Two color optical pumping, both above (anti-Stokes pump or ASP) and below (Stokes pump) the lasing wavelength, was adopted to reduce the net quantum defect (QD) in a solid-state Yb-doped fiber laser. The reduction in QD was achieved by converting a substantial portion of the gain medium's phonons directly into useful photons through a dual-wavelength excitation (DWE) mechanism. Since this is achieved through the usual processes of absorption and stimulated emission associated with lasing, high efficiency can be maintained. Both time domain and power measurements are presented, demonstrating a 13.2% reduction of the system's net QD and a 13.8% reduction in the lasing threshold power. These values were limited only by the available ASP power. Laser slope efficiency, with respect to launched ASP power, was found to be as high as 38.3%. A finite difference time domain model, developed to elucidate the role of both pumps in populating the upper states, corroborated the experimental findings. The DWE concept proposed here opens the door to an “excitation-balanced” type of self-cooled fiber laser. Simulation results also suggest that the technique is scalable and conceptually applicable to other solid-state laser systems.

Optical refrigeration via anti-Stokes fluorescence (ASF) was first postulated by Pringsheim in 1929.1 While raising a debate at the time,2–4 particularly with respect to perceived violations of the Second Law of Thermodynamics, Landau theoretically affirmed its veracity in 1946.5 With his conclusions came the caveat that, as the energy difference between pump and mean fluorescence wavelength becomes large compared to kT, the ASF intensity diminishes.5 Despite a demonstration in CO2 gas6 and several reports of “reduced heating” in solids,7,8 an observation of below-ambient ASF cooling in the latter remained elusive during the decades following Landau's contribution. In fact, it was not until 1995 when the first demonstration of ASF cooling was achieved in a small ytterbium-doped rod of fluoride glass.9 Since then, cryogenic cooling in crystalline10,11 and glass12–15 hosts has become more common, with material purity and near-unity quantum yield recognized as being enablers.

Referring to Fig. 1(a), the process of ASF cooling in an exemplar Yb-doped material is as follows. The Yb3+ system, characterized by only two energy levels (or manifolds), is optically pumped from the ground state (2F7/2) to the excited state (2F5/2). At a given temperature, there exists a fixed equilibrium population distribution in the upper state manifold, which is independent of the pumping wavelength. Following pumping, phonons will either be absorbed from, or emitted into, the host as this fixed equilibrium is reached. This process is much faster than the upper state lifetime since the maximum phonon energies in solids are typically comparable to the energetic widths of the manifolds.16 Clearly, the energy of the pump photon must be selected to be less than that of the mean spontaneous emission to realize ASF cooling. In doing so, phonons are also absorbed, leading to a movement to higher energies within each manifold. The spontaneous optical emission that follows carries thermal energy out of the material, potentially resulting in cooling.

FIG. 1.

Schematic diagrams of (a) an ASF cooling process, (b) RBL operation, and (c) DWE operation in Yb3+-doped materials. In the case of the RBL, one pump drives two processes, lasing and anti-Stokes fluorescence (FL), leading to a balancing of the QD. In the case of DWE, two pumps (SP and ASP) drive one lasing process.

FIG. 1.

Schematic diagrams of (a) an ASF cooling process, (b) RBL operation, and (c) DWE operation in Yb3+-doped materials. In the case of the RBL, one pump drives two processes, lasing and anti-Stokes fluorescence (FL), leading to a balancing of the QD. In the case of DWE, two pumps (SP and ASP) drive one lasing process.

Close modal

Aside from cryocoolers, other notable applications of ASF include radiation balanced lasers (RBLs)17,18 in which cooling through ASF offsets, or balances, the heat generated through the quantum defect (QD). Figure 1(b) represents one pumping configuration for such a process. In this case, the pump drives the production of both lasing at a longer wavelength and the anti-Stokes fluorescence. The former leads to a positive QD and the production of heat (i.e., Stokes pump or SP), while the latter (anti-Stokes pump or ASP) carries heat away from the gain medium. Ideally, no active thermal management in RBLs is necessary, but at the expense of efficiency loss through the necessary production of significant fluorescence. For instance, if the energies of the three relevant photons are uniformly separated, one fluorescence photon must be produced for every lasing photon to successfully achieve an RBL.

For practical applications, it is desirable to utilize such passive “cooling” through stimulated emission rather than fluorescence so as to increase the efficiency of a laser system. A potential approach to achieving this is through the introduction of an ASP, which has a longer wavelength than that of the laser. Considering that the shape of the emission spectrum remains invariant with respect to the pumping wavelength, a tantalizing question emerges: “Can anti-Stokes pumping contribute to stimulated emission?” Obviously, lasing at a wavelength shorter than the pump would, indeed, represent a violation of the Second Law. From a mathematical standpoint, and with deference to Boltzmann, another way to state this is that a combination of absorption and emission cross sections (σa and σe, respectively) yielding net gain at a wavelength shorter than the pump does not exist. However, if thermal energy could be removed from the host by laser emission rather than deliberately introduced fluorescence, quantum defect (QD) heating could be partly mitigated while preserving efficiency. Such a configuration, based on two pump sources (SP and ASP) driving one lasing process, is illustrated in Fig. 1(c) and is referred to as “dual-wavelength excitation” (DWE) operation.

The goal of the present work is to demonstrate that anti-Stokes pumping can, indeed, contribute to stimulated emission, and more importantly, such a process is able to offset QD heating. A simple linear cavity fiber laser configuration is employed for this initial validation. It is shown here that a combination of Stokes and anti-Stokes pumping can reduce the net QD heating associated with the lasing process. The SP and ASP are required to be mostly or completely non-overlapping in time so as to prevent undesirable amplification of the latter. As such, the pumps must operate in a pulsed regime in order to achieve this goal. The proof-of-concept experiments presented herein show contributions from the anti-Stokes pumping to stimulated emission, a concomitant reduction in the QD, and, very favorably, a lower lasing threshold.

The paper is organized as follows. First, the experimental setup is introduced, and experiments conducted in the temporal domain to investigate the influence of the anti-Stokes pumping on the lasing threshold are described. Next, a finite difference method in a time domain (FDTD) model is developed to assist in the threshold analysis. Finally, a series of power measurements are executed providing solid evidence of anti-Stokes pumping contributing to stimulated emission and a lower net QD in a solid-state laser system. In an uncanny parallel with the first observations of ASF cooling, the first successful demonstration of anti-Stokes pumping of a laser in the gas phase was reported several years ago.19 The concept proposed here could eventually find applicability as a thermal mitigation approach for high power lasers and amplifiers.

Figure 2(a) provides a schematic of the experimental setup. The SP (red dashed box) is a commercial, single-mode laser diode (LD) operating at λSP = 976.6 nm. It is driven by a pulsed current source and is followed by an isolator. The ASP (blue dashed box) is a linear-cavity CW fiber laser similar to the one in Ref. 20 with an output wavelength of λASP = 989.6 nm. It is pulse-modulated by an external acousto-optic modulator (AOM). Note that, relative to the pulse widths used in the experiments, the various rise times in the system are negligible. A multichannel digital delay/pulse generator controls the relative temporal behaviors of the two pumps, whose outputs are combined through a 50/50 coupler. One coupler output feeds directly into the laser cavity (green dashed box), while the other serves as a check point for the pumps' power and waveforms. The laser cavity comprises a wavelength-matched pair of fiber Bragg gratings (FBGs) at 985.6 nm with reflectivities of R1 = 99.02% and R2 = 39.61%, thus setting the laser wavelength, λL. Due to its favorable spectroscopic properties,21 a 12.3 cm length of Yb-doped fluorosilicate fiber is spliced between the FBGs and serves as the gain medium. The selected length of the active fiber yields the near-optimized slope efficiency as reported in an earlier study.22 The laser of Ref. 22 also provides a starting point for the present work, from which the lasing and SP wavelengths are adopted. The ASP wavelength, on the other hand, was selected to be sufficiently long to provide a significant improvement in the QD while also maintaining a relatively high absorption coefficient. This trade-off must be considered when power scaling the system.

FIG. 2.

(a) Schematic of the experimental setup. The pulse-modulated pumps are combined and injected into the laser cavity via a 50/50 coupler. The second coupler port serves as a check point for the pump power and timing. (b) Representation of the relative timing of the two pumps. The pulses overlap for a time equal to tpulseΔt.

FIG. 2.

(a) Schematic of the experimental setup. The pulse-modulated pumps are combined and injected into the laser cavity via a 50/50 coupler. The second coupler port serves as a check point for the pump power and timing. (b) Representation of the relative timing of the two pumps. The pulses overlap for a time equal to tpulseΔt.

Close modal

Figure 2(b) provides a representation of the relative timing of the two pump pulses. The ASP pulse arrives first with a width and peak power of tpulse and PASP, respectively. Following a time delay, Δt, the SP pulse arrives with the same pulse width, tpulse, but a different peak power, PSP. Note that PSP and PASP both represent power launched into the cavity and not the total absorbed power. This sequence repeats with the time interval 1/frep. Each of these timing parameters is adjustable and able to influence the output laser characteristics. Therefore, this experimental setup provides multiple degrees of freedom with which to study the system's behavior. For conciseness, however, only one set of parameters is described here (Δt = 0.8 ms, tpulse = 1 ms, and frep = 400 Hz) as the primary goal of this work is to offer evidence that anti-Stokes pumping can contribute to stimulated emission in the proposed configuration. The discussion concerning the influence of each parameter on laser behavior will be provided elsewhere. Nevertheless, a brief justification of the selected tpulse and Δt is in order and is as follows. First, since the available powers are equipment limited (maximum PASP and PSP are 29.5 and 192.4 mW, respectively), a relatively long pump pulse width is required to achieve steady state conditions. This implies, given the available powers, that tpulse must be of the same order as the upper state lifetime, τ. If more power was available, tpulse can be significantly reduced. This also sets a limit to frep that is on the order of (2τ)−1. Next, in the case where Δt is chosen such that the two pump pulses are fully, or largely, overlapped in time, the SP pulse effectively serves as a pump for the ASP pulse. In other words, energy from the SP is partially transferred to the ASP, limiting the power available to λL and enhancing the QD. On the other hand, when the SP and ASP pulses are non-overlapping, or if there exists a small temporal overlap between them (<0.1 ms), significant loss of the excited state population to spontaneous emission occurs since tpulseτ. Therefore, an intermediate temporal overlap of 0.2 ms was chosen for this experiment.

Time domain measurements are performed by placing photodiodes (PDs) at both the pump check point and the laser output. Due to the possibility of pump leakage, a bandpass filter, having a central wavelength and FWHM of 984 and 5 nm, respectively, is placed immediately at the output (after FBG2) to block both λSP and λASP. The measured temporal traces for the two pumps combined and the laser output are shown in Figs. 3(a) and 3(b), respectively. The measurements were performed with PSP = 192.4 mW and variable PASP. Referring to Fig. 3(a), the ASP pulse arrives first, and for the first 0.8 ms, it serves as the only pump, preparing the system for the arrival of the SP. Since λASP > λL, population inversion is impossible, and no laser pulse is observed during this time period. For the next 0.2 ms, the two pumps coexist, after which the ASP is turned off, and the SP brings the system above lasing threshold. Typical relaxation oscillations related to pulse pumping are observed at the beginning of the laser pulses, as shown in the insert of Fig. 3(b),23 following which the system tends toward the steady state. As clearly seen in Fig. 3(b), the time to reach lasing threshold decreases as PASP increases. This verifies the role of the ASP in populating the upper state prior to the arrival of the SP. To further quantify this process, the PSP required to reach threshold, PSPth, was measured for the five PASP values shown in Fig. 3(a) and summarized in Fig. 3(c). To reach threshold, sufficient pump energy must be absorbed, and therefore, lengthening the pumping time reduces the peak power required. Consequently, the lowest value of PSP necessary for lasing to occur is that associated with the onset of lasing at the end of the pumping cycle, or t = 1.8 ms. It is these minimal values for PSP that are given in Fig. 3(c). Note that PSPth decreases with increasing PASP, further confirming the role of anti-Stokes pumping as discussed above. Specifically, with the maximum available PASP (equipment limited), PSPth decreases from 110.5 to 95.2 mW, which is 13.8% lower than the power required by using the SP alone. It should also be mentioned that the colors of each waveform in Fig. 3 are maintained in Fig. 4 as a convenience for the reader.

FIG. 3.

For Δt = 0.8 ms, tpulse = 1 ms, and frep = 400 Hz, (a) provides the temporal trace taken at the pump check point while (b) gives the temporal traces of laser outputs. The inset in (b) shows a close-up of the laser output signal near threshold. (c) Powers required from the SP to reach threshold as a function of PASP . As discussed previously, lasing occurs at the termination of the pumping cycle so as to minimize PSP .

FIG. 3.

For Δt = 0.8 ms, tpulse = 1 ms, and frep = 400 Hz, (a) provides the temporal trace taken at the pump check point while (b) gives the temporal traces of laser outputs. The inset in (b) shows a close-up of the laser output signal near threshold. (c) Powers required from the SP to reach threshold as a function of PASP . As discussed previously, lasing occurs at the termination of the pumping cycle so as to minimize PSP .

Close modal
FIG. 4.

Simulation results for round trip gain. The power settings shown in the legend represent the threshold conditions as displayed in Fig. 3(c). They converge to the same point since GTH is a property of the cavity. More than one complete cycle is shown to illustrate how the process repeats every 1/frep.

FIG. 4.

Simulation results for round trip gain. The power settings shown in the legend represent the threshold conditions as displayed in Fig. 3(c). They converge to the same point since GTH is a property of the cavity. More than one complete cycle is shown to illustrate how the process repeats every 1/frep.

Close modal

To corroborate the experimental results, a finite difference time domain (FDTD) model was constructed from the standard rate equations to simulate both pump powers and the upper state Yb3+ population, N1, as a function of axial position, z, and time, t. The resulting equations for N1(z,t), PSP(z,t), and PASP(z,t) are

N1z,t+Δt=N1z,t+ΔtN1z,tτ+λSPσaSP+σeSPAeffhcPSPz,tN1z,t+λSPσaSPρAeffhcPSPz,t+λSPσaASP+σeASPAeffhcPASPz,tN1z,t+λSPσaSPρAeffhcPASPz,t
(1)
PSP/ASPz+Δz,t=PSP/ASPz,texp[ΓΔzN1z,tσeSP/ASPρN1z,tσaSP/ASP]
(2)

where σeSP/ASP and σaSP/ASP are the emission and absorption cross sections at the corresponding pump wavelengths, respectively, Aeff is the effective mode area, Γ is the active ion-light intensity overlap integral, and ρ is the Yb3+ number density. For the active fiber used herein, τ (= 1270 μs), σa and σe (peak values of 1.48 pm2), and ρ (= 1.65 × 1026/m3) can be found in Refs. 21 and 22, while Aeff and Γ can be calculated from the refractive index profile (found in Ref. 22) using the method outlined in Refs. 24 and 25. The results are 43 μm2 and 99% for Aeff and Γ, respectively. Finally, the round trip gain, GR, at λL was calculated by integrating the local gain over the fiber length.

For each of the five data points shown in Fig. 3(c), and with their corresponding powers, GR(t) was simulated. The results are displayed in Fig. 4. At the control setting where PASP = 0 mW, PSPth is 110.5 mW. Lasing occurs at t = 1.8 ms, i.e., the end of the pumping cycle. This is consistent with the threshold condition defined in Fig. 3(c). In other words, the threshold gain, GTH, is reached at 1.8 ms, at which time PSP is turned off and GR simply decays in accordance with the upper state lifetime. For the given PASP, the threshold gain is determined from the model to be ∼5.5 dB. Through a careful characterization of the laser cavity, including splice losses, active fiber background loss (1.36 dB/m) as well as R1 and R2, the round trip loss, α, was determined to be 5.5 dB. From laser theory, this value must be equal to GTH, which agrees with the modeling results. For the other four settings, with increasing PASP, GR(t) decays more slowly in the range from t = 0 to 0.8 ms as the ASP serves to maintain the upper state population. However, transparency (GR = 0 dB) cannot be reached since λL < λASP. The model confirms the experimental observation that less PSP is required to reach the same threshold gain when the ASP is present. Another result that builds confidence in the experimental results and model is that each of the five experimental condition sets yields the same GR = GTH at 1.8 ms (to within 0.1 dB). From the model, PSPth is predicted to be 89.3 and 84.1 mW if PASP is instead 50 and 100 mW, respectively. This result demonstrates the significance of anti-Stokes pumping if more power was available.

Finally, power measurements are performed for the pump and laser outputs, with the results provided in Fig. 5(a). The graph shows the average laser output power, P¯L, vs the launched average ASP power, P¯ASP, with each dataset corresponding to the same average SP power, P¯SP. Note that each possesses a unique color in the graph. As is evident, for the same value of P¯SP and with increasing P¯ASP, greater laser output power is achieved. Linear fitting was performed for each dataset, and the corresponding slope efficiencies, η, are also provided in Fig. 5(a), among which a maximum value of 38.3% is observed. This result serves as direct evidence that 38.3% of the launched power from the ASP is contributing to stimulated emission, cementing the answer to the question posed earlier in this Letter and offering an additional route to reducing the QD in laser systems.

FIG. 5.

(a) Average laser output power, P¯L, vs average ASP pump power, P¯ASP. Linear, least squares fits are provided for each dataset with the corresponding slope efficiency (η) listed. (b) Effective quantum defect, EQD, vs average ASP pump power, P¯ASP.

FIG. 5.

(a) Average laser output power, P¯L, vs average ASP pump power, P¯ASP. Linear, least squares fits are provided for each dataset with the corresponding slope efficiency (η) listed. (b) Effective quantum defect, EQD, vs average ASP pump power, P¯ASP.

Close modal

To further examine this impact, an effective quantum defect, EQD, is defined as

EQD=QDSP×P¯SPabsP¯SPabs+P¯ASPabs+QDASP×P¯ASPabsP¯SPabs+P¯ASPabs,
(3)

in which QDSP=1λSPλL=0.91%, QDASP=1λASPλL=0.41%, and P¯SPabs and P¯ASPabs are the absorbed pump powers from the SP and ASP, respectively. The absorbed power was determined by subtracting the measured leakage power from PSP/ASP. Using Eq. (3), the EQD values corresponding to all the data points in Fig. 5(a) are summarized in Fig. 5(b). Note that in the absence of ASP (PASP = 0 mW), EQD = QDSP. As the ASP power is gradually increased, EQD decreases monotonically to 0.79% at the maximum available P¯SP. The reason for this is, as discussed earlier, that a cooling effect is introduced through the phonon absorption associated with anti-Stokes pumping, effectively offsetting QD heating. Thus, the experimental observations of EQD reduction, in combination with the overall lasing threshold reduction and slope efficiency enhancement, provide strong evidence that the suggested pumping mechanism allows for a type of self-cooled laser system that can be characterized as an excitation balanced laser, ExBL.

In conclusion, presented here was an experimental demonstration that anti-Stokes pumping of a solid-state laser is possible and that it can contribute to stimulated emission at a higher photon energy. To achieve this, a combination of both a SP and an ASP is required. In the described proof-of-concept experiments, the pumps were pulse-modulated, partially overlapped in time, and provided excitation to a linear cavity Yb-doped fiber laser. Through time domain measurements, the roles of both pumps in populating the upper state were studied, and an FDTD model was developed corroborating the experimental analysis. Furthermore, power measurements provide direct evidence that an ASP can contribute to stimulated emission and a concomitant reduction in the net QD for the laser system. The proposed concept offers considerable potential for enhanced internal thermal management in high power lasers and amplifiers. Finally, the work presented here can be extended to other solid-state laser systems, such as Er-doped fiber lasers or crystal-based lasers. Power scaling of the current laser architecture is under way.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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