Download Pulse splitting by modulating the thickness of buffer layer of two

Pulse splitting by modulating the thickness of
buffer layer of two-layer volume holographic
grating
Xiaona Yan,1,* Mengdi Qian,1 Lirun Gao,1 Xihua Yang,1 Ye Dai,1 Xiaoyuan Yan,2 and
Guohong Ma1
2
1
Laboratory of Ultrafast Photonics, Department of Physics, Shanghai University, 200444, Shanghai, China
Department of Communication Engineering, Changchun University of Science and Technology, Changchun, China
*
[email protected]
Abstract: Based on Kogelnik’s coupled-wave theory and matrix optics,
generation of femtosecond double pulses by modulating thickness of the
buffer layer of two-layer volume holographic grating (TL-VHG) is
discussed. Expressions of diffraction field when a femtosecond pulse
incidents on the TL-VHG are deduced. Simulation results show when
thickness of the buffer layer increases from 6mm to 11mm or even larger,
one incident pulse splits into double femtosecond pulses with the same
duration and peak intensity, and pulse interval is linearly proportional to the
thickness. The reason of these phenomena is due to the interference of
diffraction waves reconstructed from two gratings and phase shift resulting
from the buffer layer thickness. Time-delay of diffracted double pulses is
explained by group time delay of periodic media. It is shown that the slope
of the pulse interval with respect to the thickness of buffer layer is 2 times
of that of pulse time-delay. Furthermore, we demonstrate it is possible to
control the output double pulses’ duration and pulse interval by varying the
grating thickness.
©2013 Optical Society of America
OCIS codes: (320.5540) Pulse shaping; (050.7330) Volume gratings; (050.1940) Diffraction.
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Received 30 Sep 2013; revised 4 Dec 2013; accepted 6 Dec 2013; published 16 Dec 2013
(C) 2013 OSA
30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031852 | OPTICS EXPRESS 31852
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1. Introduction
Multilayered diffractive optical elements offer powerful opportunity to harness both phase
and amplitude modulation for benefits in diffraction efficiency and beam shaping. Stratified
holographic optical elements (SHOEs), referred to a structure composed of a stack of thin or
thick grating layers interleaved with optically homogeneous buffer layers, are characterized
by specific properties determined by an interference of the reconstructed waves from gratings
and provide possibility to control the shape of selective response. Thin SHOEs, working in
Raman-Nath diffraction regime, possess some similar properties as those of volume
holographic gratings (VHGs), such as a strict angular selectivity that differs qualitatively
from the selectivity of conventional single-sheet volume holograms [1] and high diffraction
efficiency. For example, thin SHOEs composed of two-layer [2], three-layer [3] and fivelayer [4] thin phase gratings have diffraction efficiencies of 67%, >80% and 95%. Thin
SHOEs may be used to design waveguide grating filter [5], waveguide grating coupler [6],
multiple beam generator [7, 8], lidar beam scanner [9], holographic multiplexing and phase
multiplexing [10].
SHOEs with stacks of multiple volume gratings instead of thin gratings are commonly
called stratified volume holographic optical elements (SVHOEs) or multilayer volume
holographic gratings (MVHGs), which operate within the Bragg diffraction regime. Analysis
of MVHG is based on the coupled-wave theory of Kogelnik [11] and Matrix optics. Many
scientists have studied on the theory of MVHG. Yakimovich showed that the characteristics
of angular selectivity have a series of local maxima, width of which is determined by the sum
width of the whole system, and the envelope of the maxima coincides with the selectivity
contour of a single array [12]. A closed-form expression was derived by Vre and Hesselink to
describe the diffraction properties of layered transmission and reflection geometry of MVHG
and they also provide the possible application in dynamic multiple-wavelength filter [13].
Yan applied ultrashort pulse as the illumination to the transmission and reflective MVHGs
and showed that the spectral distributions of diffracted light depend on MVHG parameters
[14, 15]. Zhang et al. proposed a recursion formula for the reflective MVHG and studied its
applications on group velocity controlling [16]. With the development of the MVHG theory,
applications such as wavelength division multiplexers and de-multiplexers, dynamic multiple
wavelength filter have been realized by the MVHG [17].
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Received 30 Sep 2013; revised 4 Dec 2013; accepted 6 Dec 2013; published 16 Dec 2013
(C) 2013 OSA
30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031852 | OPTICS EXPRESS 31853
In this paper, based on TL-VHG, we discuss femtosecond pulse splitting by modulating
the thickness of the buffer layer. The acquired femtosecond double pulses are useful in
coherent control of quantum states and femtosecond micromachining etc [18–21]. In
femtosecond pulse measurement, such as Spectral Phase Interferometer for Direct ElectricalField Reconstruction (SPIDER) and Frequency-Resolved Optical Gating(FROG), double
pulses are also quite necessary [22, 23].
2. The structure of TL-VHG
Fig. 1. Diagram of recording and reconstruction structure of TL-VHG: (a) Recording of VHGs
in two grating layers with two coherent plane waves s and r; (b) Readout of the recorded TLVHG with a femtosecond pulse u(t), and the transmitted and diffracted pulses are denoted by
R(t) and S(t).
Figure 1 is the recording and reconstruction structure of TL-VHG, where a buffer layer is
encapsulated between two volume grating layers providing optical contact. The two grating
layers are photorefractive material, while the buffer layer is an optically homogeneous
material, which provides the phase incursion between neighboring grating layers. Ti (i = 1, 2)
and d are thickness of the two grating layers and buffer layer. n0 is the mean refractive index
of both the grating and buffer materials. VHGs in two grating layers are recorded
simultaneously with two symmetrically incident coherent plane waves s and r through
photorefractive effect, while the buffer layer does not record grating for it is not
photosensitive material. Then the TL-VHG is readout by a femtosecond pulse u(t), the
transmitted and diffracted pulses are represented by R(t) and S(t).
Two VHGs are assumed to extent infinitely in the x-y plane and have the same grating
vector and grating period Λ. Parameters of the two gratings are chosen to make Q =
2πTiλ/(n0Λ2)>>1 to guarantee that they are both VHGs, where λ is the readout wavelength.
Two VHGs are phase gratings and the corresponding refractive index distribution is
 
n = n0 + n1 cos( K ⋅ r )
n1 << n0 .
(1)
Where n1 is the amplitude of refractive index modulation; K is the grating vector, which is
parallel to axis x and the magnitude of which is K = 2π/Λ.
3. Diffraction model of TL-VHG by an ultrashort pulse
Supposing an ultrashort time-domain Gaussian pulse u ( z = 0, t ) = exp(− jω0 t − t 2 / T 2 )
incidents on the input surface of TL-VHG with angle θr, where ω0 is central frequency of
incident pulse. T = Δτ / 2 ln 2 and Δτ is the full width at half maximum (FWHM). The
Fourier transform of the incident pulse is
U (0, ω ) =
1
2π
∞
 u( z = 0, t ) exp( jωt )dt = 2
−∞
T
π
exp[−
T 2 (ω − ω0 ) 2
].
4
(2)
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Received 30 Sep 2013; revised 4 Dec 2013; accepted 6 Dec 2013; published 16 Dec 2013
(C) 2013 OSA
30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031852 | OPTICS EXPRESS 31854
It shows that the incident time-domain pulse consists of different frequency components,
and weight of each component is represented by Eq. (2).
To the ith VHG in the TL-VHG, there have two waves propagating in it, the total field can
be written as
 
 
Ei ( z , ω ) = Ri ( z, ω ) exp(− jk gr ⋅ r ) + Si ( z , ω ) exp(− jk gd ⋅ r ),
(3)
Where Ri(z,ω) and Si(z,ω) are spectral amplitudes of transmitted and diffracted waves in the
ith VHG, kgr and kgd are the corresponding wave vectors. The phase-matching condition for
Bragg diffraction is given by k gd = k gr + K .
Substituting
Eqs.
(1)
and
(3)
into
the
scalar
wave
equation
∇ 2 Ei + k 2 Ei = 0 (k = 2π n / λ ) , using the slowly varying envelop approximation and
ignoring the quadratic terms, the following coupled-wave equations are deduced
Ri ' ( z , ω ) = − jν Si ( z , ω ) Cd Cr ,
(4)
Si ' ( z , ω ) + 2 jξ Si ( z , ω ) = − jν Ri ( z , ω ) Cr Cd .
Where R’(z,ω) and S’(z,ω) represent derivatives to variable z. Cr = cos θ r and Cd = cos θ d .
ν=
π n1
λ (Cr Cd )1/ 2
is
coupling
constant;
ξ=
δ Ti
2Cd
is
off-Bragg
parameter
with
Δλ K 2
. When phase-matching condition k gd = k gr + K is satisfied, ξ = 0.
4π n0
By solving the coupled-wave Eq. (4), the transfer relation of the ith VHG is written in the
following way with [Mi] the transfer matrix,
δ = Δθ ⋅ K sin θ −
 Rir   mi11
 S  = m
 ir   i 21
mi12   Ril 
R 
×   = [ M i ]  il  .

mi 22   Sil 
 Sil 
(5)
Where Rir, Sir and Ril, Sil are spectral amplitudes of the transmitted and diffracted waves on
the right and left hand boundaries of the ith grating, respectively. Where [14]
mi11 = exp(− jξ Ti )[cos( ξ 2 + ν 2 Ti ) +
mi12 = − j
mi 21 = − j
ν
ξ +ν
2
2
ν
ξ 2 + ν2
jξ
ξ +ν 2
2
sin( ξ 2 + ν 2 Ti )],
Cd
exp( − jξ Ti ) sin( ξ 2 + ν 2 Ti ),
Cr
Cr
exp( − jξ Ti ) sin( ξ 2 + ν 2 Ti ),
Cd
mi 22 = exp( − jξTi )[cos( ξ 2 + ν 2 Ti ) −
(6)
jξ
sin( ξ 2 + ν 2 Ti )].
ξ + ν2
The buffer layer can also be represented by a transition matrix [D], the propagation of the
transmitted and diffracted waves over the buffer layer satisfies
2
 R2l 
 R1r 
 S  = [ D] ×  S  ,
 1r 
 2l 
(7)
where
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Received 30 Sep 2013; revised 4 Dec 2013; accepted 6 Dec 2013; published 16 Dec 2013
(C) 2013 OSA
30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031852 | OPTICS EXPRESS 31855
0
1

,
0 exp(−2 jζ d ) 
ζ is a defined detuning parameter in the buffer layer
[ D] = 
ζ =
(8)
k gd − k gr
.
(9)
2
TL-VHG consists of two grating layers and one buffer layer. In the input plane, the
boundary conditions are S (0, ω ) = 0 and R (0, ω ) = U (0, ω ) , relation of the incident and output
complex amplitudes is governed by
 R(T , ω ) 
U (0, ω ) 
 S (T , ω )  = [ M 2 ][ D][ M 1 ]  0  .




(10)
Where R(T, ω) and S(T, ω) are complex spectral amplitudes of the transmitted and diffracted
waves at the output plane of TL-VHG, with T the total thickness of the TL-VHG
T = T1 + d + T2 .
(11)
Inverse Fourier transform of S(T, ω), the instantaneous diffracted field and diffracted
intensity distributions on the output plane are get
∞
S (T , t ) =  S (T , ω ) exp(− jωt )d ω ,
−∞
(12)
2
I S (T , t ) = S (T , t ) .
(13)
From above discussions, we know that the instantaneous diffracted intensity is determined
by the thickness of grating layers and buffer layer, period and refractive index modulation of
two grating layers. Taking photorefractive LiNbO3 crystal as VHG material, in the next
section, we simulate the instantaneous diffracted intensity distribution with respect to the
thickness of buffer layer and discuss the conditions when diffracted double pulses generate.
4. Instantaneous diffracted intensity distribution with respect to the thickness of buffer
layer and the generation of femtosecond double pulses
In simulation, assuming the background refractive index of the grating layers and buffer layer
n0 = 3.314; refractive index modulations of the two VHGs are both n1 = 2 × 10−5; Thickness
and period of both gratings are T1 = T2 = 5.5mm and Λ = 7.3 × 10−6m. Central wavelength
and the corresponding central angular frequency of the incident pulse is λ0 = 1.5μm and ω0 =
4π × 1014rad/s, FWHM of the incident femtosecond pulse is Δτ = 100fs.
Figure 2 is the intensity distribution of the incident pulse when Δτ = 100fs. It shows that
the incident pulse includes only one pulse and the symmetric center of the pulse is t = 0.
Fig. 2. Instantaneous intensity distribution of the incident femtosecond Gaussian pulse when
Δτ = 100fs.
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Fig. 3. Distributions of instantaneous diffracted intensity of TL-VHG when thickness of the
buffer layer changes from (a): 0 mm to 0.8mm, (b): 1mm to 3.5mm.
Figure 3(a) and 3(b) show instantaneous diffracted intensity distributions of the TL-VHG
when thickness of the buffer layer changes from 0mm to 3.5mm. It is found when the
thickness d = 0, the diffracted intensity distribution is a flat-top single pulse with duration Δτ
= 206fs. Comparing to the incident pulse, duration of the temporal diffracted pulse is
broadening, which is due to Bragg selectivity of VHG. When d = 0, the TL-VHG is reduced
to a single thick volume grating with thickness T = T1 + T2. The grating bandwidth is
determined by [24]
ΔλG =
3Λ
(2n0 Λ ) 2 − λ02 .
2 T
(14)
Substituting the defined parameters, we get ΔλG = 26.3nm.
The bandwidth ΔλP of the incident pulse is determined by
ΔωP =
2π c
λ02
Δλ p .
(15)
Where Δωp = 2/T, we get ΔλP = 39.8nm. Gratings that satisfy ΔλG >> ΔλP preserve the
incident pulse spectrum, meanwhile ΔλP >ΔλG perform wavelength selectivity. In our
discussion, ΔλP > ΔλG, so some spectral components in the incident pulse are filtered out.
According to Fourier optics, in time domain, the diffracted pulse is broadened.
From Figs. 3(a) and 3(b), it is seen when thickness of the buffer layer increases from
0.2mm to 3.5mm, central intensity of all diffracted pulses decreases and gets much smaller
with the increasing of the thickness. The front edges of all diffracted pulses are overlapped,
meanwhile the back edges translate along the negative time axis. To a specific incremental
step of buffer layer thickness in Figs. 3(a) and 3(b), the relative translation displacement of
back edges of neighboring diffracted pulses are the same. However, this displacement
increase with the incremental step of the buffer layer thickness.
Moreover, all diffracted pulses are central symmetric and the symmetric center is the
center of diffracted pulse. It is found that centers of all diffracted pulses are positioned at
negative time axis and the translation displacement with respect to the origin of time axis
increases with the increasing of buffer layer thickness.
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Fig. 4. Distributions of instantaneous diffraction intensity of TL-VHG when the thickness of
buffer layer changes in the range of (a): 4mm to 6mm, (b): 7mm to 11mm.
Figure 4(a) and 4(b) show the instantaneous diffracted intensity distributions of the TLVHG when thickness of the buffer layer changes from 4mm to 11mm. It can be seen when
thickness of the buffer layer increases, the central intensity of diffracted pulse decreases
further. When thickness increases to 5.5mm, the central intensity is near zero that one
incident pulse splits into two diffracted pulses. Further increasing the thickness, all diffracted
pulses include two sub-pulses, the first sub-pulses are overlapped while the second sub-pulses
translate along the negative time axis with the increasing of buffer layer thickness. The
translation displacement is in direct proportional to the thickness of buffer layer. Moreover,
all diffracted pulses have the same peak intensity and pulse duration. Duration of one subpulse is 96fs, which is smaller than that of incident pulse, but the whole duration of one
diffracted double pulses is larger than that of incident pulse. The duration of diffracted double
pulses increases with the increasing of the thickness.
Further increasing the thickness of buffer layer from 11mm, it is found that femtosecond
double pulses shown as Fig. 4(b) will emerge again. To a specific thickness, defining pulse
interval as the separation distance between two peaks of sub-pulses, from former discussions,
we know that by modulating the thickness of buffer layer of TL-VHG, one incident pulse can
be split into two diffracted pulses with different pulse intervals.
5. Explanation on the emergence of diffracted double pulses and the relationship of
pulse interval with the thickness of buffer layer
In this section, based on the coupled-wave theory and diffracted field expressions, an
explanation on generation of femtosecond double pulses is given by taking the diffraction of
one spectral component in the input pulse as an example.
The incident femtosecond pulse can be assumed as the coherent superposition of spectral
components with different frequency and weight determined by Eq. (2). One spectral
component is equivalent to a plane wave, when it incidents on the first volume grating of the
TL-VHG, according to the coupled-wave theory of Kogelnik, one diffracted wave and one
transmitted wave with the same frequency as that of the incident plane wave will emerge on
the right output plane of the first grating. When passing through the buffer layer, according to
Eqs. (7)–(9), the diffracted wave will have a relative phase shift to the transmitted wave, and
the phase shift is in direct proportional to the thickness of buffer layer. When they incident on
the second volume grating of the TL-VHG, the diffracted wave will couple with the volume
grating, one new diffracted wave and one new transmitted wave will emerge. The new
diffracted and transmitted waves will output respectively on the transmission and diffraction
directions of the whole TL-VHG. Meanwhile the transmitted wave output from buffer layer
will couple out a new diffracted wave and a new transmitted wave in the second grating,
which will output respectively on the diffraction and transmission directions of the whole TLVHG. Thus, on diffraction direction of the output plane, there has one diffracted field and one
transmitted field, the spectral expressions of these two fields can be deduced by Eqs. (5)–(11),
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S (T , ω ) = ( M 221 M 111 + M 222 M 121e −2 jζ d )U (0, ω ),
(16)
Equation (16) shows that in frequency domain, the diffraction of the whole TL-VHG
includes two waves. Parameters M221, M111, M222 and M121 are irrelevant to the thickness of
the buffer layer d, so the second wave in Eq. (16) has a relative phase shift to the first wave
and the phase shift is in proportional to thickness d. When Eq. (16) is transformed into time
domain, according to Fourier optics, two sub-pulses will emerge and the phase shift in
frequency domain will transform into pulse interval in time domain. As the phase shift is in
direct proportional to the thickness of the buffer layer d, so is the pulse interval.
Diffracted intensity is the coherent superposition of these two sub-pulses. When thickness
of buffer layer is smaller than a specific value, the pulse interval will be smaller than the
FWHM of each sub-pulse. On this condition, these two sub-pulses will overlap and the
superposition result is one pulse with central intensity decreasing. The larger the thickness of
the buffer layer gets, the larger the central intensity decreases. It is consistent with the
evolution of diffracted intensity distributions shown in Figs. 3(a), 3(b) and 4(a). When
thickness of the buffer layer is so larger that the pulse interval between two sub-pulses is
greater than the FWHM of each sub-pulse, two sub-pulses will have no overlapped zone and
will separate with each sub-pulse keeping its own frame. The pulse interval between these
two sub-pulses increases with the increasing of the thickness. This result is consistent with the
distributions of Fig. 4(b).
Figure 5 shows relation of pulse interval with respect to the thickness of buffer layer,
which is fitted by the data acquired from Figs. 3 and 4. It can be seen that the pulse interval is
linearly proportional to the thickness of the buffer layer, just as what we discussed above. It
proves the explanation on generation of double pulses we given here is reasonable. The line
slope of Fig. 5 is βI = 22.5 fs/mm.
Fig. 5. Diagram of pulse interval of diffracted double pulses with respect to the thickness of
buffer layer.
6. Time-delay of diffracted pulse with respect to the time axis
It is seen from Figs. 3 and 4 that the center of diffracted pulse translates along the negative
time axis. In this section, based on group velocity and group time delay, we give an
explanation on the relation of translation displacement with the thickness of buffer layer.
It is well known that a periodic structure exhibits strong group-velocity dispersion and
such a dispersive property can control the time delay of diffracted pulse. The group velocity
of the diffracted pulse through the TL-VHG can be obtained by differentiating the phase shift
per unit length with respect to the angular frequency ω [25]
Vg = l (
∂φ −1
) ,
∂ω
(17)
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Where φ is the phase shift of diffracted pulse through TL-VHG, which can be calculated from
Eqs. (5)–(11). l = T / cos θ d is the propagation length of the diffracted pulse in the TL-VHG.
In our simulation, the grating period is Λ = 7.3μm, accordingly, the incident angle in vacuum
is about 6°, and in the crystal is 2°. It is reasonable to assume l approximately equal to the
thickness T of TL-VHG.
Consequently, time-delay of diffracted pulse through the VHG is
l
∂φ
=
.
(18)
Vg ∂ω
In our TL-VHG structure, the time-delay of the diffracted pulse relative to origin of the
time axis is shown in Fig. 6.
τg =
Fig. 6. Time-delay of diffraction pulse with respect to the thickness of buffer layer of TLVHG.
It is seen from Fig. 6, when the thickness of buffer layer changes from 1mm to 12mm, the
time-delay of all diffracted pulse are negative. Meanwhile, with the increasing of the
thickness of buffer layer, the absolute value of time-delay increases, this result is consistent
with the values shown in Figs. 3 and 4. Moreover, from Fig. 6 it is found that the time-delay
is in direct proportional to the thickness of buffer layer. The absolute slope of the time-delay
line is |βt | = 11.25 fs/mm, which is half of that of pulse interval line shown in Fig. 5. This
indirectly demonstrates that two diffracted sub-pulses are the same and the pulse interval
between them comes from the translation, while the translation is due to the changing of the
thickness of buffer layer.
7. Discussions and conclusions
From former discussions, we know when thickness of the buffer layer of TL-VHG increases
from 6mm, one incident femtosecond pulse will split into two diffracted pulses with the same
duration and peak intensity. Moreover, the pulse interval can be modulated by thickness of
buffer layer. Here, by changing thickness of volume grating, we show duration of diffracted
pulse can be modulated.
Figure 7 shows the instantaneous diffracted intensity distribution of TL-VHG when
thickness of buffer layer is fixed at d = 7mm, while the thickness of two gratings change from
1mm to 6mm. It is seen that the diffracted pulses are femtosecond double pulses too. To a
specific thickness of grating, the two pulses have the same pulse duration and peak intensity.
But to different thickness of grating, the duration and peak intensity of diffracted pulses are
different, which increase with the increasing of the thickness of grating layer. Figure 7 also
shows that pulse interval between diffracted double pulses changes with the thickness of
grating.
Thus, by appropriately choosing the thickness of grating layers and buffer layer, we can
get diffracted femtosecond double pulses with desired pulse interval and pulse duration.
#198606 - $15.00 USD
Received 30 Sep 2013; revised 4 Dec 2013; accepted 6 Dec 2013; published 16 Dec 2013
(C) 2013 OSA
30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031852 | OPTICS EXPRESS 31860
Fig. 7. Distributions of instantaneous diffraction intensity of TL-VHG when thickness of the
buffer layer is fixed at d = 7mm, while the thickness of two gratings changes from 1mm to
6mm.
The ultrashort pulse has a broad spectrum, thus the influence of material dispersion on the
diffraction needs to be discussed. The light dispersion in the TL-VHG occurs at the interface
of air-VHG since the refractive index of the grating layers and buffer layer are the same.
Therefore, once the incident pulse is dispersed, each spectral component maintains its
direction of propagation along the TL-VHG without noticeable change. As a first
approximation we can consider a unique background refractive index for grating layers and
buffer layer, equal to n0 [24]. In Eq. (1), the refractive index modulation n1 fulfills n1<<n0.
Hence n1 can be considered as a constant for the wavelength range of incident pulse.
Furthermore, to the VHG, the dispersion of the grating material will decrease the grating
bandwidth, thus the diffracted and transmitted pulses will broaden in time domain [14].
However, the pulse broadening resulted from dispersion effect also depends heavily on the
duration of input pulse and grating parameters. When duration of input pulse is 100fs and the
grating length is not very large, the broadening from dispersion effect is very small [26].
From two above reasons, we can neglect the influence of grating material dispersion on the
diffraction.
Furthermore, pulse splitting we discussed here is due to the interference of diffracted
pulses, so smaller pulse broadening does not affect the occurrence of pulse splitting.
However, as the duration of input pulse gets smaller or the thickness of the grating material
gets larger, the influence of dispersion effect on the diffraction should be considered. About
the influence of dispersion effect of material, laser and grating parameters on the diffraction
of TL-VHG and MVHG structures is so complicated that it needs another long paper to
compute, we will discuss it in the future.
In conclusion, generation of femtosecond double pulses by modulating the thickness of
buffer layer and grating layer is discussed when a femtosecond pulse incidents on a TL-VHG.
Results show when thickness of grating layer is fixed, while the thickness of buffer layer
changes, diffracted double pulses with the same pulse duration and peak intensity emerges.
The pulse interval of double pulses is in direct proportional to the thickness of buffer layer.
While fixing the thickness of buffer layer and changing the thickness of grating layer,
diffracted double pulses will emerge again, but the duration are modulated. From the coupledwave theory of Kogelnik and matrix optics, we give it a reasonable explanation.
Acknowledgments
This work was financially supported by National Natural Science Foundation of China
(Grants No. 60908007, 11274225, 11174195), Shanghai Leading Academic Discipline
Project (No. S30105) and Shanghai Municipal Education Commission Innovation Project
(12YZ002).
#198606 - $15.00 USD
Received 30 Sep 2013; revised 4 Dec 2013; accepted 6 Dec 2013; published 16 Dec 2013
(C) 2013 OSA
30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031852 | OPTICS EXPRESS 31861