Ultra High Speed Semiconductor Electrooptic Modulator Devices for Gigahertz Operation in Optical Communication Systems

─ The effects of electrodes geometry and temperature on high frequency radio frequency transmission characteristics are deeply investigated against semiconductor material based electro optic modulator devices such as aluminum gallium arsenide (AlGaAs) and optical waveguide parameters. On the other hand, we have developed the optimization of the electro-optic modulator parameters where the effective index plays an essential role in the evaluation of the bandwidth structure. Therefore, a theoretical analysis of the capacitance, the characteristic impedance and the effective index determine how to increase the bandwidth. The effects of design parameters on the modulating voltage and optical bandwidth are also investigated for different materials based electro-optic modulators by using rigorous transmission modeling techniques. The low-loss wide-bandwidth capability of optoelectronic systems makes them attractive for the transmission and processing of microwave signals, while the development of high capacity optical communication systems has required the use of microwave techniques in optical transmitters and receivers. These two strands have led to the development of the research area of microwave photonics. Index Terms─ Electrooptic modulator, Semiconductor material, Optical bandwidth, and High transmission performance.

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 (LiNbO 3 ). Among the integrated optical components, the contribution from electrooptic modulators using LiNbO 3 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, LiNbO 3 based ferroelectric electrooptic modulators 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  [2]. Most of the work done in the area of designing electrooptic modulators has been strongly focused on using LiNbO 3 [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, LiNbO 3 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][10][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.

II. MODELING ANALYSIS
For Al x Ga (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]: The set of the parameters is recast and dimensionally adjusted as the following [8,9]: C 1 = 10.906-2.92x, C 2 = 0.97501, C 3 =c 3 T 2 ; c 3 = (0.52886-0.735x/T o ) 2 , for x < 0.36. And C 4 =c 4 (0.93721+ 2.0857x10 -4 T); c 4 =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: 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][14][15]: Under the perfect velocity matching condition [16,17], achievable modulation bandwidth f m is: Therefore the device performance index (DPI) can be expressed as the following expression [18,19]: If a modulating voltage V m in z-direction is applied, the change in index for the TM polarization is: Therefore the product of the sensitivity and the bandwidth is not related to the signal quality factor and is given by [20]: Where r 41 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]: The material dispersion time of the single mode fiber  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]: Then the bandwidth length product within electrooptic modulator device is given by [23,24]: Gbit.μm/sec (12) The bandwidth for single mode operation within electrooptic modulator length L m is given by: , .
The signal to noise ratio (SNR) is a measure of signal quality at the receiver side, it is given by [25]: Where P 0 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 and 3), B.W sig. 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, I D is the detector's dark current, and R L 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]: Where B.W sig. 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:

III. 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. 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

IV. 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.