. G. Craighead, “Diffractive phase elements based on two-dimensional artificial dielectrics,”
Opt. Lett.
20
, 121–123 (1995).
29. P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Design and fabrication of blazed binary diffrac-
tive elements with sampling periods smaller than the structural cutoff,” J. Opt. Soc. Am. A
16
, 1143–1156 (1999).
30. M. Born and E. Wolf,
Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction
of Light
(Cambridge university press, 1999).
31.
CVI Melles Griot Optics Guide
, available at:
http://mellesgriot.com/Frontend/PDFs/TechGuide.pdf
accessed Oct.
2015.
1. Introduction
Quantum cascade lasers (QCLs) are compact and efficient sources of coherent mid-infrared
(mid-IR) radiation. Their small size, high spectral purity, and relatively low power consump-
tion enable realization of compact mid-IR spectroscopy systems with applications in chemical
sensing for environmental and medical monitoring [1–5]. Due to the wavelength-scale emis-
sion aperture of single-mode QCLs, their output beams have large divergence angles. High nu-
#248830
Received 31 Aug 2015; accepted 11 Dec 2015; published 17 Dec 2015
(C)
2015
OSA
28
Dec
2015
| Vol.
23,
No.
26
| DOI:10.1364/OE.23.033310
| OPTICS
EXPRESS
33311
merical aperture (NA) aspheric lenses made of germanium or chalcogenide compounds, such
as zinc selenide and black diamond (Ge
28
Sb
12
Se
60
), are conventionally used for collimation
and tight focusing of mid-IR radiation. Several techniques have been previously proposed to
reduce the beam divergence and to lower the cost of the collimation optics. Integration of di-
rectional antennas with the laser [6–8], and modification of the laser emission aperture [9–12]
are shown to increase the effective area of the emission aperture and reduce beam divergence
angle. Wafer scale fabrication of low NA multi-level mid-IR Fresnel lenses have been shown
using multiple lithography and etching steps [13]. Refractive mid-IR silicon lenses have been
also demonstrated using photoresist reflow and dry etching processes [14]. Here we propose
and experimentally demonstrate high NA diffractive mid-IR lenses based on dielectric metasur-
faces. Diffractive elements based on metallic and dielectric metasurfaces have recently attracted
significant attention [15, 16]. These metasurfaces are composed of two-dimensional arrays of
subwavelength scatterers that modify the wavefront, polarization, or amplitude of light. They
accurately realize lithographically defined phase, polarization, or amplitude profiles, and are
fabricated using standard micro- and nano-fabrication techniques with potential for low cost
wafer scale production. Visible and near-infrared dielectric metasurface lenses and focusing
mirrors have been recently demonstrated [17–24]. For efficient operation in mid-IR, the meta-
surface lenses should be fabricated using scatterers and substrates with low absorption. We use
hydrogenated amorphous silicon (a-Si) scatterers since a-Si has high refractive index and low
loss in mid-IR [25]. The high refractive index contrast between the scatterers and their sur-
roundings is essential for realization of high NA metasurface lenses [23]. Materials with low
refractive index and low mid-IR absorption such as zinc selenide, calcium fluoride, magnesium
fluoride, and sapphire can be used as the substrate for the metasurface lens. We chose sapphire
for its wider availability, lower cost, and low absorption at wavelengths below 5
μ
m.
A scanning electron micrograph of the mid-IR QCL we use in this study is shown in Fig. 1(a).
The QCL has a ridge width of 4
μ
m, is single mode, and emits dominantly transverse magnetic
(y polarized) mid-IR radiation with wavelength of approximately 4.8
μ
m. The sinusoidal cor-
rugation of the ridge forms a first order distributed-feedback (DFB) grating that leads to single
longitudinal mode operation of the laser. More details on the design, fabrication, and character-
ization of the laser are found in [26]. The amplitude of the electric field of the lasing mode is
shown in the inset of Fig. 1(a). The mode has subwavelength dimensions along both the x and
y directions, which results in large divergence angle of the output beam. The simulated far-field
emission pattern of the laser along the x and y directions are shown in Fig. 1(b). The far-field
profile is nearly symmetric with a full divergence angle of approximately 55
. The proposed
configuration for collimation of the QCL with the metasurface lens is shown schematically in
Fig. 1(c). The metasurface lens has a focal length of 300
μ
m and its plane is parallel to the laser
facet.
2. Design
The lens is composed of an array of a-Si posts of different diameters which are arranged on
a hexagonal lattice (inset of Fig. 1(c)). The posts are resting on a sapphire substrate. Each of
the a-Si posts can be considered as a short waveguide with circular cross section truncated on
both sides operating as a low-quality-factor Fabry-P
́
erot resonator. The circular cross section of
the posts leads to the polarization insensitivity of the lens. Because of the high refractive index
contrast between the posts and their surroundings, the posts behave as independent scatterers
with small cross coupling [23]. The phase and amplitude of the scattered light depend on the
diameter of the posts. It has been shown previously in the near-infrared region that the phase
of the transmitted light, which is the sum of the incident and forward scattered light, can be
controlled to take any value in the 0-2
π
range by properly selecting the post diameter. The local
#248830
Received 31 Aug 2015; accepted 11 Dec 2015; published 17 Dec 2015
(C)
2015
OSA
28
Dec
2015
| Vol.
23,
No.
26
| DOI:10.1364/OE.23.033310
| OPTICS
EXPRESS
33312
-90
-60
-30
0
30
60
90
0.0
0.5
1.0
Normalized intensity (a.u.)
Angle (degrees)
Along x
Along y
(b)
(c)
1
P
m
QC active region
InP
InP
SiN
x
barrier
1
P
m
QC active region
InP
InP
SiN
x
barrier
(a)
300
P
m
0
1
x
y
Intensity (a.u.)
z
y
|E
|
DFB grating
2
P
m
x
y
300
P
m
Metasurface lens
Phase (rad.)
0
-1000
300
P
m
Fig. 1. (a) Scanning electron micrograph of the laser ridge waveguide and facet of a
distributed-feedback QCL. The inset shows the simulated amplitude of the electric field
of the lasing mode. (b) Simulated far-field emission pattern of the QCL shown in (a). (c)
Schematic illustration of the QCL collimation using a metasurface lens. The inset shows
the laser intensity and phase distributions at the lens plane.
transmission coefficient of an array of posts with gradually varying diameters can be approxi-
mated by the transmission coefficient of a uniform periodic array of posts. Figure 2(a) shows
a uniform array of a-Si posts on a sapphire substrate whose diameter-dependent transmission
coefficient is used to approximate the local transmission coefficient of the metasurface lens.
The simulated intensity transmission coefficient, and the phase of the amplitude transmission
coefficient for this array as a function of the posts diameter are shown in Fig. 2(b). The post
height of 2.93
μ
m, lattice constant of 2.45
μ
m, and wavelength of 4.8
μ
m are assumed, and
the simulation is performed by using the rigorous coupled wave analysis (RCWA) technique
using a freely available software package [27]. The simulation assumes periodic boundary con-
dition for the hexagonal unit cell shown as inset in Fig. 2(a). This reduces the computational
resources required compared to simulation of scattering from a single post. The refractive index
of sapphire was assumed as 1.63 and the refractive index of a-Si was determined to be 3.37 by
extrapolating the refractive index obtained from spectroscopic ellipsometry measurements over
the 0.4
μ
m to 2
μ
m range. The norm of the reciprocal lattice vectors of the array are smaller
than the wavenumber in both sapphire and air; therefore, the array is non-diffracting for normal
incidence. As Fig. 2(b) shows, the phase imparted by the posts varies by 2
π
as the post diam-
eter changes from 685 nm to 1700 nm. By excluding the post diameters corresponding to the
reflective resonance (i.e. the transmission dip highlighted by a gray rectangle in Fig. 2(b)) from
the design, the intensity transmission is kept above 91%, and a one to one relationship between
the phase and post diameter can be obtained as shown in Fig. 2(c). Note that the metasurface
#248830
Received 31 Aug 2015; accepted 11 Dec 2015; published 17 Dec 2015
(C)
2015
OSA
28
Dec
2015
| Vol.
23,
No.
26
| DOI:10.1364/OE.23.033310
| OPTICS
EXPRESS
33313
(c)
0.00
.2
0.40
.6
0.81
.0
800
1200
1600
Phase/(2
π
)
Post diameter (nm)
0.92
0.96
1.00
Transmission
800
1200
1600
0.0
0.2
0.4
0.6
0.8
1.0
Post diameter (nm)
Transmission
Phase/(2
π
)
(a)
(b)
(d)
a-Si
Sapphire
a-Si
Side view
Top view
Fig. 2. (a) Schematic drawing of the top and side views of an array of circular posts which
is used as a basis for implementation of the metasurface lens. The inset shows a unit cell
of the array. (b) Intensity transmission coefficient and phase of the transmission coefficient
for the array shown in (a) as functions of the post diameter. (c) One to one post diameter
versus desired phase relation used in the design of the metasurface lens. The corresponding
transmission values for different phases are also presented. (d) Schematic top view of the
metasurface collimating lens.
platform does not operate in the effective index regime [28], and this enables realization of
efficient high NA lenses [29].
The subwavelength lattice constant and the large number of phase steps provided by the
continuous post diameter-phase relation, enables accurate implementation of any exotic phase
profile optimized for specific applications. To design a collimating lens for the QCL shown in
Fig. 1(a), we first found the electrical field of the lasing mode through finite element simula-
tion. As the simulated electric field of the lasing mode presented in the inset of Fig. 1(a) shows,
the lasing mode is almost circular with subwavelength full width at half maximum spot size
along both the x and y directions. Then, the electric field of the laser emission was found on
the plane of the lens (i.e. a plane 300
μ
m away from the laser) through plane wave expansion
technique [30], and by assuming that the electric field at the laser’s cleaved facet has approx-
imately the same distribution as the lasing mode’s electric field. The simulated intensity and
phase on this plane are shown as insets in Fig. 1(c). The desired phase shift imparted by the
collimating lens was set equal to the negative of the phase of the electric field of the laser at the
lens plane such that the light transmitted through the lens has a flat wavefront. To implement a
metasurface that imparts the desired spatially varying phase shift, the diameters of the posts at
each location on the metasurface were obtained from Fig. 2(c) and the corresponding desired
phase shift value at that location. A schematic drawing of the top view of the metasurface lens
is shown in Fig. 2(d). The focal length of the metasurface (which is also equal to its working
distance) was set to 300
μ
m to facilitate the alignment of the lens to the QCL while keeping
#248830
Received 31 Aug 2015; accepted 11 Dec 2015; published 17 Dec 2015
(C)
2015
OSA
28
Dec
2015
| Vol.
23,
No.
26
| DOI:10.1364/OE.23.033310
| OPTICS
EXPRESS
33314