1. Introduction

The injection-locked nanosecond pulsed laser is a unique laser that simultaneously realizes a high (MW order) peak power and the spectral purity of the Fourier transform limit [1]. This laser system is important in studies of nonlinear optical processes in isolated atomic or molecular systems [2, 3], and also in environmental metrology applications such as lidar [4]. An injection-locked laser generally operates at a single frequency; however, it can also be extended to dual and even multi-frequency oscillations [5]. In fact, dual-frequency injection-locked nanosecond pulsed lasers have been reported whose difference frequencies can be set in the THz [5–7] or GHz [8–10] regions. The noteworthy characteristic of these lasers is that two frequency beams are emitted from a single laser cavity. The temporal and spatial overlaps between the pulses generated at the two frequencies are thereby automatically satisfied [6,7]. These lasers will be a powerful tool for controlling nonlinear optical processes such as stimulated Brillouin and stimulated Raman scattering [11, 12] and for applications such as the dual-frequency lidar-radar [13].

When we apply such dual-frequency injection-locked nanosecond pulsed lasers more widely, more flexible selectivity as regards the combination of the two oscillation frequencies will be vital. However, if we are to realize stable oscillations at two frequencies we must configure two independent feedback loops to lock the two seed laser frequencies to a forced oscillator. This requirement has substantially restricted the selectivity with respect to the combination of the two oscillation frequencies [7]. In this paper, we report a novel laser system that overcomes this restriction and generates dual-frequency nanosecond pulses at arbitrary combinations of two frequencies.

2. Dual-frequency injection-locked nanosecond pulsed laser system

Our new laser system has two key features. One is that it employs two different modulation frequencies thus allowing us to configure two independent feedback loops. We pick up weak radiation leaked from a forced oscillator and detect it phase-sensitively by referencing the two modulation frequencies which are applied to the two seed frequencies. Then we produce the individual error signals corresponding to the two seeds. This process does not require the spatial separation of the two seeds to produce the error signals. The other feature is a cavity designed so that its length can be varied continuously on such a large scale that the difference between the two locked frequencies can be scanned over the free spectral range (FSR) of the forced oscillator without distorting the alignment or changing the transverse mode profile. These two features enable us to realize an arbitrary combination of the two oscillation frequencies whose difference can be extended continuously from less than 1 GHz to tens of THz.

Figure 1 illustrates the dual-frequency injection-locked pulsed laser system developed in this study. The system consists of a nanosecond pulsed titanium sapphire (Ti:Sa) laser (forced oscillator), two independent single-frequency continuous wave lasers (seed lasers) that produce two seeds with different frequencies, and two feedback loops to stabilize the injection-locked oscillation. The forced oscillator is based on a triangular ring laser configuration $\left(45°-45°-90°\right)$and additionally it contains an optical path that varies the cavity length continuously. Right-angle prism II (anti-reflection (AR) coated) in this additional optical path is mounted on a rectilinear guide rail. By sliding this prism along the rail, the cavity length can be swept from 451 mm (FSR: 0.665 GHz) to 588 mm (FSR: 0.510 GHz). This sweeping length means that the difference between the two seed frequencies can be continuously scanned over the FSR of the forced cavity, if the difference between the two seed frequencies are set at greater than 2 GHz. Prism II is slid accurately along the optical path. Thereby, the optimal cavity alignment can be maintained against this cavity length sweeping while we make slight adjustments to the prism angles as the need arises.

 

Fig. 1 Schematic illustration of the dual-frequency injection-locked nanosecond pulsed laser. PD, photo detector; GCF, green cut filter; OC, output coupler; PET, piezoelectric transducer; PSD: phase sensitive detector; ECLD, external-cavity controlled laser diode.

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The triangular ring cavity consists of two flat total-reflection mirrors (reflectivity: > 99%) and an output coupler with a curvature radius of 10 m and a reflectivity of 60%. One of the flat mirrors is mounted on a piezoelectric transducer (PET), which is used for finely adjusting and stabilizing the cavity length. The gain medium: Ti:Sa crystal (ϕ 5 mm x 20 mm, Brewster cut, Ti³⁺ dopant density: 0.15%), is placed as shown in Fig. 1. The cavity transverse mode in this design has a nearly flat beam size with a diameter of ~1.2 mm over the entire optical path. This beam size can also provide the optimum gain volume in the Ti:Sa crystal for a typical pump energy (~50 mJ), slightly below the damage threshold. More importantly, this optimum size can be nearly maintained (ϕ1.2 - 1.3 mm) over the full sweeping range (451 - 588 mm) of the cavity length.

Two independent external-cavity laser diodes (ECLDs), or the combination of an ECLD and a tunable continuous-wave Ti:Sa laser (Coherent 899-29, linewidth: < 500 kHz), serve as the seed lasers. We couple the two seed laser beams through a 3-dB fiber coupler, and inject them into the forced oscillator after we shape the beam profile to match it with the cavity transverse mode. As mentioned above, the forced oscillator is designed so that the cavity transverse mode profile is unchanged against the full sweeping range of the cavity length. Namely, the transverse mode matching between the two seeds and the forced oscillator is maintained at the optimum level.

The method of stabilizing the two seed-laser frequencies is based on a frequency modulation technique. From a function generator, we apply weak frequency modulations, ν_m1 and ν_m2 to the two ECLDs oscillating at ν₁, and ν₂, respectively. Under this condition, when we detect the weak radiation leaked from the total reflection mirror with a photo diode, we obtain an electric signal containing superposed amplitude modulations at ν_m1 and ν_m2. The respective amplitude modulations at ν_m1 and ν_m2 can be attributed to the two seeds at ν₁ and ν₂, respectively. Then, this electric signal is divided into two equivalent voltage signals, which are sent to phase-sensitive detectors (PSDs) I and II, respectively. In PSD I, we detect such voltage signals phase-sensitively at ν_m1. Thus an electric signal attributed to the seeds at ν₁ is identified. Similarly, in PSD II, we identify an electric signal attributed to the seeds at ν₂. The obtained error signals are processed in loop filters I and II, respectively and finally fed back to each of ECLDs.

The above scheme was described for a configuration in which the two seed lasers follow the “master” forced oscillator. There is another possible scheme for locking the two seed frequencies to the forced oscillator. Namely, one of the seed lasers serves as the “master”, and the other seed laser and the forced oscillator follow it by feeding back the error signals to each of the frequencies of the ECLD and the cavity length of the forced oscillator. In this latter scheme, the two error signals are not orthogonal to each other, but the scheme still performs efficiently. We employed this scheme in an experiment where we used a continuous Ti:Sa laser as one of the two seed lasers.

As described in this section, the present method has a mechanism that is independent of the selected oscillation frequencies. Therefore, the developed laser system can be adopted for arbitrary combinations of the two oscillation frequencies. (It is also possible to extend this laser system to one that generates many frequency injection-locked nanosecond pulses simultaneously [5].)

The seeding power introduced into the forced oscillator was typically 1 mW (the sum of the two seed powers). The time constant of the PSD was set at 30 - 100 ms. This time constant was determined so that the frequency locking of the seeds was not distorted by an intense pulsed oscillation. For pulse-pumping the forced oscillator, we employed the doubled output of a Q-switched Nd:YAG laser (Continuum; Surelite I-10; repetition rate, 10 Hz; pulse duration, 4 ns). The pump energy was typically 50 mJ / pulse.

3. Result

3.1 Locking of two oscillation frequencies to forced oscillator

First, we show that the two seeds are locked to the forced oscillator stably by employing the technique described in Sec. 2. Here, the two seed frequencies, ν₁ and ν₂, were set at 384.5043 THz (779.6855 nm) and 382.4391THz (783.8959 nm); cavity length: 487 mm, respectively. Also, the modulation frequencies, ν_m1 and ν_m2, were set at 5 and 3 kHz, respectively.

Figure 2a shows a typical PD output signal under this operational condition. The red line represents a case where only the feedback loop of the seed ν₁ was active. The other feedback loop of seed ν₂ was shut down, and instead, the seed frequency, ν₂, was swept over several FSRs of the forced cavity. As indicated by the red line, we confirmed the resonance profile corresponding to a long sweep of this seed frequency, ν₂, in addition to a definite offset that was produced by the seed ν₁. Figure 2b shows the monitored error signals in this case. The error signal for seed ν₁ (blue line) was fixed at 0 V (resonance condition), while the error signal for seed ν₂ exhibited a dispersion-like profile (red line), which crossed zero at the peak of the resonance profile (red line) in Fig. 2a. Next, we also activated the feedback loop of seed ν₂ and examined our designed simultaneous locking of both seed frequencies, ν₁ and ν₂. As indicated in Fig. 2a, the PD output (blue line) was fixed at the peaks of the red line. The blue and red lines in Fig. 2c are the corresponding error signals for seeds ν₁ and ν₂, respectively. Both error signals were fixed at 0 V as designed (resonance point) with a stability of better than 2MHz.

 

Fig. 2 a, Output signals of the photo detector. The red line is a case where only the feedback loop of the frequency, ν₁, was activated, and the frequency, ν₂, was swept over several FSRs of the forced cavity. The blue line is a case where both the feedback loops of the two seed lasers are activated. b, Error signals at frequencies of ν₁, (blue) and ν₂, (red), correspond to the red line in a. c, Error signals at frequencies of ν₁, (blue) and ν₂, (red) correspond to the blue line in a.

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Similar measurements were examined under various operational conditions and the available modulation frequencies were investigated. When the time constant of the PSD was set at 30 ms, and the frequency interval of the two modulation frequencies was greater than 2 kHz, the electric signals attributed to the seeds, ν₁ and ν₂, were clearly discriminated. The lower and upper limits of the modulation frequencies were determined by the time constant and the bandwidth of the feedback system, respectively. In the present laser system, the available modulation frequency was in the 1 - 10 kHz range.

3.2 Properties of dual-frequency injection-locked oscillation I: fundamental performance and spectra of dual frequency oscillation

Next, we describe the pulsed oscillation performance. While the two seeds were locked, we introduced a pump pulse into the forced oscillator and achieved injection-locked pulsed oscillation. The maximum output energy was 17 mJ at a pump energy of 51 mJ. The threshold pump energy was 21 mJ and the slope efficiency reached 57%. The output pulse had high beam quality with a Gaussian mode profile, and its pulse duration was 15 ns for the maximum pulse output [14]. This injection-locked pulsed oscillation was stably maintained.

We led the pulsed output to an optical multi channel analyzer (OMA; Oriel MS257 and Andor DU420-OE) and measured its spectrum. In Fig. 3 , we show the spectra in four cases where the spacings of the two oscillation frequencies were set at 0.615 GHz to 17.9 THz: (ν₁: λ₁, ν₂: λ₂, Δν) = (384.4874 THz: 779.7199 nm, 378.8404 THz: 791.3422 nm, 5.6469 THz), (384.4876 THz: 779.7195 nm, 374.4490THz: 800.5361 nm, 9.9980 THz), (384.5123THz: 779.6693 nm, 366.6516 THz: 817.6493 nm, 17.8607 THz), and (384.4928 THz: 779.7089 nm, 384.4934 THz: 779.7077 nm, 0.6 GHz). The seed frequency was monitored with a wavemeter (Burleigh WA1500). For any combination of the two frequencies, the broad spectrum of the free-running oscillation (gray line) was completely suppressed, and the output energy was clearly concentrated on the two seed frequencies. The inset shows a photo of the output beam taken by a digital camera after dispersing the output beam with a prism, where the two frequencies, ν₁ and ν_2, were set at 384.4957 THz: 779.7030 nm and 368.8421 THz: 812.7935 nm, respectively. Each beam profile exhibited a Gaussian single-transverse-mode profile.

 

Fig. 3 Spectra of the dual-frequency injection-locked pulsed output in four cases and that for free running oscillation (gray), observed using an optical multi-channel analyzer. The inset is a photo of the output beam taken after dispersing it by a prism.

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When the frequency interval was small: 0.6 GHz, the spectrum was not apparently resolved into the two oscillation frequencies in this OMA measurement because of the resolution. We also employed spectrum analyzer measurements to clarify this spectrum in detail (Melles Griot 13SAE025, FSR: 2 GHz, finesse: 160 - 200). As shown in Fig. 4a , two peaks corresponding to the two-frequency pulsed oscillations were clearly observed with a frequency spacing of 0.62 GHz, which coincided with the frequency difference (0.6 GHz) given for the two seeds. Although it has been reported that in a similar laser system, unstable competition occurs when two close frequencies oscillate simultaneously [15], such behavior was not observed in the present laser system.

 

Fig. 4 a, Detailed spectra of the dual-frequency injection-locked pulsed output with the two closest oscillation frequencies, measured with a spectrum analyzer. b, The temporal waveform observed with a high-speed real-time measurement system and its power spectrum (inset) obtained by a Fourier transformation of the beat waveform.

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Without any modification of the laser configuration, we confirmed the stable generation of dual-frequency injection-locked nanosecond pulses for various frequency combinations that could be extended from two close frequencies of less than 1 GHz to a wide interval of tens of THz.

3.3 Properties of dual-frequency injection-locked oscillation II: quality of two oscillation frequencies

Measurement with the spectrum analyzer had a sufficiently high resolution for us to evaluate the linewidth of the injection-locked pulsed output. The obtained linewidth of the injection-locked pulses was 32 MHz including an instrumental linewidth (> 10 ~13 MHz) and the temporal pulse duration was 18 ns. Therefore, the product of the intrinsic linewidth and the pulse duration is less than 0.4, showing that the output pulses at the two frequencies achieved the Fourier transform limit (FTL) condition.

In the time domain, the dual-frequency pulses form a beat waveform whose beat frequency coincides with the difference between the two oscillation frequencies. When the two frequencies are close together, we can directly observe the beat structure by using a high-speed real-time measurement system (consisting of a biplanar phototube: Hamamatsu Photonics R1328U, build up time, < 60 ps; and a high speed oscilloscope: Tektronix DPO7254, bandwidth, > 2 GHz; or Lecroy SDA18000, bandwidth, > 18GHz). A typical result is shown in Fig. 4b. The beat with almost full modulation was clearly observed over the entire nanosecond-pulsed envelope. The inset in Fig. 4b is a power spectrum Fourier-transformed from this beat waveform. The peak is located at 0.62 GHz, consistent to the difference of the two oscillation frequencies (0.62 GHz). Also, the width is 25 MHz (FWHM), satisfying nearly-FTL condition. In this measurement, we introduced the whole of the pulsed beam into the detector. Therefore, the result shown in Fig. 4b revealed that the generated dual-frequency injection-locked pulse has almost complete mutual coherence over both the entire pulsed envelope and the beam cross-section.

3.4 Properties of dual-frequency injection-locked oscillation III; continuous selections of two oscillation frequencies

Finally, we examined continuous selections of the two oscillation frequencies. When the cavity length of the forced oscillator is fixed, the two selected oscillation frequencies are discrete as a result of the longitudinal-mode space of the forced oscillator. As described in Sec. II, to allow continuous frequency selection, the cavity length of the forced oscillator was continuously swept by sliding prism II (457 – 589 mm). We generated dual-frequency injection-locked pulses at each cavity length and measured their beat waveforms, which were similar to that shown in Fig. 4b. Figure 5 summarizes typical examples. The dual-frequency nanosecond pulses (λ₁ = 779.714 nm, λ₂ = 779.708 nm: Δν = ~3 GHz) were generated with good mutual coherence over both the entire pulsed envelope and the beam cross-section, and their frequency intervals could be swept continuously for 0.76 GHz (2.51 - 3.28 GHz), which is sufficiently beyond the longitudinal mode space (0.510 – 0.654 GHz). In terms of continuous frequency selection, the scanning range of the forced cavity must be further extended to cover the longitudinal mode space, as the difference between the oscillation frequencies becomes smaller. Here, we showed continuous frequency selection for the two close frequencies of ~3 GHz that required the long sweeping range.

 

Fig. 5 Power spectra obtained by Fourier transformation of the beat waveforms observed for various cavity lengths of the forced oscillator, which was swept in the 457 – 589 mm range.

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4. Summary

We have developed a dual-frequency injection-locked nanosecond pulsed laser, that enables us to realize the arbitrary combination of two oscillation frequencies over the wide gain spectral range of a Ti:Sa laser. We showed that this performance was realized by employing two key methods: the electric discrimination of the error signals for the two seeds and a cavity design in which the cavity length can be varied greatly without distorting the alignment or the cavity spatial mode. We have also shown that two-frequency nanosecond pulses, produced with various frequency intervals ranging from less than 1 GHz to tens of THz, have single transverse and longitudinal modes and also good mutual coherence over the entire pulsed envelope and beam cross-section. This laser system will be a powerful tool for studying various nonlinear optical phenomena and for applications to environmental metrology.