Superimposed surface-relief diffraction grating holographic lenses on azo-polymer films

Abstract

Various superimposed chirped relief gratings, acting as diffracting holographic lenses, were photo-inscribed on azo-polymer films upon exposure to the interference pattern of a plane and a curved laser light wavefronts. Depending on the configuration used, this resulted in incident light being focused independently of polarization along the 0th or 1st diffracted order of the grating. The focal point and focalization angle of the resulting holographic lenses were easily tuned during the fabrication process. Furthermore, a dual-focus chirped holographic lens grating was fabricated and shown to exhibit a far-field interference pattern.

Full text

Superimposed surface-relief diffraction grating
holographic lenses on azo-polymer films
Ribal Georges Sabat*
Department of Physics, Royal Military College of Canada, PO Box 17000 STN Forces, Kingston, Ontario K7K7B4,
Canada
*sabat@rmc.ca
Abstract: Various superimposed chirped relief gratings, acting as
diffracting holographic lenses, were photo-inscribed on azo-polymer films
upon exposure to the interference pattern of a plane and a curved laser light
wavefronts. Depending on the configuration used, this resulted in incident
light being focused independently of polarization along the 0th or 1st
diffracted order of the grating. The focal point and focalization angle of the
resulting holographic lenses were easily tuned during the fabrication
process. Furthermore, a dual-focus chirped holographic lens grating was
fabricated and shown to exhibit a far-field interference pattern.
©2013 Optical Society of America
OCIS codes: (050.1950) Diffraction gratings; (090.2890) Holographic optical elements;
(050.1965) Diffractive lenses.
References and links
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(2004).
1. Introduction
Both reversible volume phase diffraction gratings [1] and high-efficiency surface-relief
gratings [2] can be inscribed onto cast azopolymer films by exposure to an interfering laser
pattern at an absorbing wavelength. The primary mechanism invoked in the creation of a
phase grating throughout the volume of the film is the induction of local birefringence. This
process does not involve a change in the surface profile of the film but rather a change in the
local refractive index. As for the relief gratings, a high degree of localized mass transport of
the polymer chains is responsible for the creation of a surface profile to depths nearing that of
the original film thickness. This phenomenon involves pressure gradients as a driving force,
present due to different photochemical behaviors of the azo chromophores at different regions
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Received 10 Dec 2012; revised 6 Mar 2013; accepted 6 Mar 2013; published 2 Apr 2013
(C) 2013 OSA
8 April 2013 | Vol. 21, No. 7 | DOI:10.1364/OE.21.008711 | OPTICS EXPRESS 8711

of the interference pattern. Several models have been proposed to explain the creation of
surface-relief gratings [3].
Since birefringence volume gratings can be recorded by a laser on azo films in a matter of
seconds, they become very sensitive to operating light conditions and can be erased by
exposure to randomly polarized light since the molecular alignment can be easily perturbed.
On the other hand, relief gratings take several minutes to form, and once the final shape has
been achieved, these gratings are very stable. Nonetheless, both volume phase and surface
relief gratings can be erased by heating the film above its glass transition temperature
(~130°C). A schematic of the experimental set-up used for creating these gratings is
illustrated in Fig. 1.
Fig. 1. Experimental set-up for inscribing a surface-relief grating.
Half of a collimated laser beam is reflected by a mirror oriented at 90° with respect to the
azo film, thus resulting in a sinusoidal interference pattern on the film’s surface. The depth
and spacing of the gratings can be controlled with the exposure time and laser incidence angle
respectively. This experimental set-up allows the simultaneous inscription of both
birefringence volume phase and surface-relief grating structures, but the polarized diffraction
from the birefringence gratings is largely overshadowed by the higher efficiency diffraction
from the surface-relief gratings. In addition, unlike volume gratings, the polarization of the
diffracted light is unaffected by the surface grating.
In the last decade, polymers containing azobenzene or its derivatives have been
intensively investigated for their photoresponsive properties and potential applications in
diffractive optical elements, information storage, optical switching, nonlinear optics, sensors,
and actuators. For instance, surface-relief gratings can be used to couple light either in the azo
film itself or in another adjacent medium, yielding narrowband resonant waveguide filters [4].
More recently, single-layered graphene grafted with azo polymer brushes has been used to
significantly enhance the diffraction efficiency of the photoinduced surface-relief gratings on
azo molecular glass films [5]. The azo compound has been proven to allow the inscription of
multiple superimposed relief gratings and the interactions between these gratings has been
studied [6].
Furthermore, diffraction gratings can be used to project other optical element holograms
by recording and then later retrieving the phase and amplitude of light [7, 8]. Sub-wavelength
dielectric focusing grating structures with non-periodic patterning have been fabricated from
different nano-engineered materials by chemical vapor deposition and dry etching, and their
shape provided the ability to control the focused light’s profile [9, 10]. The main advantage of
using azo-polymer for such nanostructures is that the reading and inscription of a hologram
each consist of a single fabrication step with no post-exposure adjusting or chemical
processing. Holographic volume diffracting lenses were previously recorded in azo polymer
[11] and azo liquid crystal films [12] using a different experimental set-up than the one
presented here, however, the major set-back of these lenses is that they were polarization
dependent since they rely on birefringence phase gratings. The available literature on the
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8 April 2013 | Vol. 21, No. 7 | DOI:10.1364/OE.21.008711 | OPTICS EXPRESS 8712

inscription and study of chirped relief gratings in azo polymers is very limited and only
includes single grating structures. There are no readily available published studies on the
optical interactions between superimposed linear and chirped surface-relief grating structures.
2. Experiment
The azo-polymer compound was diluted in dichloromethane with a mix ratio of 3%
weight/weight, and thoroughly mixed. Several test samples were prepared by spin-casting this
solution on a glass slide. The experimental set-up in Fig. 1 was modified as illustrated in Fig.
2.
Fig. 2. Modified experimental set-up for chirped grating inscription.
Light from a Verdi-V5 diode-pumped laser with a wavelength of 532 nm and output
power of 2 W was passed through a spatial filter and collimated to ~4.8 cm in diameter,
yielding a plane wave writing beam with an irradiance of ~27.6 mW.cm−2. A λ¤4 plate was
subsequently used to create circularly polarized light, with the size of the beam being
regulated to a diameter of ~1 cm using a variable iris. A small converging lens was placed
along the half-circle of the laser beam that was directly incident on the azo-polymer film,
hence, creating a curved wavefront which interfered with the plane wavefront from the other
laser half-circle incident on the mirror. The laser was incident at an angle which would create
a linear surface-relief diffraction grating with a spacing of 800 nm, however, any other
spacing could have equally been chosen. The laser exposure time was set to 5 minutes per
grating.
This arrangement produced a chirped holographic lens grating with an off-angle focal
point that depended only upon the location of the focal point of the physical mini-lens during
the inscription process. This mini-lens was positioned on a linear track which enabled it to be
placed at various distances away from the sample. In order to make a dual-focus chirped
holographic lens grating, an initial exposure lens hologram was inscribed for 5 minutes, then,
the mini-lens was moved a fixed distance forward or backward, followed by a second laser
inscription of a superimposed lens grating.
Subsequently, a He-Ne laser, having a power of 2 mW, was used to measure the focusing
ability of the gratings, as depicted in Fig. 3. A high dynamic range CCD camera was
positioned on a linear track and pictures of the laser beam were taken as a function of distance
travelled along the diffracted orders.
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8 April 2013 | Vol. 21, No. 7 | DOI:10.1364/OE.21.008711 | OPTICS EXPRESS 8713

Fig. 3. Experimental set-up for measuring the lens grating focusing.
3. Theory
Upon exposure to the inscribing laser beam, the interference term of the resulting irradiance
on the azo film’s surface can be written as:
2
cos ,
2
I
δ

∝

(1)
where
δ
is the phase difference between the direct and reflected beams, which can be
expressed as:
12 ,kr kr
δ
φ
=⋅−⋅+



 (2)
where 1
k

and 2
k

are respectively the direct and reflected wave vectors, r

is the position
vector and
φ
is a constant phase difference between the two beams.
Fig. 4. Laser beam geometry.
As illustrated in Fig. 4, for a linear surface-relief grating to form at point A, both direct
and reflected wave fronts must be linear. Therefore, we have that:
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()
()
1
0
2
0
ˆˆ
2ˆˆ
sin cos
2ˆˆ
sin cos ,
rxxyy
kxy
kxy
πθθ
λ
πθθ
λ
=+
=−
=− −



(3)
where 0
λ
is the free-space writing laser wavelength. Ignoring the constant phase,
δ
becomes:
0
4sin
,
L
x
πθ
δλ
= (4)
The interference term of the irradiance is now given by:
2
0
2
cos sin ,Ix
πθ
λ

∝

(5)
It can be seen that when Eq. (5) is plotted as a function of x, the period gives the grating
spacing Λ, such as:
0,
2sin
λ
θ
Λ= (6)
Now, assume a cylindrical lens is placed along the direct half laser beam with its axis along
the vertical with respect to the optical bench, as in Fig. 2. The laser beam focal point will be
at a distance f from the sample. The direct laser wavefront now becomes curved and the light
is delayed before reaching the mirror by a distance Δ, as illustrated at point B in Fig. 4. The
further away point B is located from either sides of point A on the sample’s surface, the more
the light is delayed. In order to calculate this delay, we can obtain from Fig. 4 that:
22
,
f
ft+Δ= + (7)
Using the binomial approximation, we obtain:
2
,
2
t
f
Δ≈ (8)
But, since costx
θ
=, we now have:
22
cos ,
2
x
f
θ
Δ≈ (9)
This phase delay must be added to
L
δ
in order to obtain:
22
0
2cos
,
2
cl
x
f
πθ
δδ λ

≈+ 

(10)
Therefore, in the case of a surface-relief holographic grating of a cylindrical lens, the
interference term of the irradiance becomes:
22
2
0
cos
cos 2 sin ,
2
x
Ix
f
πθ
θ
λ


∝+




(11)
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This indicates that the grating spacing changes symmetrically with respect to Point A in Fig.
4. It is those pitch variations that lead to light focalization from the holographic lens grating
upon exposure at a probing He-Ne beam. One can see that as f→∞, Eq. (11) becomes Eq.
(5). A similar development could be done for a spherical lens, but the analysis becomes more
complex since the irradiance now varies along both the ˆ
x
and ˆ
z-directions.
Fig. 5. The theoretical relative irradiance as a function distance along the sample’s surface.
Figure 5 illustrates numerical examples of how the grating spacing is affected by Eqs. (5)
and (11). It can be seen that when 0x=, both equations give the same grating spacing,
however, when 0.01 mx= , the spacing given by Eq. (5) stays the same, but that given by Eq.
(11) increases.
For superimposed linear gratings at normal incidence, light will be diffracted with wave
vectors satisfying the grating equation
12
12
22
,
light
mm
k
ππ
=± ±
ΛΛ
(12)
Where 1
mand 2
mare integers representing the diffraction orders, and 1
Λ and 2
Λare the
grating spacings. This equation is also valid for light diffraction from superimposed chirped
gratings, as the surface undulations from the first gratings are not erased, but rather added to
the second grating inscribed. Figures 6(a)-6(c) gives a graphical representation of the
excepted focalization of various combinations of superimposed chirped holographic lens
gratings.
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Fig. 6. Light focalization representation in transmission from superimposed (a) chirped lens
gratings with the same linear spacing and different focal points (b) chirped lens gratings with
different linear spacing and same focal points (c) chirped lens grating and a linear grating with
the same spacing.
4. Results and discussion
First, the circularly polarized He-Ne laser light, depicted in Fig. 3, was incident on a chirped
diffraction grating acting as a single cylindrical holographic lens. The CCD camera was
approximately placed in the focal point of the holographic lens and the computerized linear
track was zeroed. Then, various pictures were taken along the 1st diffracted order at 6.7 mm
intervals while scanning from −46.7 to 46.7 mm, as illustrated in Fig. 7. The focal point of
this chirped grating was located approximately 10 cm away from the sample’s surface.
Fig. 7. Pictures taken as a function of distance travelled along the 1st backward diffracted
order of a chirped grating of a cylindrical holographic lens.
Maximum focalization occurs at 13.3 mm, as seen in Fig. 7. Since the resulting
undulations on the azo surface are the recording light’s intensity and phase, a probing laser
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would reproduce the same light profile at the same geometry, hence, resulting in focalization
occurring only along a single diffracted order. A similar focalization was also apparent in
reflection of the same diffracted order. The polarization independence of the incident light
off-angle focalization was verified with a polarizer, hence, confirming that the focalization is
occurring due to the chirped surface-relief grating rather than any volume birefringence
grating produced. The grating’s varying pitch yields slightly different diffraction angles,
which results in light focalization at their intersection in the 1st backward diffracted order.
The focus resolution of this chirped lens grating is dictated only by that of the physical mini-
lens used during the inscription process illustrated in Fig. 2.
Then, a spherical mini-lens was substituted in the experimental set-up in Fig. 2, and a
chirped holographic grating acting as a spherical lens was inscribed. Various pictures were
taken along the 1st backward diffracted order at 7 mm intervals while scanning from −4.7 to 4
cm, as illustrated in Fig. 8. The focal point of this chirped grating was also located
approximately 10 cm away from the sample’s surface.
Fig. 8. Pictures taken as a function of distance travelled along the 1st backward diffracted
order of a chirped holographic lens grating.
A dual-focus chirped holographic lens grating was inscribed by superimposing two
chirped gratings at the same laser inscription angle, but with different positions of the focal
point of the physical mini-lens. Similar pictures were taken as a function of the distance
travelled along the 1st backward diffracted order. As seen in Fig. 9, the two focal points,
which are located approximately 8 cm apart, can be identified around −48 mm and 38.4 mm.
The minor angle eccentricity in the two focal points is due to the misalignment of the linear
track holding the physical mini-lens during the inscription process. The separation between
the focal points of the resulting chirped lens grating is equal to the movement of the physical
mini-lens during the first and second exposures.
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Fig. 9. Pictures taken as a function of distance travelled along the 1st backward diffracted
order of a dual-focus chirped holographic lens grating.
The images in Figs. 8 and 9 were digitally processed, and the light intensity profiles were
plotted as a function of the horizontal pixel position and distance travelled, as seen in Figs.
10(a)-10(b). The focal points are indicated on the figures. The CCD camera had a resolution
of 10 microns per pixel, therefore, the focal points outlined in Figs. 10(a)-10(b) are
approximately 200 microns wide.
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Fig. 10. Light intensity profile as a function of horizontal pixel position and distance travelled
for (a) single chirped holographic lens grating (b) dual-focus chirped holographic lens grating.
In Fig. 11, a first chirped holographic lens grating with a spacing of 800 nm was
inscribed, followed by a second chirped lens grating with a spacing of 700 nm. Both gratings
were written with the physical mini-lens, seen in the experimental set-up in Fig. 2, left at the
same location during both exposures. The focal points of the resulting dual-focus lens grating
are approximately 4.5 cm apart.
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Fig. 11. Pictures taken as a function of distance travelled along the 1st backward diffracted
orders of a dual-focus holographic lens grating with two different spacings.
The He-Ne laser source has been used so far to measure the off-angle focusing of these
holographic lenses because of the wavelength dependence of the diffracted light. This occurs
since
2sin ,
light m
k
πθ
λ
= (13)
where
λ
is the light wavelength in the medium and m
θ
is the diffraction angle. For a value of
light
k satisfying Eq. (12), as
λ
increases, m
θ
must decrease. Therefore, for a white light source,
the focalization of each wavelength will occur at different angles.
For the next part of this experiment, the He-Ne laser, collimating lens and quarter-wave
plate were removed from the experimental set-up illustrated in Fig. 3, and an un-polarized
white light source was used to illuminate the test sample through the variable iris. A chirped
holographic lens grating was inscribed on an azo film followed by the inscription of a
superimposed linear grating having the same spacing. In this case, one of the possible
diffraction wave vectors in Eq. (12) is when 1
mand 2
mare equal but opposite signs, which
gives a diffraction angle of zero. Hence, it was possible to observe light focalization along the
0th order for all light wavelengths, as illustrated in Fig. 12.
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Fig. 12. Pictures taken as a function of distance travelled along the 0th order for a
superimposed lens grating with a linear grating having the same spacing.
Finally, since each focal point in the dual-focus chirped lens grating acts as a point source,
an interference pattern can be observed in the far-field. For this part, a different dual-focus
holographic lens grating was inscribed with a distance of only 1 cm between the two focal
points. Figure 13 illustrates the interference pattern from a He-Ne laser source at a distance of
20 cm away from the grating along the 1st backward diffracted order.
Fig. 13. Interference pattern from the dual-focus chirped lens grating at 20 cm away from the
sample’s surface.
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5. Conclusion
A variety of superimposed chirped gratings, acting as holographic lenses, were inscribed on
azo-polymer films by interfering plane and converging laser wavefronts. These chirped
holographic lens gratings were shown to simultaneously focus incident light, independently of
polarization, along various angles, including the 0th order. The focal points of each lens and
the off-axis focalization angle were easily controlled during the single step fabrication
process. Upon inscribing a dual-focus holographic lens grating with only 1 cm separation
between the focal points, a circular interference pattern was observed in the far-field.
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8 April 2013 | Vol. 21, No. 7 | DOI:10.1364/OE.21.008711 | OPTICS EXPRESS 8723