Analysis of propagation of modulated optical signal in an integrated optic envi

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME
148
ANALYSIS OF PROPAGATION OF MODULATED OPTICAL SIGNAL IN
AN INTEGRATED OPTIC ENVIRONMENT
Yogesh Prasad K R 1
, Srinivas T 2
, Ramana D V 3
1
Department of Electrical Communications Engineering, Indian Institute of Science,
Bangalore-560012, India
2
Department of Electrical Communications Engineering, Indian Institute of Science,
Bangalore-560012, India
3
Communications Systems Group, ISRO Satellite Centre,
Vimanapura Post, Bangalore-560017, India
ABSTRACT
Propagation of an optical signal along a waveguide is traditionally analyzed on the
assumption that the signal is monochromatic. However, when an optical signal is modulated, power
gets distributed among several frequency components generated by the process of modulation.
Dispersion equation of a slab waveguide has been solved numerically to study the mode profile of a
modulated optical signal. Also, propagation of a modulated optical signal along Integrated Optic
elements has been analyzed in terms of phase variations experienced by its frequency components.
Potential of Integrated Optic structures to support very high bandwidths is demonstrated.
Keywords: Integrated optics, Sinusoidal bends, True-Time-Delay (TTD), Optical modulation
1. INTRODUCTION
The spectrum of an ideal monochromatic laser consists of a single spectral component at its
operating frequency. The entire power of the laser is contained in this spectral component. Spectrum
of a non-ideal laser having phase noise exhibits a finite non-zero linewidth as has been discussed in
our earlier paper [1]. Phase noise is significant only at frequencies very close to the laser frequency
and it falls rapidly at higher offsets from the laser frequency. As a result, power in the laser continues
to be concentrated predominantly at its frequency of operation. For this reason, propagation of an
optical signal through a waveguide is conventionally analyzed on the assumption that the signal is
monochromatic.
When a laser is subjected to modulation, it results in distribution of power among various
spectral components. The spectral width of a modulated signal and distribution of power are
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Volume 4, Issue 4, July-August, 2013, pp. 148-156
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149
dependent on modulation scheme, modulation index and the frequency of the modulating signal.
Hence, when a modulated optical signal is being analyzed, the approximation of power being
centered at carrier frequency is no longer valid. In other words, when propagation of a modulated
optical signal along a waveguide is being studied, the analysis needs to take into consideration the
frequency components constituting the signal. In this paper we analyze the propagation of modulated
optical signal along an Integrated Optic (IO) environment.
In Integrated Optic components, light is guided by films deposited on wafer-like substrates.
Theory and techniques of Integrated Optics has been extensively studied [2-4]. An IO waveguide
consists of a channel having higher refractive index compared to the surrounding material as in the
case of an optical fiber. The refractive index profile is primarily determined by the fabrication
process. For a given wavelength of operation, mode profile in the guided region is influenced by
refractive index profile, width and depth of the waveguide channel.
Different frequency components exhibit different propagation constants in an Integrated
Optic waveguide. As propagation constant determines the rate at which phase builds along the
direction of propagation, phase variations experienced by different frequency components as they
travel along an IO waveguide are not uniform. Hence, operation of any IO device has to be analyzed
over the entire range of frequencies that it is likely to encounter.
In this paper, we solve the dispersion equation of a slab waveguide (2-D waveguide) to
analyze the variation in propagation constant as a function of frequency. Phase analysis for a channel
waveguide (3-D waveguide) is carried out by extracting phase information from the beam
propagation model.
2. VARIATION IN MODE PROFILE AND PROPAGATION CONSTANT OF A SLAB
WAVEGUIDE AS A FUNCTION OF FREQUENCY
A slab waveguide on a 2-D waveguide consists of a film of refractive index nf sandwiched
between substrate of refractive index ns and cladding of refractive index nc (Fig. 1). For the structure
to act as a waveguide, the refractive indices should satisfy the condition: nf > ns > nc.
Fig. 1 Structure of a slab waveguide
Cladding (nc)
Waveguide
Substrate (ns)
d

150
Dispersion equation for TE modes in a slab waveguide is given by the equation [5]:
V(1-b)0.5
= (m+1)π - tan-1
[(1-b)/b] 0.5
- tan-1
[(1-b)/(b+a)] 0.5
(1)
Where V = k0 d (nf
2
– ns
2
)0.5
is the Normalized Frequency, (2)
b = [(N2
- ns
2
) / (nf
2
– ns
2
)0.5
] 0.5
is the Normalized Propagation Constant, (3)
k0 = 2π/λ (Free-space propagation constant), (4)
d = Thickness of the waveguide film deposited on the substrate,
nf = Refractive index of the waveguide film,
ns = Refractive index of the substrate,
N = Effective refractive index
m = mode number,
a = (ns
2
- nc
2
) / (nf
2
– ns
2
) is the waveguide asymmetry. (5)
For a given operating wavelength (or frequency) and waveguide structure whose dimensions
and refractive indices are known, the value of b can be determined numerically from the equation
(1).
Effective index N can be calculated from b as follows:
N = [b (nf
2
– ns
2
) + ns
2
] 0.5
(6)
Propagation constant is calculated as:
β = k0 N (7)
Since multiple frequency components are generated by modulation, the value of β has to be
calculated for all these components.
It is also known that for a slab waveguide, mode profile satisfies the equation:
Ey = A cos(kx) in guided region (8)
& Ey = C exp(-gx) outside the guided region (9)
where A and C are constants,
k = (k0
2
nf
2
- β2
)0.5
(10)
& g = (β2
- k0
2
ns
2
)0.5
(11)
Substituting the value of β in the above equation and calculating the values of A and C from
boundary conditions, we obtain the mode profiles for different frequency components.
Mode profile of Ey in guided region for an operating wavelength of 1550 nm is shown in Fig.
2. Figs. 3 and 4 illustrate the rapid decay of Ey on either sides of the wave-guiding region. The mode
profile in its entirety is shown in Fig. 5.
Mode profiles for operating wavelengths of 1540 nm, 1550 nm and 1560 nm have been
overlaid in Fig. 6.
Fig. 7 shows normalized propagation constant plotted as a function of frequency over a range
of 20 GHz. The frequency in the plot is centered at a frequency of 193.548 THz corresponding to
wavelength of 1550 nm.

151
Fig. 2 Mode profile of Ey in guided region
Fig. 3 Mode profile of Ey outside the guided region
Fig. 4 Mode profile of Ey outside the guided region

152
Fig. 5 Mode profile of Ey
Fig. 6 Mode profiles of Ey for 1540 nm, 1550 nm and 1560 nm
(Blue:1540 nm, Red: 1550 nm & Green: 1560 nm)
Fig. 7 Variation of Normalized Propagation Constant over 20 GHz

153
3. PROPAGATION OF A MODULATED OPTICAL SIGNAL IN IO STRUCTURES
This section analyzes the propagation of a modulated optical signal through different
Integrated Optic structures. For the sake of clarity in illustration we treat the modulated optical signal
to be composed of three components – the carrier frequency, the least lower sideband frequency and
the highest upper sideband frequency. The choice of these frequencies is such that the entire
bandwidth of the modulated signal is spanned.
Propagation of the chosen frequency components through IO elements is analyzed through
simulations. Bandwidth of 20 GHz has been considered for the sake of demonstration. The value of
20 GHz has been chosen considering the fact that most of the data communication demands are met
by this bandwidth.
Propagation of modulated optical signal is studied in terms of phase variation. The choice of
phase as the key parameter for analysis is based on the following considerations:
• Change in propagation constant affects the rate of phase change
• The amount of phase offset accrued between the highest and lowest frequency components of
the modulated signal as they propagate along the waveguide puts a limit on the maximum
bandwidth supported by the device
The phase information for simulation has been extracted from FFT based Beam Propagation
Model. Phase variation experienced by three frequency components – ‘fc - 10GHz’, ‘fc’, ‘fc +
10GHz’, representing a spanned bandwidth of 20 GHz, as they propagate through three different IO
elements is shown in Figs. 8 to 10.
3.1 PROPAGATION OF A MODULATED OPTICAL SIGNAL ALONG AN IO STRAIGHT
WAVEGUIDE
Fig. 8 Phase variation along straight waveguide over frequency range of 20 GHz
(Blue: fc-10 GHz, Red: fc, Green: fc+10 GHz; fc: 193.548 THz)

154
3.2 PROPAGATION OF A MODULATED OPTICAL SIGNAL ALONG AN IO
SINUSOIDAL-BEND (S-BEND) WAVEGUIDE
Fig. 9(a) Phase variation along an IO S-bend over frequency range of 20 GHz
Fig. 9(b) S-bend shown as reference to correlate phase variation with geometry
3.3 PROPAGATION OF A MODULATED OPTICAL SIGNAL ALONG AN IO Y-BRANCH
SPLITTER / COMBINER
Fig. 10(a) Phase variation along first arm of Y-branch over frequency range of 20 GHz

155
Fig. 10(b) Phase variation along second arm of Y-branch over frequency range of 20 GHz
Fig. 10(c) Y-branch shown as a reference to correlate phase variation with geometry
4. DISCUSSION
Variation in propagation constant as a function of frequency has been studied. Dispersion
equation for a slab waveguide has been solved numerically to obtain propagation constants and mode
profiles for different frequencies. Fig. 6 depicts the mode profile for wavelengths over a range of 20
nm. It can be seen from this figure that the variation in mode profile over the considered range is
negligible. Fig. 7 displays the plot of normalized propagation constant as a function of frequency
over a range of 20 GHz. The plot indicates insignificant change in the propagation constant thus
suggesting minimal offset in phase between signals separated in frequency by 20 GHz as they travel
along an IO environment. These predictions are verified and found to be true by simulating the phase
variations experienced by different frequency components travelling along different IO elements
(Figs. 8 to 10). The overlap in phase build-up for different frequencies conforms to the predictions.
5. CONCLUSION
Effect of variation in propagation constant over phase variation for different spectral
components of a modulated optical signal has been studied. Optical signals having bandwidth of 20
GHz have been shown to experience negligible deterioration when passed through the IO elements
proposed for the design of QPSK modulator. This paper establishes the potential of Integrated Optic
elements to support high bit-rate/bandwidth applications.

156
REFERENCES
[1] Yogesh Prasad K R, Srinivas T and Ramana D V, “A generic algorithm to numerically model
the linewidth broadening of laser due to phase noise”, International Journal of Electronics
and Communication Engineering & Technology (IJECET), Volume 4, Issue 4, 2013,
pp. 26 - 35, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472,
[2] Miller, S. E., ‘‘Integrated optics: an introduction,’’ Bell Syst. Tech. J., vol. 48, no. 7,
pp. 2059–2068, 1969.
[3] Tamir, T., Integrated Optics, Springer-Verlag, New York, 1975.
[4] Hunsperger, R. G., Integrated Optics: Theory and Technology, Springer-Verlag, New York,
1982.
[5] Nishihara, H., M. Haruna, and T. Suhara, Optical Integrated Circuits, McGraw-Hill, New
York, 1989.
[6] Rajini V Honnungar and T Srinivas, “A Novel π- Phase Shifter in Integrated Optics”,
International Journal of Electronics and Communication Engineering &Technology
(IJECET), Volume 4, Issue 3, 2013, pp. 220 - 226, ISSN Print: 0976- 6464, ISSN Online:
0976 –6472.

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