1 Introduction

A narrow spectral bandwidth laser operating at the mid-infrared wavelength regions has a variety of applications including molecular spectroscopy, remote sensing of the environment, medical diagnostics, laser radar, free space communication, etc. [1, 2]. A number of methods to produce mid-infrared laser radiation have been developed, such as HF/DF laser, optical parametric oscillator (OPO), quantum cascade laser (QCL), second harmonics generation (SHG) CO2 laser, first-overtone CO laser, Cr and Fe-doped II–VI chalcogenides solid laser [3]. Among these methods, HF laser is so far considered as the highest output power laser system [4]. Conventionally, multiline laser emission is obtained due to ro-vibrational transitions of HF molecules. Most of these laser lines will be strongly absorbed by atmosphere because of moisture. However, several spectral lines with specific ro-vibrational energy levels of HF laser have fine atmospheric transmission, especially P2(8) line that has been demonstrated without obvious optical losses and thermal blooming effects even through long distance transportation in air [5]. In general, a configuration with a blazed grating as the rear mirror of the laser cavity is usually used to select and control the spectrum of such specific radiation [6, 7]. However, it is still difficult to obtain pure P2(8) line because of the P1(11) line oscillates simultaneously. It is because that the gain coefficients of these two lines are so similar, meanwhile the wavelength difference between them is so less that it cannot be finely differentiated by a diffraction grating in the cavity. However, in the case that high temporal or spatial coherence is desirable for the laser radiation, it is necessary to enhance its monochromaticity [8]. Some techniques have been provided to generate narrow linewidth laser such as using an etalon, interferometers, and injection locking [9]. These techniques are inapplicable to high-power laser because of low power threshold of optical selection components or cavity-mode match. An Integral Master Oscillator Power Amplifier (IMOPA) concept was proposed to achieve line-selected laser for high-power HF laser [10], however, output of P2(8) pure line laser has not been experimentally verified.

In this paper we present a hybrid cavity to obtain pure P2(8) line output in a cw HF laser system. An unstable laser cavity was employed to preliminarily select the lines, which constituted a grating in the Littrow arrangement and a convex mirror. An absorption section that generated ground state HF molecules had been set close to the gain section in the cavity to suppress oscillation of P1(11) line. The characteristics, which has high efficiency of absorbing medium and needs no additional optical components, can make high-power single line laser operate in fine atmospheric window of a HF laser in more feasible way. A numerical model was developed to describe gain variations of both lines when laser operated with or without the absorption section. Experimental verification was also presented to demonstrate that output power of P2(8) single line was depended on the characteristics of the gas ejected from the absorption section.

2 Theory

The spatial distribution of gain coefficient in some point can be relative predicted by a HF laser gain model. A computational fluid dynamical codes which can integrate the complex fluid properties with the myriad chemical reactions is employed to investigate the details of the laser performance. Four processes are assumed to contribute to alteration of the gain of HF laser: (1) combustion process producing atomic fluorine by D2 reacted with NF3 (by H2 reacted with NF3 for absorption section); (2) chemical reactions forming HF molecules; (3) vibrational relaxation and V–V energy transfer (including HF molecules themselves and with other atoms or molecules); and (4) rotational relaxation process.

Numerical simulations of the mixed flow output from the combustion chamber, the subtransonic flow in the supersonic nozzle, and the chemical reactions in the gain generator were investigated. The numerical model includes the conserved forms of compressible three dimensional Navier–Stokes equations, energy equations and the transport equations of each component.

The small signal gain of a HF laser induced by stimulated transition of populations from an upper u to a lower l state is given by [11]:

$$g = \frac{{c^{2} A}}{{8\pi \nu^{2} }}g\left( \nu \right)\left[ {N_{{\text{u}}} - \frac{{g_{{\text{u}}} }}{{g_{{\text{l}}} }}N_{{\text{l}}} } \right],$$

where A is the Einstein emission coefficient, ν is the frequency, g(ν) is the spectroscopic line shape, Nu, Nl, gu and gl are the number densities and degeneracies for the upper and lower states, respectively. A can be calculated from first principles with an accurate potential energy surface and a suitable dipole moment function [12], in this paper, they are based on the values found in Refs. [5, 12].

The distribution of calculated small signal gain coefficients of P1(11) line and P2(8) line at the exit of nozzle are shown in Fig. 1, where x and y along are perpendicular to the direction of flow respectively. The laser is perpendicular to the plane consisted of x and y. The alpha value which is defined as \(\alpha = 1.5{{\left[ {{\text{NF}}_{3} } \right]} \mathord{\left/ {\vphantom {{\left[ {{\text{NF}}_{3} } \right]} {\left[ {{\text{D}}_{2} } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {{\text{D}}_{2} } \right]}}\) in the combustion chamber of the generator of atomic fluorine was set to 1.5, where [NF3] and [D2] represent the concentrations of NF3 and D2 molecules, respectively. The simulated value of average gain coefficient is 3.9% for P1(11) line and 5.7% for 2P(8) line at about 20 mm from the exit of nozzle. When the absorption section was added to the gain section, the simulated values are decreased for both lines, as shown in Fig. 2. Figure 3 shows absorption coefficients of both lines with changing of α of absorption section. Simulated values indicate that the absorption coefficients of P1(11) line is nearly an order of magnitude greater than P2(8) line when α is less than 1.8. As α further increased, absorption of both lines rise rapidly due to appearance of thermal resistance effects.

Fig. 1
figure 1

Calculated small signal gain of HF laser with α(\(\alpha = 1.5{{\left[ {{\text{NF}}_{3} } \right]} \mathord{\left/ {\vphantom {{\left[ {{\text{NF}}_{3} } \right]} {\left[ {{\text{D}}_{2} } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {{\text{D}}_{2} } \right]}}\)) set to 1.5 without absorption section: a P1(11) line; b P2(8) line

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Fig. 2
figure 2

Calculated small signal gain of HF laser with α of absorption section (α=1.5[NF3]/[H2])  set to 1.64: a P1(11) line; b P2(8) line

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Fig. 3
figure 3

Calculated absorption coefficients of both lines with changing of α of absorption section

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3 Experimental setup

A distribution feedback tunable diode(DFB) laser (2.9 μm, 2mW, Nanoplus) was used to obtain the absorption spectra of HF molecules in the absorption section, as shown in Fig. 4. The wavelength of the diode laser swept periodically by changing its current. The sweeping range of the diode laser was about 1.8 nm, which covered the spectral region of P1(11) and P2(8) lines of HF molecules. Both ends of absorption section was sealed by the laser-head sapphire Brewster windows to enhance the transmittance of diode laser. The output beam of the tunable diode laser went through the absorption region and the transmitting beam was focused on an InSb detector (J10D, Judson) which was cooled by liquid nitrogen. A digital oscilloscope (625Zi, LeCroy) was used to record the voltage signal of the detector as a function of time. The transmission spectra were obtained by comparing the absorption and non-absorption traces. It could be inferred that the absorbance of the high J lines of HF molecules would be very low at room temperature as a consequence of Boltzmann's equilibrium law. To get large absorbance of high J lines of HF molecules, the experiment had been performed on a configuration using a generator of atomic fluorine and a supersonic nozzle array, as shown in Fig. 5. NF3 and H2 was injected to the combustor, respectively, and reacted with each other to produce high temperature ground state HF molecules. The supersonic nozzle array consisted of alternative F main nozzle and H2 secondary nozzle units. The combustion products flowed through the supersonic nozzle array and entered the absorption region. The pressure of the combustor mixing gases is about 1 bar.

Fig. 4
figure 4

Schematic diagram of absorbance of two lines output from a swept DFB laser by the absorption section

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Fig. 5
figure 5

Schematic diagram of structures of F generator and nozzle

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Further experiment was carried out to investigate the behavior of laser output from the HF laser using hybrid section, as shown in Fig. 6. The geometry of generator of atomic fluorine and nozzle that generated the gain region was similar to what was described in absorption section. NF3 reacted with D2 to produce atomic fluorine in the combustor. Then the gas containing atomic fluorine was expanded and accelerated by the supersonic nozzle array and entered the gain region, in which F reacted with H2 to form excited HF molecules. Turbulators were set in each nozzle unit to enhance the mixing of reaction gas. The parameters of reagents in the experiment were in accordance with the data used in calculation previously.

Fig. 6
figure 6

Schematic diagram of the experimental setup for obtaining P2(8) single line oscillation

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A diffraction grating of 500 grooves/mm, which was placed at a Littrow angle, was employed to yield the two lines of the laser. A diffraction efficiency of over 96% was measured at P2(8) wavelength when the polarization of the laser was parallel with the direction of grooves. A 42 m radius convex mirror was used to combine with the grating to form a nonconfocal unstable resonator. The convex mirror was fixed to a sapphire window so that the laser could output from the edge of the mirror. The length of the cavity is 3 m, and the magnification is 1.7. All the optical elements were set in the vacuum chamber that was connected to the nozzle. The laser output from the chamber through a window on it ultimately. The output power of the laser was measured with a power meter (PM5K, coherent), and the wavelength was monitored with a Nicolet 6700 spectrometers (resolution in experiment was 0.25 cm−1).

4 Results and discussion

4.1 Characteristic of absorption section

Figure 7 shows the typical transmission spectra of the HF molecules emitting from the combustor of the absorption section. As seen in Fig. 7a, a notable absorption of P2(8) line was observed in the absorption section which implied the survival of vibrational excited state HF molecules in spite of frequently collisional deactivation of excited state combustion products. By controlling the deactivation process of excited HF molecules, the absorption of P2(8) line could be suppressed at a negligible level as shown in Fig. 7b.

Fig. 7
figure 7

Transmission spectra in the absorption section of the HF molecules emitting from the combustor: a P1(11) and P2(8) lines with notable absorption; b P2(8) line with negligible absorption

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It was found experimentally that P1(11) line absorbance was also suppressed while the P2(8) line absorbance was suppressed. Fortunately, the HF P2(8) line absorbance was suppressed more than P1(11) line. Figure 8 shows the ratio of P1(11) line absorbance to P2(8) line absorbance as a function of the α value. From Fig. 8, it was found that the ratio of the P1(11) line absorbance to the HF P2(8) line absorbance is strongly relevant to the α value. When the α value is smaller than 1.0, the absorbance ratio remains almost constant. On the other hand, when the α value is larger than 1.0, the absorbance ratio increases dramatically with the α value. It can be known that the gas temperature in the combustor decreases and the concentration of atomic fluorine increases with the α value when the α value is larger than 1.0. That means the combustion plays an important role in producing HF particles for absorption, and the combustion products contain not only ground state but also excited state particles that was not considered previously.

Fig. 8
figure 8

The ratio of P1(11) line absorbance to P2(8) line absorbance as a function of α

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4.2 Pure single line oscillation in HF laser

When the laser cavity consisted of only gain section and optical components, output spectra typically contained P2(8) and P1(11) lines. The power was 1 kW when the α was set to 1.56, and P2(8) line accounted for one thirds of the total power approximately, as shown in Fig. 9a. P1(11) line was depressed obviously due to presence of fundamental HF particles as the absorption section operated, as shown in Fig. 9b. With the reactant density improved further in absorption section by increasing flow rate of reactants in its combustor, P1(11) line was suppressed completely. Figure 9c shows P2(8) single line spectra with flow rate of reactants in combustor of absorption section similar to gain section, and output power of P2(8) line has little changed.

Fig. 9
figure 9

Spectra of output laser using fundamental HF particles: a P1(11) and P2(8) lines without absorption; b P1(11) absorbed by fundamental HF; c output of single P2(8) line

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As reactants in absorption section were much more than the optimal quantity, output power of P2(8) line was also reduced even suppressed. It is because the P2(8) line had been absorbed by HF(v = 1) particles produced in that condition. Figure 10a shows P2(8) single line with α of absorption section set to 1.65. However, when the flow rate of reactants was risen to 1.6 times, power of P2(8) line was reduced to less than one half, as shown in Fig. 10b.

Fig. 10
figure 10

Absorption of P2(8) line with increasing the flow rate of reactants. a Radiation of single P2(8) line; b decrease of P2(8) line as further improving absorption

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For a traditional HF laser, H2 is usually forbidden to use as fuel to react with oxidizer in combustor (D2 cannot be used for DF laser similarly) because the resulting massive HF(v = 0) particles will quench excited HF particles seriously. The principle also applies to DF laser, D2 cannot be used as fuel either. In a hybrid laser, when H2 is injected to nozzle exit region in absorption section as secondary fuel, HF(v = 2) particles produced from H2 reacted with atomic fluorine will be deexcited by HF(v = 0) particles flowed from combustor and produce HF(v = 1) particles which will lead to reduce the efficiency of P2(8) line by absorption, as shown in Fig. 11b. However, if D2 is injected to mix with atomic fluorine instead of H2, there is no significant effect on output of P2(8) line, as show in Fig. 11c. That means it is possible to obtain both a HF selected line and a DF selected line in a common laser cavity using two different gain sections and a dual-wavelength grating.

Fig. 11
figure 11

Spectra of output laser using D2 as secondary fuel instead of H2 to react with F in absorption section. a P1(11) and P2(8) lines without absorption; b using H2 as secondary fuel of absorption section; c using D2 as secondary fuel of absorption section

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5 Conclusions

We have demonstrated a hybrid configuration to achieve pure P2(8) line weakly absorbed in the atmosphere of a cw HF laser operation. Single line oscillation has been theoretically predicted using a 3D HF gain model. Experimental verification was carried out using absorbance of a swept DFB laser and output of a hybrid laser, respectively. The results indicate that P1(11) line has been absorbed significantly by fundamental HF(v = 0) particles at high J level produced from combustion, and the efficiency of P2(8) line also has been affected by a little HF(v = 1) particles. The absorbance depends on mole ratio and concentration of reactant greatly: it was improved for P1(11) line while reduced for P2(8) line as α increased; When flow rate of reactants was increased, the absorbance of both lines grew rapidly. Output laser of pure P2(8) single line was obtained with little loss when reactant concentration of absorption section was similar to gain section but α was set to 1.6. D2 as secondary fuel in the absorption has proved to be not an obvious impact on output of P2(8) line, which makes it be possible to obtain two selected lines weakly absorbed by atmosphere output simultaneously from a HF/DF dual-module laser.