Study of phase retardation in sub-wavelength metal gratings
R Zheng1*, P Lambkin1, P Hughes2
1
Tyndall National Institute, Ireland. University College, Lee Maltings, Prospect Row,
Cork, Ireland
2
SensL, Lee House, Riverview Business Park, Bessboro Road, Blackrock, Cork,
Ireland
*E-mail: fading_rz@hotmail.com
Abstract. The performance of 400nm-period Au-Ti gratings were investigated in this paper
with emphasis placed on the measurement of phase retardations (PRs), which were contributed
to the effective form birefringence of the grating and the surface plasmon resonance (SPR)
modes in the gratings. Furthermore, PR spectrum could be changed by in-filling the grating
area which changed both the form birefringence of the gratings and the position of SPR. The
PR was greatly enhanced from 10 to above 90 degree when nemetic liquid crystal was used to
fill the gratings.
Metallic gratings, operated in a regime where the grating period is less than, but not substantially less
than, the incident wavelength, manifest a number of interesting phenomena. These include
polarization conversion1 and resonant absorption or transmission2. The polarization conversion,
normally caused by the phase retardation of the gratings, was widely studied in those dielectric
gratings.3 It is seldom considered in the sub-wavelength metallic gratings (SWMGs) due to the high
reflection of TE polarization mode (the electric vector being parallel to the grating orientation).
Furthermore, for sub-wavelength metal gratings, these effects can be mediated by coupling to surface
plasmons (SP) and/or guided modes. Plasmons are associated with TM polarised light (the electric
vector being perpendicular to the grating orientation) and manifest resonantly enhanced electromagnetic fields close to the grating.4
Subwavelength Au-Ti grating structures, with an area of 1 mm2 were fabricated on transparent,
indium tin oxide (ITO) coated glass substrates. Four gratings were manufactured for testing. They are
labelled G1 to G4 in this paper. The gratings periods all are 400nm, and the other parameters are
shown in Table 1.
Characterizations of the bare Au-Ti gratings
The measured extinction (-lnT, T=transmission) spectrum of G1 is shown in Figure 1 to demonstrate
the different transmission spectra of the TE/TM modes. The peak in the TM mode response at 640nm
is the SPR of the individual gold wires. It agrees well with the SP resonance for a gold-glass interface,
and it does not appear in spectrum of the TE mode. The small but broad peak of the TM mode in the
wavelengths less than 600nm was the waveguide resonance, and a corresponding (waveguide)
resonance of TE mode appears as a peak in the wavelengths around 600nm. In addition, The cusp
around 600nm in TM mode Extinction spectrum is due to the “Rayleigh anomaly”, and it shifted to the
long wavelength a little in TE mode at the same wavelength.
Table 1
ITO thickness
Label
grating width (nm)
grating thickness (nm)
(nm)
G1
120
40
120
G2
80
40
120
G3
120
80
50
G4
120
100
50
The transmission spectrums of the TM mode of G1 to G4 are shown in Figure 2. It can be clearly
seen that the position and quality of the SPR are greatly affected by the parameters of the gratings, and
the deepest SPR appears in G1. The cusp-like Rayleigh anomaly of G1 and G2 looks sharper than that
of G3 and G4, which is due to the thicker ITO layer under G1 and G2.
2
TM
TE
Extinction
SPR
TM guided mode
1
TE guided mode
Rayleigh anomaly
0
550
600
650
700
750
800
850
900
w avelength (nm)
Figure 1 Extinction spectrum of the Au-Ti grating
(black line for TM mode, dashed line for TE mode)
The phase retardations of the
grating structures (   TM  TE )
were measured based on a Jones
matrix analysis and shown in Figure
3. It well indicates that the phase
retardation of the grating is greatly
affected by the different parameters
of the grating and the wavelength of
the incident light.
The experimental result shows
that the positive PR increases
towards longer wavelength. This is
due to the permittivity of the metal
increasing with wavelength, which
can be verified by the Drude model.
It also indicated that the effective
index of TM mode was larger than
that of TE mode in the region of
these long wavelengths (nTM>nTE).
2
G1
G2
Extinctionon
G3
G4
1
0
550
600
650
700
750
800
850
wavelength (nm)
Figure 2 Extinction spectrum (TM mode only) of the
Gratings (G1-G4)
900
In addition, at the long
wavelengths, far away from the
SPR, the PR of the grating is
proportional to the fill factor and
the thickness of the grating. That is
consistent with the classic optics
theory.
Finally, for wavelengths near the
SPR, the depth of the PR anomaly
is proportional to the quality of the
SPR. In other words, the resonance
in the PR spectrum of G1 is deepest
due to the best quality of SPR in G1
(see Figure 2). Furthermore, the
value of PR for some wavelengths
in the resonance became negative
80
70
60
50
PR(degree)
40
30
20
10
0
550
-10
600
650
700
750
800
850
900
-20
wavelength (nm)
G1
G2
G3
G4
Figure 3 The phase retardations of the gratings (G1-G4)
(   0 ), which indicated that
the effective index of TE mode
was larger than that of TM mode
in the region of these wavelengths
(nTM<nTE).
In conclusion, the phase
retardations of the gratings are
due to two contributions, the form
birefringence of the binary
metallic gratings and the resonant
surface modes. However, both of
these two contributions are not
strong enough to generate great
phase retardation in ultra-thin
gratings. To solve this problem, it
was considered that to fill some
nonlinear materials into the
gratings.
Characterizations of the Au-Ti gratings filled with nemetic liquid crystals
It is well known that the electromagnetic field near to metal surfaces can be substantially increased by
SPR. Consequently, nonlinear optical effects, associated with an SPR, can be observed when a
periodically nano-structured metal film is embedded in a nonlinear optical material. 5 The nonlinear
optical material we chose in this work is nematic liquid crystals (NLCs). Therefore the strong electric
fields might be used to resonantly orientate the NLC deposited on the grating and, thereby, enhance
the form birefringence of the whole sample.
In this work we used a NLC named E63 which was purchased from Merck. E63 is a kind of
nematic liquid crystal mixture with large birefringence (ne=1.7444, no=1.5172@589nm, clearing
point=82 0C). A minimal quantity of NLC was filled into the grating area. Some of them was
remaining above the gratings and the thickness of the remaining NLC layer was measured to be about
120nm. For simplification, only
the properties of G1 filled with
E63 was discussed there.
2
Extinction
TM
TE
1
0
550
600
650
700
750
800
850
900
wavelength (nm)
Figure 4 The extinction of the transmission spectra of G1
when filled with NLC (back for TM mode, grey for TE mode)
The extinction spectra of the
grating filled with NLC were
measured and are shown in
Figure 4. The SPR, present only
in the TM spectrum, has been
red shifted since the gold-air
interface is now a gold-NLC
interface. Additional structure
at short wavelengths is now
also
present
in
both
polarisations. This is suspected
to be attributed to enhanced
coupling to substrate and
waveguide modes mediated by
the grating.
PR (degree)
The phase retardation of
G1
filled with NLC is also
50
shown in Figure 5 and shows
a
substantially
different
Bare grating
behavior.
Large
phase
0
retardation
(more
than
90
550
600
650
700
750
800
850
900
degree)
was
observed
in
the
NLC film
-50
ultra-thin
(40nm)
metal
Filled with NLC
gratings filled with E63,
which was much larger than
-100
the phase retardation in the
bare metal grating plus the
retardation in the bare LC
-150
film. It is noticed that the PR
wavelength (nm)
of the sample was totally
negative after filled with
Figure 5 The phase retardation of G1 when filled with NLC,
NLC. It indicates that the
comparing with that of the NLC film and the bare grating
effective index of TE mode
was larger than that of TM
mode for all of these wavelengths (nTM<nTE). It could only happen when the rod-like LC molecules
were well aligned and parallel to the orientation of the grating. It is also named “strong surface
anchoring” in the sub-wavelength grating structure.6 This result is contrast to the original hypothesis
that the NLC might be directed by the E-field generated by the SPR. The inability of the E-field of the
SPs to reorientate NLCs is suspected to be due to the relatively large gap between the grating wires in
G1. In addition, although a small resonance did appear at the same wavelength as the SPR position,
the influence of SPR is merely perturbative on the much stronger background in the PR spectrum.
Discussion and Further work
In conclusion, a series of 400nm-period Au-Ti gratings with different parameters were fabricated, the
performances of the gratings are investigated in detail, including the SPRs in the transmission spectra
of the gratings and the phase retardation in these gratings. Two factors are found to be attributed to the
phase retardation of the gratings, namely, the form birefringence of the gratings and the position of the
SP modes; the latter only affects the wavelengths near the SPR. The polarization conversion of the
sub-wavelength gratings due to form birefringence increases in proportion to the grating thickness.
However, the influence of the SPR depends on the quality factor of the resonance.
Since the phase retardation in the gratings is not enough to generate great phase, to overcome this
shortage, it was considered that to fill NLC into the gratings.
The origin of the large effective birefringence observed in the NLC filled grating is obtained. The
morphology of the grating is similar to that produced by the rubbing or photo-induced processes on
polymer substrates normally used to align liquid crystal molecules.6 However, even with perfect
alignment induced by the grating structure, the film thickness is not sufficient to account for the
magnitude of the measured retardation. The only possibility is that the birefringence of the NLC was
enhanced by the surface modes of the grating structures. Future work will consider simulating the
performance of the NLC in an effort to establish the origin of this extraordinary effect.
References
[1] S.J.Elston, GP Bryan-Brown and JR Sambles Phys.Rev.B 44 6393 (1991)
[2] J.A.Porto, F.J.Garcia-Vidal and J.B.Pendry Phys. Rev. Lett 83 2845 (1999)
[3] N.Bokor, R.Shechter, N.Davidson, Asher A.Friesem and E.Hasman Applied Optics 40 2076
(2001)
[4]
[5]
[6]
H.Raether Surface Plasmon on Smooth and Rough Surface and on Gratings (Springer-Verlag,
Berlin, 1988)
I.I.Smolyaninov,A.V.Zayats,A.Stanishevsky and C.C.Davis Phys. Rev. B 66 205414 (2002)
P.G. de Gennes The physics of liquid crystals (Oxford: Clarendon, 1974)