EFFECTS OF GEOMETRICAL
STRUCTURE ON MICROWAVE AND
OPTICAL PROPERTIES OF
TRAVELING WAVE
ELECTROABSORPTION
MODULATORS BASED ON
ASYMMETRIC COUPLED STRAINED
QUANTUM WELLS ACTIVE LAYER
KAMBIZ ABEDI
Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Shahid Beheshti University, G. C., Evin 1983963113, Tehran, Iran
http://ece.sbu.ac.ir/Desktopmodules/Sbu_ProfessorsPage/SP.aspx?userid=1603 Abstract :
This paper presents the effects of geometrical structure on microwave and optical properties of traveling wave electroabsorption modulators (TWEAMs) based on asymmetric intra-step-barrier coupled double strained quantum wells (AICD-SQW) active layer. The AICD-SQW active layer structure has advantages such as very low insertion loss, zero chirp, large Stark shift and high extinction ratio in comparison with the intra-step quantum well (IQW) structure. Firstly, the influences of the intrinsic (active) layer thickness and width on effective optical index and confinement factor are analyzed. Furthermore, the effect of the intrinsic layer thickness on their transmission line microwave properties such as microwave index, microwave loss, and characteristic impedance are evaluated. The thickness and width of active layer are changed from 0 μm to 1.4 μm and 1 μm to 3 μm, respectively. Finally, the frequency response of TWEAM based on AICD-SQW active layer is calculated using circuit model.
Keywords: Traveling wave electroabsorption modulator; AICD-SQW; microwave and optical properties; frequency response.
1. Introduction
EAM bandwidth because of the limitation of RC time constant [1, 3]. If the traveling wave electrode is not appropriately terminated, there will be microwave reflection at the termination end. The optical wave will be
Fig. 1. Schematic diagram and the principle of operation for a traveling wave electroabsorption modulator.
modulated by both the forward traveling microwave and the reflected backward traveling microwave. The magnitude of the reflected microwave is influenced by the reflection coefficient at the load end, which is determined by the impedance mismatch between the EAM electrode transmission line and the termination load [6]. Similarly, there will be reflections at the input end if the characteristic impedance of the transmission line is not matched to the source impedance. Therefore, the total modulation efficiency of the EAM is influenced by the impedance mismatch. Furthermore, in the ideal case, the forward traveling microwave should keep in pace with the modulated optical wave packet, so that the modulation is always being increased during the propagation. This requires matching the microwave phase velocity with the optical group velocity [6, 7]. This velocity matching becomes especially important for the TWEAM with a long waveguide. The microwave loss in the transmission line should also be minimized, since it generally increases with the modulation frequency, which is unfavorable to the modulation bandwidth. For a TWEAM, the modulation bandwidth is no longer limited by the RC-time constant, but by the above mentioned impedance mismatch, velocity mismatch and microwave loss [8-12].
Unfortunately, an ordinary TWEAM has complex characteristic impedance because of lossy transmission line with real part only ~ 20 Ω. This impedance is microwave frequency dependent, which is much less than the commonly used 50 Ω. These actualities make the impedance matching difficult. The TWEAM electrode also has very slow microwave velocity with phase velocity index ~ 7, which is a large mismatch with the optical group index, i.e. 3.4-3.6 [1-4]. The frequency-dependent microwave loss in the TWEAM transmission line is also exceptionally large. All of these unpleasant factors compound the difficulty of TWEAM design [6, 7].
Recently, TWEAMs based on asymmetric intra-step-barrier coupled double strained quantum well (AICD-SQW) active layer with advantages such as large Stark shift, very low insertion loss, zero chirp, high extinction ratio, and higher figures of merit in comparison with the IQW structure have been introduced [13-18].
Since microwave properties such as the characteristic impedance, microwave loss and the microwave effective index and optical properties such as effective optical index and confinement factor of a TWEAM are influenced by the geometrical structure of the device [9], In this article, we intend to investigate the geometrical structure such as thickness and width of active layer on microwave and optical properties of TWEAMs based on AICD-SQW active layer for the first time. For this purpose, the thickness and width of active layer are considered from 0 μm to 1.4 μm and 1 μm to 3 μm, respectively. Finally, the frequency response of a TWEAM based on AICD-SQW active layer is calculated using circuit model.
2. AICD-SQW Structure for active layer of TWEAM
A schematic illustration of the compositions and the thicknesses of the active region layers of TWEAMs based on multi-period of AICD-SQW structure are shown in Fig. 2 [13]. The undoped AICD-SQW structure has In0.52Al0.48As barriers, which are lattice matched to the InP substrate, as well as one lattice-matched
In0.53Ga0.33Al0.14As intra-step-barrier. The In0.525Ga0.475As wide well is under 0.05% of tensile strain, and the
barriers is 10 nm, while the thickness of the middle barrier is 1.5 nm. The thicknesses of the wide well, the narrow well and the intra-step-barrier are 6.8 nm, 3.5 nm and 4 nm, respectively. The middle barrier layer and strain amount of wells cause the electron and heavy hole wave functions are distributed dominantly in the wide and narrow wells, respectively. As a result, the insertion loss significantly decreases at zero electric field [13].
Fig. 2. Schematic of layers for TWEAM (Abedi et al. 2008).
3. Circuit Model and Frequency Response of TWEAM
A TWEAM can be modeled based on the supposition of quasi-TEM waves propagating along the electrical waveguide as a transmission line comprised of many unit cells. Each unit cell is assumed to be so small that it can be taken into account as an electronically lumped element. Fig. 3 shows the circuit model of unit cells for a unit length of TWEAM transmission line. The circuit model of unit cells contains the metal conduction resistance Rcon which changes with frequency due to the skin effect, the inductance Lm, the vertical series resistance RS, the junction capacitance Cm, an outer parasitic capacitance Co, and a differential resistance Ro parallel to Cm which is caused by photo-generation of carriers in the intrinsic layer. The effect of junction resistance Ro becomes significant only at high incident optical power [7, 14].
' ' i i
V , Z ' '
n n V , Z
i V L Z O C m C O R S R m L con R S Z
Fig. 3. Circuit model for a unit length of TWEAM transmission line.
The circuit model elements for a unit length of TWEAM transmission line can easily be extracted from the TWEAM transmission line microwave properties Z0 (characteristic impedance) and γµ (propagation constant), which are obtained via full-wave simulations of the given geometry using HFSS simulator based on finite element method [7, 9].
0
2
ser con m
Z Z R j L
(1)
0
2 2
2 2 2 2 2 2
1 1 1 m P o S m
S m m
o
S m S m
j C
Y j C
Z j R C
R C C
j C
R C R C
(2)
The small signal frequency response for TWEAM can be obtained as follows [1, 9]:
1 22 0
1
j no eff i l
n c
Pac V ei l
i
(3)where Vi is the modulating voltage in i section. The calculation of the small signal modulation response requires the knowledge of the effective optical index no-eff and the circuit model elements for calculation of Vi.
4. Results and discussion
In this section, we investigate the effects of geometrical structure such as the active layer thickness (hi) and
width (wa) on optical and microwave properties of TWEAM based on AICD-SQW such as effective optical
index no-eff, confinement factor Γ, microwave index nμ, microwave attenuation αμ and characteristic impedance
Z0. The thickness and width of active layer are changed from 0 μm to 1.4 μm and 1 μm to 3 μm, respectively. In
this study, the thicknesses of the p- and n-layer within the mesa are taken as 1.5 μm and 1.7 μm, respectively. In
order to improve the junction capacitance, we use a small intrinsic buffer layer, i-InP on top of the active layer with thickness of 0.2 µm. Modeling is performed for a wavelength of 1.55 μm. The corresponding geometry values and typical material data are in [14]. For our case study, we use data for the InP/InGaAsP material system according to published devices [7, 14].
The effective optical index defines the optical speed, which should be known in the analysis of a traveling wave modulator and calculation of modulation response. Fig. 4 shows the calculated effective optical index as a function of the active layer thickness using full-vectorial finite difference method for fundamental mode of TE polarization with wa=2 μm. As shown in this figure, the value of effective optical index versus active layer
thickness changes from 3.495 to 3.584 when the active layer thickness changes from 0 μm to 1.4 μm.
Fig. 4. Effective optical index for fundamental mode of TE polarization versus active layer thickness.
Fig. 5 shows the calculated effective optical index as a function of active layer width for fundamental mode of TE polarization for different combinations of active layer thickness. In view of the fact that narrowing of the horizontal dimension of active layer in order to decrease the capacitance is limited by the process and the constraints for optical waveguiding and coupling, therefore typical values of wa are considered 1–3 μm [9]. The
value of effective optical index draws near a constant level for active layer width above 2 μm. It can be observed that as the active layer thickness and width are increased, the effective optical index value is increased.
Fig. 7 shows the calculated real part of characteristic impedance Re(Z0) over frequency for different values
of active layer thickness hi. The real part of characteristic impedance draws near a constant level for frequencies
above 10 GHz. This value is usually mentioned to as the modulator impedance. It can be observed that as the
Fig. 5. Effective optical index for fundamental mode of TE polarization versus active layer width.
Fig. 6. Confinement factor (Γ) for fundamental mode of TE polarization versus active layer thickness.
Fig. 7. Calculated real part of characteristic impedance Re(Z0) versus frequency for different active layer thickness.
of the thickness of active layer, the circuit model elements Rcon, Lm, and Co are not affected since the magnetic
field path length and ohmic losses don’t change. Moreover, the junction capacitance Cm is affected by changing
wa. Therefore, by thickening the active layer, the junction capacitance decreases. The main effect of active layer thickness can be depicted best by considering an ideal transmission line without any losses. In this case characteristic impedance is obtained as Z0= (Lm/Cm)0.5. Increasing the active layer thickness decreases the
junction capacitance Cm in waveguide and increases thereby the characteristic impedance.
Fig. 8 shows the calculated microwave index over frequency for different values of active layer thickness hi.
As the active layer thickness increases, the microwave index value decreases. In ideal transmission line without any losses case, microwave index is obtained as nµ=c0(LmCm)½. Increasing the active layer thickness only
decreases the junction capacitance Cm in waveguide and decreases thereby the microwave index. Therefore, the
microwave velocity increases.
Fig. 8. Calculated microwave index versus frequency for different active layer thickness.
Fig. 9 shows the calculated microwave loss over frequency for different values of active layer thickness hi. It
Fig. 9. Calculated microwave loss versus frequency versus frequency for different active layer thickness.
Fig. 10 shows the calculated frequency response of TWEAM based on AICD-SQW with different lengths and ZL=25 Ω. The overall waveguide loss and velocity mismatch increase as the device length increases. The
microwave loss and velocity mismatch reflect the decrease in optical modulation, as shown in the plot. The 3dB bandwidth for TWEAM based on AICD-SQW is about 83 GHz for 100 μm, 44 GHz for 200 μm and 22 GHz for 400 μm waveguide length, respectively.
Fig. 10. Frequency response for TWEAM based on AICD-SQW with different waveguide lengths.
5. Conclusions
for TWEAM based on AICD-SQW is about 83 GHz for 100 μm, 44 GHz for 200 μm and 22 GHz for 400 μm waveguide length, respectively.
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