Applications of Prepared MnMoO₄ Nanoparticles as Saturable Absorbers for Q-Switched Erbium-Doped Fiber Lasers: Experimental and Theoretical Analysis

Abstract

This study presents the synthesis of manganese molybdenum tetraoxide (MnMoO₄)-based nanoparticles and then their experimental demonstration as saturable absorbers (SAs) in erbium-doped fiber lasers (EDFLs). The MnMoO₄ nanoparticles were prepared and then embedded between the fiber ferrule to act as an SA to generate Q-switched pulsed operation in EDFLs. For the characterization, scanning electron microscopy (SEM) was employed to confirm the particle size of the prepared MnMoO₄ nanoparticles, and the SA optical properties were further investigated by measuring their modulation depth and saturation intensity. By implementing the prepared SA within the cavity, the measured results revealed that under pump power ranging from 28 to 312.5 mW, the laser exhibited Q-switched pulse durations varying from 15.22 to 2.35 µs and repetition rates spanning from 24.98 to 88.11 kHz. The proposed EDFL system delivered an average output power between 0.128 and 2.95 mW, pulse energies ranging from 5.12 to 33.49 nJ, and peak power from 0.281 to 6.26 mW. The laser stability was also confirmed by continuously noticing the pulse duration, emission wavelengths, and pulse repetition rates for 4 h. Finally, a numerical model based on a nonlinear Schrödinger equation (NLSE) was employed to validate both experimental and theoretical results of the passive Q-switched EDFL. These findings highlight the potential of EDFLs utilizing MnMoO₄-based SAs for potential applications in pulsed laser sources.

1. Introduction

Pulsed lasers have attracted major attention due to their compact design, durability, and ability to deliver a high average output power with minimal maintenance [1]. Their applications span telecommunications [2,3], microfabrication, sensing [4], and industrial processes such as precision cutting, cleaning, and surface texturing. Among these, passively Q-switched (PQS) fiber lasers are particularly promising due to their cost-effective and stable pulse operation and suitability for high-precision applications [5,6]. Erbium-doped fiber lasers (EDFLs), operating at 1550 nm, are advantageous due to their broad bandwidth and high gain efficiency. Their low transmission loss over long distances makes them ideal for optical communication, ensuring superior signal integrity [7].

Additionally, EDFLs exhibit excellent beam quality, making them suitable for high-precision applications in various scientific and industrial domains. Pulse generation in fiber lasers is primarily achieved through mode-locking and Q-switching. In Q-switched fiber lasers, pulse formation is controlled by typical passive and active techniques. Active Q-switching relies on external modulators to regulate intracavity losses and enhance energy storage [8]. In contrast, PQS utilizes a saturable absorber (SA) to modulate cavity losses automatically, offering a simpler and more compact laser design. A SA contains a material that absorbs light at low intensities but becomes transparent as intensity increases, allowing light to pass through. As incident light intensity rises, electrons in the valence band absorb energy and jump to the conduction band, leaving the valence band empty. These excited electrons then undergo de-excitation, and the interaction between high-intensity light and electron relaxation plays a crucial role in modulating pulse shaping, improving pulse efficiency, and enhancing overall pulse performance.

Various types of SAs have been explored for PQS lasers, including black phosphorus [9], carbon nanotubes [10], MXenes [11], MAX phases [12], metal-organic frameworks (MOFs) [13], semiconductor saturable absorber mirrors (SESAMs) [14], transition metal dichalcogenides (TMDs) [15], and graphene [16]. Each material possesses a specific bandgap, distinct electronic states, and varying nonlinear optical properties. However, they also have certain drawbacks as SAs. Black phosphorus degrades rapidly under ambient conditions due to oxidation, requiring protective encapsulation. Carbon nanotubes tend to aggregate, leading to inconsistent optical performance. MXenes are highly susceptible to oxidation, which degrades their optical response over time, and their fabrication process is complex. MAX phases exhibit a relatively weak nonlinear optical response, which limits their efficiency in pulse generation. MOFs often suffer from lower thermal stability and mechanical robustness, affecting their long-term reliability in laser systems. SESAMs have high fabrication costs and relatively slow recovery times, restricting their potential use in ultrashort laser applications. TMDs exhibit layer-dependent optical properties, leading to performance inconsistencies, and their fabrication remains challenging. Graphene, despite its efficiency, lacks a direct bandgap, resulting in a weaker modulation depth and limiting its ability to generate high-energy pulses. These limitations highlight the need for further research to develop SAs with improved stability, efficiency, and durability for fiber laser applications. Among them, metal oxides serve as effective SAs due to their strong nonlinear optical response, allowing for PQS in fiber lasers. Their high thermal stability supports reliable performance under intense operating conditions, while their broad optical transparency enables adaptability across different wavelengths. Oxygen vacancies and defect states contribute to enhanced light absorption and nonlinear interactions between intense pulses and oxide materials, improving pulse generation. Their ability to be processed into various forms, such as thin films and nanocomposites, ensures easy integration into laser systems. Compared to other materials, metal oxides provide long-term structural stability, making them well-suited for photonic applications. MirerShadi et al. examined the nonlinear optical behavior of MoS₂ nanoflakes employing the Z-scan approach with a 532 nm CW laser, and it was found that nonlinear refraction dominates, and they explored the impact of MoS₂ thickness on self-focusing and self-defocusing effects. The high third-order susceptibility (~10⁻⁷ esu) and second-order hyperpolarizability (~10⁻³² esu) highlight the material’s potential for photonic applications [17]. Sharma et al. synthesized molybdenum oxide thin film (250–260 nm) via thermal deposition under high vacuum conditions. XRD and Raman spectroscopy confirmed their amorphous nature, with key peaks at ~805 cm⁻¹ and ~986 cm⁻¹. The optical bandgap was determined as 3.16 eV using Tauc’s plot, and optical dispersion was analyzed using the Wemple–DiDomenico model. AFM revealed a uniform surface with ~10 nm peak-to-valley variation. Nonlinear optical properties were estimated using the generalized Miller’s rule, highlighting the material’s potential for photonic and optoelectronic applications [18]. Most recently, Ahmed et al. implemented a MoS₂-SA in an EDFL-based ring cavity and investigated the performance of the laser both experimentally and theoretically [19]. The current study demonstrates the synthesis of MnMoO₄ structures and their implementation in an EDFL cavity to act as an SA. The MnMoO₄ nanoparticles were characterized using SEM. Once implemented inside the laser cavity to act as a SA, the EDFL based on a MnMoO₄ SA yielded a minimum pulse duration of 2.35 µs, maximum repetitions of 88.11 kHz, and a maximum average output power of 2.95 mW at a maximum pump power of 312.5 mW. Moreover, the stability of pulsed EDFL was further explored for 4 h, confirming the system’s reliability. Additionally, a numerical model was further implemented to investigate the efficacy of the proposed EDFL.

2. Synthesis and SEM Analysis of MnMoO₄ Nanoparticles

A solid-state route was preferred for the synthesis of single-phase manganese molybdenum tetraoxide. For this purpose, manganese nitrate tetrahydrate [Mn(NO₃)₂·4H₂O] and molybdenum trioxide [MoO₃] (purity ≥ 99% Sigma Aldrich, St. Louis, MO, USA) were selected as precursors. A properly stoichiometrically calculated and measured quantity of the salts mentioned above were placed in the ball-milling chamber and crushed thoroughly at 25 Hz for 210 min with a milling time span of 30 min each. The crushed material was then calcined at 800 °C for three hours to obtain a proper phase and structure. Finally, the powder was ground to produce fine powder for further characterization.

The SEM image of MnMoO₄ at 1000× magnification displays an agglomerated microstructure with irregular particles forming a porous network. The structural characteristics observed could influence the material’s interaction with light, affecting its optical performance, as shown in Figure 1a. Further, based on SEM analysis, the synthesized MnMoO₄ nanoparticles exhibit well-defined crystalline grains with an estimated size range of approximately 80 nm to 200 nm, as shown in Figure 1b. Most particles are comparable to or slightly larger than the 100 nm scale bar, with minor variations due to aggregation and orientation. Additionally, the size and concentration of MnMoO₄ nanoparticles significantly influence the saturable absorption behavior and pulse dynamics of the Q-switched EDFL. In this work, the synthesized nanoparticles, with sizes ranging from 80 to 200 nm, are within the nanoscale regime favorable for supporting effective nonlinear optical interactions. While smaller particles typically enhance nonlinear effects and recovery times, larger particles may increase scattering losses.

The experimental arrangements for the measurement of modulation depth are presented in Ref. [13]. Figure 2 displays the modulation depth characterization of MnMoO₄, where the experimental transmission data are represented by blue spheres, and the corresponding nonlinear fitting curve, derived from the saturable absorption model, is shown as a red line. The saturable absorption behavior of the EDFL laser based on MnMoO₄ SA is modeled using the following equation:

T(I) = 1 − ΔT × exp(−I/V) − α_ns

(1)

where each parameter plays a critical role in defining the material’s nonlinear optical response. The modulation depth, ΔT = 9.77%, quantifies the maximum change in transmission under high-intensity illumination, directly influencing the efficiency of pulse formation in Q-switched lasers. Additionally, the saturation intensity (I) and non-saturable loss (α_ns) were measured to be 74.08 MW/cm² and 64.15%, respectively. These parameters govern the suitability of MnMoO₄ as an SA.

3. Theoretical Modeling and Simulations of the EDFL

Figure 3a–d illustrate the results of numerical simulations conducted on a Q-switched EDFL cavity using a nonlinear Schrödinger equation (NLSE) to examine pulse propagation dynamics within the laser cavity. This equation is as follows:

$${\displaystyle \frac{\mathit{\partial }\mathit{A}}{\mathit{\partial }\mathit{Z}}}=-\mathit{i}{\displaystyle \frac{{\mathit{\beta }}_2}{2}}{\displaystyle \frac{{\mathit{\partial }}^2\mathit{A}}{\mathit{\partial }{\mathit{\tau }}^2}}+\mathit{i}\mathit{\gamma }{\left|\mathit{A}\right|}^2\mathit{A}+{\displaystyle \frac{{\mathit{g}}_{\mathit{c}}}{2}}\mathit{A}$$

(2)

where A($\mathsf{\tau }$,z) indicates the electric field envelope; $\mathbf{Z}$ is the propagation distance along the fiber axis; $\mathit{\beta }$, $\mathit{\gamma },$ and ${\mathbf{g}}_{\mathbf{c}}$ denotes the dispersion coefficient in the cavity, nonlinearity, and gain saturation, respectively. As the gain in a passive fiber is zero, we assume the loss in a passive fiber is also zero [19]. It is pertinent to mention here that this theoretical calculation does not consider high-order dispersion and nonlinear effects due to minimal contributions in the experiment. In the active fiber, ${\mathit{g}}_{\mathit{c}}$ represents the saturation gain, which varies spectrally. The saturation gain of the active fiber is defined by the following equation [20]:

$${\mathit{g}}_{\mathit{c}}={\displaystyle \frac{{\mathit{g}}_0}{1+\frac{{\mathit{P}}_{\mathit{a}\mathit{v}\mathit{g}}}{{\mathit{P}}_{\mathit{S}\mathit{a}\mathit{t},\mathit{G}}}}}$$

(3)

where ${\mathit{g}}_0$ represents the small signal gain and ${\mathit{P}}_{\mathit{a}\mathit{v}\mathit{g}}$ and ${\mathit{P}}_{\mathit{S}\mathit{a}\mathit{t}}$ represent the average signal power (over one round trip) and the saturation power of the gain medium, respectively. The value ${\mathit{g}}_0$ is calculated by the pump. It is derived from the steady-state solution of the coupled population density rate equations, as described in [19,21], along with the pump and signal propagation equations. White noise is used to initialize the electric field, representing intracavity optical radiation for the initial conditions. After initializing the field, it then propagates through the cavity components in a round-trip manner [21,22]. By utilizing the split-step Fourier approach, the evolution of the electric field is simulated in active and passive fibers. Note that all numerical simulations exhibited here were conducted using custom code executed in MATLAB [23,24].

The plot in Figure 3a shows the prominent peak centered at 1.563 µm, which is the typical operating wavelength of EDFLs, indicating coherent output and a wavelength close to the central wavelength reported in the actual experimental measurement (1559.14 nm). The precise nature of the peak represents spatial coherence and a high degree of temporal coherence. This peak also suggests that the laser emits strongly at 1.563 µm. The stability at the central wavelength, 1.563 µm, represents good control over the Q-switching mechanism and laser medium, which ideally should not result in a shift in the peak emission wavelength [19,25]. The variation in theoretical and experimental peak profiles can be attributed to factors such as non-negligible background noise in the experimental setup or slight variations in the gain characteristics of the laser cavity [26,27]. Figure 3b illustrates the evolution of the spectral intensity of the Q-switched fiber laser cavity over 500 roundtrips within the laser cavity. The spectral intensity is highest at the central wavelength (1.563 µm) and gradually decreases symmetrically on either side of this central peak. This signifies that the gain is strongest near its peak emission wavelength, leading to the dominance of this wavelength in the spectrum. Figure 3c shows the temporal profile of a conventional Q-switched pulse generated in the Q-switched EDFL cavity. The plot displays a single symmetric pulse with a peak at zero microseconds, indicating the localized and stable nature of the pulse in the time domain. Figure 3d provides a spectrogram of the pulse depicted in Figure 3a. The prominent line denoting stable roundtrips at a constant wavelength of approximately 1.563 µm, demonstrating strong and stable emission. This plot captures characteristics of pulse progression like pulse width and pulse intensity due to intracavity dynamics managed by dispersion, gain saturation, and nonlinearities. The consistency of the roundtrips to the central wavelength at 1.56 µm shows the spectral purity and stability of the laser.

4. Experimental Setup

The experimental configuration for the MnMoO₄ SA-based EDFL is illustrated in Figure 4. A 980 nm semiconductor diode laser with a maximum output power of 1 W serves as the optical pump source. The pump is introduced into the laser cavity via a 980/1550 nm wavelength division multiplexer (WDM), which efficiently combines and transmits optical signals at both wavelengths. A 2 m long EDF is connected to the WDM, acting as the gain medium to provide amplification at the lasing wavelength. After the gain medium, MnMoO₄-based SA, is integrated into the cavity by placing MnMoO₄ nanoparticles on the fiber ferrule to enable the nonlinear absorption required for the PQS operation. Next to SA, a polarization controller (PC) was implemented in the cavity, aiming to control the polarization state of light. To ensure stable, unidirectional light propagation and suppress unwanted back reflections, a polarization-insensitive optical isolator (PI-ISO) is placed after the PC. A 90:10 optical coupler is then employed to manage the power split; 90% of the light is circulated back into the cavity to sustain population inversion, while the remaining 10% is extracted for laser characterization. The extracted 10% output is further split equally into two channels. One channel is analyzed using a YOKOGAWA AQ6370D optical spectrum analyzer to examine the emission spectrum, and GW-INSTEK GDS-3504 digital oscilloscope to record the pulse train and temporal characteristics. The second channel is directed to a power meter to measure the average output power, thus providing a comprehensive evaluation of the laser performance.

5. Results and Discussions

Figure 5a presents the optical spectrum analyzer (OSA) measurement of the QS EDFL using a MnMoO₄ nanoparticle-based SA. Continuous-wave (CW) emission (red) occurs at a wavelength of 1569.33 nm, whereas QS operation with the MnMoO₄ SA exhibits an emission wavelength of 1559.14 nm, corresponding to a blue-shift of 10.19 nm. In EDFLs using MnMoO₄ SA, the blue shift observed when transitioning from CW to QS operation is physically interpreted as a result of dynamic gain competition and SA effects. During Q-switching, the MnMoO₄ SA enables the rapid extraction of stored energy, causing a sudden depletion in the population inversion. This abrupt energy release shifts the gain peak toward shorter wavelengths, as the gain for longer wavelengths is depleted more quickly, and the effective gain spectrum transiently favors shorter wavelengths (blue shift). This shift indicates an optimization of pulse energy and other pulse regime parameters. Additionally, the 3 dB bandwidth for PQS operation using the SA was observed to be 1.49 nm. Figure 5b presents the relationship between repetition rate and pulse width as the pump power increases from 28 mW to 312.5 mW. The results show an almost linear rise in repetition rate from 24.98 kHz to a maximum of 88.11 kHz, with pulse width gradually decreasing from 15.22 µs to a minimum of 2.35 µs. The microsecond-range pulse width observed in the QS EDFL is primarily governed by the interplay of cavity design, pump conditions, and gain dynamics, all of which influence the temporal characteristics of the pulses. Notably, despite the longer pulse duration, the laser exhibited stable QS operation over a wide range of pump powers. This indicates reliable energy modulation and confirms the overall effectiveness of the system configuration for generating a stable pulsed output in the microsecond regime. The steady and predictable changes in these parameters indicate a stable QS regime, confirming the SAs’ effectiveness in maintaining consistent pulse generation [23]. Figure 5c illustrates the relationship between pump power and average output power, as well as the variations in pulse energy and peak power vs. pump power for the PQS operation. The pulse energy (red triangles) increases from 5.12 nJ at 28 mW to 33.49 nJ at 312.5 mW. However, beyond 186 mW, a slight fluctuation in pulse energy is observed between 186 mW to 197.6 mW and 255.5 mW to 267.1 mW. This fluctuation can be primarily linked to the early saturation of the SA, where the material reaches saturation at lower intensities, leading to a reduction in pulse energy [28]. Additionally, the decrease in pulse energy from 33.75 nJ to 33.49 nJ, between 301.2 mW and 312.5 mW, is attributed to nonlinear optical effects. Figure 5c demonstrates that the peak power (blue triangles) in the PQS regime increases from 0.28 mW to 6.26 mW as the pump power varies from 28 mW to 312.5 mW. This enhancement in peak power highlights the MnMoO₄ SA’s ability to effectively suppress CW operation while simultaneously compressing the pulse duration, ensuring stable pulse energy. The SA accumulates intracavity energy and releases it in short bursts as it becomes transparent at higher intensities, facilitating efficient pulse generation. As the pump power gradually increases from 28 mW to 312.5 mW, the average output power (black spheres) exhibits a steady rise from 0.128 mW to 2.95 mW. Figure 5d presents the long-term performance evaluation of a Q-switched EDFL incorporating MnMoO₄ as a SA, illustrating the variations in pulse repetition rate and pulse width over a continuous four-hour (240 min) operation under a constant pump power of 134 mW. The pulse repetition rate, indicated by blue spheres, demonstrates remarkable stability, fluctuating slightly around a mean value of 58.38 kHz with a standard deviation of ±0.29 kHz. The recorded minimum and maximum values are 57.85 kHz and 58.99 kHz, respectively, reflecting only minor temporal deviations and confirming the SA’s ability to sustain consistent pulse generation. This minimal variation underscores the reliability of MnMoO₄ for maintaining a stable pulse train, a critical parameter for applications demanding high temporal precision. Likewise, the pulse width, represented by red spheres, remains stable throughout the measurement period, varying within a narrow range of 5.16 µs to 6.24 µs, with a mean of 5.67 µs and a standard deviation of ±0.28 µs. These fluctuations are well within acceptable limits, indicating excellent long-term operational uniformity. Moreover, the absence of significant broadening or compression demonstrates that MnMoO₄ maintains efficient saturable absorption, ensuring steady pulse shaping without degradation over time. The minor fluctuations observed in the pulse width parameter highlight the excellent optical stability of MnMoO₄, which resists thermal-induced effects and nonlinear distortions. The low uncertainty in both repetition rate and pulse width further highlight the robustness and suitability of MnMoO₄ as an effective SA for PQS, enabling consistent laser output essential for practical deployment in precision-demanding optical systems.

The material’s high damage threshold and strong nonlinear response contribute to maintaining a steady QS mechanism over extended operation. The four-hour stability test confirms that MnMoO₄ is a highly stable and efficient SA for QS EDFLs. It should be noted that when the pump power was increased beyond 312.5 mW, the laser started operating in the CW mode, and when the pump power was reduced to 312.5 mW, the pulse operation was again retained. The high damage threshold of MnMoO₄ was not measured directly due to the limitation of the fiber components employed in the cavity not having the capacity to operate beyond 312.5 mW. However, operating the laser at such a higher pump power, 312.5 mW in pulse mode, indicates a higher threshold for the SA employed in the system.

The pulse train spectrum at a pump power of 51.6 mW is presented in Figure 6. At a pump power of 51.6 mW, the time interval between consecutive pulses is 27.07 µs, corresponding to a repetition rate of 36.9 kHz.

The table below shows a comparison of metal oxides, metal dioxides, and composite metal tetraoxides used as SAs in QS EDFLs. MnMoO₄ achieves a pulse width of 2.35 µs, positioning it between ZnO- and rGO-Ag/PVA-based SAs in terms of pulse duration. Its high repetition rate of 88.11 kHz exceeds all SAs presented in

Table 1. Comparison of important pulse parameters of metal oxides, metal dioxides, and composite metal tetraoxides.

Saturable Absorbers (SAs)	Technique	Cavity	Pulse Width (μs)	Repetition Rate (kHz)	Pulse Energy (nJ)	Reference
ZnO	PQS	EDFL	5.6	79.37	74	[29]
AZO	PQS	EDFL	2.2	86	47.3	[30]
Fe2O3	PQS	EDFL	13.8	22.7	36.9	[31]
NiO	PQS	EDFL	5.2	52.18	31.5	[32]
Co3O4	PQS	EDFL	5.02	70.92		[33]
TiO2	PQS	EDFL	4.12	81.04	22.63	[34]
rGO-Ag/PVA	PQS	EDFL	1.38	76.63		[35]
MnMoO4	PQS	EDFL	2.35	88.11	33.49	This work

, making it well-suited for applications requiring rapid pulse generation. One of its key strengths is maintaining a consistent pulse generation for 4 h, demonstrating long-term reliability. The data suggest that MnMoO₄ SA is a valuable addition to the range of available SA materials, with potential applications in optical communication and precision sensing.

6. Conclusions

In summary, a MnMoO₄-based saturable absorber demonstrated stable Q-switched pulse generation in an EDFL, maintaining consistent performance over 4 h of continuous operation. The MnMoO₄ nanoparticles were prepared, and their particle size was confirmed using SEM, while the SA’s optical properties were characterized using a balanced twin-detector method. The saturation intensity, nonsaturable absorber losses, and modulation depth were measured to be 64.15%, 74.08 MW/cm², and 9.77%, respectively. With a minimum pulse width of 2.35 µs, a repetition rate of 88.11 kHz, and a pulse energy of 33.49 nJ, the laser exhibited excellent stability and efficiency. Additionally, to evaluate the performance of a passive Q-switched EDFL, a numerical model based on the nonlinear Schrödinger equation (NLSE) was employed, showing good agreement with experimental measurements. These results suggest that the broadband nonlinear absorption, fast recovery time, and high damage threshold of MnMoO₄ nanoparticles as an effective SA make it suitable for mode-locked fiber lasers, generating ultrafast femtosecond pulses for applications in optical communications, sensing, and material processing.