Abstract—We design, manufacture and characterize large numerical aperture lenses for the THz frequency range. Binary metallic lenses focus off-axis a selected narrow band part from a wide band incident signal. Double-side dielectric Fresnel lenses exhibit low absorption and almost no aberration.

I. INTRODUCTION MAGING applications in the terahertz (THz) frequency range are subject to a huge development activity as the first

THz matrix sensors (hot electron or room temperature bolometers, plasma-effect nano-transistors) are becoming available, at least in laboratories. Among these applications, the security domain is of the highest interest. It requires imaging people or items located up to a few meters from the THz camera. If one desires to avoid mechanically scanned systems, or if a high spatial diffraction-limited resolution is required, it is necessary to use large numerical aperture optics due the proximity and the dimension of the scene. The requested size of classical refractive lenses leads to large thicknesses (several cm) that induce large absorption especially at high THz frequencies as most of the dielectric materials exhibit a residual tail of absorption due to a phonon peak or a phonon-like boson peak at higher frequencies. On the other hand, reflective optics using mirrors, like telescopes, exhibits large geometrical aberrations, in particular for non-paraxial rays, which makes impossible the optics to work off-axis together with a good spatial resolution. Diffractive optics may overcome these problems of size and aberrations. In addition, such elements are easy to manufacture for sub-millimeter wavelengths.

Fig. 1: Left: The diffractive binary metallic lens; Right: The double-side Fresnel lens. In this paper, we present two different diffractive lenses (Fig. 1). The first one is a binary metallic lens, which focuses off axis the signal at ~0.5 THz when illuminated by a broadband beam, like the thermal ones radiated by the scene in passive

imagery. The second is a double-side Fresnel lens made with polyethylene (HDPE), which exhibits low absorption and low aberrations.

II. EXPERIMENTAL PROCEDURE Both devices are characterized using a THz time-domain

setup with LTG-GaAs photoconductive antennae. The fibered receiving antenna is attached to a rotating arm (goniometer setup) and the device is located at the rotation center, allowing us to record signals deflected in the plane of incidence. The beam delivered by the emitting antenna exhibits a spectral width ranging from 0.1 to 2.5 THz. Its shape, determined from a knife-edge measurement, is practically Gaussian at any frequency of the radiated spectrum. At the sample location, the beam waist is typically 7.4 mm at 0.5 THz (5.8 mm at 1 THz).

0

2

4

6

8

0 10 20 30 40 50 60 70

THz

sign

al a

mpl

itude

Angle (degree)

0.41 THz

0.44 THz

0.46 THz

0.60 THz

0.50 THz

0.80 THz

1.00 THz

0.90 THz

0.70 THz

Fig. 2: Left: THz signal deflected by the binary structure versus the deflection angle at different frequencies; Right: Contour map of the THz field in the vicinity of the focus point, calculated (a) and deduced from measurement (b).

III. BINARY METALLIC DIFFRACTIVE LENS The lens is designed to image an object located 36 cm in

front of the lens onto the detector at 5 cm behind the lens and 5 cm below the optical axis (45° off axis detection). The design of the lens corresponds to 2 Fresnel binary lenses, one for making parallel the incident rays and the second one to focus them off-axis, which are combined together to form a single component. The lens is calculated to work for the 0.5 THz frequency in a non-paraxial regime. Therefore this component acts as both a spatial and spectral filter, hence it is especially suitable for separating THz signal from broad-band thermal load in passive detection systems. The lens is manufactured in a stainless steel slab by laser cutting of curved stripes whose varying periodicity has a 0.81 mm average value. Fig. 2-left shows the THz signal recorded at the

Maciej Sypek1,2, Micha� Makowski1, Izabela Ducin1, Agnieszka Siemion1, Andrzej Siemion1, Jaros�aw Suszek1, Frédéric Garet3, Emilie Hérault3, and Jean-Louis Coutaz3

1 Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00 662 Warsaw, Poland 2 Orteh Sp. z o.o., Ilskiego 25, 04 479 Warsaw, Poland

3 IMEP-LAHC, UMR CNRS 5130, University of Savoie, 73 376 Le Bourget du Lac Cedex, France

Large aperture diffractive lenses for the THz domain

I

30 35 40 45 50 55 60 65 70 75 80 85 9030

35

40

45

50

55

60

65

70

75

80 a)

0.8-10.6-0.80.4-0.60.2-0.40-0.2

30 35 40 45 50 55 60 65 70 75 80 85 9030

35

40

45

50

55

60

65

70

75

80 b)

0.8-10.6-0.80.4-0.60.2-0.40-0.2

80 mm

70 mm

60 mm

������������������ �����������

Abstract—We design, manufacture and characterize large numerical aperture lenses for the THz frequency range. Binary metallic lenses focus off-axis a selected narrow band part from a wide band incident signal. Double-side dielectric Fresnel lenses exhibit low absorption and almost no aberration.

I. INTRODUCTION MAGING applications in the terahertz (THz) frequency range are subject to a huge development activity as the first

THz matrix sensors (hot electron or room temperature bolometers, plasma-effect nano-transistors) are becoming available, at least in laboratories. Among these applications, the security domain is of the highest interest. It requires imaging people or items located up to a few meters from the THz camera. If one desires to avoid mechanically scanned systems, or if a high spatial diffraction-limited resolution is required, it is necessary to use large numerical aperture optics due the proximity and the dimension of the scene. The requested size of classical refractive lenses leads to large thicknesses (several cm) that induce large absorption especially at high THz frequencies as most of the dielectric materials exhibit a residual tail of absorption due to a phonon peak or a phonon-like boson peak at higher frequencies. On the other hand, reflective optics using mirrors, like telescopes, exhibits large geometrical aberrations, in particular for non-paraxial rays, which makes impossible the optics to work off-axis together with a good spatial resolution. Diffractive optics may overcome these problems of size and aberrations. In addition, such elements are easy to manufacture for sub-millimeter wavelengths.

Fig. 1: Left: The diffractive binary metallic lens; Right: The double-side Fresnel lens. In this paper, we present two different diffractive lenses (Fig. 1). The first one is a binary metallic lens, which focuses off axis the signal at ~0.5 THz when illuminated by a broadband beam, like the thermal ones radiated by the scene in passive

imagery. The second is a double-side Fresnel lens made with polyethylene (HDPE), which exhibits low absorption and low aberrations.

II. EXPERIMENTAL PROCEDURE Both devices are characterized using a THz time-domain

setup with LTG-GaAs photoconductive antennae. The fibered receiving antenna is attached to a rotating arm (goniometer setup) and the device is located at the rotation center, allowing us to record signals deflected in the plane of incidence. The beam delivered by the emitting antenna exhibits a spectral width ranging from 0.1 to 2.5 THz. Its shape, determined from a knife-edge measurement, is practically Gaussian at any frequency of the radiated spectrum. At the sample location, the beam waist is typically 7.4 mm at 0.5 THz (5.8 mm at 1 THz).

0

2

4

6

8

0 10 20 30 40 50 60 70

THz

sign

al a

mpl

itude

Angle (degree)

0.41 THz

0.44 THz

0.46 THz

0.60 THz

0.50 THz

0.80 THz

1.00 THz

0.90 THz

0.70 THz

Fig. 2: Left: THz signal deflected by the binary structure versus the deflection angle at different frequencies; Right: Contour map of the THz field in the vicinity of the focus point, calculated (a) and deduced from measurement (b).

III. BINARY METALLIC DIFFRACTIVE LENS The lens is designed to image an object located 36 cm in

front of the lens onto the detector at 5 cm behind the lens and 5 cm below the optical axis (45° off axis detection). The design of the lens corresponds to 2 Fresnel binary lenses, one for making parallel the incident rays and the second one to focus them off-axis, which are combined together to form a single component. The lens is calculated to work for the 0.5 THz frequency in a non-paraxial regime. Therefore this component acts as both a spatial and spectral filter, hence it is especially suitable for separating THz signal from broad-band thermal load in passive detection systems. The lens is manufactured in a stainless steel slab by laser cutting of curved stripes whose varying periodicity has a 0.81 mm average value. Fig. 2-left shows the THz signal recorded at the

Maciej Sypek1,2, Micha� Makowski1, Izabela Ducin1, Agnieszka Siemion1, Andrzej Siemion1, Jaros�aw Suszek1, Frédéric Garet3, Emilie Hérault3, and Jean-Louis Coutaz3

1 Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00 662 Warsaw, Poland 2 Orteh Sp. z o.o., Ilskiego 25, 04 479 Warsaw, Poland

3 IMEP-LAHC, UMR CNRS 5130, University of Savoie, 73 376 Le Bourget du Lac Cedex, France

Large aperture diffractive lenses for the THz domain

I

30 35 40 45 50 55 60 65 70 75 80 85 9030

35

40

45

50

55

60

65

70

75

80 a)

0.8-10.6-0.80.4-0.60.2-0.40-0.2

30 35 40 45 50 55 60 65 70 75 80 85 9030

35

40

45

50

55

60

65

70

75

80 b)

0.8-10.6-0.80.4-0.60.2-0.40-0.2

80 mm

70 mm

60 mm

focus versus the angle relative to the normal direction of the lens. A strong signal is seen for f=0.5 THz at 45°. For other frequencies far from 0.5 THz, the signal is not concentrated in a given direction. The contour map of the field of the THz beam at 0.5 THz is drawn on Fig. 2-right. The upper curve is calculated, while the one below is deduced from the waist measured at different distances from the lens. The focusing and filtering properties of the lens are clearly observed and they are in good agreement with the modeling. In the sub-wavelength regime, the device deflects the beam that is not diffracted (zero order of diffraction) and thus should go straight through the device [2]. The angle of deflection varies roughly linearly with the frequency. This dispersive property is related to the variation of the periodicity along the device, which induces a gradient of its effective refractive index. Thus the device behaves as a 2D prism for THz frequencies. For a similar device with a constant period, no deflection is observed.

-5

0

5

10

15

20

25

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Varying periodConstant period

Dev

iatio

n an

gle

(deg

ree)

Frequency (THz) Fig. 3: Angle of deflection of the non diffracted beam versus frequency for 2 lenses with respectively a varying periodicity and a constant periodicity.

IV. DOUBLE-SIDE FRESNEL-TYPE DIELECTRIC LENS This lens is especially designed for reducing absorption

losses and chromatic aberrations for frequencies above 0.5 THz, while keeping a large numerical aperture (diameter 100 mm, back focal length 80 mm). This forces us to find a compromise, as achromaticity requires a thick Fresnel lens while absorption is weaker for thin lenses. The lens was machined in a HDPE substrate. The sharp step between the regions of the lens is 1.8 mm high on each side. It corresponds to a total phase jump of ~35π at 1 THz, which will lead to a weak spectral dependence of the focusing properties. Each region of the lens exhibits a spherical shape with the same radius of curvature, which makes its manufacturing easy. The almost parallel and narrow beam delivered by our TDS setup permits to characterize the ray deviation from any location of the lens, but not the focal spot size, which requires illuminating the whole lens area (in this case, the calculated focal spot size is of the order of the wavelength). Fig. 4 shows the THz amplitude versus the angle of the detector and the frequency when the beam impinges the lens at 20 mm from the axis. We can see that the angle does not depend on frequency and thus the lens is achromatic. The angular shape versus frequency obeys nicely the Gaussian beam theory. Ripples around the main beam are due to diffraction by the emitting antenna holder.

0

10

20

30

-10

0.2 0.4 0.6 0.8 Frequency (THz)

Angle (degree)

0

10

20

30

-10

0

10

20

30

-10

0.2 0.4 0.6 0.8 Frequency (THz)0.2 0.4 0.6 0.80.2 0.4 0.6 0.8 Frequency (THz)

Angle (degree)

Fig. 4: Experimental amplitude of the deflected beam versus frequency and versus the angle of detection, when the incoming beam impinges the lens at 20 mm from the optical axis.

The ray tracing picture at 1 THz deduced from measurements is presented in Fig. 5 (left). Similar results, independent on frequency, are obtained in the range 0.2-1.5 THz. The quite large geometrical aberrations originate from the not-optimized (spherical) shape of the Fresnel zones. So we designed another Fresnel lens, still with spherical zones (multi-spherical), but whose radii of curvature are different. Thus the geometrical aberrations are strongly reduced, as seen in Fig. 5 (right).

Fig. 5: Ray tracing picture of the Fresnel lens deduced from the measurements shown in Fig. 5. Left: Zones with the same radius of curvature. Right: Zones with different radii of curvature. Finally, we compare the transmission of the Fresnel lens with the one of a plano-convex Teflon lens (Thorlabs LAT 100). Thanks to the smaller thickness of the Fresnel lens, and because of the absorption of the materials (0.2-0.5 cm-1), the Fresnel lens transmits 3 times more THz energy than the classical lens (Fig. 6).

Frequency (THz)

THz

ener

gy s

pect

ral

dens

ity (A

.U.)

Frequency (THz)

THz

ener

gy s

pect

ral

dens

ity (A

.U.)

Fig. 6: Transmission spectra of the Fresnel lens (upper curve) and of a classical lens (lower curve).

REFERENCES [1] A. Siemion et al., “Off-Axis Metallic Diffractive Lens for Terahertz

Beams,” Optics Lett. 36, 1960 (2011). [2] E. Hérault et al., “Prism-Like Behavior at Terahertz Frequencies of a 2D

Metallic Grid with a Varying Periodicity,” J. Infrared Milli. Terahz. Waves 32, 403-406 (2011).