Ultra broadband phase measurements on nanostructured metasurfaces
Ekaterina Pshenay-Severin, Matthias Falkner, Christian Helgert, and Thomas Pertsch
Here we give more detailed description of our technique. The developed interferometric setup provides
simultaneous measurements in transmission and reflection. The interferometric measurements are
performed with a supercontinuum light source SuperK Versa from NKT Photonics (operating spectral
range is from   0.4 µm to   1.7 µm). The broadband generation of this source is based on the
supercontinuum generation in an optical fiber. The principal scheme of the interferometer is presented in
Fig 1. The linear polarizer P1 (operating spectral range is from   0.65 µm to   2 µm) serves to
control the polarization state of the input light. In the first birefringent beam displacer B1 (operating
spectral range from   0.35 µm to   2.3 µm) linear polarized light is split into two orthogonally
polarized beams forming the two arms of the interferometer. The intensity distribution between the
sample and reference arm is controlled by the rotation of the linear polarizer P1. The second beam
displacer B2, which serves to recombine the two beams, is followed by the linear polarizer P2, providing
interference of the sample and reference beams. The recombined beam is coupled into a photonic crystal
fiber (PCF) which is single-mode for   0.6 µm . The analysis of the interference signal is performed
with an optical spectral analyzer (OSA) Yokogawa AQ6370B featuring a grating spectrometer. To avoid
spatial overlapping of the higher diffraction orders of smaller wavelengths with the second diffraction
order of larger wavelengths, an optical low pass filter F is used during the measurements in the VIS
spectral range.
Measurements of the phase in reflection are realized with the beam splitter BS (operating spectral range
is from   0.42 µm to   1.7 µm). The sample and reference beams reflected from the sample are
recombined in the first calcite beam displacer B1 and are guided to the part of the setup for the reflection
measurements with a polarizing beam splitter BS.
1
The mirror symmetrical arrangement of the beam displacers causes an optical path difference of about
5.2 mm between the interferometer arms. To this phase difference corresponds an interference pattern
(0.2 nm around   1 µm) which is close to the spectral resolution of the OSA. Therefore, the optical
length difference between the arms was decreased to a value of 1 mm to enable a high sampling rate of
the interference signal. This was realized by placing compensating plates D1 and D2 made of BK7, each
6 mm thick, in the sample arm of the interferometer. The period of the corresponding interference
pattern was about 1 nm at   1 µm.
As the measurements of signals are done in the wavelength domain, the measured signal has to be
transformed to the frequency domain (   2 c /  ) and regularly sampled. The influence of the data
interpolation, required to transform the spectra, on the accuracy of the phase definition has been
investigated. It was shown that, if the sampling rate of a signal is close to the Nyquist limit, linear
interpolation of the signal causes a noisy background in the retrieved phase. In the experiment, in the
VIS spectral range the period of the interference pattern is about 0.5 nm at   0.7 µm. To provide an
appropriate signal-to-noise-ratio, the signal acquisition is done with a resolution of 0.1 nm. To increase
the sampling rate, a so-called zero-fitting procedure is applied to the signal. This technique is based on
the Fourier transformation of the spectra from the wavelength space to an inverse space  . Then the
window size N is increased by adding additional points with zero amplitudes. In the experiments the
window size was increased by a factor 4 . The backward Fourier transformation gives the initial
spectrum with an increased sampling rate. Thereafter, the spectrum is linearly interpolated and the
Fourier transformation can be performed.
2