1. Introduction

For several last years there is a strong demand on a development of laser systems based on Fe²⁺ ions operating in a spectral range of 4–5 µm pumped by a convenient laser source. Such 4–5 µm laser systems are interesting for a variety of possible applications in medicine diagnostics and treatment, spectroscopy, air pollutants measurement, free-space communications, target illumination, and industrial technologies [1]. In general, laser radiation in this wavelength range can be also obtained using difference frequency generation (DFG), hydrogen Raman lasers [2], CO lasers [3], or free-electron lasers [4]. DFG based on solid state lasers utilizing various non-oxide nonlinear crystals has been proven to be the efficient method for tunable mid-IR lasing within pulse duration range from femtosecond up to continuous-wave [5,6]. Radiation can be further amplified by optical parametric amplification (OPA), optical parametric chirped pulse amplification (OPCPA), or ZnSe:Fe²⁺ multi-pass amplifier [6–8]. Practical applications of these devices are somewhat limited by their complexity. Semiconductor lasers present other interesting and applicable alternative with the most recent output power at a level of several Watts [9,10]. Nevertheless, there is still strong interest in Fe²⁺:II-VI solid-state lasers broadly tunable in the mid-IR region. These lasers are usually pumped by ∼3 µm sources fitting the Fe²⁺ ions absorption maximum. Up to now, pumping at ∼3 µm generated mostly by free-running or Q-switched YAG:Er³⁺ (YSGG:Er³⁺), second D₂ Raman Stokes of YAG:Nd³⁺, or electric discharge HF laser is used [11–16]. Other interesting pump source is presented by an Er³⁺ doped ZBLAN fiber laser. A liquid-nitrogen-cooled (LN₂), continuous-wave (CW) ZnSe:Fe²⁺ laser pumped by such fiber laser was presented recently with the maximum output power of 2.1 W and slope efficiency of 59% [17]. As for Cr²⁺ pumping, ZnSe:Cr²⁺ laser tuned to 2.94 µm was proved to be an efficient source for 9.2 W continuous-wave (CW), liquid-nitrogen-cooled ZnSe:Fe²⁺ laser [18]. All these pumping sources are usable but not as simple as laser diode pumping.

Other possible way to simplify the pumping scheme is a combination of Fe²⁺ ions with other active transitional metal ions inside the active medium and utilization of an energy transfer process. Up to now, some research was made to realize this pumping scheme of Fe²⁺ ions through the energy transfer from Co²⁺ or Cr²⁺ ions. Self-lasing at 3.9 µm from ZnSe:Co²⁺,Fe²⁺ and ZnS:Co²⁺,Fe²⁺ crystals was proven experimentally for temperatures below ∼24 K [14,19,20].

In the case of the energy transfer from Cr²⁺ ions, mid-IR luminescence of Fe²⁺ in ZnSe:Cr²⁺,Fe²⁺ at room temperature excited by 1.56 µm was documented in [21] at first. The Cr²⁺ → Fe²⁺ energy transfer was further confirmed also in ZnS:Cr²⁺,Fe²⁺ or under 1.77 µm excitation [11,22,23]. In-depth analysis of room temperature kinetics and energy transfer rate in the ZnSe:Cr²⁺,Fe²⁺ was published recently in [24]. Fe²⁺ luminescence was also detected under visible (532 nm) excitation [11,25] at cryogenic temperatures.

Cr²⁺ ions (donors) fluorescence spectrum should overlap Fe²⁺ ions (acceptors) absorption spectrum in order to obtain the energy transfer. In [26] Doroshenko et al. previously shown that absorption and fluorescence spectra of Cr²⁺ ions in Zn_1-xMn_xSe solid solutions with manganese ions presence are shifted towards longer wavelengths compared to a ZnSe crystal. At the same time, the shape of the Fe²⁺ ions absorption spectrum remains practically unchanged at the short-wavelength part with a steady shift of a long-wavelength part with absorption maximum towards longer wavelengths with increasing content (x) of manganese ions in the matrix. The Cr²⁺ → Fe²⁺ energy transfer process was investigated and Fe²⁺ ions gain-switched Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.3) laser operation under short pulse (200 ns) 1.73 µm excitation in a temperature range 78–150 K was presented by us [27]. Most recently, Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.3) laser operation under long pulse (1 ms, 10 Hz) 1.94 µm Tm:fiber pumping was also demonstrated [28].

2. Cr²⁺ → Fe²⁺ ions energy transfer process characteristics

In this paper, the energy transfer from excited Cr²⁺ to Fe²⁺ ions followed by the laser emission is presented. The lasing was obtained in the Cr²⁺, Fe²⁺ co-doped Zn_1-xMn_xSe (x = 0.05) single crystal within a temperature range from 78 K up to 110 K. The Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ active medium was synthesized by solid-phase synthesis and grown by HPBM (High Pressure Bridgman Method) with active ions doping during the synthesis process. A 3.9 mm thick experimental sample was cut from a crystal boule and its faces were optically polished. There was no antireflective coating on the sample. The refractive index was measured using a prism-coupled refractometer and its value is 2.4404 at 1.7 µm. This value is for about 0.004 lower than that for the ZnSe crystal at the same wavelength. The concentrations were C(Cr) = 5×10¹⁸ cm⁻³ and C(Fe) = 2×10¹⁸ cm⁻³. Dopant ion concentrations in the synthesized sample were measured using inductively coupled plasma–optical emission spectrometry element analysis. In [27] Doroshenko et al. investigated the Cr²⁺ → Fe²⁺ energy transfer process in a highly-Mn-concentrated Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.3) crystal with about 1:2 Cr²⁺ to Fe²⁺ ions concentrations ratio. Here we present the results on low Mn concentrated Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal with about inverse (2.5:1) Cr²⁺ and Fe²⁺ ions concentration.

The absorption spectrum of Cr²⁺ and Fe²⁺ ions measured at 78 K in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal is presented in Fig. 1. For comparison the absorption spectrum of Cr²⁺ and Fe²⁺ ions in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.3) crystal at 78 K is also presented. The spectra were measured using a FTIR spectrometer (Infralum FT-08). As follows from this figure, Fe²⁺ ions concentration in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal is about 2.5 times lower than that for the x = 0.3 sample.

 

Fig. 1. Absorption spectra of Cr²⁺ and Fe²⁺ ions in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ crystals with Mn content x = 0.05 (red) and x = 0.3 (blue) at 78 K.

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Fluorescence spectra of the Cr²⁺ ions together with the Fe²⁺ ions absorption spectra normalized to a unit area are plotted in Fig. 2. The Cr²⁺ ions fluorescence spectra were measured in Cr²⁺ doped samples (in the absence of the Fe²⁺ ions). As Nemec et al. discussed in [29], lower Mn content in the Zn_1-xMn_xSe results in a smaller shift of Cr²⁺ ions fluorescence maximum towards longer wavelengths. Also, higher Mn content results in both long wavelength shift and broadening of Fe²⁺ ions absorption lines. Both these facts lead to a significantly lower overlap of Cr²⁺ ions fluorescence with Fe²⁺ ions absorption at 78 K in the crystal with low Mn content x = 0.05 compared to the crystal with Mn content x = 0.3 (see hatched areas in Fig. 2). The overlap integral for the x = 0.05 was calculated to be about ∼ 3% of a normalized unit area and for the x = 0.3 this value was about 10% which should result in higher Cr²⁺ → Fe²⁺ energy transfer efficiency for crystal with higher Mn content.

 

Fig. 2. Fluorescence spectra of Cr²⁺ ions and absorption spectra of Fe²⁺ ions in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ crystals with Mn content (a) x = 0.05 (red) and (b) x = 0.3 (blue) at 78 K. All spectra were area normalized. Hatched areas mark the overlap between donor (Cr²⁺) ions fluorescence and acceptor (Fe²⁺) ions absorption.

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Fe²⁺ ions fluorescence spectra are also modified depending on Mn content x with similar (to absorption spectra) shift of Fe²⁺ fluorescence maximum towards longer wavelengths with an increase of Mn content x as shown in Fig. 3. The fluorescence spectra were measured using a monochromator (Oriel 77250) together with a LN₂-cooled mercury-cadmium-telluride (MCT) detector (Judson-Teledyne J15).

 

Fig. 3. Comparison of Fe²⁺ ions fluorescence spectra in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ crystals with Mn content x = 0.05 (red) and x = 0.3 (blue) at 78 K.

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The fluorescence decay curve of Cr²⁺ ions measured at 78 K in the Zn_1-xMn_xSe:Cr²⁺ (x = 0.05) crystal was single exponential with a decay time of 5.3 µs as shown in Fig. 4 (pink hollow dots). In the presence of Fe²⁺ ions (in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal), the decay curve was observed to become non-exponential due to the nonradiative Cr²⁺ → Fe²⁺ ions energy transfer. It has to be noted that deviation from single exponential decay was not so pronounced as in the case of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.3) crystal with about 2.5 times higher Fe²⁺ ions concentration [27].

 

Fig. 4. Decay curves of Cr²⁺ ions in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal without (pink hollow dots) and with (black hollow dots) Fe²⁺ ions co-doping measured at 78 K. Green line shows single exponential approximation.

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The efficiency of Cr²⁺ to Fe²⁺ (donor-acceptor) energy transfer (η_DA) can be directly evaluated from Fig. 4 by using equation η_DA = 1-<τ_Cr-Fe>/τ_Cr, where τ_Cr is the Cr²⁺ ions lifetime in the sample without Fe²⁺ ions co-doping and <τ_Cr-Fe> is the average Cr²⁺ ions lifetime in the co-doped sample [14,27]. The average lifetime can be obtained from the decay curve as <τ_Cr-Fe> = $\mathop \smallint \nolimits_0^\infty {\textrm{I}_{\textrm{D}}}(t )\textrm{d}t/{\textrm{I}_{\textrm{o}}}$ and the energy transfer efficiency can be therefore expressed using following equation:

Energy transfer function Ln(I_R)-Ln(I_N) plotted in $\sqrt t $ axis similar to [27] shows the first “ordered” exponential decay in the beginning (see inset in Fig. 5) which linearizes further for “disordered” Forster energy transfer stage. As follows from Fig. 5 the first exponential stage is much less pronounced compared to that in the case of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.3) crystal with about 2.5 times higher Fe²⁺ ions concentration. The value of maximal decay rate W_max obtained from the first “ordered” part was about 0.8×10⁵ s⁻¹ which is about an order of magnitude lower than in the case of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.3). The average decay rate at the “disordered” energy transfer stage was calculated from the measured γ = 145 s^−1/2 value to be W_F = γ_F² = 0.2×10⁵ s⁻¹. This value is again nearly an order of magnitude lower than that for the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.3) crystal [27] and again should be a result of 2.5 times lower acceptors (Fe²⁺ ions) concentration. It should be noted that W_max to W_F ratio in both cases is quite similar and it is close to 4. Moreover, critical time (when “ordered” stage is exchanged by “disordered one”) was also quite similar in both cases being close to 0.7 µs (see Fig. 5).

 

Fig. 5. Nonradiative Cr²⁺ → Fe²⁺ energy transfer function in $\sqrt t $ axis in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) and (x = 0.3) crystals at 78 K.

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Donor-acceptor energy transfer efficiency was estimated for the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal according to [30] as

Serious advantage of the Zn_1-xMn_xSe (x = 0.05) crystal is a much lower nonradiative quenching of Fe²⁺ ions fluorescence resulting in sufficiently longer Fe²⁺ ions fluorescence lifetime especially at 78 K. In Fig. 6 measured decay curves of Fe²⁺ ions at 78 K are shown for two Mn contents x = 0.05 and 0.3. Both decay curves were observed to be double exponential (fits are shown in Fig. 6 by the dashed lines) with fluorescence lifetimes at initial and tail stages presented in this figure. As follows from Fig. 6 iron ions fluorescence lifetime is shortened about 4× at both stages when Mn content is increased from x = 0.05 to x = 0.3. Such longer iron fluorescence lifetime (63 µs at the tail which is quite similar to that for a ZnSe crystal ∼60 µs at ∼78 K [26,31,32]) for lower Mn content should result in higher quantum yield of Fe²⁺ ions fluorescence with respect to the Zn_1-xMn_xSe (x = 0.3) crystal. It should be noted that fluorescence decay times in Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ crystals were measured and analyzed at 78 K and can differ from radiative lifetimes which were shown in [31–33] to be shorter for temperatures below 14 K.

 

Fig. 6. Fluorescence decay curves of Fe²⁺ ions in the Zn_1-xMn_xSe:Fe²⁺ crystals with Mn content x = 0.05 (red) and x = 0.3 (blue) at 78 K.

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Pumping at ∼1.7 µm is quite efficient from the point of view of Cr²⁺ ions excitation as it well fits Cr²⁺ absorption maximum in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal (see Fig. 1). On the other hand, such short wavelength pumping should increase the quantum defect for Fe²⁺ ions excitation. For ordinarily used ∼2.9 µm pumping with Er³⁺ ions-based excitation sources, theoretical efficiency for generation at ∼4.1 µm as high as 70% could be achieved. It should be noted that Fe²⁺ ions lasing with a slope efficiency up to 59% was demonstrated in the ZnSe crystal recently [17]. For 1.7 µm pumping theoretical limit decreases more than twice down to ∼30%. Though ∼1.7 µm excitation through the Cr²⁺ → Fe²⁺ energy transfer simplifies the pump scheme and enlarge the number of commercially available compact pump sources allowing to obtain cheap and compact Fe²⁺ ions based tunable lasers.

3. Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) laser results

The Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) laser properties were investigated under two different pumping sources around ∼1.7 µm. The first pumping source was based on a Q-switched YLF:Er laser and the second source was a commercial laser diode (LD).

3.1 Pumping by a 1.73 µm Q-switched YLF:Er laser

In the first experiments Fe²⁺ ions lasing under 1.73 µm Q-switched YLF:Er laser excitation similar to [27] was tested. The laser cavity and mirrors were the same as described in [27]. The pumping beam was focused by a 150 mm CaF₂ lens. Both the pumping flat mirror (PM) and concave (r = 500 mm) output coupler (OC) were placed outside the cryostat and the cavity length was ∼10 cm. The cryostat was equipped by CaF₂ windows with no antireflective coating. Pumping mirror transmittance at 1.73 µm was ∼95% and reflectivities at 2.4 µm and 4.2 µm were 8.5% and >98%, respectively. The output coupler reflectivity at the same wavelengths were 92% and 94%, respectively. The YLF:Er laser generated 200 ns pulses with the repetition rate of 1 Hz. The experimental arrangement is presented in Fig. 7(a) with a detail of YLF:Er pumping in Fig. 7(b).

 

Fig. 7. (a) Experimental arrangement of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) laser. Pumping sources: (b) YLF:Er pumping, (c) laser diode pumping. PM – pumping mirror, OC – output coupler, HR – high reflectivity mirror at ∼1.7 µm, PC – Pockels cell.

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Unlike in the case of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.3) crystal used in [27], relatively low Cr²⁺ → Fe²⁺ energy transfer efficiency in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal resulted in simultaneous Cr²⁺ and Fe²⁺ ions lasing at 78 K (see Fig. 8(a) as an example).

 

Fig. 8. Temporal profiles of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (a) x = 0.05 and (b) x = 0.3 [27] laser radiation at 78 K for the output mirror reflectivity of 94% in intracavity pumping mode operation. Inset in (a) presents the Fe²⁺ laser beam spatial profile.

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Fe²⁺ ions intracavity pumping mode (most probably followed by the Cr²⁺ → Fe²⁺ energy transfer stage) resulting in about 6 µs long Fe²⁺ ions oscillation pulse – Fig. 8(a) was realized in this case with the highest output energy of 83 µJ, which corresponds to about 1% of optical-to-optical efficiency (absorbed pumping energy was ∼7 mJ).

Oscillation pulse of the Fe²⁺ ions in the x = 0.3 sample for the case of the Cr²⁺ → Fe²⁺ intracavity pumping is shown in Fig. 8(b). Unfortunately, pure Cr²⁺ → Fe²⁺ energy transfer mode like in the x = 0.3 sample [27] was not achieved for the x = 0.05 sample. The oscillation spectra of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) laser were measured by the monochromator Oriel 77250 described above and Vigo PVI-4TE-6 photodetector. The laser generated in a temperature range from 78 K up to 200 K and the generated spectra examples are presented in Fig. 9. A drop in the oscillation spectra around 4.25 µm is caused by the CO₂ absorption because the cavity mirrors were placed outside the evacuated cryostat. As it could be seen from this figure, the central oscillation wavelength red-shift was observed to be similar to direct 2.94 µm Fe²⁺ ions excitation [26].

 

Fig. 9. Oscillation spectra of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ x = 0.05 laser under 1.73 µm Q-switched YLF:Er laser pumping in a temperature range from 78 K up to 200 K.

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3.2 Pumping by a 1.71 µm laser diode

Oscillation properties of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal were also tested in more interesting case of commercial 1.71 µm laser diode (LD) pumping. This LD generated maximum CW power of 35 W. This type of optical excitation provides much lower pumping rate compared to Q-switched laser pumping. Also, a specific LD driver was characterized by relatively long build up time (∼2 ms) of the excitation pulse which resulted in a noticeable delay between the laser diode pump and Fe²⁺ ions oscillation pulse start. Therefore, an optical chopper (Thorlabs MC2000B) was used to get ∼1 ms (FWHM) pumping pulses at 10 Hz from CW operation of the LD. It should be noted that for available LD pumping levels, no Cr²⁺ ions lasing was observed for the same mirror set as in the case of the YLF:Er Q-switched laser. The experimental setup of the LD pumping system is shown in Fig. 7(c).

Oscillation pulse of Fe²⁺ ions was measured by the MCT detector behind a bandpass filter (Thorlabs FB4250-250). Generation was achieved in the temperature range from 78 K up to 110 K. Typical temporal profiles of the pump and Fe²⁺ ions laser oscillation pulses at 78 K are shown in Fig. 10. This is the first demonstration, to our best knowledge, of Fe²⁺ ions laser generation under direct commercial 1.71 µm laser diode excitation.

 

Fig. 10. Oscillogram of the 1.71 µm pump pulse (green curve) and the 4.19 µm Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) laser output pulse at 78 K (red curve).

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The oscillation spectra were measured again by the monochromator and MCT described above. The Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) laser oscillation spectra for temperatures of 78 K and 100 K are shown in Fig. 11. The oscillation spectrum maximum of the Fe²⁺ ions in the crystal was observed to be slightly shifting towards longer wavelengths with temperature increase. The output spectra were quite strongly influenced by CO₂ absorption at ∼4.25 µm. The central output laser wavelength was ∼4190 nm at 78 K.

 

Fig. 11. Oscillation spectra of the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ x = 0.05 laser under 1.71 µm laser diode pumping for temperatures of 78 K and 100 K.

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The mean output power was measured by a power probe (Coherent PM3) behind the LP3000 and LP3750 long-pass filters (Spectrogon, transmittance of each filter ∼92% @ 4.2 µm). Laser mean output power as a function of absorbed pump power for the active medium temperature of 78 K is presented in Fig. 12. The slope efficiency was η ≈ 2.3%. The maximum mean output power was 4.1 mW (single pulse energy ∼0.41 mJ) for the absorbed pump power of ∼240 mW corresponding to the optical-to-optical efficiency of 1.6%. The output beam spatial profile was measured by a pyroelectric camera (Spiricon Pyrocam III) behind a long-pass filter LP4095 (Spectrogon). The output beam shape was observed to be distorted compared to fundamental Gaussian mode most likely due to high active crystal thermal loading due to high Cr²⁺ ions absorption.

 

Fig. 12. Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) mean laser output power as a function of the absorbed laser-diode pump power. Inset presents the beam spatial profile for the maximal output power of 4.1 mW.

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4. Summary

To conclude, to our best knowledge, the Fe²⁺ ions lasing in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) single crystal under direct commercial 1.71 µm laser diode and YLF:Er Q-switched laser excitation was demonstrated for the first time. A nonradiative Cr²⁺ → Fe²⁺ ions energy transfer parameters in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal were determined and compared to those previously shown for x = 0.3 crystal [28]. Five times lower (compared to x = 0.3 crystal) Cr²⁺ → Fe²⁺ energy transfer efficiency of about 10% in the Zn_1-xMn_xSe:Cr²⁺,Fe²⁺ (x = 0.05) crystal was demonstrated for used Cr²⁺ and Fe²⁺ ions concentrations which seems to result from an order of magnitude lower energy transfer rate at both the first “ordered” and second “disordered” stages due to 2.5 times lower Fe²⁺ acceptor ions concentration.

Short pulse excitation by a Q-switched YLF:Er laser (1.73 µm, 200 ns, 1 Hz) has demonstrated only intracavity Cr²⁺ → Fe²⁺ ions pumping mode (most probably followed by the Cr²⁺ → Fe²⁺ ions energy transfer stage) resulting in the Fe²⁺ ions oscillations. The oscillations were achieved in a temperature range from 78 K up to 200 K and the central oscillation wavelength increased from 4.1 µm to 4.4 µm depending on the active medium temperature. The highest output energy of 83 µJ and optical-to-optical efficiency of about 1% at 78 K were achieved.

Under 1.71 µm commercial laser diode pumping (1 ms, 10 Hz), Fe²⁺ ions excitation through the Cr²⁺ → Fe²⁺ ions energy transfer mode was realized. In this case the maximum mean laser output power of 4.1 mW and slope efficiency of 2.3% with respect to the absorbed power were obtained at 78 K. Laser was observed to operate within a temperature range from 78 K up to 110 K with central oscillation wavelength shift from 4.19 µm to 4.23 µm.

These results seem to be a good demonstration of a future possibility to develop a compact diode-pumped mid-infrared coherent laser source generating in the range of 4.1–4.3 µm. Further optimization of absolute Cr²⁺ and Fe²⁺ ions concentrations as well as Cr²⁺ to Fe²⁺ ions concentration ratio should allow to optimize energy transfer process and increase further the Fe²⁺ ions oscillation efficiency.