Features of the super prism effect in multilayer dielectric coatings
We demonstrate that the strong change of reflected beam intensity in the
 spectral range of the super-prism effect not allow to use periodic multilayer coatings as
 effective wavelength division multiplexing devices. But using chirped mirrors that are
 one of the key elements...
Gespeichert in:
| Veröffentlicht in: | Semiconductor Physics Quantum Electronics & Optoelectronics |
|---|---|
| Datum: | 2008 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2008
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/119079 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Features of the super prism effect in multilayer dielectric coatings / Yu.O. Pervak, V.M.Onitchuk, V.Yu. Pervak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 4. — С. 345-351. — Бібліогр.: 23 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860257655404101632 |
|---|---|
| author | Pervak, Yu.A. Onitchuk, V.M. Pervak, V.Yu. |
| author_facet | Pervak, Yu.A. Onitchuk, V.M. Pervak, V.Yu. |
| citation_txt | Features of the super prism effect in multilayer dielectric coatings / Yu.O. Pervak, V.M.Onitchuk, V.Yu. Pervak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 4. — С. 345-351. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | We demonstrate that the strong change of reflected beam intensity in the
spectral range of the super-prism effect not allow to use periodic multilayer coatings as
effective wavelength division multiplexing devices. But using chirped mirrors that are
one of the key elements in ultrafast optics can solve this problem with success.
|
| first_indexed | 2025-12-07T18:50:54Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 345-351.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
345
PACS 42.79.Bh, 42.79.Wc
Features of the super prism effect in multilayer dielectric coatings
Yu.O. Pervak*, V.M. Onishchuk and V.Yu. Pervak
Taras Shevchenko Kyiv National University, Radiophysics Department;
e-mail: yupervak@univ.kiev.ua
Abstract. We demonstrate that the strong change of reflected beam intensity in the
spectral range of the super-prism effect not allow to use periodic multilayer coatings as
effective wavelength division multiplexing devices. But using chirped mirrors that are
one of the key elements in ultrafast optics can solve this problem with success.
Keywords: chirped mirror, multilayer coating.
Manuscript received 02.09.08; accepted for publication 20.10.08; published online 11.11.08.
1. Introduction
The polychromatic light incident at an angle onto one of
the prism surfaces is dispersed within the prism; i.e.,
light rays of different wavelengths propagate at different
angles in the prism [1]. Splitting the light by a
conventional prism relies on the dispersion of material.
Due to fact that the changes in the refractive index with
wavelength are rather weak for transparent materials, the
achievable level of the dispersion in multilayer coatings
is limited. Based on optical transparent (dielectric)
materials, created were artificial structures that are
known as photonic crystals [2-6]. They can be used to
obtain much higher spatial dispersion. In certain
conditions, photonic crystals exhibit much higher
dispersion than that of the material of a conventional
prism. Close to the photonic band edge, photonic
crystals exhibit chromatic dispersion caused by gradual
changes of the apparent refractive index, due to the
curvature of the photonic bands. This can be interpreted
as the prism effect, i.e. as a change in diameter of the
iso-frequency lines within the band structure. If the iso-
frequency contours change their shape with the
frequency, the dispersion can be increased by orders of
magnitude. Such ultra-strong dispersive properties called
super-prism effects (SPE) allow us to produce compact
optical filters that are highly attractive for wavelength
division multiplexing (WDM) applications [7-8].
Recently, SPE in one-dimensional thin-film structures
was investigated [9-12]. Four approaches of designing
the structures with a high spatial dispersion were
reported. First, the strong spatial dispersion of periodic
thin-film structures close to the stop-band edge was
reported. Second, it was shown that the wavelength-
dependent penetration depth of double chirped structures
can be used to obtain spatial dispersion. Third, the
coupled-cavity structures employ a wavelength
dependent amount of stored energy to obtain dispersion.
Fourthly, structures that use a combination of a
wavelength-dependent turning point and stored energy
were discussed. However, a problem of WDM intensity
was not considered.
In this paper, we demonstrate that strong changes
in the reflected beam intensity within the spectral range
of the super-prism effect don’t allow us to use periodic
multilayer coatings as effective WDW devices. But
using chirped mirrors can efficiently solve this problem.
2. The periodic dielectric multilayer structures
Let’s consider the stratified infinitive media that
includes infinitive repetition of two-component period
LH. Here L and H are layers of different optical material
with the refractive index nL and nH, thickness dL and dH,
respectively. This stratified media is a one-dimensional
photonic crystal. The optical waves with the
wavelengths close to λ0 = 2(nLdL + nHdH) cannot spread
in this media, in accordance with the theory of photonic
crystals [2-6]. Generally, the full ranges of the forbidden
wavelengths are obtained by methods of Bloch’s waves
or couple-mode theory [6]. However, the edge of a
forbidden gap can be obtained by the method of
equivalent layers [13]. The method of equivalent layers
can be applied after a modification of the stratified
infinitive media. The properties of stratified infinitive
media are not changed, if we assume that media begin
and finish with the layers of one eight wave optical
thickness. This modification can be written as
(LH)m → (0.5LH0.5L)m, where m→∞.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 345-351.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
346
But now the stratified infinitive media can be
considered as one infinitive media with equivalent
refractive index of Ne, its properties and position of
forbidden gap of wavelengths easy can be obtained by
analysis of the characteristic matrix period
,
cossin
sincos
cossin
sincos
cossin
sincos
2221
1211
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
δδη
δ
η
δ
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
δδη
δ
η
δ
×
×
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
δδη
δ
η
δ
=⎥
⎦
⎤
⎢
⎣
⎡
LLL
L
L
L
HHH
H
H
H
LLL
L
L
L
i
i
i
i
i
i
MiM
iMM
(1)
where Lδ , Hδ and Lη , Hη are phase thicknesses and
admittances of layers L and H, respectively. Here
LLLL dN θ
λ
π
=δ cos ; HHHH dN θ
λ
π
=δ cos ;
rrr N θcosη vacχ= for TE wave and rrr N θcosχη vac=
for TM wave; rrr iknN −= ; angles Lθ , Hθ can be
obtained from Snell’s law HHLL nn θ=θ sinsin ; r = L
or H; vacχ – vacuum admittance.
Equivalent admittance is ee Nvacη χ= , where the
equivalent refractive index
1221 MMNe = . (2)
The equivalent refractive index is a real quantity in
the case when 111 ≤M . This condition defines the
passband regions of the multilayer coating. In contrast,
for 111 >M the equivalent refractive index becomes
complex and these wavelength regions are called stop
bands or forbidden gaps. If stratified media is limited in
such a manner that its reflectivity consist of the
alternating high and low reflectivity ranges. Close to
stop bands, Ne has the high dispersion. It is the range of
SPE.
Fig. 1 demonstrates reflectivity and spectral
dependences of the real part of Ne for the multilayer
structure S0(0.5LH0.5L)mS, where S0 –media of light
incidence (air), S – substrate (fused silica, nS ≈ 1.48-
500 nm), L and H – layers with optical thickness λ0/4
(λ0 = 800 nm) from silica dioxide (SiO2) and niobium
oxide (Nb2O5), m = 15 – a number of periods. The angle
of incidence is 30°. The reflectivity was calculated by
the matrix method [13]. Reflection is
∗
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
−
=
CB
CB
CB
CB
R
0
0
0
0
η
η
η
η
, (3)
where
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
η⎥
⎦
⎤
⎢
⎣
⎡
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
S
m
MiM
iMM
C
B 1
2221
1211 , (4)
0η and Sη – admittance of air and substrate,
respectively. The phase change ϕ at the reflection was
calculated by expression [13]
500 600 700 800 900 λ, nm
0
0
Ne
(b)
(a)
10
0,1
140
R, %
80
40
R, %
80
500 600 700 800 900 λ, nm
10
0,1
1
Fig. 1. Reflectivity spectra and spectral dependences of the real
part of Ne for the multilayer structure S0(0.5LH0.5L)15S at the
angle of incidence 30°: (a) s-polarization of light; (b) p-
polarization of light. S0 –air, S – substrate (silica), L and H –
layers with optical thickness λ0/4 (λ0 = 800 nm) from silica
dioxide (SiO2) and niobium oxide (Nb2O5).
( )[ ]
∗∗
∗∗
−
−
=ϕ
CCBB
CBBC
2
0
0
η
ηImtan . (5)
The group delay (GD) is described as
λ
ϕ
⋅
π
λ
=
ω
ϕ
−=
d
d
cd
d
2
GD
2
, (6)
where с = 3·108 m/s is the speed of light.
The group delay dispersion (GDD) is
( ) ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
λ
ϕ
λ+
ω
ϕ
λ
π
λ
−=
ω
ϕ
−=
d
d
d
d
d
d 2
2
GDD 2
2
2
2
2
2
2
. (7)
The material dispersion of SiO2 and Nb2O5 was
considered for all calculations. The Cauchy formula for
the refractive index of SiO2 layers is nL = 1.46 +
(3.35⋅10-3/λ2) + (1.41⋅10-5/λ4) and for Nb2O5 layers is
nH = 2.22 + (2.18⋅10-2/λ2) + (4⋅10-3/λ4), if the unit of λ is
µm. The stop band for TM waves (p-polarization) is
narrower than that for TE waves (s-polarization). Note
that Ne changes from 0 to ∞ and it cannot be physically
interpreted as a refractive index, but it is useful in
analysis and synthesis of the multilayer coatings.
In the case when the angle of incidence is zero, the
real part of Ne is zero in the spectral range from 705.1 to
922.4 nm, and the photonic forbidden gap is 217.3 nm.
When the angle of incidence equals to 30°, the position
and width of the forbidden gap depend on light
polarization. For TE wave, the width of the forbidden
gap is 226.1 nm, and it is expanded from 669.6 to
895.7 nm. For TM wave these values are 190.1, 683 and
873.1 nm, respectively. The longwave range to the right
of the forbidden gap is the first permitted photonic band,
and the shortwave range from to the left of the forbidden
gap is the second permitted photonic band. The spectral
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 345-351.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
347
60
120
0
662 668 674 λ, nm
GD, fs
80
40
R, %
Ne
0.3
0.2
0.1
0
Ne
GD
(a)
0
885 895 λ, nm
GD, fs
R, %
Ne
25
15
5
Ne
GD
(b)
40
80
40
80
100
200
0
675 680 685 λ, nm
GD, fs
80
40
R, %
Ne
0.3
0.2
0.1
0
Ne
GD
(c)
0
860 870 λ, nm
GD, fs
R, %
Ne
20
10
0
Ne
GD
(d)
40
80
40
80
880
Fig. 2. Spectral dependences of R, GD and Ne for the multilayer structure S0(0.5LH0.5L)15S at the angle of incidence 30°. (a),
(b) s-polarization of light; (c), (d) p-polarization of light. Parameters of the structure are identical to those in Fig. 1.
dependences of Ne are different and have high dispersion
close to forbidden gap (Figs. 2 and 3). The multilayer
structures have more periods with the shape of high
reflective band close to rectangular and with higher time
and spatial dispersions. The difference in the type of
dispersion in the first and second permitted photonic
bands causes the different dependences of the group
delay in those bands. GD is the time dispersion, and it is
in proportion to the spatial dispersion. The spatial shift s
is [9-12]
1
constω
βGDGD
−
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
⋅=⋅=
K
gxvs . (8)
Here, vgx is a component of the group velocity
along the x direction, if x is in the plane of incidence and
parallel to layer interfaces. If z is perpendicular to layer
interfaces, then the wave vector K has components only
in the x and z directions and is thus given by K = βx +
Kz [9]. Calculations for the test structures show that the
group velocity vgx is approximately constant with
changing the wavelength, and the group delay is thus
proportional to the spatial shift. This result is not
completely surprising, as vgx is the group velocity along
the layers. Within a WKB-type approximation the spatial
shift and the group delay are exactly proportional, as vgx
is independent of the wavelength [9]. This result
provides physical insight and has practical
consequences. The spatial and the temporal dispersion
are approximately proportional; an existing structure
with temporal dispersion can be modified to obtain
structures with spatial dispersion. The WKB
approximation (quasi-classical approximation in
quantum mechanics) states that if the local wavelength
λ(z), which is linked to the local wave vector K(z),
changes slowly with z, the accumulated phase change
can be calculated by integrating the wave vector K(z)
from the start position z1 to the end position z2 [9]. This
result is exactly true for uniform media as well as for
infinite periodic media, where the wave vector K is
obtained from the Bloch theory and is independent of z.
In according to WKB approximation
θsinω
β1 2
eff
constappr c
n
v
K
gx
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∂
∂
=
=
, (9)
where
[ ]{ }
[ ]{ }∑
∑
−
−
=
i
ii
i
iii
nd
ndn
n 2122
21222
2
eff θsin
θsin
. (10)
In (10) the summation is over all the layers of
multilayer structure and θ is the angle of incidence,
when external media is air.
For the structure S0(0.5LH0.5L)mS, where S0 –
media of incidence (air), S – substrate (silica, nS ≈ 1.48-
500 nm), L and H – layers with the optical thickness λ0/4
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 345-351.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
348
100
200
0
668 669 670 λ, nm
300
GD, fs
80
40
R, % Ne
0.15
0.10
0.05
0
Ne
GD
(a)
100
200
0
894 896 898 λ, nm
300
GD, fs
20
40
R, % Ne
25
20
15
10
Ne
GD
(b)
100
200
0
682 684 λ, nm
300
GD, fs
80
40
R, %
Ne
0.15
0.10
0.05
0
Ne
GD
(c)
0
2
4
6
8
1
0
870 872 λ, nm
GD, fs R, %
Ne
20
10
Ne
GD
(d)
100
200
40
80
874
300
Fig. 3. Spectral dependences of R, GD and Ne for multilayer structure S0(0.5LH0.5L)30S at the angle of incidence
30°. (a), (b) s-polarization of light; (c), (d) p-polarization of light. Parameters of the structure are identical to those
in Fig. 1.
(λ0 = 800 nm) from silica dioxide (SiO2) and niobium
oxide (Nb2O5), it was obtained that vgx = 50 nm/fs at
θ = 30°. The expression (8) permits to calculate the
spatial shift. Our analysis of Figs. 2 and 3 showed that
the increase in layer quantity permits to increase the
dispersion but decreases the spectral range with this
increasing dispersion.
0 15 30 45 60 75 90
0 15 30 45 60 75 90
0 15 30 45 60 75 90
0 8 nd, µm
E2
, r
el
at
iv
e
un
its
4
(a)
1000
0
160
0
0
0
2000
60
(b)
(c)
(d)
Fig. 4. Penetration of electric field through the
multilayer structure of S0(0.5LH0.5L)30S for four
wavelengths: 899 nm (a), 898 (b), 897 (c) and 896 (d).
Light is incident from the left at the angle 30°, and the
structure extends from 0 to 12 µm (optical thicknesses).
It is obvious that SPE in periodic structures is
associated with the wavelength dependence of the wave
penetration in the structure. In a certain sense, Fig. 4
confirms this opinion. In Fig. 4, penetration of electric
field through the multilayer structure S0(0.5LH0.5L)30S
is shown for four wavelengths.
Essential imperfection of the periodic structure is a
strong change of the reflectivity in the spectral range of
SPE. Another imperfection is nonlinearity of the spectral
dependence of GD and spatial shift. Both imperfections
can be avoided, if using the chirped mirrors for
demultiplexing.
3. A chirped mirrors
A chirped mirror is a dispersive optical interferential
coating usually designed by optimizing the initial
multilayer design [15-22]. A chirped mirror is
characterized by a certain value of the GDD, the second
derivative of the phase shift on reflection with respect to
the angular frequency. A chirped mirror can provide the
broadband spectrum with support, broader as for prism
and grating pairs, in addition chirped mirror offers
control of the third- and higher-order dispersions and
higher efficiency (reflectivity) together with better beam
stability. In general, the mirror GDD should compensate
the material (through which the initially short pulse
passes) or the (nonlinear) pulse chirps so that the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 345-351.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
349
1
0
0 20
nd
,
in
u
ni
t
λ 0
/4
40 60
(a)2
3
Number of layer
40
0
1200 1600
(b)
λ, nm
R, %
80
1400
2200
0
1500 1540
- -2⋅ 104
(c)
λ, nm
GD, fs
400
1520
-1⋅104
1
GDD, fs2
40
0
1535 1545
(d)
λ, nm
R, %
80
1540
2
1
0
0
0
0
GD_phi_TE
GD_phi_TM
GDD_phi_TE
GDD_phi_TM4
3
2
200
0
1500 1540
(e)
λ, nm
GD, fs
400
1520
1 GDD, fs2
-1⋅104
-2⋅104
-4⋅103
4
3
2
200
0
1480 1520
(f)
λ, nm
GD, fs
400
1500
1
GDD, fs2
-1⋅104
-3⋅104
0
600
-5⋅104
Fig. 5. Structure of the chirped mirror and spectral dependences of its reflectivity, GD and GDD at various angles of incidence:
a) optical thicknesses of layers, numeration of layers begins from external media (air); b) reflectivity spectrum at normal
incidence; c) spectral dependences of GD and GDD for normal incidence; d) reflectivity spectrum at the angle of incidence 20°:
s- (1) and p- (2) polarizations of light; e) spectral dependences of GD and GDD at the angle of incidence 10°: 1 – GD,
s-polarization, 2 – GD, p-polarization, 3 – GDD, s-polarization, 4 – GDD, p-polarization; f) spectral dependences of GD and
GDD at the angle of incidence 20°: 1 – GD, s-polarization, 2 – GD, p-polarization, 3 – GDD, s-polarization, 4 – GDD,
p-polarization.
residual dispersion fluctuations are acceptably small in
all the relevant spectral range. Usually, during design
optimization, unavoidable residual oscillations of GDD
drop to a low level. The unavoidable GDD oscillations
can broaden the pulse and lead to energy transfer from
the initial single pulse to satellites. The period of the
oscillations in the spectral domain determines the
position of the satellite in the temporal domain, and the
amplitude of these oscillations determines the amount of
energy which transfered to the satellite(s).
For aims of demultiplexing, most of the problems
related with chirped mirrors are not essential, and
technique of chirped mirror creation is useful to obtain
multilayer structures with a high dispersion. We found
the nonperiodic structure that has a high dispersion and
linear dependence of GD, optimization procedures are
described in [15, 18]. The structure consists of 77
alternating layers of SiO2 and Nb2O5 on the silica
substrate. All odd layers are Nb2O5. The optical
thicknesses of layers are shown in Fig. 5a. Most of the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 345-351.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
350
layers have the optical thickness close to λ0/4 (λ0 =
1550 nm), a thickness of 17-th layer is 17.6 nm, 33-
rd layer – 86.5 nm, 77-th layer – 1177 nm. The structure
looks similar to the classical Bragg stack, it doesn’t
consist of the layers with a thickness close or multiple of
λ0/2, and nevertheless the sharp peak of transmission is
obtained in the high reflective spectral range
(Figs. 5b, d). The position of this peak is 1575.7 nm at
normal incidence, 1545.9 nm for s-polarized light at the
angle of incidence 20° and 1542 nm. This important
result permits to assume that the narrowband filter can
be created not only on the base of Fabry-Perrot
structures.
GD behaves linearly within the spectral range from
1530 to 1570 nm at normal incidence (Fig. 5c). Using its
CM at oblique incidence allows to receive almost linear
spectral dependence of GD in more shortwave range.
Also GD behaves linearly within the spectral range from
1520 to 1560 nm at the angle of incidence 10°
independently of polarization (Fig. 5e). GD behaves
linear in spectral range from 1500 to 1540 nm at the
angle of incidence 20° only for p-polarization (Fig. 5f).
The x component of the group velocity calculated using
(9) and (10) is 17.37 and 34 nm/fs for the angles of
incidence 10° and 20°, respectively. To obtain the higher
group velocity, one has to use the bigger angle of
incidence. The linearity of GD provides the high
negative GDD within the spectral range from 1500 up to
1570 nm.
As in the case of periodic structures, the high
dispersion of chirped mirror is associated with
wavelength dependence of the wave penetration in the
structure. In Fig. 6, penetration of electric field through
the multilayer structure of chirped mirror is shown for
four wavelengths. The longwave light penetrates into the
structure of chirped mirror deeper. Also, it is worth
noting that the certain dispersive mirror utilizes a
resonance effect, which can bring about 50 % in addition
to the main value of GDD obtained by the penetration
depth effect [23].
0 8 d, µm
E2
, r
el
at
iv
e
un
its
4
(a)
(b)
(c)
(d)
1
0.01
0.1
0.01
1
0.1
100
1
10
105
103
104
12
Fig. 6. Penetration of electric field through the multilayer
structure of chirped mirror that is shown in Fig. 5a for four
wavelengths: 1560 nm (a), 1540 (b), 1520 (c) and 1500 (d).
Light is incident from the left at the angle 20°, and the
structure extends from 0 to 16.5 µm (physical thicknesses).
4. Conclusion
The periodic multilayer structures allow us to achieve a
high dispersion within the spectral range of several
nanometers. The increase in dispersion is possible when
essentially increasing the number of layers. Essential
drawbacks of the periodic structures demonstrate a
strong change in the reflectivity and nonlinearity of the
spectral dependence of GD and spatial shift in the
wavelength range of SPE. Both drawbacks can be
avoided by using demultiplexing the chirped mirrors.
References
1. M. Born, E. Wolf, Principles of Optics. Pergamon
Press, Oxford, 1984.
2. J.D. Joannopoulos, R.D. Meade, and J.N. Winn,
Photonic Crystals. Princeton University Press,
Princeton, 1995.
3. S.G. Johnson, J.D. Joannopoulus, Photonic
Crystals: The Road from Theory to Practice.
Kluwer Academic Publ., 2002.
4. K. Sakoda, Optical Properties of Photonic
Crystals. Springer, Berlin, Heidelberg, 2001.
5. K. Busch, S. Lolkes, R.B. Wehspohn, N. Foll (ed.),
Photonic Crystals. Willey, New York, 2004.
6. K. Inoue, K. Ohtaka (ed.), Photonic Crystals.
Springer, 2004.
7. R. Marz, S. Burger, S. Goika, A. Farchel, C.
Hermann, C. Jamois, D. Michaelis, and K. Wandel,
Planar high index-contrast photonic crystals for
telecom applications, In: Photonic Crystals.
Advances in Design, Fabrication, and Charac-
terization. Wiley-VCH Verlag GmbH&Co.KGaA,
Weinheim, p. 308-328, 2004.
8. B. Momeni, A. Adibi, Optimization of photonic
crystal demultiplexers based on the superprism
effect // Appl. Phys. B 77, p. 555-560 (2003).
9. M. Gerken and D.A.B. Miller, Multilayer thin-film
structures with high spatial dispersion // Appl. Opt.
42, p. 1330-1345 (2003).
10. M. Gerken and D.A.B. Miller, Wavelength
demultiplexer using the spatial dispersion of
multilayer thin-film structures // IEEE Photon.
Technol. Lett. 15, p. 1097-1099 (2003).
11. M. Gerken, Wavelength multiplexing by spatial
beam shifting in multilayer thin-film structures //
Electrical Engineering Ph.D. Dissertation,
Stanford Univ., Stanford, Calif., 2003.
12. M. Gerken, D.A.B. Miller, Limits on the
performance of dispersive thin-film stacks // Appl.
Opt. 44, No.16, p. 3349-3357 (2005).
13. H.A. MacLeod, Thin-Film Optical Filters. Institute
of Phys. Publish., Philadelphia, Pa., 2001.
14. N. Matuschek, F.X. Kärtner, and U. Keller, Theory
of doublechirped mirrors // IEEE J. Sel. Top.
Quantum Electron. 4, p. 197-208 (1998).
15. A. Fernandez, A. Verhoef, V. Pervak, G. Lermann,
F. Krausz, A. Apolonski, Generation of 60-nJ sub-
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 345-351.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
351
40-fs pulses at 70 MHz repetition rate from a
Ti:sapphire chirped pulse-oscillator // Appl. Phys. B
87, p. 395-398 (2007).
16. R. Szipöcs, K. Ferencz, C. Spielmann, and
F. Krausz, Chirped multilayer coatings for
broadband dispersion control in femtosecond lasers
// Opt. Lett. 19, p. 201-203 (1994).
17. V. Pervak, S. Naumov, G. Tempea, V. Yakovlev,
F. Krausz, A. Apolonski, Synthesis and manu-
facturing the mirrors for ultrafast optics // Proc.
SPIE 5963, p. 490-499 (2005).
18. V. Pervak, A.V. Tikhonravov, M.K. Trubetskov,
S. Naumov, F. Krausz, A. Apolonski, 1.5-octave
chirped mirror for pulse compression down to sub-
3 fs // Appl. Phys. B 87, p. 5-12 (2007).
19. G. Steinmeyer, G. Stibenz, Generation of sub-4-fs
pulses via compression of a white-light continuum
using only chirped mirrors // Appl. Phys. B 82,
p. 175-181 (2006).
20. G. Steinmeyer, Femtosecond dispersion compen-
sation with multiplayer coatings: toward the optical
octave // Appl. Opt. 45, p. 1484-1490 (2006).
21. N. Matuschek, L. Gallmann, D.H. Sutter,
G. Steinmeyer, U. Keller, Back-side-coated chirped
mirrors with ultra-smooth broadband dispersion
characteristics // Appl. Phys. B 71, p. 509-522
(2000).
22. F.X. Kärtner, N. Matuschek, T. Schibli, U. Keller,
H. A. Haus, C. Heine, R. Morf, V. Scheuer, M.
Tilsch, and T. Tschudi, Design and fabrication of
double-chirped mirrors // Opt. Lett. 22, p. 831-833
(1997).
23. V. Pervak, C. Teisser, A. Sugita, S. Naumov,
F. Krasz, A. Apolonski, High-dispersive mirrors for
femtosecond lasers // Optics Express 16, No.14,
p. 10220-10233 (2008).
|
| id | nasplib_isofts_kiev_ua-123456789-119079 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T18:50:54Z |
| publishDate | 2008 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Pervak, Yu.A. Onitchuk, V.M. Pervak, V.Yu. 2017-06-03T05:11:56Z 2017-06-03T05:11:56Z 2008 Features of the super prism effect in multilayer dielectric coatings / Yu.O. Pervak, V.M.Onitchuk, V.Yu. Pervak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 4. — С. 345-351. — Бібліогр.: 23 назв. — англ. 1560-8034 PACS 42.79.Bh, 42.79.Wc https://nasplib.isofts.kiev.ua/handle/123456789/119079 We demonstrate that the strong change of reflected beam intensity in the
 spectral range of the super-prism effect not allow to use periodic multilayer coatings as
 effective wavelength division multiplexing devices. But using chirped mirrors that are
 one of the key elements in ultrafast optics can solve this problem with success. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Features of the super prism effect in multilayer dielectric coatings Article published earlier |
| spellingShingle | Features of the super prism effect in multilayer dielectric coatings Pervak, Yu.A. Onitchuk, V.M. Pervak, V.Yu. |
| title | Features of the super prism effect in multilayer dielectric coatings |
| title_full | Features of the super prism effect in multilayer dielectric coatings |
| title_fullStr | Features of the super prism effect in multilayer dielectric coatings |
| title_full_unstemmed | Features of the super prism effect in multilayer dielectric coatings |
| title_short | Features of the super prism effect in multilayer dielectric coatings |
| title_sort | features of the super prism effect in multilayer dielectric coatings |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119079 |
| work_keys_str_mv | AT pervakyua featuresofthesuperprismeffectinmultilayerdielectriccoatings AT onitchukvm featuresofthesuperprismeffectinmultilayerdielectriccoatings AT pervakvyu featuresofthesuperprismeffectinmultilayerdielectriccoatings |