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Laser produced thin metallic planar mini-flyer generation
using fiber optic plate
MAYANK SHUKLA, SACHIN SAWANT, ASHISH AGRAWAL, YOGESH KASHYAP, TUSHAR ROY,
AND AMAR SINHA
Neutron and X-ray Physics Facilities, Bhabha Atomic Research Centre, Mumbai, India
(RECEIVED 13 January 2013; ACCEPTED 21 March 2013)
Abstract
Laser produced planar mini flyer generation has widely gained importance owing to its wide ranging applications in the
field of condensed matter, astrophysics, material research, shock phenomenon, etc. Flattop smooth laser beam profile as
driver is the primary requirement for planar flyer generation besides special multilayered target geometry. We present here
laser produced thin metallic planar mini-flyer generation using afiber optic plate (FOP) of 8 mm thickness and about 6 μm
fiber dimension. This technique is unique in the sense that it doesn’t require large length as compared to optical fiber. A
Gaussian shape laser beam from a laser oscillator was allowed to fall on the FOP generating a speckle pattern. This pattern
was relayed and amplified using lenses and laser amplifiers to achieve energy of about 400 mJ. The beam was focused on a
substrate (fused silica) based multilayered target on which flyer disks of different materials such as Al. Cu, Br, and Ta were
attached. Velocities as high as 400 m/s was measured for Al flyer of 1.5 mm diameter and thickness 50 μm. Flyer disks
were completely recovered after the laser shot. We also present a theoretical analysis along with experimental results of the
laser beam smoothing technique using a He-Ne laser and FOP. Each channel of the FOP acts as a small single mode optical
fiber. The basic idea was to divide the incoming coherent beam into many beam-lets introducing random distribution in
length or/and diameter of optical fibers of FOP. The individual FOP channel acts as a diverging source because of single
mode fiber with natural divergence λ/d. However, due to the small randomness in length or diameter, the individual
diffraction sources are not in phase. This results in the generation of speckles in both near (Fresnel) and far field
(Fraunhoffer) destroys the spatial coherence of the beam.
Keywords: Fiber optic plate; Flattop beam profile; Planar mini-flyer; Smooth beam; Speckle
INRODUCTION
Flyers have been widely used by many researchers in the field
of material science (Asay, 1990), impact studies (Roybal et al.,
1995), astrophysics (Roybal et al.,1995), condensed matter
physics (Paisley et al.,1991; Swift, 2002; Swift et al.,2005;
Bushman et al.,1993). The areas where they have specially
gained importance are: achieving sufficient velocities for com-
pression of inertial confinement fusion target (Labaste et al.,
1995;Decosteet al.,1979;Krehlet al.,1975), ultrafast
ignition of secondary explosives (Asay et al.,1990; Bourne,
2001), measurement of equation of state (EOS) and high
pressure induced phase transitions (Swift, 2002), measurement
of dynamicspall strength of various metals (O’Keefe & Skeen,
1972;Okadaet al.,2003; Robbins & Sheffield, 2000;Paisley
et al.,2001;Wang2002;Watsonet al.,2000). In one of the
experiments, X-ray driven flyers have been used to generate
EOS data in the pressure regime of 0.75 Gbar (Cauble et al.,
1993). Flyers have also been used for meteorite impact studies
of space micro-debris and dust on spacecraft material (Roybal
et al.,1995), estimation of strength of thin films (Robbins &
Sheffield 2000;Paisleyet al.,2001;Wang,2002). The ability
of a flyer to investigate the compressed as well as impacted
material under cold conditions (without pre-heating), makes
it an ideal tool for such research. Laser produced mini-flyers
offers several advantages over the other techniques such as
gas gun, exploding wires (Burr, 1967;Neffet al.,2009)and
chemical explosives (Swift et al.,2007) for investigating the
dynamic properties of materials. In particular, the small dimen-
sions involved (of millimeter order) and the low cost of laser
shots offers advantages such as good repetition rate, reduction
in experimental length and time, high shot throughput, simpli-
fied experimental apparatus and reasonably moderate energy
(few hundreds of mJ) requirement to achieve flyer velocities
of few km/s.
289
Address correspondence and reprint requests to: Mayank Shukla, Neutron
and X-ray Physics Facilities, Bhabha Atomic Research Centre, Mumbai
400085, India. E-mail: mayank@barc.gov.in
Laser and Particle Beams (2013), 31, 289–300.
© Cambridge University Press, 2013 0263-0346/13 $20.00
doi:10.1017/S0263034613000256
Twoapproachoflaserbasedgenerationandaccelerationof
thin metallic flyers have been generally used. The first one in-
volves direct laser irradiation of thin metallic foils. In this
method, a high power pulsed laser beam is focused at high inten-
sity on a solid target. The plasma created at the surface liberates
and acceleratesthe rear target to velocities up to few km/sbythe
process of ablative acceleration (Decoste et al.,1979; Ripin
et al.,1980). Research on ablative acceleration of thin foil targets
by intense pulsed lasers began in 1970’s. Since then several re-
searchers have utilized thistechnique to study various phenom-
enon associated with laser matter interaction. Velocities as high
as 13 km/s have been achieved by the direct laser irradiation
method (Tanaka et al.,2000). Though direct laser irradiation
of targets have been used to achieve high flyer velocities
(tens of km/s), it has some limitations. For example, the preheat-
ing of the target rear surface due to the thermal heat transport va-
porizes the material of the flyer. The second method involves
indirect laser irradiation of thin metallic targets attached to an op-
tically transparent substrate (Greenway et al.,2003;Paisley,
1991). In this method, a moderate power laser pulse is focused
at the substrate-target interface through transparent side. The
plasma created at the interface is confined by the massive sub-
strate (providing the necessary tamping effect) that liberates
the target by stress induced spallation (Paisley, 1991; Setchell
et al.,2002). The advantage of this method over the direct
laser irradiation is that velocities as high as km/s can be achieved
using a moderate power laser that is limited by the damage
threshold of the substrate material. Use of multi-layered targets
involving efficient laser energy absorbing material and thermal
insulator material helps in minimizing the heat transport to the
rear of the target, thus allowing flyers to be accelerated in solid
from in both direct (Tanaka et al.,2000) and indirect drive
methods (Miller et al.,2009; Watson et al.,2000). Another
advantage of indirect method is that the laser beam doesn’t
require to be tightly focused. A few mm spot size focusing is
sufficient (as compared to about 100 μm in direct drive
method) to achieve high velocities.
A Gaussian laser beam profile irradiates the target surface
non-uniformly. This results in non-uniform acceleration of
material with peak at the center of the target. Another phenom-
enon that is common to non-uniformlaser energy deposition is
the hot spot generation in the plasma. This leads to pre-heating
of the target material before it is compressed and launched re-
sulting in fast vaporizing of the material (Honrubia et al.,
1998). The requirement of beam smoothing for planar shock
generation and uniform illumination of inertial confinement
fusion targets has made this subject extensively studied.
Many techniques have been reported for laser beam smooth-
ing such as random phase plate (RPP) and phased zone-plate
(PZP) (Batani et al.,2002; Bennuzi et al.,1998;Dixitet al.,
1994;Katoet al.,1984;Koeniget al.,1994;Lehmberg&
Obenschain, 1983; Skupsky et al.,1989; Stevenson et al.,
1994), multiple lens array (Deng et al.,1986), diffuser (such
as ground glass or integrating sphere) and optical fiber (Green-
way et al.,2003). Each method has some advantages over
other. The phase modulators (such as RPP or RPZ), which
converts the coherent wave to random-phased wave, has to
be kept very close to the target that makes conducting exper-
iment inconvenient. Moreover, theses plates are expensive too.
The multiple lens array assembly requires precise lenses with
high numerical aperture and low aberration to be fabricated,
which makes it difficult to design. In the case of speckle pat-
tern generated by ground glass, reflections from a rough sur-
face of glass are the combination of both scattering and
interference phenomena. As surface roughness increases, the
scattering effect plays a dominant role that reduces the laser
beam intensity. Also, there is no precise control on the speckle
generation. Integrating sphere involves the multiple diffuse re-
flections of laser in it and produces speckle pattern for modu-
lation transfer function testing of detectors. Step index
multimode optical fiber has also been used by many research-
ers (Greenway et al.,2003; Paisley, 1991) for laser beam
smoothing. Incident laser beam propagating through such a
fiber excites many optical modes travelling at different vel-
ocities. However, the small random fluctuations in the core
radius or the refractive index affect the propagation by introdu-
cing random phases into the modes. As a consequence the op-
tical modes interfere at the output of the fiber and their overlap
produces a speckle pattern. This profile has fine-scale intensity
variations (“modal noise”) due to interference between propa-
gating fiber modes, with the amplitude of these variations de-
pendent on the temporal coherence of the laser. Inside a
multimode fiber, the optical radiation is distributed between
all the possible propagation modes thus acting to smooth out
“hot spots”and non-uniform features within the beam profile.
In this paper, we present generation of planar mini-flyer gen-
eration using a fiber optic plate for laser beam smoothing. This
technique is unique in the sense that it doesn’trequirelarge
length as compared to the optical fiber (few tens of meters).
A fiber optic plate is a bundle of fibers with individual fiber di-
mension of few microns and overall length of a few mm. The
diffraction pattern from each fiber overlaps to from a smooth
laser beam profile (both in near and far field patterns). We
have used this technique to produce planar mini-flyers of
materials such as Al, Cu, Br, and Ta. A solid state Nd:Glass
laser with energy about 300 mJ to 400 mJ and duration 2 ns
was used as a driver. The laser was focused to a spot size of
about 1.5 mm on the target kept in air to achieve flyer velocities
of about 0.4 km/s. Accelerated flyers were recovered in solid
form after the laser shot. Laser beam profile smoothing achieved
using FOP has been compared with the theoretical modeling.
Diffraction theory for overlapping beamlets emerging out of
the FOP was used to model the laser smoothing. The results
corroborates well both experimentally and theoretically.
EXPERIMENT
Laser Beam Smoothing Study Using 2 mw He-Ne Laser
When coherent pulse propagates through a random media, the
scattered waves interfere randomly to give a fine, peculiar,
high-contrast, granular virtual objective pattern called
M. Shukla et al.290
“Speckle.”It exhibits an interference image that contains lots of
information about the characteristics of the illuminated scatter-
ing object and the process being analyzed. Being optical
non-contact pattern the important aspects of speckles are deter-
mining the activity quantity from the materials under study
(Braga et al.,2011). The time varying speckle pattern also
plays an important role in many physical phenomena like in
measurement of dynamic object (Semenov et al.,2010), metro-
logical and stress corrosion analysis (Chiang & Kin, 1982;Lu
&Zou,2010), surface deformation and roughness measure-
ment (Ling et al.,1986), bio-speckle study in seed analysis
(Nobre et al.,2009) besides smoothing of the laser beam
(Veron et al.,1988).
In an optical fiber, the number of speckle spots is given by
the number of modes of the fiber and is limited by the accep-
table angular spread of the beam, while the time delay is pro-
portional to the length of the fiber (Garnier & Videau, 1997).
The length of the optical fiber is chosen such that it generates
number of independent interference patterns simultaneously
superimposed on the target resulting in a smooth laser beam
profile. To achieve this the laser pulse duration should be con-
siderably larger than the coherence time and the light ray
should be delayed as per the equation (Veron et al.,1988),
Δt=Lθ2
2nc .(1)
Where Lis the length of the optical fiber, nis the refractive
index, θis the angle of incidence in radians. Thus to obtain a
delay of 1 ns for n=1.5 and θ=0.12 radian the length of op-
tical fiber required is 50 m.
We have used a FOP plate to produce a flat intensity laser
profile. The main advantage of this technique is that it
doesn’t require large length as compared to optical fiber. To
achieve a reasonable flat profile, the FOP should have some
degree of randomness either in individual fiber length or in
diameter. This has been explained by the diffraction analysis
of both ordered and random FOP’s as explained in the next
section to understand their operation for a Gaussian beam.
Figure 1 shows the experimental setup used for laser gener-
ated speckle analysis using fiber optic plate. The study of laser
beam smoothing using FOP was carried out with 630 nm
He-Ne laser (instead of 1064 nm) so as to avoid the damage
of CCD camera chip. An expanded beam was used that exactly
matched the laser beam size at 1064 nm used for mini-flyer
generation. The beam was expanded to about 20 mm and
then focused at spot size of about 1.3 mm with the help of
lens L
3
(f=50 mm) on a FOP. We have used two types of
FOP’s to study the laser beam smoothing. Figure 2a shows
the photograph of the FOP of 25 mm diameter and thickness
8 mm taken using high resolution optical microscope. The
individual fiber dimension was found to be about 6 μm. The
output from the rear end of the FOP was collected using lens
L
4
(f=30 mm) and imaged on the chip of a high resolution
CCD camera. Figure 2b shows the recorded speckle pattern
using lens L
4
and a high resolution monochrome CCD
camera. This FOP was designated as random FOP as it gener-
ated speckle pattern that corroborates well with the diffraction
analysis for the random plate as presented in the next section.
Lens L
4
was adjusted to obtain the expanded (speckle) as
well as focused intensity pattern. Figure 3 shows the recorded
intensity profile of the speckle pattern at the focal plane using
the experimental setup of Figure 1. The flatness of the profile
can be clearly seen. The high frequency ripples at the flattop
has reduced sensitivity for laser produced plasma at 1064 nm
at the focal plane. Besides this lateral energy transport due to
thermal conduction also helps in mitigating the effect caused
by these ripples.
Figure 4 shows the microscope image and the pattern re-
corded for second type of FOP with 25 mm diameter and
individual fiber dimensions of about 6 μm. This plate was de-
signated as ordered FOP as it generated pattern that corrobo-
rates well with the ordered diffraction pattern through a
bunch of optical fibers. The analysis of this is also presented
in the next section. At the focal plane of the lens L
4
(Fig. 1),
multiple spots were obtained.
Planar Mini-flyer Generation Using FOP Laser
Smoothing Technique
The final laser smoothing was done for 1064 nm Nd:Glass
laser using the FOP technique described above. The
Fig. 1. (Color online) Schematic of experimental setup for laser generated speckle using He-Ne laser and FOP.
Laser produced thin metallic planar mini-flyer generation 291
technique was employed for generating planar thin mini-flyer
generation. For this purpose, driven indirect drive approach
was adopted as shown in Figure 5. The target for this ap-
proach consisted of thin metal flyer disks (diameter 5mm
and thickness 50–80 μm of different materials such as Al,
Br, Cu, and Ta) attached to the optical substrate (fused
silica). A moderate power laser pulse (up to about 400 mJ)
was focused at the substrate-target interface through transpar-
ent substrate side. The plasma created at the interface was
confined by the massive substrate and provides the necessary
tamping effect. The stress wave generated exerts pressure on
the un-vaporized material and ejects it in the form of flyer
due to spallation (Lehmberg & Obenschain, 1983). Figure 6
shows the schematic diagram of experimental setup. It con-
sists of a Q switched Nd:YAG laser oscillator capable of de-
livering laser pulse of energy 150 mJ and duration 2 ns. This
oscillator was a part of the 2 J laser chain consisting of beam
expander, two 25 mm diameter silicate Nd:Glass laser ampli-
fiers in double pass configuration, Faraday isolator. The laser
chain was modified by introducing the random FOP with
lenses L
3
,L
4
, and L
5
as shown in Figure 6. Lens L
3
was
used to obtain a focal spot of about 1.3 mm diameter at the
Fig. 2. (Color online) Random FOP (a) microscopic image, (b) corresponding diffraction pattern.
Fig. 3. (Color online) Focused speckle pattern and intensity profile.
Fig. 4. (Color online) Ordered FOP (a) microscopic image, (b) corresponding diffraction pattern.
M. Shukla et al.292
input of the FOP. The speckle pattern generated at the exit of
FOP was relayed using lenses L
4
and L
5
through the two am-
plifiers as shown in Figure 6. Amplified beam was finally fo-
cused to a spot size of about 1.3 mm at the substrate based
target interface using lens L
6
. The energy was measured to
be about 400 mJ. Figure 7 shows the burn pattern of the
beam just after the amplifiers and at the focal plane of lens
L
6
, respectively. Three ICCD high speed framing cameras
were used to record the flyer motion. These cameras were
capable of recording minimum frame duration of 200 ps. A
xenon flash lamp driven by high voltage capacitive discharge
powersupply was used as a back lighting source. Target image
was split into three parts using beam splitter before imaging on
the ICCD cameras as shown in Figure 6. It was imaged on the
photocathodes of the cameras with the help of tele-magnifying
lens system assembly consisting of a fiber plate, tele-lenses,
and camera lenses. Multi-layered substrate based targets
were used to study the flyer motion. We had used fused
silica optical substrate of dimension 65 mm (Length) ×
5 mm (Width) ×1 mm (Thick) on which thin metal disks
(Al, Cu. Br, or Ta) of diameter 1.5 mm were fixed using
epoxy glue suitably diluted in acetone. These flyer disks
were glued on the substrate pre-deposited with thin layer of
carbon (3 μm) and alumina (Al
2
O
3
–5μm). These layers
were deposited using DC RF sputtering technique. Carbon
was deposited to increase the laser absorption whereas alumina
layer helped in providing heat shield to the flyer disks from the
plasma due to its low thermal conducting properties. Figure 8
shows the recorded image of the recorded frames of the
motion of planar mini-flyer made of 50 μmaluminacircular
disk (1.5 mm diameter) at different times. These times were
set by adjusting the ICCD’s trigger delay. The images were re-
corded for frame duration of 5 ns. Planar flyer motion in solid
form is clearly visible from these snap shots. The flyer disks
were completely recovered in intact form after the laser shot.
Maximum velocity of the flyer was measured to be about
400 m/s for alumina. Similar frames were recorded for differ-
ent flyers made of Cu, Br, and Ta. Measured velocities for
different targets are represented in Figure 9 and the recovered
flyer disks after the shot is shown in Figure 10.
The experiment was also performed with Gaussian laser
beam profile without FOP. Figure 11 shows the recorded
images of alumina flyer disk of diameter 1.5 mm and thick-
ness 50 μm at incident laser energy of about 300 mJ. It can be
seen that the flyer plate emerges from the substrate in intact
form. It follows the laser beam profile with some vaporized
material behind it. However, the motion of the flyer is not
Fig. 5. Substrate based laser driven mini-flyer using indirect drive approach.
Fig. 6. (Color online) Experimental setup for indirect drive scheme for planar mini flyer generation and tele-magnifying lens arrangement.
Laser produced thin metallic planar mini-flyer generation 293
uniform with peak motion at the center than at wings. After
laser shot, flyer plate was not recovered. This infers that
excess heat is transported to the other side of the foil
during motion that completely vaporizes the material. In
one of the shots at laser energy about 500 mJ the flyer
plate was observed to be shattered with the fragments
going in all the directions as shown in Figure 12.
Theoretical Analysis of Laser Beam Smoothing Using
FOP
An optical fiber (of diameter d) acts as a single mode optical
fiber if its diameter is on the order of the wavelength (λ)of
the incoming light. For a bunch of optical fibers (FOP)
each individual channel generates a diverging source with
natural divergence given by λ/d. This divides the incoming
beam into many beamlets which, when allowed to propagate
Fig. 7. (a) Beam after the amplifiers. (b) Beam after the focusing lens L
6
.
Fig. 8. Frame shots of planar mini-flyer launch made of 50 μm Al using laser smoothing by random FOP at incident laser energy of about
300 mJ.
Fig. 9. Measured Flyer velocity as a function of laser energy.
M. Shukla et al.294
through space interfere with each other and generate a diffrac-
tion pattern. If the phases of individual beamlets generated by
the given fiber optic plate are not synchronized, the random
phase difference between them causes to make a diffraction
pattern, which is the desired speckle pattern. The diverging
speckle pattern when focused using a lens gives a smooth
laser profile at the focal plane of a lens.
To study the feasibility of the concept, the process of
speckle formation was simulated using a source TEM
00
mode of Gaussian beam with wavelength 630 nm of He-Ne
laser beam. Ray optics was applied for the propagation of
the beam through the fibers while diffraction theory has
been used for its further propagation in space.
Let us consider a wave-front of the incident beam with am-
plitude A
in
(x, y) and phase distribution e
iφ(x,y)
given by,
Fin x,y
=Ain x,y
eiφx,y
()
.(2)
When this wave-front passes through the bunch of fibers
(FOP), then due to multiple interactions (refraction and re-
flection) the amplitude and phase get modified. This modifi-
cation of incident beam is characterized by optical transfer
function of the fiber optic plate.
The single mode fiber optic plate considered for this study
has been modeled with a two dimensional distribution (opti-
cal transfer function) is given by,
OTX′
,Y′
=MTX,Y()eiφTx,y
()
.(3)
Where, M
T
(X,Y) characterizes the modification in the am-
plitude and and φ
T
(x,y) characterizes the modification in
the phase of the incident wave front.
Modification in the amplitude of the beam depends only
upon the structure of the fiber optic plate and distribution of
individual fiber in it. We have model it with a matrix possessing
Fig. 10. Recovered flyer disks after the shot with smooth laser beam profile using FOP.
Fig. 11. Image of flyer motion for Gaussian beam laser profile at incident
laser energy of about 300 mJ. Fig. 12. Image of shattered flyer material for Gaussian beam laser profile at
incident laser energy of about 500 mJ.
Laser produced thin metallic planar mini-flyer generation 295
the region of beam transmission with a value one and rest of the
region with a value zero (Figure 13a). The modification in
phase of the incident beam depends upon number of reflection
and refraction of wave in the individual fiber which conse-
quently depends upon several parameters like incidence
angle-θ,length-Land diameter of the fiber-d(Fig. 13b). Thus
the distance between any two reflection points would be d/
tanθ. So the number of times a ray undergoes reflection
Ltanθ/d. As each reflection would change the phase of wave
by πrad, hence change in the phase of wave due to reflection
can be modeled by equation π(Ltanθ/d). Similarly path length
travelled by ray between entry and exit of the waveguide is L/
cosθ,whereLis the total length of fibre. If L
0
is the mean
length of the fibers then the phase difference between the
rays can be modeled as 2π
λ(L/cos θ−L0)whereλis the wave-
length of the incident light. Thus total phase part of the optical
transfer function can modeled according to following equation,
φT(x,y)=[π(Ltan θ/d)] due to diameter,(4)
=2π
λ(L/cos θ−L0)
due to length.(5)
After modification due to its passage through FOP the wave-
front at exit of FOP is given by the product of incident wave
front and the optical transfer function of FOP which is
Fout(x′
,y′)=Ain(x,y)eiφ(x,y)OT(X′
,Y′).(6)
As this modified beam propagates through the space, it gen-
erates diffractions pattern due to the mutual interference of
the beam at various distances from FOP depending upon
the fulfillment of the required criteria of the diffraction.
The overall result of this interaction is each individual fiber
acts as a diverging source with natural divergence λ/d.If
d
2
/λz~1, the diffraction pattern obtained is said to be near
field diffraction (Fresnel diffraction) while if d
2
/λz<1,
the diffraction pattern obtained is said to be far field diffrac-
tion (Fraunhoffer diffraction). The problem was investigated
for both near (Fresnel) and far (Fraunhoffer) region of
diffraction.
For Fresnel diffraction region, the diffraction pattern is ob-
tained by multiplying the beam wave function by Fresnel
propagator and the propagated wave-front is given by,
QFres(x,y)=c∫∫ Fout (x′
,y′)e−2πi(x−x′)2+(y−y′)2/λz
[]dx′dy′.(7)
The intensity distribution at the image plane is given by
Io=|QFres(x,y)|2.(8)
With zas a propagation distance and xand yare the co-
ordinates of image plane. In Fraunhoffer diffraction region
(d
2
/λz<1), the diffraction pattern is given by,
I0=|QFraun(l,m)|2
,(9)
QFraun(l,m)=∫∫ Fout (x,y)e2πik[(lx+my)]dx dy.(10)
Eq. (8) indicates clearly that both Fraunhoffer diffraction pat-
tern is nothing but the Fourier transform of beam wave func-
tion at the exit plane of the FOP.
Both near field and far field cases were analyzed using the
code. However, we present here the simulation results of
Fraunhoffer (far field) region only since the experiment
was performed in the far field geometry. This is the limit-
ations because, for experimental fulfillment of the condition
in near field, the detector has to be kept in impossibly close
proximity with the FOP.
The function O
T
(x,y) in Eq. (3) is not always an ordered
function of (x,y) but can also be a random function. This is
possible because of small randomness in the arrangement of
fibers or due to the variation in length and diameter that may
cause a random modification in the incident beam. Depend-
ing upon the available fiber optic plate there is a possibilityof
randomness in M
T
(x,y) due to randomness in interspacing
between individual fibers or in φ
T
(x,y) due to randomness
in length, diameter of fiber or in both.
To study this effect the simulations were carried out for
following cases:
a. FOP with equal diameter and length of all individual
fibers (No randomness),
b. FOP with randomness in length and diameter of indi-
vidual fibers (Randomness in the Phase part of the op-
tical transfer function).
The optical transfer function of a FOP ordered in amplitude
as well as in phase is shown in Figure 14a. For such FOP’s,
the diverging beamlets coming out of FOP interfere to make
a regular diffraction pattern, i.e., normal Nslit diffraction pat-
tern as shown in the simulated pattern in Figure 14b. This
pattern corroborates well with the pattern obtained exper-
imentally for the ordered FOP as shown in Figure 4.
Fig. 13. (Color online) (a) Multi-fiber construction with core transmission
taken as 1 and cladding transmission taken as zero. (b) Beam propagation
through an optical fiber. L =length of the fiber, d =diameter of fiber
core. θ
C
=acceptance angle.
M. Shukla et al.296
Phase part of optical transfer function of FOP is possible to
be random because of two reasons —the randomness of
length or the randomness of diameters of various fibers. To
study the effect of their individual contribution in the ran-
domness of the optical transfer function, the two cases has
been studied separately. Figure 15a shows the optical transfer
function with randomness in the length (0.008%) of the
fibers of equal diameters. The scale of the figure varies
from –πto +π, which is the range of phase changes intro-
duced in the various portions of the incident wave-front
over the FOP. Corresponding diffraction pattern for this
case is shown in Figure 15b. Similarly, Figure 16a shows
the optical transfer function with randomness in diameter
(15%) of the fibers of equal length. The corresponding dif-
fraction pattern is shown in Figure 16b.
Various values of randomness were introduced in above
studied cases (Fig. 17) and it was observed that there exists
a minimum required randomness to achieve the required
speckle pattern. If the randomness introduced was lesser
than this value then a certain ordered structure was found.
The quantification of this randomness in under study and
will be presented separately. For the present case it was
found that to achieve a complete speckle pattern a minimum
randomness on the order of 0.0008% in the length of fibers or
3% in diameter of fibers is required.
These simulation results show that it is possible to generate
a speckle pattern if there is randomness in length and diam-
eter of the fibers. The randomness in the FOP plate used for
the experiment could not be measured due to experimental
limitation. However, it is predicted that the FOP used for gen-
erating smooth laser profile has some randomness either in
length or in diameter or in both. The experimental results cor-
roborates well with the theoretical results. As the experiment
was performed specially in the context of generating incoher-
ent flattop smooth laser profile for uniform illumination of
target, the effect on pulse duration is the prime issue. In a
long length (>10 km) single mode optical fiber transmission,
the pulse broadening has been observed due to the group vel-
ocity dispersion (GVD) (Kawana et al.,1978; Nakatsuka &
Grischkowsky, 1981). However, since the length of each
Fig. 14. (Color online) (a) Simulated optical transfer function of an ordered FOP. (b) Corresponding diffraction pattern.
Fig. 15. (Color online) (a) Optical transfer function due to 0.008% randomness introduced in length. (b) Corresponding diffraction
pattern.
Laser produced thin metallic planar mini-flyer generation 297
fiber of FOB plate used in this study was only 8 mm (where
GVD is negligible), no change in the pulse width is pre-
dicted. The main phenomenon is controlled by the diffraction
generated speckle pattern.
CONCLUSION
To conclude, it can be said that planar mini-flyers of different
materials such as Al, Cu, Br, and Ta were produced using
FOP based laser smoothing technique. The technique is
unique in the sense that it doesn’t require long length optical
fiber (about tens of meters). Instead a FOP plate (∼8mmin
thickness) with some randomness in length or/and in diam-
eter of the individual fibers can be used for generation of
planar mini-flyers. A moderate energy (few hundred mJ)
solid state laser is required for achieving flyer velocities of
km/s in substrate based targets on which flyer disks are at-
tached. However, velocities ranging from 50m/s to about
400 m/s were achieved for different materials in the present
experiment described. A multilayered target geometry on an
optical substrate consisting of Carbon layer (few microns)
followed by alumina layer (few microns) has helped in in-
creasing the laser energy absorption and providing thermal
barrier to the flyer material. However, the laser energy coup-
ling can further be increased by using anti-reflection coatings
on the optical substrate. For the present case, no anti-
reflection coating was done on the fused silica optical sub-
strate. The results corroborates well with theoretically simu-
lated results using the diffraction theory for laser light
interacting with a bunch of optical fibers, i.e., a FOP. The ef-
ficiency of the FOP can be increased by use of proper FOP
material which has high laser transmission. Anti-reflection
coating at the both input and output face of the FOP can
further add up to efficiency.
ACKNOWLEDGEMENT
We would like to thank Dr. H.S. Vora, RRCAT, Indore, India for
providing the image processing software PROMISE for this study.
Fig. 16. (Color online) (a) Optical transfer function due to 15% randomness introducedin diameter. (b) Corresponding diffraction pattern.
Fig. 17. (Color online) Simulated results of speckle for randomeness (a) 0.006% in length & 3% in diameter of individual fibers, (b)
0.006% in length and 5% in diameter of individual fibers.
M. Shukla et al.298
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