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Abstract
Fourier-limited nanosecond pulses featuring narrow spectral bandwidths are required for applications in spectroscopy, sensing, and quantum optics. Here, we demonstrate a direct and simple route for the generation of single-frequency light relying on phonon-resonant Raman interactions within a monolithic diamond resonator. The technique enables the production of nearly Fourier-limited nanosecond optical pulses (15 ns), with an overall spectral bandwidth of down to 180 MHz, which is nearly two orders of magnitude narrower than the pump laser linewidth used (12 GHz). The power conversion efficiency was 47%, yielding a power spectral brightness enhancement of ${\gt}50 \times$ compared to the pump. Our results pave the way to the integration of pulsed widely tunable, power scalable, narrow linewidth light sources into integrated photonic platforms. Furthermore, the device does not need elaborate mechanical feedback loops for cavity length or frequency stabilization, or any additional optical components.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
The frequency synthesis and spectral content of lasers have been topics of investigation since the invention of the laser. Narrow linewidth and single longitudinal mode (SLM) lasers have become the prime tools for modern applications where high stability and precision are required. These include the development of atomic clocks [1], atomic matter and antimatter cooling [2], high-resolution spectroscopy [3], physics beyond the standard model [4], or lidar [5], to name a few. Applications on laser spectroscopy of radioactive elements [6–8] and the increasing interest for the study of chemical elements where no atomic information is known [9], is just another example where SLM laser sources with MHz-class linewidths are of imperative importance.
The advent of quantum-technology-based sensing and photonic sources has increased the interest in producing and integrating pulsed narrow linewidth lasers [10]. Here, the main challenge is in the complexity of producing widely tunable, high-performance narrowband lasers (in the kHz to hundreds of MHz) at a range of wavelengths that are used to cool, trap, and manipulate ions [11]. Eventually, photonic integrated circuits (PICs) are expected to provide the scalability and simplicity required to enable quantum-technology-based sensing systems and applications, but multiple advances are still needed. Among these, improvements in active materials (e.g., direct gain and laser output in the green-yellow spectral range) and passive materials (low-loss waveguides, especially in the UV blue range) could enable a viable path for wafer-scale integration [12].
While many methods to generate a stable phase-coherent train of ultrafast laser pulses are available now [13–15], these methods only provide limited access to the generation of stable coherent nanosecond pulses. By using injection-locking in Ti:sapphire [16], VCSEL [17], and fiber-based [18] lasers or external electro-optic modulation of single-frequency fibers [19], nearly Fourier-limited ns pulses have been achieved with flexible pulse durations, repetition rates, and tunability ranges. However, such schemes are usually associated with significant experimental complexity and cost, typically produce outputs with high noise figures and no pulse-to-pulse temporal coherence, and are usually not integrable on a chip.
Alternatively, taking advantage of the traditionally superior noise characteristics of passive mode-locking techniques, graphene-based saturable absorbers have been used for mode-locking ns pulses [20–22]. However, these systems produced chirped pulses with linewidths in the few-GHz range, caused mainly by the disadvantageous operation timescales of saturable absorbers, as well as by the low strength of the nonlinear effects reachable through ns pulses with moderate energies. More recently, nonlinear amplifying loop mirrors have been used to achieve Fourier-limited ns laser pulses with a corresponding spectral bandwidth in the MHz regime, although its operation was restricted to the IR and provided very low peak powers in the tens of mW [23].
An interesting alternative is to generate SLM light through stimulated Raman scattering (SRS) because it provides wide wavelength diversification at high efficiency in a simple manner. However, generating single-frequency light has only been employed in continuous wave (CW) mode [24–28] or pumped by narrow linewidth nanosecond lasers [29]. Ostensibly, pulse Raman systems are not typically amenable to SLM output. A likely reason is that the cavity designs and gain bandwidths place a large number of modes under the gain bandwidth. As a result, seeding or narrowband tuning elements are needed for mode selection. Even a homogeneous Raman gain profile is not sufficient to enable stable SLM output in the presence of transient thermal and optical processes in the timescale of the interacting pulses.
In this work, we overcome these problems and demonstrate that it is possible to produce directly stable single-frequency coherent ns pulses at any given wavelength without complicated arrangements or equipment. We present the experimental results of a power-scalable, compact, and efficient integrated Raman laser that can funneling the broad multimode output of high-power nanosecond lasers to a Fourier-limited SLM output by using a monolithic diamond resonator. We believe that this system will find many applications across different sciences, and here we show a schematic depiction of how to use it for ion trapping and spectroscopy experiments (see Fig. 1), featuring different possible ways to couple the pumping light into the diamond resonators.
Fig. 1. Example of how monolithically integrated diamond Raman lasers can be used for spectroscopy experiments in an ion trap. The broadband pumping sources can be arranged in a fiber coupler, direct waveguiding, or free space (longitudinally or side pumping). The multimode light from the pump sources is directly converted to a single-frequency tunable Stokes pulse, while the resonators can be used at any wavelength from the UV to the IR. Tuning can be performed by adjusting the bulk temperature. The output light is then directed to the interaction point by transmissive gratings. The wavelength flexibility provides access to a wide variety of ionic species employing the same optical system.
2. STOKES SPECTRAL COMPRESSION TO THE FOURIER LIMIT VIA RESONANT PHONON INTERACTIONS
One key advantage of SRS is that the gain is mediated by propagating pump photons rather than via energy storage in localized inverted ions, so there can be no local regions of unextracted pump energy and therefore no spatial hole burning [24]. The phase-matching condition between pump and Stokes beams is automatically satisfied, and therefore the energy transfer relationship between fields is dictated in great part by the shape of their temporal envelopes rather than their spectral phase characteristics or modal content. In this section, we cover the theoretical aspects involved and identify the conditions for maximal spectral compression of the Stokes pulse.
The energy transfer dynamics between pump and Stokes fields in SRS media has been a subject of study for several decades and, as a consequence, there is a wide range of modeling strategies available. Of those, a convenient methodology to study the spectral characteristics of the fields involved is to model the SRS process entirely in the frequency domain [30]. In this approach, the field from a laser is represented by the amplitude and phase of the longitudinal modes of the laser cavity. The superposition of these modes in the time-domain gives a laser signal repeating with a period of the round-trip time of the laser cavity ${t_{\textit{rt}}} = 2\pi /\Omega = 2{L_{\rm{eff}}}/c$, where ${L_{\rm{eff}}}$ is the optical path length of the resonator.
The noisy temporal structure of multimode laser fields–both in amplitude and phase on timescales faster than the cavity round-trip time–is caused by the interference of its spectral modes. These modes, however, generally vary in amplitude and phase on the timescale of the round-trip time or slower. This is equivalent to saying that the linewidth of any individual mode is much smaller than the mode spacing $\Omega$. Since the longitudinal modes vary slowly (at least much slower than the phonon dephasing time), we can in most cases model the Raman gain and loss for each mode using steady-state Raman theory, even if interference of the modes produces a structure that would need transient Raman theory if modeled in the time domain. This approach has been used by many authors to analyze SRS with broadband lasers [30–36], and we now use this method to model phonon-resonant Raman interactions.
To construct the frequency domain model, we start by writing the multimode fundamental field ${\tilde E_F}$ (also called “pump” in the following) with $2m + 1$ modes spaced in frequency by $\Omega$, and a single-mode Stokes field ${\tilde E_S}$:
in which $cc$ represents the complex conjugate of the preceding term, and ${\omega _{F(l)}} = {\omega _{F(0)}} + \Omega l$. In these equations, ${S_0}$ and ${F_l}$ are complex amplitudes describing, respectively, the amplitude and phase of the Stokes and fundamental modes. The approximation for the mode wavevector ${k_{F(l)}} \approx {k_{F(0)}} + \Omega l/{u_F}$ accounts for the group velocity difference between the fundamental wave packets, but neglects the group velocity dispersion within each wave packet.The key to produce a spectral “funneling” effect is to find a mechanism in which each fundamental mode efficiently transfers its energy to a single Stokes spectral mode. This effect can be described by
where the term $({\omega _R} \pm l\Omega)$ accounts for a phonon that resonantly interacts with the fundamental field mode ${\omega _{F(l)}}$, and is within the Raman linewidth ($\Delta {\omega _R} \gt \Omega l \forall l$). Here, we define “phonon-resonant” Raman conversion to the processes that fulfill Eq. (3). A visual interpretation of this mechanism is depicted in Fig. 2. Here, the broadband pump photons must interact with phonons of the exact energy so that the resulting Stokes photon energy is constant. This process can be efficient, provided the pump linewidth is narrower than or equal to the Raman linewidth $\Delta {\omega _R}$. The conditions to satisfy this equation will be described at the end of this section.Fig. 2. Virtual energy states of a Raman process highlighting a resonant phonon interaction. A fundamental field composed by multiple longitudinal modes interacts with phonons of specific energy such that the scattered Stokes photons form a purely monochromatic beam.
To describe the coupling between the fundamental and the Stokes modes, we use SRS in steady-state relations and write it in a doubly degenerate phase-matched form. Note that nondegenerate modal interaction is not possible if Eq. (3) is satisfied because there are no Stokes sidebands:
The condition expressed mathematically in Eq. (3) cannot be attained unless the SRS process is set in an environment that prevents Stokes side modes from being amplified. In free-space lasers, this is normally achieved by introducing spectrally selective components such as etalons, gratings, or birefringent filters. Another solution is to design a resonator that predominantly amplifies the Stokes central frequency, where pump depletion mechanisms decrease the gain available for Stokes sidebands [24]. In a monolithic design, this can be achieved implementing a standing wave resonator that operates as a Raman-active etalon, provided that the combination of net gain and finesse ${\cal F}$ is enough for effective spectral selectivity. For very high intensity fundamental fields, Raman gain narrowing can further assist in producing a reduced effective gain linewidth and ensure single-mode operation.
Taking the aforementioned effects into account, a sufficient condition to satisfy Eq. (3) is that the free spectral range (FSR) of the resonator is then larger than the overall effective Raman gain linewidth of the resonator (${\rm{FSR}} \gt \Delta {\omega _g}$). Here, the effective gain with a linewidth of $\Delta {\omega _g}$ is approximately the result of the convolution of the natural Raman spectrum and the pump laser spectrum. For Lorentzian lineshapes, this is $\Delta {\omega _g} = \Delta {\omega _F} + \Delta {\omega _R}$. Such broad gain linewidth typically requires microresonators with sub-mm optical path lengths to produce a SLM output, being often implemented in toroidal or racetrack architectures that require high-Q factors to operate efficiently [37,38]. Consequently, the operation of such lasers is restricted to CW mode and very low average powers in the µW range.
A workaround for high-power nanosecond pulses is to operate in the high Raman gain regime [32,39,40]. Here, the Stokes spectrum is driven to duplicate the pump spectrum. This normally occurs for Raman lasers exhibiting high single-pass gain in combination with relatively low $Q$ cavities. In this case, the sufficient condition that satisfies Eq. (3) becomes
which allows for the use of manageable mm-scale resonators, if pumped by lasers with $\Delta {\nu _F}$ in the tens of GHz. We now define the quantity $\eta$ that accounts for the combined effects of the power conversion efficiency and the ratio of spectral widths:For $\eta \gt 1$, the net effect is of an enhancement of the power spectral density (PSD) or an apparent spectral funneling effect. Values of $\eta \lt 1$ are common in the literature and correspond to previous realizations of CW (in intracavity [28] and external cavity [24–27] arrangements) and pulsed nanosecond SLM Raman lasers [29]. Note that substantial enhancement in spectral density was observed in the CW laser of [26]; however, details of the SLM output linewidth were not reported. In this work, we demonstrated, for what we believe is the first time, a monolithic system that can produce large $\eta \gt 50$, while its linewidth approached the Fourier limit.
3. MONOLITHIC DIAMOND RESONATORS
As an almost ideal quantum photonic material, diamond holds the promise to combine in a single platform all the required components for large-scale quantum PICs with the potential to operate at an ambient temperature [26,37,41]. Integrated photonic systems realized in single-crystal diamonds are poised to benefit from the extraordinary material properties, including an ultrawide transparency range, high Raman gain [42,43], and extremely high thermal conductivity [44]. These unique characteristics enable the construction of power-scalable optical devices beyond the kW average power [45].
The fact that diamond has a very low thermal expansion coefficient (${\sim}1.1 \times {10^{- 6}}\;{{\rm{K}}^{- 1}}$) provides a naturally stable environment to construct integrated resonators. Diamond is also among the stiffest materials known and possesses extremely low thermoelastic mechanical damping [46]. Therefore, monolithic diamond resonators are a natural choice to produce frequency stable light without the need for external mechanical feedback loops to control the resonator length, given that the temperature of the crystal is stable.
Compared to integrated ring resonators, a monolithic linear Fabry–Perot design prevents depolarization due to the anisotropic nature of the SRS interaction in diamond and provides easy access to the maximal Raman gain [47]. It also allows for the scaling of the output power by simply increasing the transversal pump mode size, and temperature adjustments can be directly used to fine tune the center frequency of the output Stokes within the FSR of the resonator. Ultrawide tunability, however, is attained by coarsely adjusting the pump laser wavelength.
We carried out simulations for a pump laser and a diamond resonator resembling the one used for the experiments. The model is described in more detail in Supplement 1. For the calculations, a pump source producing pulses with a duration of 15 ns (FWHM) and a multimode spectral profile with variable linewidth $\Delta {\nu _F}$ ranging from 1–45 GHz and centered at 570 nm was used. The intensity of the pump laser was set to $0.7\; {\rm{GW/c}}{{\rm{m}}^2}$ for all simulations. The Fabry–Perot resonator is as depicted in the inset in Fig. 3. Here, ${{\rm{L}}_{{\rm{eff}}}}$ is the effective resonator length at ${\omega _S}$, which in each case was adjusted to satisfy Eq. (6), and ${{{R}}_{{1}}}$, ${{{R}}_{{2}}}$ are the reflectivities of the end surfaces at the Stokes wavelength.
Fig. 3. Results of simulations of a Fabry–Perot diamond resonator using a phonon resonant interaction model. The Stokes linewidth ($\Delta {\nu _S}$) is shown as a function of the pump field spectral linewidth and resonator finesse ${\cal F}$. Results are shown for pump linewidths from 1 GHz (blue, average of 10 simulations) – 45 GHz (red, average of 10 simulations) in steps of 5 GHz (gray lines, single simulations). Fourier-limited linewidth of the pump pulse (yellow).
The results of the simulations are shown in Fig. 3. It is apparent that for values of ${\cal F} \gt 6$, the output Stokes linewidth is reduced to $\Delta {\nu _S} \lt 200 \;{\rm{MHz}}$ for any given pump linewidth up to the Raman linewidth $\Delta {\nu _R}$. As ${\cal F}$ is further increased, the resonator photon lifetime extends beyond the fast variations of the pump temporal envelope, producing an integration effect that allows $\Delta {\nu _S}$ to be smaller than the Fourier-limited transform of the pump pulse. In the experiments, we show that for moderate pump linewidths of around $\Delta {\nu _F} \approx 12\; {\rm{GHz}}$, even uncoated diamond surfaces (${\cal F} \approx 1$) are reflective enough to produce a narrow linewidth SLM output. In general, Eq. (S.14) in Supplement 1 allows for the calculation of the Stokes field for a given combination of pump laser and diamond resonator, while the narrowest attainable Stokes linewidth depends on resonator characteristics (length, finesse) and the pump pulse linewidth and temporal envelope.
4. EXPERIMENTS
For our experiments, we used the setup depicted in Fig. 4. The pump source was a tunable dye laser (Credo, Sirah Lasertechnik GmbH) pumped by a frequency-doubled DPSS ${\rm{Nd:YV}}{{\rm{O}}_4}$ laser (Blaze, Lumera Laser GmbH) producing up to 40 W at 532 nm, with a repetition rate of 10 kHz and a pulse duration of ${\sim}15 \;{\rm{ns}}$. The gain media of the dye laser was rhodamine 6G dissolved in ethanol, which generated a tunable laser output from 563 nm to 597 nm, with a linewidth of $\Delta {\nu _p} \sim 11.9\; {\rm{GHz}}$ measured at 570 nm (time-bandwidth product of $\approx 180$), and Gaussian in lineshape. The maximum output power at this wavelength was 2.5 W. The losses of the dye laser light due to the components used for matching the beam to the diamond resonator were up to 20%.
Fig. 4. Schematic layout of the experimental setup: A monolithic diamond resonator is pumped by a widely tunable broadband rhodamine 6G dye laser. The output Stokes pulse was characterized temporally and spectrally with a set of high-resolution Fizeau interferometers (Lambdameter), a SFPI, and a large bandwidth oscilloscope. HWP, half-wave-plate; PBS, polarizing beam splitter; FL, focusing lens; PM, power meter; PD, photodiode; and SFPI, scanning Fabry–Perot interferometer.
The diamond that constitutes the Fabry–Perot resonator was 5 mm in length (low birefringence, low nitrogen, CVD-grown single crystal, Element Six Ltd.) and repolished to achieve an end-face parallelism better than $0.5\; {{\unicode{x00B5}{\rm m}/{\rm mm}}}$. The resonator length was chosen so that its FSR (12 GHz) was approximately equal to the dye laser linewidth (11.9 GHz) following Eq. (6). The resonator was directly pumped at 568 nm by means of a 15 cm focal length lens, as shown in Fig. 4, that produced a Stokes pulse at 614 nm. Initially the experiments were performed with an uncoated diamond sample (${R_1}$, ${R_2} \approx 17\%$), although subsequent experiments were carried out after deposition of multilayer dielectric coatings at each end, and with the resonator placed in an oven that was temperature stabilized with a precision ${ \lt 0.01^ \circ}{\rm{C}}$ and at around 40°C. A tuning slope of $3 \;{\rm{GHz}}{/^ \circ}{\rm{C}}$ was observed when adjusting the oven temperature. Note that for further integration into PICs, thermal tuning pads maybe used instead of an oven [48]. In all cases, a tunable nearly Fourier-limited output was produced.
To obtain large power spectral density enhancement factors $\eta$, the output linewidth must approach the Fourier limit and the conversion efficiency must be comparable to the quantum defect ${\omega _S}/{\omega _F}$. To characterize the conversion efficiency of the Raman process, we measured the slope efficiency curve. We varied the pump power by changing the power sent to the diamond resonator by means of HWP1 and PBS, as shown in Fig. 4. The resulting beam was the polarized parallel to the ${\langle}{{111}} \rangle $ diamond crystallographic axis using HWP2. The observed instabilities in the laser power are due to instabilities in the pump laser power. A linear fit to the experimental data revealed a slope efficiency of 56%, with a conversion efficiency of 47% at maximum pump power (combining all resonator outputs), while the measured beam quality was ${{\rm{M}}^2} \lt 1.2$. During these measurements, the output linewidth of the Stokes pulse did not vary significantly. (See Supplement 1, Section 2 for more details.) The results were achieved using a high-power widely tunable dye laser. Even though this laser system is relatively large and powerful, the requirements for pulse energy and intensity are relatively modest (${\lt}100\;\unicode{x00B5}{\rm{J}}$ pulse energy in a 15 ns pulse focused to a $35 \times 36\;{{\unicode{x00B5}}}{{\rm{m}}^2}$ spot and an intensity of $0.7\;{\rm{GW/c}}{{\rm{m}}^2}$). Such performance can also be attained by employing compact microchip lasers operating at lower repetition rates and with pulse durations in the few ns range. Moreover, using higher finesse resonators, the requirement for pump laser intensity can be further reduced, down to the mW regime in diamond PIC platforms, as was demonstrated in [37].
A. Time-Bandwidth Product Reduction by 100× to Nearly the Fourier Limit
The temporal response of the device was characterized using an ultrafast photodiode (UPD-50-SP, Alphalas GmbH) with a bandwidth ${\gt}\;{{7}}\;{\rm{GHz}}$ and a 16 GHz bandwidth oscilloscope (SDA 18000, Teledyne LeCroy). The calibrated minimum rising time of the combined photodiode and oscilloscope was measured to be 150 ps, enabling the temporal characterization of optical waveforms with linewidths of up to $\Delta {\nu _S} \approx 6.5\; {\rm{GHz}}$. The experimental measurements from where the previous results were extracted are presented in Supplement 1. The observed amplitude modulation with a period of 2 ns in both Stokes and pump pulses result from longitudinal mode beating in the pump laser cavity ($\approx 30\; {\rm{cm}}$ long), and are independent of the pump source of the dye laser. Since the resonator finesse used in the experiments is relatively low (${\cal F} \lt 2$), the combination of short cavity photon lifetime and high Raman gain allows the Stokes envelope to quickly follow the amplitude modulations of the pump pulse. In such case, the output Stokes linewidth is approximately the Fourier transform of the pump pulse temporal profile (${S_0}(\omega) \propto F\{|F(t{)|^2}\}$). The calculated Fourier transform of the Stokes temporal envelope at maximal pump power resulted in a bandwidth of $95 \pm 15\; {\rm{MHz}}$ (FWHM).
To determine the spectral characteristics of the pump and Stokes pulses, we used two instruments: a spectrum analyzer (Lambdameter LM-007, Cluster Ltd., Moscow) based on a set of four Fizeau interferometers and a scanning Fabry–Perot interferometer (SFPI, SFPI 100, instrumental width ${\sim}34\; {\rm{MHz}}$, Toptica Photonics AG). The free spectral ranges of the highest resolution Fizeau interferometer and the SFPI were 3.75 GHz and 4 GHz, respectively. A detailed report of the results and methods used to perform the measurements can be found in Supplement 1. The dye laser linewidth was measured with a Fizeau interferometer with a FSR of 59 GHz, yielding a $\Delta {\nu _F} \approx 11.9 \pm 0.3 \;{\rm{GHz}}$, with a Voigt-like convolved lineshape. The Stokes linewidth measured with the SFPI yielded a value of $\Delta {\nu _S} \sim 180 \pm 33\; {\rm{MHz}}$, which is Lorentzian in lineshape.
The same measurement using the Fizeau interferometers resulted in a linewidth of $\Delta {\nu _S} \sim 220 \pm 50\; {\rm{MHz}}$, measured for approximately 100 consecutive pulses over a period of 10 ms. The weighted mean value of the Stokes linewidth was estimated to be $\overline {\Delta {\nu _S}}\; 200 \pm 40\; {\rm{MHz}}$. It is expected that during this relatively short period of time ${{\rm{L}}_{{\rm{eff}}}}$ remains constant. The measured linewidth of 200 MHz was comparable to the Fourier-transform-limited bandwidth of ${\sim}96 \;{\rm{MHz}}$ retrieved from oscilloscope traces. From these measurements, we conclude that the time bandwidth product was reduced by nearly two orders of magnitude ($180 \to 1.9$) from pump to Stokes pulses.
B. Enhancement of the Power Spectral Density $50 \times$
It is possible to estimate the average PSD of the pump and Stokes pulses by scaling the deconvolved spectral profiles with the average power measurements. In this case, the PSD of the dye laser was estimated to be approximately 0.08 W/GHz, whereas the one for the output Stokes was ${\sim}4\;{\rm{W/GHz}}$ (a ${\gt}50 \times$ PSD enhancement), as depicted in Fig. 5.
Fig. 5. Power spectral density and linewidth comparison between the pump and Stokes pulses. The produced Stokes pulse is $50 \times$ more spectrally bright than the pump pulse.
Note that the absolute maximum theoretical $\eta$ attainable with this experimental setup corresponds to $\eta \approx 115$, which corresponds to 100% of the pump photons being funneled into monochromatic Stokes photons. In general, the maximal PSD enhancement is attainable if $\Delta {\omega _R} \sim \Delta {\omega _p}$, assuming pulse temporal shape preservation.
C. Center Frequency Stability
To test the stability of the produced single-frequency output, we scanned the pump laser wavelength continuously for a range of more than 20 nm and measured the Stokes center frequency using a set of Fizeau interferometers. The accuracy of the wavelength measurement setup was better than $1 \times {10^{- 4}}\;\unicode{x00C5}$, corresponding to $\delta \nu \lt 8 \;{\rm{MHz}}$ at 617 nm.
Figure 6(a) shows results for a small tuning range to highlight the mode-hopping nature of the Stokes output. The results show that the device operates in a mode-locked fashion, producing a stable frequency regardless of the pump laser center wavelength. Beyond the FSR of the resonator (12 GHz) the Stokes frequency jumped to the next longitudinal mode with higher gain, but mostly maintaining a narrow output linewidth a stable frequency.
Fig. 6. Stokes wavelength as a function of the pump wavelength. (a) The mode hopping between the resulting Stokes wavelength. (b) The stability of the single-mode center frequency while the pump laser wavelength is tuned. The variation in center frequency in combination with the linewidth of the laser produced an overall convoluted resolution of around 300 MHz (red line).
The shallow slope observed in the plateau sections of the Stokes wavelength in Fig. 6(a) possibly are produced by pump beam steering due to the tuning of the dye laser grating. A lateral displacement of the beam, even if in the ${{\unicode{x00B5}{\rm m}}}$ scale, can in principle produce a small frequency tuning due to the imperfect parallelism of the diamond faces. The instability observed in the edges of each mode hop is possibly associated with a sporadic multimode laser operation when the center frequency is close to edge of the free spectral range, producing a less accurate reading in the wavemeter.
Figure 6(b) shows a sequence of simultaneous Stokes linewidth and wavelength measurements as a function of pump laser frequency. A free running measurement at a fixed pump wavelength showed a Stokes frequency standard deviation of ${\sim}150\; {\rm{MHz}}$ over ${10^6}$ shots. The combined effect of the linewidth and wavelength instabilities yielded an integrated spectral linewidth of 300 MHz, which was independent of the pump laser center wavelength stability. This fluctuation is already small enough for atomic hyperfine structure and nuclear spectroscopy [6–8], where the spectral resolution required is on the order of 100–300 MHz. Reduced frequency noise, which may be required for some applications, may be achieved by employing pump lasers with a higher pulse to pulse energy stability and lower temporal envelope noise.
5. CONCLUSIONS AND OUTLOOK
We show experimental evidence of Stokes spectral squeezing via a phonon resonant interaction. This effect was exploited to produce near Fourier-limited linewidth mode-locked nanosecond pulses employing a monolithic diamond resonator, without the need for mechanical feedback loops to stabilize the length or additional optical arrangements.
The output Stokes linewidth was 200 MHz in contrast to 11.9 GHz for the pump laser, while the power conversion efficiency was 47%, resulting in a power spectral density enhancement of $50 \times$. Moreover, taking advantage of the phase-independent characteristics of the Raman scattering process, the resonator directly produces pulse-to-pulse temporally coherent pulses without additional effort. This technique is power scalable, and is widely applicable to commercially available nanosecond lasers operating at nearly any wavelength from the UV to the IR.
The combination of very narrow spectral bandwidth and the resulting high spectral density, alongside the large transparency range of diamond, make this technique very versatile and useful for a large number of applications. The compact architecture and modest requirements in terms of resonator quality factors, readily allow for stable and portable operation, while opening up a route toward the full integration of the laser system in PICs. Further studies using careful temperature adjustments of the diamond resonator are underway to allow for full continuous tunability. We believe this device, together with the possibility to combine this technique with widely tunable Ti:sapphire or dye lasers, will pave the way toward novel sensing and high-resolution spectroscopy implementations across the optical spectrum.
Funding
CERN (Knowledge Transfer Fund, Singular Light).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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