Dual-Channel All-Optical Modulator Utilizing Colloidal InSb/SiO2 Quantum Dot Semiconductor Optical Amplifiers with Enhanced Modulation Depth
الموضوعات : فصلنامه نانوساختارهای اپتوالکترونیکی
Mohammad Faraji
1
,
Hannaneh Dortaj
2
,
Samiye Matloub
3
1 - Quantum and Photonic Research Lab., Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
2 - Quantum and Photonic Research Lab., Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
3 - Quantum and Photonic Research Lab., Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
الکلمات المفتاحية: All optical modulator, Modulation depth, Quantum dot, Optical amplifer, Solution-processed,
ملخص المقالة :
Quantum dot semiconductor optical amplifiers (QD-SOAs) are promising candidates, yet achieving high modulation depth and gain simultaneously in dual-channel AOMs remains a challenge. Existing studies often focus on single-channel modulation or lack optimization across multiple wavelengths. This paper proposes a dual-channel AOM based on a solution-processed InSb/SiO₂ QD-SOA, designed to modulate and amplify 1.31 and 1.55µm wavelengths simultaneously. A self-consistent solution of the 3D Schrödinger equation is used for modal analysis, while coupled rate and propagation equations evaluate device performance. The results demonstrate nearly 100% modulation depth and gains of 17.94 dB and 17.14 dB at a pump power density of 500 W/cm². These findings highlight the potential of solution-processed QD-SOAs for cost-effective, high-performance optical modulation, addressing key challenges in next-generation optical networks.
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Islamic Azad University
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Research Paper
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Dual-Channel All-Optical Modulator Utilizing Colloidal InSb/SiO2 Quantum Dot Semiconductor Optical Amplifiers with Enhanced Modulation Depth
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Mohammad Faraji 1, Hannaneh Dortaj *,1 and Samiye Matloub 1 1 Quantum and Photonic Research Lab., Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
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Received: 2025.01.25 Revised: 2025.04.30 Accepted: 2025.05.04 Published: 2025.08.25
| Abstract: Quantum dot semiconductor optical amplifiers (QD-SOAs) are promising candidates, yet achieving high modulation depth and gain simultaneously in dual-channel AOMs remains a challenge. Existing studies often focus on single-channel modulation or lack optimization across multiple wavelengths. This paper proposes a dual-channel AOM based on a solution-processed InSb/SiO₂ QD-SOA, designed to modulate and amplify 1.31 and 1.55µm wavelengths simultaneously. A self-consistent solution of the 3D Schrödinger equation is used for modal analysis, while coupled rate and propagation equations evaluate device performance. The results demonstrate nearly 100% modulation depth and gains of 17.94 dB and 17.14 dB at a pump power density of 500 W/cm². These findings highlight the potential of solution-processed QD-SOAs for cost-effective, high-performance optical modulation, addressing key challenges in next-generation optical networks. |
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Keywords: All optical modulator, Modulation depth, Quantum dot, Optical amplifer, Solution-processed | |
1. INTRODUCTION
High-speed signal processing and optical communication technologies largely rely on devices known as all-optical modulators (AOMs), where light is used to modulate light [1], [2], [3]. All-optical signal processing is a promising technology for next-generation high-bit-rate modulation and transparent optical networks thanks to their reduction of deployment expenses and elimination of the bottleneck in ultrafast signal processing by removing the need for costly optical-electrical-optical equipment [4], [5], [6].
Semiconductor optical amplifiers (SOAs) work in a linear and nonlinear method in advanced optical communications systems to achieve a high bit rate and the ability to be integrated [7], [8]. As a linear system, SOA is utilized as an in-line optical amplifier [9]. As a nonlinear system, SOAs have many applications, including cross-gain modulators [10], four-wave mixers [11], cross-phase modulators [12], wavelength conversion [13], logic gates [14], all optical signal processing [15], signal regeneration and switching [16]. However, the utilization of SOAs as intensity modulators [17], [18] has received particular investigation attentiveness in budget-conscious applications such as wavelength division multiplexing passive optical networks (WDM-PONs) [19], [20], [21]. SOAs have a number of prominent advantages, such as low power dissipation, controllable modulation linearity, large-scale monolithic integration capability, low modulation power, full coverage of the entire fiber transmission window, small footprint, and potentially low cost [22]. In addition, SOAs are utilized appropriately as intensity modulators because they can perform the modulation and the amplification simultaneously, and these are an ideal option to increase the speed and efficiency of optical networks [23].
Quantum dot semiconductor optical amplifiers (QD-SOAs) have illustrated a great number of remarkable properties for utilization in numerous applications from all-optical signal processing to optical communication systems [24], [25]. The most salient features enabling their implementation in next-generation high-speed optical access networks include WDM [26], [27], large saturation power [28], potential cost-effectiveness [29], high operation speed [30], patterning-free optical amplification [31], ultrafast gain recovery [32], and the potential for monolithic integration with other optoelectronic devices [33].
A comparison between two structures of SOA intensity modulator and QD-SOA intensity modulator has been accomplished in [34]. In this research, in 60km single mode fiber, the bit rate is 30 (Gb/s) for SOA in 15-24 dBm probe power and 50-200mA bias current and is 32(Gb/s) for QD-SOA in 10-25dBm probe power and 50-200 bias current. In addition, the gain in the input probe of 10dBm and the bias current of 900mA is about 15dB, and the extinction rate in the structure is 0.55. A structure with three electrodes for injecting bias current is presented for an intensity modulator based on QD-SOA [24]. They reported that this structure solves the nonlinearity defects related to one or two electrode structures. Therefore, at a telecommunication distance of 20-40km with the probe power of -10dBm and the bias current of 300mA, it achieves the bit rate of 35(Gb/s) and the modulation depth of 80%. The saturation gain in this structure is reported 20dB.
Recent advancements in QD-SOA technology and related optical systems have focused on improving modulation depth, bandwidth, and tunability to meet the demands of next-generation optical communications. For instance, optofluidic laser sensors and tunable plasmonic photodetectors in the near-infrared range have demonstrated high sensitivity and efficient light manipulation, highlighting the potential of integrated photonic systems for high-speed signal processing [35]. In this context, graphene-based devices, such as broadband polarization converters, enable dynamic optical control over a wide frequency range, emphasizing the significance of tunable optical components in modern communication networks [36]. Moreover, perovskite metasurfaces have facilitated ultrafast all-optical modulation, achieving an unprecedented signal modulation depth of 2500% with a femtosecond-scale response time, paving the way for high-speed optical computing [37]. Additionally, recent advancements in QD-SOAs have led to the development of polarization-independent designs, such as the polarization-independent quantum dot semiconductor optical amplifier (PIQS) with a fiber-to-fiber gain of 22 dB, addressing critical challenges in optical amplification [38].
Despite these advancements, achieving both high modulation depth and gain simultaneously in dual-channel AOMs based on QD-SOAs remains a major challenge. Most existing studies focus on single-channel modulation, and optimizing modulation performance across multiple wavelengths has yet to be fully realized. Furthermore, the potential of solution-processed quantum dots for enhanced absorption and tunability in dual-channel AOM architectures has not been extensively explored. This research aims to bridge these gaps by introducing a solution-processed InSb/SiO₂ QD-SOA structure capable of simultaneously modulating and amplifying two distinct telecommunication wavelengths (1.31 µm and 1.55 µm), providing a practical approach for high-speed optical communication applications.
This paper presents a novel concept for a dual-channel all-optical modulator utilizing QD-SOAs. The proposed device is developed using a solution-processed InSb/SiO2 quantum dot core/shell structure, offering advantages such as enhanced absorption, high efficiency, cost-effective fabrication, room temperature processing, ease of large-area production, and excellent tunability. [39], [40], [41], [42], [43], [44]. For the first time, two different wavelengths within the telecommunication windows have been modulated and amplified simultaneously by applying two pump signals with two different wavelengths of visible range at a high temperature of 300K. Unlike most previous studies, the two-channel AOM based on QD-SOA in this novel approach can be adjusted to modulate and amplify selective wavelengths by tuning QDs’ sizes. Moreover, some non-idealities of fabrication conditions have been analyzed in this modulator to propose a practical device. The introduced two-channel AOM is adjusted to absorb two visible wavelengths of 519nm (green) and 663nm (red) and two independent probe signals with wavelengths of 1.31µm and 1.55µm are applied to enable stimulated emission and amplify the modulated signal. This high-speed two-channel AOM based on QD-SOA with a high modulation depth and high optical gain can utilize in several applications, including thermal imaging, signal processing, high-speed computing systems, night vision cameras, wavelength de-multiplexing (WDM), optical communication networks based on dense wavelength division multiplexing (DWDM) technology, free-space communication, online learning systems, and online medical services [21], [45], [46].
2. THE PROPOSED TWO-CHANNEL AOM BASED ON QD-SOAS
In this study, two distinct sizes of core/shell QDs, fabricated using the solution process method, have been employed to design a high-contrast all-optical modulator based on QD-SOAs. It has been exploited InSb as the core and SiO2 as the shell to form the absorber layer for the suggested structure. As depicted in Fig. 1(A), laser beams with different wavelengths are used as pump and probe signals, applied through separate channels. Dots with radiuses R1 and R2 are related to channel-1 and channel-2, respectively.
Interband and intersubband transitions between quantized energy levels of the valence band and the conduction band are very considerable in the modulation and amplification process. Two Square pulses, as the information pump signals with the wavelengths of 519nm (green) and 663nm (red), also two continuous waves (CW) as the probe signals with the wavelengths of 1.31μm and 1.55μm (NIR spectra) are applied simultaneously which are adjusted for the QD radiuses of R1=2.65nm and R2=3.15nm, respectively. By applying pump signals, electrons absorb from the excited state of the valence band (ESv) to the excited state of the conduction band (ESc). Then, the excited electrons descend to the ground state of the conduction band (GSc) rapidly due to the small amount of relaxation time. At the moment, two CW probe signals lead to stimulated emission of electrons from GSc to the ground state of the valence band (GSv) because of the population inversion happened in the conduction band. Eventually, many photons are generated, and the probe signals will be modulated and amplified. The absorption, emission, and recombination process have been demonstrated in Fig. 1 (B). The time constants corresponding to these carrier transition procedures are depicted in Fig. 1(B) as τgev (electron decay time from the GSv to the ESv), τegc (electron decay time from the ESc to the GSc), τgr (carrier lifetime from the GSc to the GSv), τer (carrier lifetime from the ESc to the ESv), the time constants according to FRET mechanism are illustrated as τdown-trans-g(e) (electron transition time from the GSc (ESc) of channel-1 to the GSc (ESc) of channel-2) and τup-trans-g(e) (electron transition time from the GSc (ESc) of channel-2 to the GSc (ESc) of channel-1).
Fig. 1. A) Schematic of two different sizes of QDs arrayed by core/shell InSb/SiO2 structure. B) The simulated energy band structure of the proposed device by representing the modulation and amplification mechanism
3. The theoretical Modeling of the proposed structure in the rate equation framework
In this section, for modal analysis of two-channel AOM based on QD-SOA, the 3D Schrodinger equation has been solved to achieve eigen-energies, wavefunctions, and the energy band diagram. Subsequently, to analyze the performance of the two-channel AOM based on QD-SOA and characterize the key metrics of the modulator, the coupled rate and propagation equations are solved. In addition, the impacts of the homogeneous and inhomogeneous broadening and the fluorescence resonance energy transfer (FERT) are involved in coupled rate equations.
By considering the effective mass approximation method and solving the 3D Schrödinger equation by use of the values referred to in Table 1, the energy band diagram of the structure is obtained, as illustrated in Fig. 1(B). Also, eigen-energies and the corresponding wavefunctions of the GSc, ESc, GSv, and ESv have been obtained using the Finite Element Method (FEM) software. The periodic boundary condition is applied for extending the simulated device to the practical system. As Fig. 1(B) displays, the variety between the ESv and ESc in determined QDs is 2.39eV for channel-1 and 1.87eV for channel-2, appropriately adjusted for interband absorption of the pump signals at 519µm (green) and 663µm (red) wavelengths, respectively. Moreover, the variety between the GSc and GSv is 0.94eV for channel-1 and 0.79eV for channel-2, that is proper for the stimulated emission of 1.31μm and 1.55μm wavelengths, respectively. The 3D computed wavefunctions corresponding to each state of the main mode for both channels are similar to our previous work depicted clearly in [47].
TABLE I Materal properties used in calculating the 3D Schrodinger equation. [48], [49], [50], [51], [52].
| ||||||||||||||||||||||
Due to the restriction of synthesis conditions during the solution process method, the designed exact size of QDs cannot be achieved [45], [53], [54], [55]. Therefore, the non-uniformity of the QDs size will affect the absorption spectra, and the created distribution of energy states is modeled by the Gaussian profile whereat the QDs ensemble is partitioned to 2M + 1 groups of uniform QDs with an energy spacing of ΔE=1meV [29], [56], [57], [58].
| (1) |
| (2) |
here, 
the transfer energy corresponds to the most probable size of QDs (M+1-th QD group), with the index 𝑖 fixed at 1 for channel-1 and 2 for channel-2 The index n refers to the number of active modes, and ξ0 represents the QD coverage defined as ξ0 =(1/2.35)FWHM [29], [45].
Furthermore, intrinsic effects such as pressure or temperature lead to interactions between carrier-carrier and phonon-carrier which homogeneously affect all groups, so homogenous broadening will appear on the energy levels. This HB is modeled by a Lorentzian profile with 
=20meV as its FWHM at room temperature [47], [59].
| (3) |
In consideration of the broadenings acquired, the linear interband absorption coefficient from ESv to ESc arising from applied pump power is attained by [60]:
| (4) |
Here, c denotes the speed of light in free space, and ε0 represents the permittivity of free space, 
is the refractive index related to pump wavelengths, ħ is the reduced Planck’s constant, e is the electron charge, and 
is the volume of the QD. The term 
is the interband transition dipole moment. In final, the total interband absorption is attained through:
| (5) |
Similarly, the gain as a result of the stimulated emission from GSc to GSv by applying probe power is obtained by:
| (6) |
Here 
is the refractive index related to probe wavelengths and the term 
is the interband transition dipole moment. In final, the total gain is obtained through:
| (7) |
On the other hand, Fluorescence (or Förster) resonance energy transfer (FRET) is a non-radiative energy transfer procedure in which a donor (a dot with a smaller radius) transfers the energy to an acceptor (a dot with a larger radius) through dipole-dipole interactions [61]. The transmission rate depends on the distance between two dots and the spectral overlap. In the proposed two-channel AOM based on QD-SOA due to utilizing two distinct groups of QDs, this transfer procedure is assumed as a transmission rate (
) attained through:
| (8) |
Here, 
is the effective volume of QDs with different sizes, and
. The time constants related to transfer between two different sizes of QDs are computed by 
and involved in coupled rate equations.
4. THE RATE AND PROPAGATION EQUATIONS
The performance of the designed two-channel AOM based on QD-SOA is primarily determined by the dynamics of carriers and photons. For analyzing and modeling, the semiconductor Bloch equation can be used, which provides a more accurate approach for these characteristics. However, in order to avoid the difficulty and time-consuming of calculating the equations, the rate and propagation equations have been solved, and these equations have reported acceptable results. The square pulse train of pump signals and the CW probe signals are propagated along the z-direction. The coupled rate and propagation equations for the proposed structure employing the parameters of Table 2 are represented as:
| (10) |
| (11) |
| (12) |
| (13) |
| (14) |
| (15) |
| (16) |
Where 
, 
, 
, and 
are the number of electrons in GSc, ESc, GSv, and ESv, respectively. Additionally, 
and 
are the optical pump power and the CW probe power, respectively. The corresponding carrier occupation probabilities are illustrated as 
, 
, 
, and 
, respectively. Additionally, the number of electrons corresponding to their respective occupation probabilities are calculated by
, 
. All the time constants are explained in detail in Section 2. Furthermore, the time constants related to the electron escape process in the valence and the conduction bands are acquired as:
| (17) |
TABLE Ⅱ The parameters required in calculating rate and propagation equations [62], [63], [64].
| |||||||||||||||||||||||||||||||||||||||||||||||||||
is the energy interval between ESc(v) and GSc(v) [65], [66], [67]. Degeneracies are determined by 
,
, 
, and 
. The total number of electrons of each state, GSc, ESc, GSv, and ESv are demonstrated with 
, 
, in which NQD,i is the density of QDs and Vd is the volume of the active region for both channels.
5. SIMULATION RESULTS
In this section, the performance of the proposed two-channel AOM based on QD-SOA has been determined by evaluating the coupled rate and propagation equations (9-16) according to the parameters referred in Table2. The most critical metrics in the characteristics of an intensity modulator based on SOA are the gain and modulation depth (MD). So, these parameters are achieved, and the effects of some non-idealities of fabrication condition on the performance of the structure are investigated as follow.
Fig. 2. A) Applied pump power signals with the frequencies of 3GHz for channel-1 and B) 4GHz for channel-2. C) Output modulated probe power signals as a function of time for channel-1 and D) for channel-2. E) Calculated gain versus time for both channels. F) Calculated linear absorption versus time for both channels
According to Fig. 1(A, B), two square pump power signals with different frequencies have been applied for each channel. In order to explain the synchronicity and asynchrony of the activation of the channels, the output modulated probe power have been represented in Fig. 2(C, D). Channel-1 (smaller QD) has a frequency of 3GHz, and channel-2 (larger QDs) has a frequency of 4GHz. As the results show in Fig. 2(E, F), when the pump power is applied to just one channel, in the gain and the absorption profile, the value of the channel with zero input power has moved away from its stable state, which indicates that the two channels are correlated to each other because of the FRET mechanism.
Fig. 3. The gain profile versus the pump power density for both channels at the probe power of -20dBm
Due to the increase in input pump density for the fixed probe power value of -20dB, it is expected that the gain will ascend because of the enhancement in carrier absorption from the valence band to the conduction band, which causes an increment in excited carriers in the conduction band. Increasing carriers in ESc leads to increasing in the stimulated emission in the presence of the probe power and thus increases the gain. Furthermore, as the pump power density increases, the gain increases until ESc is not saturated with excited carriers. As seen in Fig. 3, with the increase of the pump power density up to 500W/cm2, the gain changes almost linearly. From this value onwards, as the pump power density increases, the changes in the output gain are small, which shows the saturation of ESc.
As a result, the output probe power and the gain will be stable at high pump power densities.
Fig. 4(A) displays the saturation of the gain in low probe power values, and it indicates that with increasing the input probe power, the gain goes out of the saturated state (linear) and moves to the nonlinear state. For amplification, probe powers that are specific to the saturation regime are used, and for signal processing, probe powers that are greater than the saturation input probe power of 3dB are utilized. It can also be realized that up to the probe power of 0dBm, this structure with a pump power density of 500W/cm2 is still able to amplify the input probe power. The saturated gain in this structure is 23.6dB and 24.8 dB for channel-1&2, respectively. Fig. 4(B) represents the modulation depth (MD) as a function of the input probe power, which can be concluded that until the probe power of 20dBm MD has a suitable value after that, it reduces by increasing the probe power.
Fig. 4. A) Gain of the proposed device as a function of probe power for both channels. B) MD of the proposed device as a function of probe power for both channels
One of the parameters that affect the gain of the device is the carrier recombination time. This parameter is completely dependent on the conditions of QDs’ fabricating process. Due to the presence of traps that modify the recombination process time, it is possible to control the recombination time by engineering the construction of these QDs. Fig. 5(A, B) shows the output probe power in different carrier lifetimes for channel-1&2 which indicates that by increasing the lifetime, the output probe power increases.
Fig. 5. Output probe power versus time for different values of carrier lifetime A) for channel-1 and B) for channel-2. C) The gain of the device as a function of carrier lifetime
This is because with the increase of lifetime, the probability of spontaneous emission of electrons decreases. As a result, the noise arising from the creation of unwanted photons from spontaneous emission is reduced. In this case, there will be more time and more carriers to perform stimulated emission by applying the probe signal. Fig. 5(C) illustrates the gain variation with respect to the different lifetimes, and it indicates that the gain converges as the lifetime increases from 1ps to 1ns. The life time in all simulations is fixed for the optimal value of 10ns.
Another parameter that affects the gain are the volume density of QDs (Nd) which depends on the QDs synthesis process. According to Fig. 6(A, B), it can be emphasized that for both channels, the amount of Nd should not be more or less than a value, which directly affects the gain and subsequently reduces the output probe power. According to this figure, the gain has the maximum value in Nd=0.5×1015 for both channels.
Fig. 6. Output probe power versus time for different values of Nds A) for channel-1 and B) for channel-2
On the other hand, ΓIHB defined as the FWHM of the non-uniform distribution of QDs also affects the gain of the proposed device. Fig. 7(A) indicates that with the increase of ΓIHB up to 25meV, the gain increases for both channels, and then with a further increase of ΓIHB a decrease in the gain can be observed. In addition to the gain has its maximum value when ΓIHB=25meV, another point is that this amount of FWHM in the inhomogeneous broadening does not cause a lot of complexity and difficulty in the synthesis and construction of this device, and this is very valuable.
In the end, the effect of changes in the input pump frequency on the MD is depicted in Fig. 7(B) for both channels. Given that with the increase in the frequency, the carriers have little chance to recover themselves and return to a stable state; therefore, the MD, which is defined as the distance between the ON and OFF state at the output, is reduced. In other words, at high frequencies, some carriers exist in the conduction band even when the pump power is not present, which causes a gain when the pump power is OFF. Eventually, the distance between the ON and OFF state in the output probe power is reduced, and thus, the MD is reduced.
The structural parameters of the proposed dual-channel AOM were carefully selected based on quantum confinement effects, optical absorption characteristics, and practical telecommunication standards. The quantum dot (QD) radii (R₁ = 2.65 nm, R₂ = 3.15 nm) were determined by solving the 3D Schrödinger equation, ensuring that their absorption peaks align with the chosen pump wavelengths (519 nm, 663 nm) and their emission matches the telecommunication probe wavelengths (1.31 µm, 1.55 µm). These wavelengths were selected to maximize optical gain and modulation efficiency while maintaining compatibility with standard fiber-optic systems. Additionally, the pump power density (500 W/cm²) was optimized through numerical simulations of coupled rate and propagation equations to achieve high modulation depth (~100%) and gain (~17.94 dB and 17.14 dB).
Fig. 7. A) Calculated gain as a function of ΓIHB for channel-1 and channel-2. B) MD has been reduced by increasing the pump frequency for both channels.
Fabrication imperfections introduce slight variations in structural parameters [68]. To assess the robustness of the proposed AOM, we analyzed its sensitivity to deviations in key design values. A ±5% change in QD radius results in less than a 1% shift in absorption/emission wavelengths, ensuring stable operation. The device also tolerates pump power fluctuations of ±10% with minimal impact on gain (~1 dB variation) and maintains >90% modulation depth. Additionally, a ±5 nm misalignment in pump or probe wavelengths leads to only a ~5% reduction in modulation depth, demonstrating the flexibility of the proposed structure. These findings confirm that the device remains functional under realistic fabrication constraints, making it feasible for experimental implementation.
6. Conclusion
In this study, a new conception of a two-channel AOM employing the colloidal InSb/SiO2 structure based on QD-SOAs with the solution process method is introduced. The proposed structure is suggested to modulate and amplify two distinct wavelengths of telecommunication windows (1.31µm, 1.55 µm) simultaneously by applying two pump signals with two different wavelengths of the visible range (519nm, 663nm) through two separate channels. For modal analysis of the designed two-channel AOM based on QD-SOAs 3D Schrodinger equation has been solved, and to appraise the theoretical analysis the coupled rate and propagation equations have been calculated. From the simulation results, it can be accomplished that the modulation depth is obtained 100 % and the gain is about 17.94 dB and 17.14 dB in the pump power density 500W/cm2 and probe power -20dBm for channel-1 and channel-2, respectively.
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