1. Introduction

Present communication technology relies on fiber-optic systems which include light sources such as a laser, optical fiber, integrated optical components such as modulators and switches, and optical detectors. The lasers and detectors are fabricated using semiconductor materials, and the integrated optical components are generally fabricated using electrooptic single crystal materials such as lithium niobate (LiNbO₃). Among the integrated optical components, the contribution from electrooptic modulators using LiNbO₃ waveguide structures has been significant in the last several decades due to their high speed and chirp-free nature[1]. The essential requirements for efficient electrooptic modulation are low half-wave(switching) voltage and broad 3-dB bandwidth. The optical modulator is a key component for photonics. Optical fiber communications, microwave photonics, instrumentation, and optical signals processing all require optical modulators. Several different technology platforms can be used for the realization of optical modulators. Of these, LiNbO₃ based ferroelectric electrooptic modu-lators provide the most mature technology. Electro-optic polymers and compound semiconductors are also attractive technologies for optical modulators. High-speed integrated electro-optic modulators and switches are the basic building blocks of modern wideband optical communications systems and represent the future trend in ultra-fast signal processing technology. As a result, a great deal of research effort has been devoted to developing low-loss, efficient and broadband modulators in which the radio frequency signal is used to modulate the optical carrier frequency[2]. Most of the work done in the area of designing electrooptic modulators has been strongly focused on using LiNbO₃[3]. Interest in research in this field has arisen as lithium niobate devices have a number of advantages over others[4], including large electro-optic coefficients, low drive voltage, low bias drift, zero or adjustable frequency chirp, and the facility for broadband modulation with moderate optical and insertion losses and good linearity . However, on the other hand, LiNbO₃ devices cannot be integrated with devices fabricated using other material systems such as semiconductors and as a result they are best suited to external modulation applications. However, with the recent developments in semiconductor technology, modulators based on semiconductor materials have been receiving increasing attention. In particular, AlGaAs/GaAs material offers the advantage of technological maturity and potential monolithic integration with other optical and electronic devices in creating better optoelectronic integrated circuits(OEIC). Recently, electrooptic polymer modulators have also emerged as alternatives for optical modulators, particularly for low-cost applications for the next–generation metro and optical access systems. Today 2.5 Gb/s and 10 Gb/s modulators are standard commercial products and 40 Gb/s modulators are also being developed for the market after successful prototype demonstrations: however, the continuous demand to increase the data rate further will push their operating frequency well into the millimeter wave range[5].

High-speed optical modulators are essential for dealing with the current explosive growth in network traffic. These modulators are based on two types of physical effect: the electro absorption (EA) effect and the electro-optic (EO) effect. EA modulators have been widely used in recently developed 2.5 and 10 Gbit/s optical transmission systems, because they have a small driving voltage of around 2 Volt [6], a small size and they are easily integrated with laser sources. However, it is difficult to apply EA modulators to high-bit-rate transmission systems because of their chirp characteristics. EA modulators can only be applied to very-short-reach (VSR) systems at 40 Gbit/s[7,8]. In contrast, the interferometric Mach Zehnder (MZ) modulator provides more flexibility than the EA modulator in terms of chirp controllability. Moreover, MZ modulators are capable of controlling the optical phase. The MZ modulator is the most widely used device employing the EO effect. The optical phase can be controlled by supplying the EO waveguides with a voltage[8]. High-bit rate transmission systems require a phase controlled modulation format, such as a carrier-suppressed return-to-zero(CS-RZ) or optical duo binary signal format[9-11]. These formats are capable of improving the transmission performance because of their dispersion tolerance resulting from the fact that there is less spectral width broadening during modulation.

In the present study, Aluminum gallium arsenide(AlGaAs) semiconductor material based electrooptic external modulators have been developed for extensive use in high speed and long distance optical fiber transmission systems. This is because they can offer the advantages of modulation exceeding multi Gbit/sec combined with a low driving voltage, and they can eliminate the dynamic laser wavelength chirping which limits the span-rate system product due to their fiber dispersion characteristics. Modulators fabricated on semiconductor substrates such as (AlGaAs) and silicon doped materials are particularly attractive in that these exists the possibility of monolithic integration of these devices with other optoelectronic components.

2. Modeling Analysis

For Al_xGa_(1-x)As, the parameters required to characterize the ambient temperature and operating signal wavelength dependence of the refractive-index, where Sellmeier empirical equation is under the form of[12]:

(1)

The set of the parameters is recast and dimensionally adjusted as the following[8, 9]: C₁= 10.906-2.92x, C₂= 0.97501, C₃=c₃T²; c₃= (0.52886-0.735x/T_o)², for x < 0.36. And C₄=c₄ (0.93721+ 2.0857x10^-4T); c₄=0.002467(1.14x+1). We have taken into account the value of x=0.2, then the first and second differentiation of above empirical equation with respect to operating optical signal wavelength λ gives:

(2)

(3)

The switching voltage V_π or the voltage required to change the output light intensity from its maximum value to its minimum value can be expressed as the following [13-15]:

(4)

Where λ is the operating optical signal wavelength in μm, Γ is the confinement factor, d is the modulator thickness in μm, L_m is the modulator length in μm, and r₄₁ is the electrooptic coefficient for used semiconductor material.

Under the perfect velocity matching condition[16,17], achievable modulation bandwidth f_m is:

(5)

Where α is the power absorption coefficient in dB/μm.

Therefore the device performance index (DPI) can be expressed as the following expression [18,19]:

(6)

If a modulating voltage V_m in z-direction is applied, the change in index for the TM polarization is:

(7)

Therefore the product of the sensitivity and the bandwidth is not related to the signal quality factor and is given by [20]:

(8)

Where r₄₁ is the electrooptic coefficient for aluminum gallium arsenide material based EO modulator devices.

The total system rise time is the square root of the sum of the squares of the transmitter, optical fiber connection, and receiver rise times. That is given by[21]:

(9)

The material dispersion time of the single mode fiber τ_mat. which is given by the following equation:

(10)

In addition to providing sufficient power to the receiver, the system must also satisfy the bandwidth requirements imposed by the rate at which data are transmitted. A convenient method of accounting for the bandwidth is to combine the rise times of the various system components and compare the result with the rise time needed for the given data rate and pulse coding scheme. The system rise time is given in terms of the data rate for non return to zero pulse code by the expression[22]:

(11)

Then the bandwidth length product within electrooptic modulator device is given by [23, 24]:

(12)

The bandwidth for single mode operation within electrooptic modulator length L_m is given by:

(13)

The signal to noise ratio (SNR) is a measure of signal quality at the receiver side, it is given by [25]:

(14)

(15)

Where P0 is the received or output optical power, ρ is the detector’s unamplified responsivity, G is the detector gain if an avalanche photodiode(APD) is used, n accounts for the excess noise of the APD (usually between 2,3), B.Wsig. is the signal bandwidth at the receiver, k is Boltzmann’s constant(k = 1.38 x 10–23 J/K), e is the magnitude of the charge on an electron(1.6 x 10–19 coulomb), T is the ambient temperature in K, ID is the detector’s dark current, and RL is the resistance of the load resistor that follows the photodetector. The maximum transmission bit rate or capacity according to modified Shannon technique is given by[26,27]:

(16)

Where B.Wsig. is the actual bandwidth of the optical signal, and SNR is the signal to noise ratio in absolute value (i. e., not in dB). Where the Shannon Bit rate length product can be given by:

(17)

3. Simulation Results and Performance Analysis

We have investigated ultra high speed semiconductor electrooptic modulator devices for gigahertz system operation over wide range of the affecting operating parameters as shown in Table 1.

Based on the model equations analysis, assumed set of the operating parameters, and the set of the Figs.(1-14), the following facts are assured as the following results:

i) As shown in the series of Figs. (1-3), as both modulator length and confinement factor increase, and operating optical signal wavelength decreases, this results in decreasing of switching voltage.

Table 1. Proposed operating parameters for our suggested electrooptic modulator device Parameter Definition Value and unit T Ambient temperature 300 K ≤ T ≤ 330 K Lm Modulator length 2 μm ≤ Lm ≤ 5 μm d Modulator thickness 0.1 μm ≤ w ≤ 0.5 μm τt Rise time of the transmitter 0.8 nsec τr Rise time of the receiver 1 nsec P0 Output power 0.1 ≤ P0, Watt ≤ 0.6 T0 Room temperature 300 K λ signal operating wavelength 1.3 μm ≤ λ ≤ 1.65 μm Δλ Spectral line width of the optical source 0.1 nm r41 Electoptic coefficient for AlxGa(1-x) As 18 Pm/volt L Inductance 20 μH C Capacitance 0.2 pF RL Load resistance 5 kΩ G Detector gain 20 dB α Power absorption coefficient 0.1–0.5 dB/μm Δne Effective refractive index difference 0.01 ≤ Δne ≤ 0.09 Г Confinement factor 0.8 ≤ Г ≤ 0.95 ID Detector dark current 8 nA ρ detector responsivity 0.8 A/Watt η Modulator efficiency 90 % c Speed of light 3x108 m/sec

ii) Fig. 4 has assured that as both modulator length and relative refractive index difference increase, this leads to increase in modulating voltage.

iii) As shown in Fig. 5 has demonstrated that as both power absorption coefficient and modulator length increase, this results in decreasing of modulation device bandwidth.

iv) Figs. (6, 7) have indicated that as both operating optical signal wavelength and modulator thickness increase, and confinement factor decreases, this leads to decrease in device performance index.

v) As shown in Fig. 8 has assured that as operating optical signal wavelength increases and confinement factor decreases, this results in decreasing of device sensitivity bandwidth product.

vi) Fig. 9 has proved that as both modulator length and optical output power increase, this results in increasing of signal to noise ratio.

vii) As shown in Figs. (10, 11) have demonstrated that as both modulator length and output power increase, this results in increasing of transmission bit rate length product. As well as modulator length increases, and output power decreases, this leads to decrease in transmission bit rates with Shannon transmission technique.

viii) Fig. 12 has indicated that as ambient temperature decreases operating optical signal wavelength increases, this leads to increase in transmitted signal bandwidth.

ix) Figs. (13, 14) have demonstrated that as both modulator length and operating optical signal wavelength increase, and ambient temperature decreases, this results in increasing transmission bit rate length product. As well as both modulator length and ambient temperature increase, and operating optical signal wavelength decreases, this results in decreasing of transmission bit rates with non return to zero coding formats.

Figure 1. Variations of switching voltage versus confinement factor at the assumed set of parameters

Figure 2. Variations of switching voltage versus confinement factor at the assumed set of parameters

Figure 3. Variations of switching voltage versus signal wavelength at the assumed set of parameters

Figure 4. Variations of modulating voltage against relative index difference at the assumed set of parameters

Figure 5. Variations of Modulation bandwidth against modulator length at the assumed set of parameters

Figure 6. Variations of Device performance index against optical signal wavelength at the assumed set of parameters

Figure 7. Variations of Device performance index against optical signal wavelength at the assumed set of parameters

Figure 8. Variations of sensitivity bandwidth product against optical signal wavelength at the assumed set of parameters

Figure 9. Variations of signal to noise ratio against modulator length at the assumed set of parameters

Figure 10. Variations of Shannon transmission bit rate against modulator length at the assumed set of parameters

Figure 11. Variations of Shannon bit rate length product against modulator length at the assumed set of parameters

Figure 12. Variations of transmitted signal bandwidth versus ambient temperature at the assumed set of parameters

Figure 13. Variations of transmission bit rate versus ambient temperature at the assumed set of parameters

Figure 14. Variations of transmission bit rate length product against modulator length at the assumed set of parameters

4. Conclusions

In a summary, we have presented ultra high speed semiconductor electrooptic modulator devices for multi gigahertz operation systems. It is theoretically found that the increased confinement factor and modulator length, and the decreased operating optical signal wavelength, this leads to the decreased switching device voltage. It is evident that the decreased operating optical signal wavelength and modulator thickness, and the increased confinement factor, this results in increasing of device performance index. As well as the increased output received power and modulator length, and the increased operating optical signal wavelength, and the decreased ambient temperature, this results in the increased transmission bit rate length product with using both Shannon transmission technique and NRZ coding formats.