Download Analysis of Tilted Grating Etalon for DWDM Demultiplexer Sommart Sang-Ngern, Non-member

Analysis of Tilted Grating Etalon for DWDM Demultiplexer
71
Analysis of Tilted Grating Etalon for DWDM
Demultiplexer
Sommart Sang-Ngern, Non-member and Athikom Roeksabutr, Member
ABSTRACT
This paper theoretically analyses the characteristic of a Tilted Grating Etalon (TGE) in the first order coupled wave formalism for the consideration of
DWDM (Dense Wavelength Division Multiplexing)
demultiplexer. This theory could be used to investigate the characteristic of shifting Bragg wavelength
on the effect of device structure parameters such as
etalon thickness (L), refractive index (n), grating pe0
riod (Λ), the angle between z axis and z axis (Φ)
and the variation of incident angle. The results will
be useful for consideration of device design as well as
determination of the suitable operating conditions.
riod, etalon thickness and the transmission spectral
as the angle of incident wave (incident angle).
2. TILTED GRATING ETALON (TGE)
In the order to understand the operating principle
of the TGE, the characteristic of both tilted grating
and FP needs to be reviewed in combination.
Keywords: Tilted Grating Etalon, Bragg Grating,
Etalon
1. INTRODUCTION
In the recent years, the demand of bandwidth in
optical network has been significantly increasing because of the growing of high-speed data communications. One system called DWDM has been improved
in order to support all the bandwidth expansion. A
tunable optical filter is a key device in such DWDM
systems. Since the selective filters are one of the key
components, many techniques have been researched.
For examples they include, a Fiber Bragg Grating
(FBG) [1]-[2], Fabry-Perot Ti-diffused LiNbO3 [3]
and Tilted grating structure [4]. The latter one was
first demonstrated in 1999 and it is one of our interesting topics. Fig. 1 illustrates the structure of
the Tilted Grating Etalon (TGE) that is formed by
Fabry-Perot etalon (FP) with tilted grating inside. In
TGE, the direction is the propagation wave vector of
grating inside the etalon. This direction of the period
index modulation is not parallel to the -axis normal
to the boundaries. The investigation of such a device
when the internal angle of reflected light in the etalon
is varied was reported in ref. [4]. However, it lacks of
the intensive details. In this paper, we report the informative investigation on the characteristic of Tilted
Grating Etalon (TGE) on the effect of other parameters such as the average refractive index, grating peEL5R40: Manuscript received on August 12, 2004 ; revised
on February 22, 2005.
The authors are with Optical Communication Research Lab
Department of Telecommunication Engineering, Mahanakorn
University of Technology 51 Cheum Sampan Rd., Nong Chok ,
Bangkok , Thailand 10530 Tel: (662)-988-3655 EXT. 271, Fax:
(662)-988-4040, E-mail: [email protected].
Fig.1:
(TGE).
The structure of Tilted Grating Etalon
Let A0 , A1 denote the slowly varying amplitude
of incident (forward mode) wave and diffracted wave
π
(backward mode), respectively. βbragg = Λ
is the
Bragg wave vector, where Λ is the grating period.
The total field of the incident wave inside the tilted
grating can be expressed as
E(z)
−
= Ef+orward + Ebackward
[−iβz]
= A0 e
(1)
[−i(β−2βbragg )z]
+ A1 e
Consider the same notation, the coupled-wave equations can be formed as [5]
dA0
dz
dA1
dz
= −iKA1
=
(2)
e 0
2iξA1 + iKA
where
K=
K0
cos θ
(3)
72 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.3, NO.1 FEBRUARY 2005
(4)
(5)
2nΛ
cos (Φ − θ)
(6)
λ
εsi is dielectric permittivity of sil-
χ=
where:
ica. (εsi = 1.5),
n is average refractive index,
θ is the internal angle,
0
Φ is the angle between z axis and z axis,
λ is wavelength,
K0 is coupling coefficient for period grating
seen at θ = 0.
It is worth noting that the coupling between A0
and A1 is not symmetrical which appears somewhat
uncommon for a pure index coupling first order modulation. The transfer function in terms of transmission coefficient for the incident wave (Ti ) in TGE can
be found as:
Ti =
Ωi exp (−iβbragg L)
Ωi cosh (Ωi L) + iξi sinh (Ωi L)
3. THE CHARACTERISTICS OF TGE ON
THE EFFECT OF DEVICE STRUCTURE
To investigate the characteristic of the TGE,
Equation (10) will be used with the variation of the
physical parameters of the device. The simulation
is performed as a function of wavelength to examine
the effect of device structures such as etalon thickness
(L), refractive index (n) of grating, and grating period (Λ). The initial practical parameter values used
in this work are as follows [4]: the angle between
0
z axis and z axis (Φ) is π6 , refractive index outside
etalon (n0 ) is 1, average refractive index of grating
(n) is 3.5, grating period (Λ) is 250 nm, internal angle
(θ) is 0.2 degree, and coupling coefficient for period
grating K0 is L3
3. 1 Effect of etalon thickness (L)
Influence of etalon (L)
0.9
0.8
(7)
In the same way, the transmission coefficient for the
diffracted wave (Tr ) can be found by replacing θ =
−θ in to equations (2)-(6). Finally, the expression of
transmission coefficient for the diffracted wave (Tr )
can be obtained as
0.7
Transmission Spectral
nΛ
λ cos Φ − nΛ cos θ
nΛ
πλ(χ − 1)
ξ=
2nΛ2
λ cos Φ − nΛ cos θ
e = πεsi
K
2nλ
0.6
0.5
0.4
L= 30 um
L= 35 um
L= 40 um
L= 45 um
L= 50 um
0.3
0.2
Ωr exp (−iβbragg L)
Tr =
Ωr cosh (Ωr L) + iξr sinh (Ωr L)
where
Ωi = Ωr =
r
e − ξ2
KK
(8)
(9)
The TGE is described as a Fabry-Perot etalon
modified by the internal tilted grating. The overall intensity transfer function of TGE can be derived
by taking into account the transmission coefficient Ti
and Tr . The calculation is therefore similar to that
of the usual Airy function for a FP [6] except for the
particular form taken here by internal losses. As a
result, the intensity transfer function (Transmission
spectral) can be written as
T =
where
Ψ=
T0
1 + Ψ sin2 ( Φ2 )
(10)
1.56
1.565
1.57
1.575
Wavelength (um)
1.58
1.585
1.59
-6
x 10
Fig.2: Relationship between the Transmission of
TGE and the wavelength on the etalon effect (L) .
Fig.2 shows the transmission spectral of TGE as
a function of wavelength in the range of 1555-1590
nm when the etalon thickness is varied from 30 to 50
nm. The difference between peak and valley of transmission light is reduced as increasing etalon length
and wavelength. The peak wavelength is finely either
up-shifted or down-shifted whereas the free spectral
range (FSR) seems to be reduced as the etalon length
is increased. The etalon length does not have much
effect on the finesse of the etalon such that the minimum output light cannot easily be suppressed.
3. 2 Effect of average refractive index (n)
4Rref τ 2
(11)
2
(1 − Rref τ 2 )
2
τ 2 = |Ti Tr |
(12)
2
T0 =
0.1
1.555
2
(1 − Rref ) |Ti |
2
(1 − Rref τ 2 )
(13)
where Rref = [(n − n0 )/(n + n0 )]2 is the intensity
reflection coefficient
Fig.3 shows the transmission spectral of TGE as
a function of wavelength in the same range when the
average refractive index of grating in the etalon is
varied from 3.50 to 3.58. As can be seen from the
figure, when increasing the index, the starting point
of the first transmission optical peak is up-shifted.
For example, for n = 3.56 the optical peak starts to
transmitted at the wavelength of about 1569 nm but
Analysis of Tilted Grating Etalon for DWDM Demultiplexer
73
Influence of Grating Period
0.9
0.8
0.7
Grating Period = 257 nm
Grating Period = 256 nm
Grating Period = 255 nm
Grating Period = 254 nm
Grating Period = 253 nm
0.6
Transmission Spectral
for n = 3.58, the first optical peak appears at the
wavelength of about 1577 nm. Besides, the output
light at the wavelength below this starting point is
totally suppressed, i.e. no output light. This property
is very interesting. If the appropriate refraction of
grating is chosen, the desired wavelength in DWDM
can be selected. It should be noted that the FSR of
the etalon tends to be extended as the wavelength
increases.
0.5
0.4
0.3
0.2
Influence of Refractive index (n)
0.1
0.9
n = 3.50
n = 3.52
n = 3.54
n = 3.56
n = 3.58
0.8
Transmission Spectral
0.7
0
1.555
1.56
1.565
1.57
1.575
Wavelength (um)
1.58
1.585
1.59
-6
x 10
0.6
Fig.4: Relationship between the Transmission of
TGE and the wavelength on the grating period effect
(Λ) .
0.5
0.4
0.3
0.2
0
1.555
1.56
1.565
1.57
1.575
Wavelength (um)
1.58
1.585
1.59
x 10
-6
Fig.3: Relationship between the Transmission of
TGE and the wavelength on the average refractive index effect (n) .
3. 3 Effect of grating period (Λ)
Fig.4 shows the transmission spectral of TGE as
a function of wavelength in the same range when the
grating period is varied from 253 to 257 nm. The
property comes from the variation of grating period
is similar to the previous. When increasing the grating period the starting point of the first transmission
optical peak is up-shifted. For example, for Λ = 253
nm the optical peak starts to transmitted at the wavelength of about 1562 nm but for Λ = 257 nm, the first
optical peak appears at the wavelength of about 1587
nm.
As the grating period changes of 4 nm, the start
transmission optical peak is up-shifted for about 25
nm. This implies that the optical signal in DWDM
system can be finely selected by the variation of grating period. In comparison with the case of varying
refractive index in which small index variation gives
large range of start optical peak difference, the change
in grating length gives more feasible in practical control of desired wavelength.
3. 4 Effect of the angle between z axis and z
axis (Φ)
from the variation of the angle can be seen from the
figure, when increasing the angle, the starting point
of the first transmission optical peak is up-shifted.
For example, for Φ = 0.46 rad the optical peak starts
to transmitted at the wavelength of about 1585 nm,
but for Φ = 0.47 rad, the optical peak appears at
the wavelength of about 1572 nm, 1576 nm and 1586
nm, respectively. It should be noted that the FSR
of the TGE tends to be extended as the wavelength
is similar to the previous. By choosing appropriate
angle of the TGE structure, the desired wavelength
as in DWDM system.
We also examined the transmission spectral as the
angle of incident wave or incident angle. The result is
interesting. Additionally, this paper will discuss the
transmission spectral as the incident angle in section
4.
Influnce of the angle (z,z')
0.9
0.8
0.7
Transmission Spectral
0.1
0.6
the angle (z,z') = 0.54 rad.
the angle (z,z') = 0.52 rad.
the angle (z,z') = 0.50 rad.
the angle (z,z') = 0.48 rad.
the angle (z,z') = 0.46 rad.
0.5
0.4
0.3
0.2
0.1
0
1.555
1.56
1.565
1.57
1.575
Wavelength (um)
1.58
1.585
1.59
-6
x 10
0
Fig.5 shows the transmission spectral of TGE as
a function of wavelength in the same range when the
0
angle between z axis and z axis (Φ) is varied from
o
0.46 rad (26 ) to 0.54 rad (31o ). The property comes
Fig.5: Relationship between the Transmission of
TGE and the wavelength on the angle between z axis
0
z and axis (Φ).
74 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.3, NO.1 FEBRUARY 2005
0.8
0.8
0.7
0.7
0.6
0.6
Transmission Spectral
Transmission Spectral
4. TRANSMISSION SPECTRAL AS THE
ANGLE OF INCIDENT WAVE (INCIDENT ANGLE)
0.5
Incident angle
0 degree
0.4
0.3
0.2
Incident angle
10 degree
0.4
0.3
0.2
0.1
0
1.35
0.5
0.1
1.4
1.45
1.5
Wavelength (um)
1.55
0
1.35
1.6
1.4
1.45
1.5
Wavelength (um)
−6
x 10
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.4
Incident angle
20 degree
0.3
0.2
0.5
Incident angle
30 degree
0.4
0.3
0.2
0.1
0
1.35
0.1
1.4
1.45
1.5
Wavelength (um)
1.55
0
1.35
1.6
1.4
1.45
1.5
Wavelength (um)
−6
x 10
(c)
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.4
Incident angle
40 degree
0.3
0.2
1.6
−6
x 10
0.5
Incident angle
50 degree
0.4
0.3
0.2
0.1
0
1.35
1.55
(d)
Transmission Spectral
Fig.6 shows the simulation model for investigating
the characteristic of TGE for the variation of the incident angle. The simulation is performed as a function
of wavelength in the range of 1350 – 1600 nm when
the incident angle is varied from 0-50 degree. The
physical parameter values used in this simulation are
the etalon thickness is 25 um, grating period is 250
nm, average refractive index is 3.5, refractive index
0
outside etalon is 1, the angle between z axis and z
axis is 0.645 rad, internal angle is 0.2 degree and coupling coefficient for period grating is 0.2/L.
Fig.7 shows the transmission spectral of TGE as
a function of wavelength in the range of 1350-1600
nm when the incident angle is varied 0-50 degree.
The TGE can act as a variable band stop wavelength
as the incident angle varied. In Fig.7(a), the incident angle is 0 degree which leads to the band stop
(center bragg wavelength [7]) at the wavelength of
about 1399 nm. As can be seen from the Fig.7(b) to
Fig.7(f), when increasing the incident angle, the center bragg wavelength is up-shifted. For Fig.7(c) the
center bragg wavelength at the wavelength of about
1490 nm but for Fig.7(e) the center bragg wavelength
at the wavelength of about 1557 nm. Furthermore,
the relation between the center bragg wavelength and
the incident angle is illustrated in Fig.8.
Fig.8 shows the relationship between the center
bragg wavelength of transmission of TGE shift and
incident angle. In Fig.8, as the incident angle changes
of 5 degree, the center bragg wavelength is up-shifted
for about 23 nm. These results will be useful for
the design and consideration of a wavelength demultiplexer in DWDM system.
Fig.9 presents transmission spectral of the Fabry
Transmission Spectral
Fig.6: The simulation model of transmission spectral as the incident angle .
1.6
−6
x 10
(b)
Transmission Spectral
Transmission Spectral
(a)
1.55
0.1
1.4
1.45
1.5
Wavelength (um)
(e)
1.55
1.6
−6
x 10
0
1.35
1.4
1.45
1.5
1.55
Wavelength (um)
1.6
1.65
1.7
−6
x 10
(f)
Fig.7: Relationship between the transmission of
TGE and wavelength on the incident angle: (a) 0
degree, (b) 10 degree, (c) 20 degree, (d) 30 degree, (e)
40 degree and (f ) 50 degree
Perot etalon without grating (general Fabry Perot)
compared to that of TGE. The numerical parameters are the same as in section 3 except etalon thickness is 15 um. It can be seen from the figure that
peak-to-valley ratio and FSR of general Fabry Perot
transmission spectral are exactly constant. These results are the same as in theory of Fabry Perot etalon
[8]. On another hand, peak-to-valley ratio and FSR of
TGE transmission spectral are variable. For example,
from wavelength of about 1350 nm to about 1480 nm,
peak-to-valley ratio slightly increases. In the same
wavelength duration, FSR slightly decreases. From
wavelength of 1550 nm to 1600 nm peak-to-valley ratio trends decrease while FSR slightly increases. The
transmission spectral is zero from wavelength of 1480
nm to 1550 nm.
It could be seen from figures 2, 3, 4, 5, and 7 peakto-valley ratio and FSR of TGE transmission spectral
are adjustable. These results indicate that it is pos-
Analysis of Tilted Grating Etalon for DWDM Demultiplexer
75
dition, it is possible to build grating etalon components by placing acoustic waves into the etalon area
of Fabry Perot etalon.
1600
Center Bragg Wavelength (nm)
1550
References
1500
1450
1400
1350
0
5
10
15
20
25
30
Incident angle (degree)
35
40
45
50
Fig.8: The relation between the center bragg wavelength and the incident angle .
1
0.9
0.8
Transmission Spectral
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.35
[1] L. R. Chen, “Design of flat-top bandpass filters
based on symmetric multiple phase-shifted longperiod fiber gerating’, Opt. Commun., vol.205,
pp.271-276, May 2002.
[2] C. S. Goh, S. Y. Set and K. Kikuchi, “Widely
Tunable Optical Filters Based on Fiber Bragg
Grating”, IEEE Photon. Technol. Lett., vol.14,
pp.1306-1308, Sep. 2002.
[3] T. Saito, Y. Endo, M. Yamamoto, K. Oyamada,
“Study on Fabry-Perot Ti-diffused LiNbO3 optical waveguide filter”, Technical Report of IEICE,
pp.7-11, July 1998.
[4] Y. Boucher, T.Fessant, A. V. Uskov, “Angular
and spectral filtering in tilted-grating structures”,
IEE Proc. Optoelectronics, vol.146, pp.35-38, Feb.
1998.
[5] T. K. Gaylord, M. G. Moharam, “Analysis and
application of optical diffraction by grating”,
Proc. IEEE, vol.73, no.5, pp.894-937, 1985.
[6] Ammon Yariv, “Optical Electronics”, 3rd Edition., pp.88-95, CBS College Publishing, 1985.
[7] K. O. Hill, G. Meltz, “Fiber Bragg Grating Technology Fundamentals and Overview”, J. Lightwave Technol., vol.15, pp.1263-1276, 1997.
[8] E. Hecht, “Optics”, 3rd Edition., pp.409-418, Addison Wesley, 1998.
Fabry Perot etalon without grating
Tilted Grating Etalon (TGE)
1.4
1.45
1.5
Wavelength (um)
1.55
1.6
-6
x 10
Fig.9: The transmission spectral of Fabry Perot
etalon without grating and TGE.
sible to adjust the parameters to build grating etalon
components for DWDM demultiplexers.
Sommart Sang-Ngern received the
B.Eng. and M.Eng. degrees in Electrical Engineering (Telecommunication)
from Mahanakorn University of Technology, Bangkok, Thailand, in 1997 and
2001, respectively. He is currently the
lecturer of Department of Telecommunication Engineering at Mahanakorn University of Technology.
His research
interests cover fiber optic component,
fiber bragg grating (FBG), optical ring
resonator, and nonlinear optics.
5. CONCLUSION
The investigation of the characteristic of a Tilted
Grating Etalon (TGE) on the effect of varying physical structures such as etalon thickness, average refractive index, grating period, the angle between axis
and axis (grating angle) and incident angle, has been
intensively reported. If the parameters of device
structure are appropriately chosen, the device can be
used as the DWDM demultiplexer for photonic networks or optical communication systems. The same
scheme can also be applied to spectral filtering in Integrated Optoelectronics (IO). This proposed structure can perform narrow channel spacing, which can
be a promising candidate for DWDM system. In ad-
Athikom Roeksabutr received the
B.Eng. degree from King Mongkut’s
Institute of Technology, Ladkrabang,
Thailand, in 1984, the M.S. (Electrical) degree from the Florida Institute
of Technology, Melbourne, FL, USA, in
1989, and the Ph.D. degree from the
school of Electrical Engineering, University of New South Wales, Australia, in
1997. Currently he is Vice-president and
Dean of Faculty of Engineering at Mahanakorn University of Technology. His research interests cover
fiber optic component, optical communication system, and
acousto-optic fiber devices.