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Design and fabrication of constant-pitch
diffraction gratings on disperse red 1 glass
James Leibold,1Peter Snell,1Olivier Lebel,2and Ribal Georges Sabat1,*
1Department of Physics, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston, ON, K7K7B4, Canada
2Department of Chemistry and Chemical Engineering, Royal Military College of Canada, P.O. Box 17000,
STN Forces, Kingston, ON, K7K7B4, Canada
*Corresponding author: firstname.lastname@example.org
Received March 12, 2014; revised May 2, 2014; accepted May 2, 2014;
posted May 5, 2014 (Doc. ID 208089); published June 5, 2014
Circular surface-relief diffraction gratings with a constant pitch were photo-inscribed on thin films of a disperse red
1 functionalized glass-forming compound using a novel holographic technique. Various light-interfering metallic
fixtures, which consisted of annular rings with a sloped and polished inner surface, were designed and fabricated.
Each of them allowed the inscription of stable and high-quality circular diffraction gratings with pitches ranging
from approximately 600–1400 nm and depths up to 250 nm. This was accomplished by exposure to a collimated
laser beam with an irradiance of 604 mW∕cm2for 350 s. The resulting gratings had a diameter of 11.4 mm and had the
advantage of being produced in a simple single-step procedure with no postprocessing or specialized equipment.
The pitch and diameter of these circular gratings were dependent on the fixture geometry, while the depth was
related to the exposure time. © 2014 Optical Society of America
OCIS codes: (050.1950) Diffraction gratings; (050.1970) Diffractive optics; (050.2770) Gratings; (050.6875) Three-
dimensional fabrication; (090.1970) Diffractive optics; (310.6860) Thin films, optical properties.
Surface relief diffraction gratings (SRGs) can be pro-
duced by a variety of methods. Patterns can be directly
imprinted onto a resist through electron beam lithogra-
phy  or directly engraved into materials with focused
ion beams  or laser milling . These methods can be
time consuming for large grating areas since each line is
drawn individually. Photolithography is widely used in
industry and involves using a photomask to expose an
entire pattern onto a photoresist. It is convenient for cre-
ating large, complex patterns and can be combined with
other microfabrication techniques , but it requires
multiple processing steps. Nanoimprinting involves
production of a mold, sometimes from a method listed
above, which is then pressed into a polymer surface
. Although it is appropriate for mass production of a
pattern, it is also a multiple step process that is ill suited
for rapid development of new grating patterns. Direct
laser interference patterning utilizes interference of
coherent light to directly engrave surface patterns on
commercially available polymers . This method is a
single step process, but the ablation of material requires
a high-powered pulsed laser.
The production of SRGs using materials containing
azobenzene chromophores has proven to be an interest-
ing area of study . A thin film of an azo–polymer
material, such as disperse red 1 (DR1) Poly(methyl meth-
acrylate) (PMMA), has the ability to record holographic
information in surface relief because of its photosensitive
mass transport properties. These SRGs also have the abil-
ity of being thermally erased and optically rewritten .
Although the mechanism is not fully understood, there
are successful models which explain the material trans-
port as the result of changes to the elastic properties of
the material when it is exposed to light . Other papers
have reported on the properties of DR1-functionalized
glass-forming compounds . Our group has recently
synthesized a new azo–glass compound, which possesses
the added benefits of easier purification, higher yield, and
the production of high-quality thin films and SRGs .
The goal of this Letter is to introduce a novel method of
inscribing circular SRGs onto azo–glass films using a
three-dimensional (3D) beam splitting technique with a
fixture called a circular diffraction grating generator
(CDG). There have been other publications on the forma-
tion of circular diffraction gratings using interference
patterns from standing spiral waves , Bessel beams
, and fiber optic modes ; however, our technique
is novel in its production method, and our circular gra-
tings are created on a much larger scale than previously
reported. Possible applications for this new technique
may include: optical sensors , enhancement of LEDs
, improvements in solar cell efficiency , plas-
monic lenses , circular grating distributed feedback
dye laser , and optical measuring techniques .
Assume a mirror in the shape of a hollow truncated
cone. The inner surface of this shape is reflective and
is the basis for a theoretical CDG. When a collimated la-
ser beam, with a diameter sufficiently large to illuminate
the entire reflective surface, is incident normally, the
CDG will reflect the light toward the smaller aperture
end, creating interference at the center with the directly
incident light. This interference yields a pattern of circu-
lar constant-pitch concentric rings with sinusoidal
intensity variation that can be photoinscribed on an
azo–glass film placed at the back of the CDG along
the smaller aperture end.
If the angle of the mirrored surfaces of the CDG could
be changed, it would modify the circular grating pitch.
Figure 1shows a schematic of a planar wave front inci-
dent onto a CDG where θis the angle of the mirrored
surface from the normal. At points Aand B, the colli-
mated wave front will be in phase. Using the law of sines
June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS 3445
0146-9592/14/123445-04$15.00/0 © 2014 Optical Society of America
with triangle ACD, it can be shown that AC DC cot θ.
Using triangle ABC, it can be shown that BC
AC cos 2θ. Substituting these two equations to find the
difference in path length AC −BC, along with the use
of trigonometric identities, gives
AC −BC DC sin 2θ:(1)
The phase difference δis related to the optical path
length difference as δkAC −BCπ, where kis
the wavenumber for the light source k2π∕λ, and the
additional term of πis the phase change from the reflec-
tion on the CDG mirror. In order to find the pitch
between each maxima or minima, we can state that
2πkAC −BC. By substituting Eq. (1) and isolating
the length DC, it can be found that for a given CDG angle
θ, the grating pitch Λis given by
This equation demonstrates a practical limit to the small-
est grating pitch that can be generated, which is depen-
dent on the wavelength of the light source and is limited
to Λ≈λas θapproaches 45 deg. At CDG angles greater
than or equal to 45 deg, the reflected light will never
reach the sample surface, and no interference pattern
will be generated.
A similar geometric analysis of Fig. 1shows that a
maximum height yof the CDG is constrained by the ra-
dius of the smaller CDG aperture xand is dependent on
the angle of the CDG θ. This is given by the following
tan 2θ−tan θ:(3)
If the actual height of a CDG is larger than the maximum
height ypredicted by Eq. (3), then the reflected beams
will pass the center point of the sample. This will cause
cross interference with the reflected beam from the op-
posite side of the CDG and will decrease the quality of the
SRG being generated. If the actual height of the CDG is
smaller than yfrom Eq. (3), then the resulting interfer-
ence pattern will not reach the center of the sample re-
sulting in a ring grating with a smooth circular center.
Several CDG fixtures were machined and polished us-
ing manual equipment found in common machine shops.
Care was taken to ensure that the reflecting conical
surface was a true truncated cone, finishing at a knife
edge on the minor aperture, with its central axis
perpendicular to the flat face. The material used was
high-quality annealed carbon steel. After machining,
the CDG fixtures were washed with solvent and dried
with air. Approximately 500 nm of silver was then sputter
coated onto each CDG in order to create a mirror-like
finish. A total of five CDGs were machined with angles
θof 12.5, 20.8, 23.5, 31.2, and 40.4 deg.
Azo–glass was synthesized according to . Solutions
of azo–glass were then prepared from powder by mixing
with dichloromethane at 3 wt. % concentration. The sol-
ution was subsequently mechanically shaken and filtered
with a 50-μm filter. Solid films were fabricated by spin
casting the solution onto cleaned and dried microscope
slides. At a rate of 1500 rpm, the solid films had a thick-
ness of approximately 400 nm, as measured with a
An azo–glass sample was placed directly on the CDG
facing the small aperture. The beam from a Verdi diode-
pumped laser with a wavelength of 532 nm was passed
through a spatial filter, collimated, and circularly polar-
ized by a quarter-wave plate. The resulting collimated
beam had an irradiance of 604 mW∕cm2. The beam diam-
eter was controlled by a variable iris and was projected
onto the CDG and sample.
Real-time data of the diffraction efficiency at a local-
ized point of the circular SRG is shown in Fig. 2as a func-
tion of exposure time. This was accomplished by shining
a low-powered He–Ne laser onto the sample where
the grating was forming. This laser was mechanically
chopped, and the first-order diffraction beam was
incident onto a silicon photodiode. The signal from the
photodiode was amplified by a lock-in amplifier and plot-
ted as a function of time on a computer. The diffraction
efficiency was calculated by dividing the first-order dif-
fracted signal by that of the incident beam, which was
measured in a similar manner. The steady increase
and eventual plateau of the diffraction efficiency for ex-
posures up to about 300 s is likely due to the physical
migration of the molecules of the azo–glass as they are
being displaced to form peaks and troughs of greater
depths. Based on the results of this plot, efficient circular
SRGs can be generated with exposure times greater than
Fig. 1. Schematic demonstrating the optical geometry of a
cross section of a CDG.
Fig. 2. Typical localized diffraction efficiency of circular SRG
in real time as it is inscribed by a CDG. The sudden drop just
after 600 s is attributed to when the inscribing laser is turned
off. Inset (a): Circular SRG produced in azo–glass and coated
with gold. Inset (b): Circular diffraction pattern from SRG.
3446 OPTICS LETTERS / Vol. 39, No. 12 / June 15, 2014
300 s. Nonetheless, for the remainder of this experiment,
an exposure time of 350 s was arbitrarily chosen.
Circular SRGs, with a diameter of approximately
11.4 mm, were inscribed using the method described
above, as seen in Fig. 2, inset (a). To verify that circular
gratings were actually created, a collimated beam from a
He–Ne laser was used to illuminate the SRG resulting in
the circular diffraction pattern photographed in transmis-
sion 1 cm away from the sample, as seen in Fig. 2,
Atomic Force Microscopy (AFM) imagery of the sur-
face profile of a circular SRG was taken, and an example
is presented in Fig. 3. The AFM scans show a regular sine
wave pattern aligned radially from the center of the
circular SRG. The generated SRGs had depths of up to
250 nm, depending on laser exposure time. The total dis-
tances between multiple peaks were obtained from the
AFM imagery and divided by the number of complete
waves to get an average grating pitch for each scan.
To further improve the accuracy of the results, scans
were taken at the 0°, 90°, 180°, and 270° positions of each
circular grating, and these results were averaged again.
The black circle points in Fig. 4represent AFM measure-
ments of grating pitches taken by this method. AFM
scans of the smooth center area of circular SRGs created
with a CDG having a height less than the theoretical y
from Eq. (3) do show evidence of random self-structuring
formations; however, these are on the order of 20 times
shallower then the gratings formed in the interference
In order to verify that there were no unpredicted large-
scale effects, a scanning electron microscope (SEM) was
used to image larger SRG areas (on the order of 150 μm),
as seen in Fig. 5. Circular SRGs, generated from the 12.5,
20.8, 31.2, and 40.4 deg CDGs, were sputter coated with
approximately 60 nm of gold and observed in the SEM.
Individual gratings could still be visually resolved at
magnifications of up to 2000 times. The grating pitches
were measured at a magnification level of 15000 times,
and these data points are included on Fig. 4as crossed
The third and last method for obtaining the grating
pitch of these circular SRGs was done by measuring
the diffraction angle from a low-powered He–Ne laser in-
cident on a small portion of the grating. The resulting
first-order diffracted beam was an arc of a circle. How-
ever, since the laser beam illuminated only a small area
near the edge of the circular grating, it can be approxi-
mated as a linear diffraction grating since the radius of
curvature of the grating is relatively large compared to
the small area being illuminated. Therefore, the well-
known grating equation for normal incidence was used
to calculate the grating pitch Λ. Accurate measurements
of the first order diffraction angle were obtained using a
Velmex rotary stage connected to a computer. Hollow
square points in Fig. 4represent grating pitches calcu-
lated by this method.
The results in Fig. 4demonstrate that the three inde-
pendent methods of measuring the circular grating
pitches written on azo–glass samples by CDGs are con-
sistent and correlate very well with the predicted theory
given by Eq. (2).
Five circular SRGs, with pitches from 600 to 1400 nm
and depths of up to 250 nm, were photoinscribed onto
azo–glass films using a novel holographic technique
made possible with a fixture called a CDG. The fact that
the SRGs formed are circular is supported by the
Fig. 3. AFM scan of circular SRG generated by a 20.8 deg
Fig. 4. Theoretical and measured results of the SRG pitch ver-
sus CDG mirror angle θ. Measured results include data points
taken from AFM, SEM, and diffraction angle measurements.
The theoretical curve is plotted using Eq. (2).
Fig. 5. SEM image of circular SRG generated from a 20.8 deg
CDG. (a) At 2000 times magnification, the grating peaks can be
visually resolved showing a highly regular grating pattern.
(b) At 15000 times magnification gratings are clearly resolved.
June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS 3447
orientation of the gratings measured in the AFM scans as
well as the circular diffraction pattern produced by illu-
minating the SRGs. The SRG depth and, to a certain ex-
tent, the diffraction efficiency can be varied depending
on the inscribing laser irradiance and the amount of
exposure time. The SRG pitches were measured using
a variety of techniques and agreed very well with the
theoretical predictions, which are dependent on the
CDG geometry and wavelength of the inscribing light.
The inside and outside diameters of the circular SRGs
generated by this method can also be controlled by
varying the size of a CDG’s smaller aperture xand height
y. The main advantages of this method are that it is a
single step, direct inscription process that produces
SRGs that can be thermally erased and optically rewrit-
ten. It has relatively fast SRG production times on the
order of 300 s with grating sizes only limited by the
diameter of the collimated laser beam used to inscribe
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