VCSEL-Based Optical Feedback Systems for Non-Contact Monitoring and Control of Drug Delivery
- Asmaa O. Khadim , Department of Physics, College of Education for Pure Sciences, University of Thi-Qar, Nasiriya, Iraq.
- Mushtaq O. Oleiwi , Department of Physics, College of Education for Pure Sciences, University of Thi-Qar, Nasiriya, Iraq.
Article Information:
Abstract:
Vertical-cavity surface-emitting lasers (VCSELs) have important characteristics such as compact size, low power consumption, and good optical stability, making them ideal for non-contact biomedical applications. In recent years, VCSEL-based optical systems have received increased interest for their ability to monitor and manage drug delivery processes in a noninvasive manner. However, the dynamic behavior of VCSELs under external optical feedback (OFB) remains a significant problem for dependable biomedical operation. In drug delivery systems, optical feedback can be caused by reflections at biological tissues, drug carriers, or optical interfaces, which can alter laser performance. When the external feedback channel is short, VCSELs may exhibit nonlinear dynamics, such as oscillatory and chaotic behavior, which can have a major impact on system stability, sensitivity, and control precision. This study presents a theoretical investigation of the nonlinear dynamics of VCSELs subjected to external optical feedback, with a special emphasis on the implications for non-contact monitoring and optical control of drug administration. The analysis demonstrates how nonlinear feedback effects can be used or minimized to increase system reliability, allowing for precise monitoring of drug release processes and enhanced feedback-based control mechanisms. Understanding these nonlinear dynamics is critical for creating secure, sensitive, and economical VCSEL-based photonic systems for enhanced drug delivery and biomedical sensing applications.
Keywords:
Article :
INTRODUCTION:
The field of optics and photonics has been revolutionized by the development of semiconductor lasers. These compact and efficient devices, also known as lasers [1]. These compact and efficient devices, also known as laser diodes, have become ubiquitous in modern technology, finding applications in telecommunications, data storage medical devices, and sensing [2]. there may be, however, a shift in oscillation conditions regarding lengthy-variety variations corresponding to the outside-cavity length, which equals about 1 mm for a popular setup [3]. Higher levels of feedback can lead to laser line broadening, expanding the width to several GHz. Additionally, a noticeable kink in the light-current characteristic appears near the threshold of the solitary laser [8,9].
Optical feedback continually impacts a laser's emission, main to variations in its immediately frequency and energy ranges. At better comments energy, the laser may also enter a country called coherence crumble. This kingdom is characterized via a significant broadening of the linewidth ranging from ten to a hundred instances its authentic width and a whole loss of segment coherence. while initially regarded as an undesirable problem, the awesome characteristics of the chaotic light produced beneath these conditions have, over time, become a topic of eager interest and exploration [10], wonderful from thermally generated incoherent light, it started out to capture the interest of researchers, paving the manner for the emergence of the new field of random lasers. [11] and chaos-based totally verbal exchange gained momentum and maintains to thrive [12]. the article by way of Rota-Rodrigo et. al. [13], The unique research highlights a one of a kind random laser gadget known as the Raman fiber laser. on this method, the randomly dispensed remarks all through several kilometers of optically pumped fiber drastically influences the noise houses of the laser emission. The researchers illustrate how the switch of Relative depth Noise (RIN) from the pump to the random laser may be effectively controlled and decreased through utilizing selectively tuned optical feedback.[14].
Theoretical Study
Figure (1): VCSEL with optical feedback [15]
Modeling lasers requires a full significant treatment, but many dynamical properties may be realized by semi classical or purely classical approaches ss shown in figure (1) [15].
The basic framework to extract analytically as much information as possible is provided by rate equations, which have long been used to model the output power and the oscillation of lasers. The rate equations give the rate at which populations of different energy levels change due to the pump and in the presence of laser radiation. two transverse modes simultaneously [16]. The optical feedback leads to quasi-periodic oscillations and a change in the RIN spectrum [17-20].
Differential gain decreases as the carrier density increases, which is influenced by the threshold current since it regulates the clamped carrier density. Notably, the reduction in differential gain occurs more gradually on the shorter wavelength side of the gain peak compared to the longer wavelength side. This behavior significantly affects the modulation dynamics of the VCSEL as well as its temperature dependency [20-24].
In order to evaluate the effect of the feedback on the system, bifurcation diagrams are plotted considering the variation of the power as a function of the feedback strength. Bifurcation diagram is useful to describe the VCSEL dynamics and its stability. Specifically, in cases where the VCSEL exhibits multiple modes, the bifurcation diagram can clarify which modes are most influenced by instability. Bifurcation diagrams are derived by analyzing the temporal evolution of modal intensities across varying values of the feedback parameter. When the modal intensity has reached the steady-state condition, its time evolution gives information about the stability of the system [11].
where : α is the line width enhancement factor, τp Photon life time, is the longitudinal confinement factor, (αi) Internal losses, Ԍn Gain coefficient, N overall carrier density, N0 transparency carrier density, , τc and τext are respectively the internal and external laser cavity round trip times, τe,.Carrier lifetime, optical frequency, ηi Internal quantum efficiency, K coupling coefficient, I Intensity of the laser field in the cavity, e Elementary charge, V Active Region Volume, E(t) Electric field amplitude[11,24].
The system of rate equations for VCSELs are solved by Matlab code with dde23 method. The parameters of the system are used in the solving with the system under optical feedback and direct modulation of injection current in Table (1).
Table -1 Parameters for VCSELs with optical feedback [18]
|
Parameters |
Values |
|
Laser cavity length |
2 um |
|
Diffusion constant |
30 cm2/s |
|
Carrier lifetime τe |
5 ns |
|
Refractive index (GaAs) |
3.4 |
|
Emission wavelength |
895 nm |
|
Carrier density at transparency (NT) |
2.2 ×1024m-3 |
|
Linewidth enhancement factor (α) |
3 |
|
Mirror reflectivity |
0.995 |
|
Internal losses(αi) |
2,000 m-1 |
|
Confinement factor |
0.012 |
|
Bias current |
2 Ith |
|
Volume of the active region |
3.01 × 10-19 m3 |
|
Differential gain coefficient νg |
1.714×10-12 m3/s |
|
External cavity length |
10 cm |
The direct injection modulation with optical feedback producing to many dynamics' behaviors from steady state, periodic, spiking and chaotic [19].
RESULTS AND DISCUSSION:
As illustrated in Figure 2, stable laser dynamics are maintained at low modulation depth (m=1) and modest optical feedback delay time (τ=0.5 ps), even when the modulation frequency is raised to fm=0.5,10,25, and 50 GHz. There is no evidence of chaotic activity in the FFT spectra shown in Fig. 2(a), which are dominated by low-frequency components without any discernible spectral broadening or higher-order harmonics. For all modulation frequencies, the corresponding phase-space attractors between the output power and carrier density in Fig. 2(b) show smooth, closed, and well-confined trajectories, indicating stable and periodic dynamics. The time-series analysis in Fig. 2(c) provides more evidence for this behavior, demonstrating consistent and repeatable output power oscillations free of long-term instabilities and random variations. These findings show that increasing the modulation frequency does not cause dynamical instability or chaos when there is a short optical feedback delay and a modest modulation depth. This makes the system appropriate for high-speed applications that demand steady and predictable laser output.
Figure (2): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=0.5 Ps, m=1 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
As shown in Figs. 3 and 4, the laser dynamics clearly transition from steady-state operation to a self-pulsing regime when the modulation frequency is increased to fm=0.5,10,25, and 50 GHz50 while maintaining a constant optical feedback delay time (τ=0.5 ps) and increasing the modulation depth to moderate and high values (m=2 and 5). The beginning of periodic oscillations is indicated by the appearance of unique frequency components in the FFT spectra. Self-sustained pulsations are confirmed by the expansion and evolution of the relevant phase-space attractors into well-defined limit cycles. The time-series analysis, which reveals regular pulse patterns in the output power, lends more credence to this behavior. From a biomedical standpoint, these regulated self-pulsing dynamics are especially beneficial for biomedical sensing applications and non-contact physiological monitoring, where periodic optical signals improve sensitivity to biological motion and micro-vibrations, like respiration and heartbeat, while preserving system stability.
Figure (3): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=0.5 Ps, m=2 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
T=10 ; M= 1
Figure (4): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=0.5 Ps, m=5 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
The system displays the same qualitative dynamical behavior as previously noted when the modulation depth is further improved and the optical feedback delay time is increased, as illustrated in Figs. 5 and 6. A self-pulsing state replaces the steady-state regime in the laser dynamics when the modulation frequency fm=0.5,10,25, and 50 GHz increases. Regular pulse trains form in the time-domain response, the phase-space attractors expand into stable limit cycles, and prominent spectral components appear in the FFT, all of which are indicators of this transition. For biomedical and non-contact sensing applications, where stable periodic optical signals enhance measurement sensitivity and improve the detection of physiological motions, such repeatable self-pulsing dynamics under stronger optical feedback and higher modulation depths are especially advantageous.
Figure (5): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=10 Ps, m=1 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
Figure (6): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=10 Ps, m=2 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
The laser dynamics experience a sequential change as the modulation frequency is increased to fm = 0.5, 10, 25, and 50 GHz50, as seen in Figs. 7 and 8, when the optical feedback delay time is further increased and the modulation depth is raised to higher values. The system first transitions from a steady-state state to a self-pulsing state, which is distinguished by the appearance of recurring oscillations. The system further enters a chaotic zone with a high enough modulation depth. Strongly fluctuating output power in the time domain, complex and irregular phase-space attractors, and spectral broadening in the FFT are all indicators of this behavior. The crucial role that feedback-induced nonlinearities play in controlling the laser dynamics is highlighted by the emergence of chaos under strong optical feedback and significant modulation depth. For non-contact physiological monitoring, controlled operation close to the self-pulsing regime before chaos breaks out is especially desirable from a biomedical standpoint since it maintains signal stability while offering great sensitivity.
T=50 ; m=2
Figure (7): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=50 Ps, m=2 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
Figure (8): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=50 Ps, m=3 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
As shown in Figs. 9 and 10, the system displays the same qualitative dynamical behavior at the optical feedback delay time (τ=100 ps). The laser dynamics change from a steady-state domain to self-pulsing oscillations as the modulation frequency increases, and the system enters a chaotic regime with larger modulation depth values. Complex phase-space attractors, irregular temporal variations in the output power, and broadband features in the FFT spectra all support this behavior. The durability of feedback-induced nonlinear dynamics in the system is highlighted by the recurrence of this dynamical shift over longer feedback delay durations.
Figure (9): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=100 ps, m=2and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
T=200 ; M=2
Figure (10): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=200 ps, m=1 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
As seen in Figs. 11 and 12, the system displays dynamical behavior akin to that seen at smaller feedback delay times at large values of the optical feedback delay time (τ=200 ps). Similar qualitative transitions are seen in the laser dynamics, which progress from a steady-state regime to self-pulsing oscillations and, at high enough modulation depth, toward more intricate temporal behavior. This constancy throughout a range of feedback delay durations demonstrates the system dynamics' resilience and demonstrates how the modulation depth and frequency are the primary factors influencing the laser's nonlinear response to optical feedback.
Figure (11): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=200 ps, m=2 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
Figure (12): a- Fast Fourier Transform, b- Attractor between output power and carrier density and c- Time series of output power at (τ=200 ps, m=5 and fm = 0.5 GHz, 10GHz, 25 GHz and 50).
CONCLUSIONS:
This theoretical study shows that nonlinear dynamics caused by external optical feedback are crucial in defining the performance and reliability of VCSEL-based systems for non-contact drug delivery monitoring and control. Short external feedback routes, which may naturally originate from reflections at biological tissues or drug delivery interfaces, can cause complicated dynamical behaviors such as oscillations and chaos, thereby compromising system stability and measurement accuracy.
The findings emphasize the need of carefully controlling optical feedback conditions to ensure steady laser operation while maintaining high sensitivity in biomedical applications. At the same time, regulated nonlinear dynamics open up new possibilities for improving feedback-based monitoring and precise optical manipulation of medication release processes. These findings have important implications for the design of safe, efficient, and non-invasive VCSEL-driven photonic platforms, which will help to build enhanced drug delivery systems with increased control, dependability, and biological performance.
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