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Laser-induced controllable chirped-pitch circular
surface-relief diffraction gratings on AZO glass
James Leibold and Ribal Georges Sabat*
Department of Physics, Royal Military College of Canada, PO Box 17000, STN Forces, Kingston, Ontario K7K7B4, Canada
*Corresponding author: sabat@rmc.ca
Received March 4, 2015; revised May 13, 2015; accepted May 14, 2015;
posted May 15, 2015 (Doc. ID 235622); published June 12, 2015
Chirped-pitch nanoscale circular surface-relief diffraction gratings were photoinscribed on thin films of a Disperse
Red 1 functionalized material using a holographic technique. A truncated conical mirror splits and redirects a
converging or diverging laser beam, resulting in an interference pattern of concentric circles with a chirped pitch
that can be controlled by varying the wavefront curvature. The resulting circular gratings have a diameter of 12 mm
and have the advantage of being produced in a fast, single-step procedure with no requirement for a master grating,
photomask, or milling equipment. © 2015 Chinese Laser Press
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.
http://dx.doi.org/10.1364/PRJ.3.000158
1. INTRODUCTION
Chirped linear surface-relief diffraction gratings (SRGs) are
useful in a variety of applications such as spectral filters
[1] and light focalizers into waveguides [2]. Chirped circular
SRGs can serve similar functions as their one-dimensional
linear counterparts, but have the advantage of acting in
two dimensions. This allows for the design of a wide variety
of diffractive optical elements, such as diffractive lenses or
kinoforms [3], specialized lensacons [4], and hybrid lenses
[5]. Other possible applications for circular SRGs include sur-
face-emitting distributed feedback lasers [6], surface plasmon
enhanced optical sensors [7], and the miniaturization of
instruments such as spectroscopes [8].
A literature review revealed a wide range of techniques to
manufacture chirped circular SRGs. Photolithography is a
common microfabrication technique which uses a photomask
or interference pattern to project light onto a photoresist
material. This is normally a multistep process that involves
coating the material with a photoresist, exposing it to a source
of patterned light, etching it, and then cleaning it. In one
paper, a circular SRG was generated using a linear grating pat-
tern on a wedge-shaped mask that was rotated at a certain
step interval and exposed to create a circular grating [7].
Direct milling techniques such as diamond turning [5],
focused ion beams [8], or electron beam milling [9] have been
used to create circular gratings onto a mold, masking material,
or directly onto a desired substrate. These techniques are
capable of nanometer-scale resolutions; however, they gener-
ally have a low throughput since each line of the grating is
machined one at a time.
Furthermore, soft lithography uses a flexible mold to trans-
fer a surface-relief pattern onto a desired substrate [10]. The
resulting patterns can further be modified by mechanically
bending, compressing, or stretching the mold [11]. Although
this technique is good for mass production, it relies on the
fabrication of the original mold pattern through either a
direct milling or a photolithography technique, as previously
described.
In this paper, we use a three-dimensional laser beam split-
ting technique with a custom-built fixture called a circular
diffraction grating generator (CDG), pictured in Fig. 1,to
inscribe large-scale, chirped-pitch circular diffraction gratings
using a single-step process. An incident laser beam on the
CDG is simultaneously split and redirected to form an inter-
ference pattern of concentric circles of laser light inside the
aperture. This pattern is then photoinscribed onto an exposed
AZO glass thin film by means of the photomechanical behav-
ior of the AZO glass molecules. This occurs due to the
trans-cis photochemical isomerization of the azobenzene
chromophores [12]. Herein, we also present a theory that
was successfully fitted to experimental results, which enables
understanding of how the pitch variations within each circular
grating can be controlled with the geometry of the CDG, the
wavelength of the inscribing light, and the curvature of the
laser wavefront.
Other researchers have reported the generation of circular
SRGs in azobenzene-functionalized materials using optical
sources such as a Bessel beam [13] or interference patterns
from the end of an optical fiber [14]. The method introduced
in this paper has several advantages over other techniques in
that the size of the circular SRG produced is scalable and
the pitch and chirp of the grating are controllable within the
limitations of the theory.
2. THEORY
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 point source of light is positioned on
the axis of symmetry of the CDG at some distance s, the
spherical wavefront will be reflected by the mirrored surface
towards the smaller aperture end of the CDG. This reflected
light will interfere with the directly incident light, creating a
158 Photon. Res. / Vol. 3, No. 4 / August 2015 J. Leibold and R. G. Sabat
2327-9125/15/040158-06 © 2015 Chinese Laser Press
pattern of concentric rings with sinusoidal intensity
variations.
A schematic of the cross-section of the CDG and a point
source is shown in Fig. 2. The mirrored surface of the CDG
will create a reflected image at the coordinates X; Y. A geo-
metric analysis of the diagram results in the expression
X;Y2lcos θ;s−2lsin θ;(1)
where θis the angle between the mirrored surface and the
normal of the sample and lis the length of the line normal
to the mirror to the point source. The variable lcan be
expressed in terms of the CDG mirror angle θ,s, and minor
radius m, giving lssin θmcos θ. Substituting this equa-
tion into Eq. (1) and simplifying using trigonometric identities
gives the equations
Xmcos2θmssin2θ;
Yscos2θ−msin2θ:(2)
At a given distance δfrom the center of the sample, the
optical path difference (OPD) between the two rays of light
that strike that location can be given by
OPDδρ2−ρ2
X−δ2Y2
q−
δ2s2
p:(3)
In order to find the grating spacing Λat a particular dis-
tance from the center δ, the change in the phase difference
between paths ρ1and ρ2at the point δand δΛmust be
2π. By a similar argument, the change in OPD must be equal
to one wavelength of the inscribing light λ, giving
OPDδΛ−OPDδλ:(4)
Substituting Eq. (2) into (3) and then Eq. (3) into (4) yields a
result that is very complicated to isolate for the variable Λ. For
this reason, a ray-tracing computer simulation was used to
generate graphs of the grating pitch Λversus distance δusing
the given experimental parameters θ,s,m,λ, as well as the
height of the CDG, h. It is also possible to achieve a numerical
approximation of Λin terms of δfrom Eq. (4) for a given set of
parameters θ;s;m;λby using commercially available alge-
braic math software. This was done to independently verify
the accuracy of the ray-tracing simulation, proving that the
results of both methods are, for all practical purposes,
equivalent.
3. EXPERIMENT
A CDG fixture was machined and polished using manual
equipment found in common machine shops. Care was taken
to ensure that the reflecting conical surface was a true trun-
cated 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 fixture was washed with solvent and
dried with air. Approximately 500 nm of silver was then
sputter-coated onto the CDG in order to create a mirrorlike
finish. The CDG dimensions were measured using a digital cal-
iper and an analog traveling microscope. It was found to have
an angle θof 28.9°1° and a small aperture radius m
of 5.95 mm.
Dispersed Red 1 AZO glass was synthesized according to
[15]. Solutions of AZO glass were then prepared from powder
by mixing with dichloromethane at a 3% concentration by
weight. The solution 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 thickness of approximately 400 nm, as measured with
a profilometer.
An AZO glass sample was placed against the small aperture
face of the CDG. The beam from a Verdi diode-pumped
laser, at a wavelength of 532 nm, was passed through a spatial
filter, collimated, and circularly polarized by a quarter-wave
plate. The resulting collimated beam had an irradiance of
607 mW∕cm2. The beam diameter was controlled by a varia-
ble iris and was passed through a spherical convex lens with a
known focal length to create a point source image, as seen in
Fig. 3. This point source was placed at a known distance s
from the sample and was used to inscribe the concentric
interference pattern directly onto the AZO glass films with
an exposure time of 450 seconds. This was repeated four
more times to create SRGs from distances sof 3, 6, 9, −10,
and −20 cm.
Real-time diffraction efficiency measurements for the first-
order diffraction were taken as a circular SRG was being writ-
ten. This was accomplished by shining a 405 nm wavelength
probe laser onto the sample as the SRG was being inscribed.
The probe laser was incident on a small part of the grating and
Fig. 1. CDG.
Fig. 2. Schematic demonstrating the optical geometry of the cross-
section of a CDG.
J. Leibold and R. G. Sabat Vol. 3, No. 4 / August 2015 / Photon. Res. 159
light was diffracted along an arc of a circle. The probe laser
was mechanically chopped and the first-order diffraction arc
of a circle was incident on a photodiode. The signal from the
photodiode was then fed through a lock-in amplifier and re-
corded on a computer. The diffraction efficiency in percent
was calculated by dividing the first-order diffraction signal
by the signal from the directly incident beam and multiplied
by 100.
4. RESULTS
Figure 4shows the real-time diffraction efficiency of a chirped
pitch circular SRG as it was being inscribed using a CDG. Care
was taken to place the photodetector close to the sample
in order to collect as much light as possible from the first
diffraction order mode, but loss of light outside the area of
the detector may have resulted in a slight underestimation
of the diffraction efficiency. The maximum observed diffrac-
tion efficiency was observed to be 4% after a 700 s exposure,
with an inscribing laser irradiance of 1209 mW∕cm2.
Atomic Force Microscope (AFM) measurements of the
grating pitches were taken using a Pacific Nanotechnology
Nano-R O-020-0002 scanning probe microscope. The AFM
was calibrated using a sample with known dimensions, and
has a measurement accuracy of 2%. The distance between gra-
ting peaks was measured at intervals of 0.5 mm, starting from
the outside edge of the circular SRGs. Each measurement was
taken a second time from the opposite side of the circular
SRGs, and the two measurements were averaged. An example
of the AFM imagery can be seen in Fig. 5. Although a profile
depth of 0.09 μm is quite shallow, the depth and diffraction
efficiency of the circular grating can be increased with a com-
bination of stronger irradiance and longer exposure time, as
demonstrated in Fig. 4.
The resulting graphs of the grating pitch Λas a function of
distance δfrom the center of the circular grating are illus-
trated in Figs. 6–10. The lines in these graphs show the results
of the computer simulation for a CDG with θ29°, as well as
two additional lines at 1° to illustrate the range of error from
the physical measurements of the CDG angle. The hollow
circle points represent data taken from the numeric solution
from algebraic computer software to verify the fidelity
of the ray-trace simulation. The black squares with error
bars are physical measurements of the grating pitch from
the AFM.
The measurement data largely agree with the predicted
theoretical pitches for all tested values of s. All five graphs
in Figs. 6–10 show the common feature that the pitch is
slightly higher than predicted near the outside edge of the
SRG. It is believed that this observation is the result of the
manufacturing process of the CDG. The interior radius of
the CDG is finished to a knife-edge, however, and because
the material supporting this area is very thin, it is susceptible
to deformation during the polishing process. This results in a
Fig. 3. Experimental setup for writing concentric chirped gratings
using a CDG. a) If the point source is on the left sample film, then
sis positive and the inscribing light is divergent. b) If a lens with a
longer focal length is used to place the image of the point source
on right of the CDG, then sis negative and the light is convergent.
Fig. 4. Real-time diffraction efficiency of a chirped circular SRG as it
is being inscribed in AZO glass. The inscribing laser with a measured
irradiance of 1209 mW∕cm2was turned on shortly after the 0 s mark
and turned off after 700 s of exposure time. The small dip in diffraction
efficiency after 700 s can be attributed to the turning off of the inscrib-
ing laser. It is possible that the subsequent rise in diffraction efficiency
can be attributed to the relaxation of the AZO glass material after the
inscribing laser was turned off.
Fig. 5. AFM imagery at 1 mm from the edge of a circular SRG
inscribed using a 28.9° CDG with a point source of inscribing light
at s−10 cm.
160 Photon. Res. / Vol. 3, No. 4 / August 2015 J. Leibold and R. G. Sabat
slight decrease in the effective CDG angle θnear the interior
radius, effectively increasing the grating pitch at the edge of
the resulting SRGs.
The accuracy of the resulting interfering wavefronts, and
therefore the quality of the resulting circular SRGs, is entirely
dependent on the quality and alignment of the optical ele-
ments used in the experimental setup. The prototype CDG
was the only optical element that was manufactured in-house.
Quantitative measurements of the optical performance of
this mirrored fixture are not known; however, the results in
Figs. 6–10 demonstrate the sensitivity of the resulting
grating pitch when the angle of the CDG mirror is altered
by 1° or more. Improvements in the manufacturing process
of the CDGs could help reduce this potential source of error.
Alternately, it may also be possible to intentionally introduce a
curve to the CDG mirror surface in the radial direction as an
additional method of controlling the rate of chirp in the result-
ing circular SRGs.
Once the ray-trace computer simulations were validated
through physical data measurements, a larger range of values
of swere simulated to demonstrate the range of pitches and
degree of chirping that are theoretically possible. Figure 11
shows the simulated grating pitch dependence on the distance
δfrom the center of the SRG for a range from s−10 mto
s10 m. When the distance from the point source of light to
the CDG and sample is large, the radius of curvature in the
spherical wavefront of inscribing light is similarly large. In
these cases, the model approaches a constant-pitch circular
SRG as generated by a collimated light source, as depicted
in Fig. 10 for the lines for s10 m and s−10 m. When
the distance to the point source of inscribing light is de-
creased, the degree of chirping in the grating becomes more
pronounced, as seen by the increase in positive slope for s
with a negative value and decrease in negative slope for swith
a positive value.
Fig. 6. Theory and measurements for a circular SRG inscribed from a
28.9° CDG with diverging point source 3 cm away from sample.
Fig. 7. Theory and measurements for a circular SRG inscribed from a
28.9° CDG with diverging point source 6 cm away from sample.
Fig. 8. Theory and measurements for a circular SRG inscribed from a
28.9° CDG with diverging point source 9 cm away from sample.
Fig. 9. Theory and measurements for a circular SRG inscribed from a
28.9° CDG with converging point source -10 cm away from sample.
AFM measurements are not made for the values of δsmaller than
4 mm because the height hof the CDG prohibits the formation of gra-
ting lines in the center of the SRG, as discussed in Section 4.
J. Leibold and R. G. Sabat Vol. 3, No. 4 / August 2015 / Photon. Res. 161
When running the simulation for different values of s, it be-
came apparent that the results are very sensitive to selecting
the proper height of the CDG h. There exists a critical value
for the CDG height hcfor optimum circular SRG inscription. If
his larger than hc, the interference pattern will cross over the
center line of the SRG, destroying the SRG in that area.
Conversely, no grating is formed in the center of the SRG if
his smaller than hcbecause the interference pattern does
not reach the center. For a planar wave inscription, the value
of hccan be readily obtained from geometry:
hm
tan2θ−tan θ:(5)
For a divergent or convergent source, the equation for the
critical height hcof the CDG is given by
hc−
mcos θmsin2θ−scos2θ
2mcos θsin θ:(6)
For large distances s, Eq. (6) converges to Eq. (5). In Figs. 9
and 10, the AFM was unable to detect grating structures near
the center of the SRG written at s−10 cm and s−20 cm.
This is because the height of this particular CDG h
4.342 mmwas insufficient to reach the center at a configura-
tion with a small negative distance to the point source. For the
cases where the CDG would have been too tall, the variable
iris illustrated in Fig. 3was closed so that less of the CDG
was illuminated, reducing the effective height of the CDG
exposed to light. This illustrates a capability of adjusting not
only the pitch of the gratings, but their geometrical form.
5. CONCLUSION
Five circular SRGs were photoinscribed onto AZO glass films
using a 28.9° CDG and a point source of either converging or
diverging laser light at various distances from the film. The
resulting grating pitches were measured as a function of dis-
tance from the center of the grating, and had a controllable
chirped pitch in agreement with the theoretical predictions.
A ray-trace simulation confirmed that the chirped-pitch
slope is dependent on the value s, which is the distance from
the sample to the point source along the optical axis. The gra-
ting pitches and the SRG diameters can further be controlled
by varying the CDG geometry with parameters such as θ,m,h
and the wavelength of the light source λ. The simulation dem-
onstrated that chirped-pitch slopes from −30.1to 34.1 nm/mm
are possible and that a slope of zero corresponds to a con-
stant-pitch grating generated by a distant point source.
The chirped-pitch circular SRGs generated by this method
were found to be sensitive to imperfections in the CDG manu-
facturing process as well as the overall height hof the CDG.
This is especially true for small values of swhere the geometry
amplifies the sensitivity of the control parameters. For this
reason, special care must be taken in the selection of dimen-
sions of the CDG in order to ensure that circular SRGs are
generated with predictable pitches.
Despite the somewhat complex nature of the optical ray
path geometry of this experiment, relatively large-scale
chirped circular SRGs could be designed and easily manufac-
tured using a simple and inexpensive reflective fixture such as
the CDG. This is done in a single-step process without the
need for specialized lithography or milling equipment. The cir-
cular chirped SRGs were manufactured fairly quickly, on the
order of 450 s with a laser irradiance of 607 mW∕cm2. The
circular SRGs generated in this experiment had a diameter
of 12 mm, but the size of the SRGs that this technique can
produce is theoretically limited only by the size and power
of the collimated laser beam as well as suitably sized focusing
lens and CDG. It should therefore be possible, using the
method described here, to generate circular SRGs with
much larger diameters but equally fine subwavelength resolu-
tions. Because of the ease, speed, and economy of this new
production method, it may be possible for other researchers
Fig. 10. Theory and measurements for a circular SRG inscribed from
a 28.9° CDG with converging point source −20 cm away from sample.
AFM measurements are not made for the values of δsmaller than
3 mm because the height hof the CDG prohibits the formation of gra-
ting lines in the center of the SRG, as discussed in Section 4.
Fig. 11. Dependence of grating pitch on distance from the center for
14 simulated circular SRGs inscribed with a 28.9° CDG using different
distances to the point source of light swith a wavelength of 532 nm. A
positive value of sdenotes a divergent source while a negative value
indicates a convergent source. As the distance to the point source
increases, whether positive or negative, the slope of the grating
approaches zero. Small absolute values of sresult in steeper slopes
and nonlinear curves. The grating pitch can be further controlled
by changing the CDG angle θor the wavelength of light λ. Curves
are derived from a ray-trace computer simulation discussed in
Section 2.
162 Photon. Res. / Vol. 3, No. 4 / August 2015 J. Leibold and R. G. Sabat
to have access to customized circular SRGs to meet their own
application-specific research in the field of photonics.
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