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Abstract
We report on an 888 nm-pumped Nd:GdVO$_4$ ring laser operational over a wavelength range from 1340.3 nm to 1342.1 nm with a maximum output power of 7.4 W at 1341.2 nm and a beam quality parameter $M^2 < 1.1$. To our knowledge this is the highest single-longitudinal-mode power obtained with a Nd:GdVO$_4$ crystal laser. We use a commercial frequency-doubling cavity to achieve 1.2 W at 671.0 nm and 4.0 W at 670.6 nm for use in lithium cold atom experiments. Respectively, these wavelengths are approximately resonant with and 250 GHz blue-detuned from the lithium $D$-lines. Thus, this source provides ample power for laser cooling of lithium atoms while also offering substantial power for experiments requiring light 10’s to 100’s of GHz blue-detuned from the primary lithium transitions.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laser sources near 671 nm are the workhorses of lithium atom experiments; they are used for optical cooling and trapping [1], driving Raman transitions [2], Bragg scattering in lithium atom interferometers [3,4], and isotope separation [5]. Moreover, a multi-Watt source of light blue-detuned from the lithium $D$-lines has the potential to form a pinning lattice for a lithium quantum gas microscope [6] or provide a near resonant lattice in which to produce ultra-cold lithium atoms at high phase space density [7] when the lattice is used in combination with gray molasses [8,9] or Raman sideband cooling [2]. Further applications of high-power 671 nm light include its use as a low noise pump for Cr:LiSAF based lasers [10] and the generation of entangled photon pairs in the O-band of commercial silica fibers by optical parametric down conversion [11].
Traditionally, external cavity diode lasers followed by tapered amplifiers have been used to produce several hundred milliWatts of continuous wave (CW) single longitudinal mode (SLM) light at wavelengths near 671 nm. However, due to poor spatial mode quality, deterioration of the tapered amplifiers over time, and the limited attainable power, development of other laser sources is desirable, and frequency doubled 1342 nm solid state lasers have emerged as a promising alternative.
The two main choices of laser crystal for producing light near 1342 nm are Nd:YVO$_4$ and Nd:GdVO$_4$. The emission cross section at 1342 nm is slightly larger for Nd:YVO$_4$ than for Nd:GdVO$_4$, so most of the development of these lasers has focused on Nd:YVO$_4$. However, Nd:GdVO$_4$ has a larger thermal conductivity and thus may be a promising alternative at higher pump powers [12–14]. Furthermore, the emission spectrum of Nd:GdVO$_4$ is shifted in wavelength relative to that of Nd:YVO$_4$, making it useful for providing light at wavelengths not accessible with Nd:YVO$_4$.
Frequency-doubled, single-longitudinal mode Nd:YVO$_4$ ring lasers have seen significant progress in recent years. In 2010, Camargo et al. demonstrated the first single-frequency operation of an 808 nm pumped Nd:YVO$_4$ ring laser with an output power of 1.55 W at 1342.5 nm. Through intra-cavity second harmonic generation, they obtained 680 mW at 671.1 nm tunable with a thin etalon over a wavelength range of 1.25 nm [15]. In 2012, using an 808 nm pumped Nd:YVO$_4$ ring laser with comparable performance, Eismann et al. demonstrated the utility of this laser in lithium cold atom experiments [16]. Later in 2013, they significantly improved the power of their laser by pumping at 888 nm. A pump wavelength of 888 nm results in a lower quantum defect and a lower absorption coefficient; this significantly reduces heating in the crystal and distributes the heat over the entire crystal length allowing for higher pump powers before thermal lensing becomes detrimental [17]. With the new setup, they reached powers of 2.5 W at 1342 nm and 2.1 W at 671 nm [18]. In 2015 Koch et al. achieved even greater power by using an injection locked Nd:YVO$_4$ ring laser pumped at 888 nm. They demonstrated 17.2 W at 1342 nm, the highest yet reported, and, after frequency doubling, 5.7 W at 671 nm [19]. Recently in 2018, Cui et al. improved upon the effectiveness of second harmonic generation, reporting a conversion efficiency of 93% and 5.2 W at 671 nm [20].
Nd:GdVO$_4$ lasers have also seen progress. In the 2000’s, multiple groups demonstrated 1341 nm light using Nd:GdVO$_4$ standing wave lasers [12,21,22]. However, due to reduced mode competition from spatial hole burning in standing wave lasers, these lasers were not single longitudinal mode. In 2013, Wang et al. demonstrated an 808 nm pumped CW single longitudinal mode Nd:GdVO$_4$ ring laser emitting 3.1 W at 1341 nm [23]. In 2014, they frequency doubled their laser to achieve 1.3 W at 670 nm [24]. In 2015, that same group improved the power of their 1341 nm Nd:GdVO$_4$ laser to 4.6 W by using a crystal with un-doped endcaps [25]. The undoped endcaps serve to reduce the effects of thermal lensing. In that work, neither frequency doubling nor a value for the beam quality ($M^2$) were reported.
In this article, we investigate power scaling of Nd:GdVO$_4$ single-longitudinal mode ring lasers by employing a pump laser with a wavelength of 888 nm. As with Nd:YVO$_4$ lasers, pumping at 888 nm reduces the quantum defect and distributes the heat load over the length of the crystal, reducing the detrimental effects of thermal lensing. We characterize the thermal lensing and describe its behavior with a simple model. Management of thermal lensing allows us to demonstrate an SLM output power of 7.4 W at 1341.2 nm. Further, we provide a high-resolution measurement of the gain and excited state absorption spectrum near 1342 nm and demonstrate the tunability of this laser with a thin etalon in order to evaluate the usefulness of this laser for lithium cold atom experiments. We demonstrate tunability over a wavelength range from 1340.3 nm to 1342.1 nm. The peak power is attained at 1341.2 nm which, after frequency doubling, produces light approximately 250 GHz to the blue of the $D$-line transitions in lithium. A powerful laser source at this wavelength is of value for lithium experiments requiring far-off-resonance light in order to reduce photon scattering. For example, lithium atom interferometers using off-resonant light for Bragg scattering would benefit from the high power at a detuned wavelength offered by this laser [3,4], as would blue-detuned optical lattices used to form a pinning lattice for a quantum gas microscope [6] or a high-phase-space-density source of lithium atoms [7]. The Nd:GdVO$_4$ laser is at the same time also useful for providing near resonant laser cooling and trapping light since it can achieve an output power of 2 Watts at 1342.0 nm, twice the wavelength of the $D$-line transitions in lithium. Watt-level laser power at 671.0 nm is sufficient even for demanding applications such as gray molasses cooling [8,9]. In addition to demonstrating its tunability, we also characterize the laser’s linewidth, spatial mode quality, as well as long- and short-term power stability. Finally, we demonstrate frequency doubling with an efficiency of 66% using a commercial build-up cavity.
2. Optical characterization of the Nd:GdVO$_4$ crystal
Neodymium-doped vanadate crystals are amenable to diode-laser pumping with 808 nm light as they exhibit strong absorption features near this wavelength corresponding to transitions from the ground Stark sublevel of the $^4I_{9/2}$ manifold in Nd$^{3+}$ to the $^4F_{5/2}$ manifold (see Fig. 1(a)). The peak absorption coefficient at 808.4 nm for Nd:GdVO$_4$ is $57 \, {\mathrm {cm}}^{-1}$ for 1 % at. Nd doping concentration and light polarized along the $c$-axis of the crystal [26]. Unfortunately, the large quantum defect for a laser emitting at 1342 nm combined with the small volume over which pump light is absorbed poses challenges for management of the heat load in the crystal when scaling lasers pumped with 808 nm light to high power. Heat deposited in the crystal causes thermal lensing due to the temperature dependence of the index of refraction, stress and strain in the crystal, and bulging of the end face which can ultimately result in fracture.
Fig. 1. (a) Energy level diagram of Nd$^{+3}$ in a GdVO$_4$ host material. The relevant transitions for pumping, lasing, and excited state absorption are labeled. (b) Absorption coefficient for a 0.5% at. doped Nd:GdVO$_4$ crystal near the 880 nm and 888 nm pumping transitions. (c) Gain and excited state absorption spectrum.
Intra-band pumping directly into the laser emitting level with 880 nm light (see Fig. 1(a)) is a promising alternative and has been used to demonstrate a 5.1 W multi-longitudinal mode intra-cavity frequency-doubled laser operating at 670 nm with an $M^2 < 2$ [22]. Here, the quantum defect compared to 808 nm pumping is significantly reduced. Further, the absorption coefficient is reduced compared to 808 nm light resulting in the absorbed power being spread over a somewhat larger volume. Alternatively, 888-nm pumping from the thermally occupied second Stark level in the $^4I_{9/2}$ manifold should be possible (see Fig. 1(a)). Pumping with 888 nm light in Nd:YVO$_4$ has been demonstrated to result in a significant reduction in the absorption coefficient, allowing the pump light to be absorbed over the entire length of a 30 mm long crystal [17,19]. Here, we demonstrate, for the first time, an 888-nm-pumped Nd:GdVO$_4$ laser.
We begin by characterizing the optical properties of the Nd:GdVO$_4$ crystal starting with a measurement of its absorption coefficient for intra-band pumping with 880 nm and 888 nm light. The measurement is made with a 0.5% at.-doped Nd:GdVO$_4$ crystal that is $a$-cut and 5 mm in length. The absorption coefficient as a function of wavelength is shown in Fig. 1(b). The measurement is made using a low power (10 mW) fiber-coupled diode laser (Thorlabs, L880P010) that is temperature tuned in order to control its wavelength. The wavelength is measured with a multi-wavelength meter (Agilent, 86120B). For a wavelength of 880 nm, light polarized along the $c$-axis of the crystal is most strongly absorbed, with an absorption coefficient of nearly $8\,{\mathrm {cm}}^{-1}$. Light at a wavelength of 888 nm, on the other hand, is more strongly absorbed if it is polarized along the $a$-axis of the crystal and the peak absorption coefficient of $0.9 \, {\mathrm {cm}}^{-1}$ is reduced from that of 880 nm light by nearly an order of magnitude. Thus, as with Nd:YVO$_4$, pumping an Nd:GdVO$_4$ crystal at 888 nm allows the absorbed pump power to be spread over the length of a crystal several cm in extent. In fact, the ability to completely absorb all of the pump light over the length of the crystal requires the use of exceptionally long crystals or higher Nd doping concentrations than what is explored here.
We then measure the gain and excited state absorption coefficient at wavelengths near 1342 nm for an Nd:GdVO$_4$ crystal pumped with high power 888 nm light. In this case we use the crystal that is ultimately used for constructing the laser, which is a $4 \times 4 \times 25 {\mathrm {mm}}^3$ Nd:GdVO$_4$ crystal that is $a$-cut and has 0.5% at. doping. The crystal is wrapped in indium foil and mounted in a water cooled block of copper which is maintained at a temperature of $17^\circ \, {\mathrm {C}}$. The high-power pump source capable of 60 W output is a fiber-coupled diode bar (QPC Lasers, BrightLase Ultra-100) with a spectral full-width at half maximum of 2.3 nm which is operated at an output power of 50 W for this measurement. The output fiber core diameter is $400 \, \mu {\mathrm {m}}$ with a 0.22 numerical aperture (NA). The output of the fiber is imaged onto the crystal with a 75 mm and a 175 mm lens so that a top-hat pump beam profile approximately $1 \, {\mathrm {mm}}$ in diameter propagates through the gain medium. Of the 50 W incident, nominally 40 W of 888 nm pump light is absorbed by the crystal. The gain and excited state absorption is measured with light from a 1342 nm extended cavity diode laser (ECDL) that is based on a fiber-coupled single-angled facet gain chip (Thorlabs, SAF1174P). (The design of this laser is similar to that presented in [27].) The gaussian beam from the ECDL is focused to a $400 \, \mu {\mathrm {m}}$ waist ($1/e^2$ intensity radius) at the location of the gain medium. Approximately 15 mW of 1342 nm light is incident on the crystal.
The natural logarithm of the power gain, $G(\lambda )$, as a function of wavelength is shown in Fig. 1(c). This quantity, $\ln \left [ G(\lambda ) \right ]$, is proportional to $\sigma _e - \sigma _{\mathrm {esa}}$ where $\sigma _e$ is the stimulated emission cross section and $\sigma _{\mathrm {esa}}$ is the excited state absorption cross section. The gain features near 1341 nm are associated with stimulated emission from the $^4F_{3/2}$ manifold to the $^4I_{13/2}$ manifold. The excited state absorption features near 1337 nm are associated with transitions from the $^4F_{3/2}$ manifold to the $^4G_{7/2}$ manifold (see Fig. 1(a) and 1(b)). Note that the peak of the gain is approximately 0.8 nm (130 GHz) to the blue of $2 \times \lambda _{\mathrm {Li}}$ where $\lambda _{\mathrm {Li}}$ is the wavelength of the $D$-line resonances. Also, note that there is still significant gain at the location of $2 \times \lambda _{\mathrm {Li}}$. This can be contrasted with the gain observed in Nd:YVO$_4$ lasers where the peak of the gain curve lies approximately 0.14 nm (25 GHz) to the red of $2 \times \lambda _{\mathrm {Li}}$ [16,18]. Thus, while Nd:YVO$_4$ lasers can supply high-power light near-resonant with $2\times \lambda _{\mathrm {Li}}$, the Nd:GdVO$_4$ laser can be used in applications requiring high-power light far-detuned from the lithium resonances and moderate power for light at resonance.
3. Experimental setup
A schematic of our laser setup is shown in Fig. 2. Our pump source is the same fiber coupled diode bar described above which can provide up to 60 W at 888 nm in a top hat profile. Lenses L1 (75 mm) and L2 (175 mm) focus the pump light onto the laser crystal with a spot size radius of $467 \mu {\mathrm {m}}$. The gain medium is the 0.5% doped $4 \times 4 \times 25 {\mathrm {mm}}^3$ Nd:GdVO$_4$ laser crystal described above. The Nd:GdVO$_4$ crystal is anti-reflection coated for 888 nm, 1064 nm and 1342 nm light. Four flat mirrors form the ring cavity. Our total cavity length is 450 mm giving a free spectral range of 670 MHz. Because all the mirrors are flat we rely on the thermal lens from the Nd:GdVO$_4$ crystal to produce a stable cavity. At our maximum pump power of 60 W, the crystal absorbs 46 W which produces a thermal lens with a focal length of 19 cm (see Sect. 4 which describes thermal lensing in our gain medium). Mirrors M1 – M3 are highly reflective for 1342 nm light and transmissive for 888 nm light. Our output coupler (M4) has a reflectivity of 96% which is close to optimal for our cavity losses. To ensure unidirectional operation we use a home made optical diode consisting of an optical faraday rotator (OFR) (described below) and zero order half-waveplate. For control of the wavelength we use a single uncoated etalon made of undoped yttrium aluminum garnate (YAG) that is $250 \, \mu {\mathrm {m}}$ thick. To reduce the effects of acoustic noise we house our fundamental laser in an acrylic box.
Fig. 2. A schematic of the laser setup. The laser is pumped by a fiber-coupled diode bar. Lenses L1 and L2 image the end of the pump fiber onto the Nd:GdVO$_4$ crystal. Mirrors M1 – M4, which are all flat, form a bow-tie cavity with a round trip path length of 450 mm. The physical distance between mirrors M1 and M2 is 45 mm and that between M3 and M4 is 156 mm. M4 is the output coupler. Uni-directional operation is enforced by the combination of the $\lambda /2$ waveplate and the TGG crystal placed in a high magnetic field to provide Faraday rotation. The rotatable thin etalon is used to tune the operating wavelength. The beam output from M4 is collimated by L3 and passes through an optical isolator before being sent to a commercial build-up cavity for second harmonic generation.
We send the 1342 nm light from this fundamental laser to a commercial frequency-doubling enhancement cavity (unmodified Toptica, SHG Pro) to attain light at 671 nm. Backscatter from the frequency doubler occasionally breaks the unidirectional operation of our fundamental laser. To prevent loss of unidirectional operation we insert an optical diode (which has approximately 10% insertion loss) between our fundamental laser and the frequency doubler.
The Faraday rotator used to ensure uni-directional oscillation is home built following the design outlined by Gauthier et al. in [28]. It consists of an assembly of three right cylindrical neodymium ring magnets with an anti-reflection coated terbium gallium garnet (TGG) crystal 5 mm in diameter and 7 mm in length placed inside the bore. The central right cylindrical ring magnet has an outer diameter of 38.1 mm, an inner diameter of 6.35 mm, and a thickness of 19.05 mm. Two right cylindrical magnets with their magnetization opposite that of the central magnet are placed at either end. These outer right cylindrical magnets have the same outer and inner diameter as that of the central magnet and each have a thickness of 12.7 mm. Each magnet is grade N38. An aluminum housing holds the assembly together. The purpose of the two outer magnets is to increase the field at the center of the central magnet by 54%. Along the axis of the TGG crystal, this magnet assembly provides an integrated magnetic field of $I_B = \int _0^{\ell _{\mathrm {TGG}}} B(z) dz = 6.8 \, {\mathrm {T}} \, {\mathrm {mm}}$. For the Verdet constant ${\mathcal {V}} = 20.3 \, {\mathrm {rad}} \, {\mathrm {T}}^{-1} \, {\mathrm {m}}^{-1}$ measured at a wavelength of 1342 nm by Eismann et al. in [16], the predicted rotation provided by our Faraday rotator is $\phi = 7.9^{\circ }$. The compact design of this Faraday rotator allows the total round trip length of the ring resonator to be relatively small (450 mm).
Figure 3 shows the power output from the Nd:GdVO$_4$ laser as a function of absorbed pump power. Below an absorbed pump power of 19 W, the laser is unstable presumably due to the focal length provided by the thermal lens being too large. For absorbed pump powers between 19 W and 45 W, the output power nominally follows a straight line from which we can determine a threshold power of $P_{\mathrm {th}} = 13.1 \, {\mathrm {W}}$ and a slope efficiency of $\eta _{\mathrm {sl}} = 24 \%$. The maximum output power is 7.4 W. The peak output powers near the maximum absorbed pump power may show signs of saturation. Unfortunately, higher pump powers could not be provided as the thermoelectric cooler used to regulate the temperature of the pump diode bar could not maintain the temperature needed to operate at 888 nm at higher diode current.
Fig. 3. Output power as a function of absorbed pump power. The line is $P_{\mathrm {out}} = \eta _{sl} (P_{\mathrm {abs}} - P_{\mathrm {th}})$ where the threshold power $P_{\mathrm {th}} = 13.1\, {\mathrm {W}}$, the slope efficiency $\eta _{sl} = 24 \%$ and $P_{\mathrm {abs}}$ is the absorbed pump power.
4. Thermal lensing
In end-pumped solid-state lasers, a fraction of the power from the pump beam is deposited as heat in the laser crystal leading to thermal lensing, thermal induced diffraction losses, and eventually to thermal fracture of the laser crystal. Accounting for these thermal effects presents a significant challenge for the construction of solid-state lasers; in particular, in 1342 nm solid-state lasers these thermal effects quickly become sever due to the high quantum defect between the pump wavelength and the laser wavelength and are often the limiting factor in attaining higher power operation. In this section, we quantify the thermal effects in our system by measuring the dioptric power as a function of the absorbed pump power and compare our measured values to a theoretical model taking into account the fractional thermal load due to both lasing and fluorescence.
Figure 4 shows our measured dioptric power. To determine the dioptric power, we measured the output parameters of our 1342 nm laser with a beam propagation profiler (Coherent ModeMaster PC). Complex paraxial resonator analysis of our laser cavity [29] then gives the thermal lens necessary to produce the measured laser output mode. This method, while accurate and simple to implement, cannot determine the thermal lens without laser action. Hence our data in Fig. 4 begins at the onset of lasing. At our maximum output power, we measure a thermal lens of 19 cm. The solid line in Fig. 4 is our theoretical model presented below.
Fig. 4. Dioptric power as a function of absorbed pump power. The curve is Eq. (1) with the fractional thermal heat load $\eta _h$ given by Eq. (5). These equations provide a model of the thermal lensing in our system with no free parameters.
The dioptric power for a laser crystal optically pumped by a top hat distribution is given by [30]
where $\eta _h$ is the fractional thermal load, $d n/ d t = 4.7 \times 10^{-6} {\mathrm {K}}^{-1}$ is the thermo optic coefficient of Nd:GdVO$_4$, $P_{\mathrm {abs}}$ is the absorbed pump power, $K_c = 11.7 \, {\mathrm {W}}/{\mathrm {m}}{\mathrm {K}}$ is the thermal conductivity of Nd:GdVO$_4$, and $w_p$ is the average pump radius inside the laser crystal [13,14]. The average pump beam radius is given by the average of $w_p(z)$ weighted by the absorption in the crystal:Here we derive the fractional thermal load of end-pumped Nd:GdVO$_4$ laser lasing at 1342 nm taking into account both laser action and fluorescence. Following similar derivations [31,32], we start with the rate equation for a 4-level system given by
Now we can consider the power densities associated with pumping, lasing, fluorescence, and ultimately heating. Power densities can be derived by multiplying the rate of the process by the associated photon energy. The power densities are $Q_p = \alpha _p I_p$ (from pumping), $Q_f = \frac {1}{t_{\mathrm {rad}}} \frac {h c}{\lambda _f} N$ (from fluorescence) where $t_{\mathrm {rad}}$ is the radiative life time and $\lambda _f$ is the fluorescence wavelength, and $Q_l = \sigma _e \frac {\lambda _l}{h c} I_{\mathrm {circ}} N$ (from lasing). The power density associated with heating is the difference between that of the pump power and that of the florescence and laser powers: $Q_h = Q_p - (Q_f + Q_l)$. Finally, the total fractional thermal load is the ratio between the heat power density and the pump power density and is given by
At maximum pump power, the focal length of the thermal lens in the Nd:GdVO$_4$ crystal is found to be 190 mm. The paraxial resonator analysis used to determine this thermal lens from the measured output mode of our laser beam also predicts the waist radius of the lasing mode at the center of the gain medium. This waist radius is found to be $426 \, \mu {\mathrm {m}}$. This radius is 81% of the average pump radius $w_p$. This is an appropriate ratio for the mode to pump radius as it is small enough to avoid diffraction losses [34,36] yet large enough to ensure suppression of transverse modes.
5. Characterization of the fundamental and frequency-doubled laser
5.1 Single longitudinal mode operation and linewidth
Single-longitudinal mode operation of the fundamental laser was first verified using a scanning Fabry-Perot (FP) interferometer with a free spectral range of 300 MHz (see Fig. 5(a)). Reliable single-mode operation could be achieved even in the absence of an intra-cavity etalon, only the Faraday rotator and half-wave plate are required. Whereas other groups have reported needing one or more etalons to achieve single-mode operation, we ascribe the robustness of the single-frequency behavior in our laser to the relatively short cavity length of the fundamental laser which gives a free spectral range of 670 MHz. The linewidth of the 1342 nm radiation measured with the FP interferometer is limited by its finesse.
Fig. 5. (a) Fabry-Perot spectrum showing single-longitudinal mode operations. (b) Beat note between the free-running Nd:GdVO$_4$ and an extended cavity diode laser demonstrating an upper bound on the fundamental laser linewidth of $450 \, {\mathrm {kHz}}$.
To more accurately determine an upper limit on the linewidth of the free-running fundamental laser, we measure a beat note between the 1342 nm solid-state ring laser and the extended cavity diode laser that is based on a fiber-coupled single-angled facet gain chip which was described above. As the ECDL is acoustically well isolated from the environment, we expect that its free-running linewidth is quite narrow. The linewidth of an ECDL laser with a similar design has been shown to be $< 10 \, {\mathrm {kHz}}$ [27]. Both lasers are made to illuminate an InGaAs amplified detector with a 150 MHz bandwidth (Thorlabs PDB450C). The resulting beat note between the two free running lasers as measured on a spectrum analyzer is shown in Fig. 5(b). The resolution bandwidth of the spectrum analyzer is 300 kHz and its video bandwidth is 10 kHz. The sweep time is set to 50 ms. The measured beat note is fit to a gaussian and found to have a full-width at half maximum (FWHM) of 450 kHz. This linewidth is sufficient for use of this laser in cooling and trapping experiments with lithium as the natural linewidth of the $D$-line transitions is $5.9 {\mathrm {MHz}}$.
5.2 Mode quality of fundamental and second harmonic
To evaluate the mode quality of our fundamental laser beam, we use a commercial beam propagation profiler (Coherent ModeMaster PC). This beam profiler utilizes the knife edge method to measure the beam width along two orthogonal directions. To measure the beam width at different positions along the propagation axis the profiler moves a telescopic lens so that different planes along the propagation axis are imaged onto the moving knife edge. After determining the widths at the location of the knife edge, the widths of the propagating beam external to the profiler can be determined from the known focal length and principal plane of the telescopic lens. When measuring the beam propagation with the profiler we place a 1000 mm focal length lens following lens L3 in Fig. 2. The $1/e^2$ intensity radius as a function of position external to the profiler is shown in Figs. 6(a) and 6(b). The origin in these figures corresponds to the input bezel of the beam profiler. A fit to the function
is shown for each of the directions. Here, $w_0$ is the beam waist, $z_0$ is the location of the beam waist, $z_R = \pi w_0^2/\lambda$ is the Rayleigh length of a gaussian beam, $\lambda = 1342 \, {\mathrm {nm}}$, and $M^2$ is the beam quality parameter. The fit parameters are $z_0$, $w_0$, and $M^2$. Propagation of the beam in the horizontal direction is consistent with that of an ideal gaussian beam for which $M^2 = 1$. The beam quality in the vertical direction is less than ideal but is still very good with $M^2 < 1.1$. The laser beam is slightly astigmatic with astigmatism given by $(z_{0,{\mathrm {horiz}}} - z_{0,{\mathrm {vert}}})/\bar {z}_R = 23 \%$ where $\bar {z}_R$ is the average Rayleigh length for the two directions. Also, the beam is close to circular with a waist asymmetry given by $w_{0,{\mathrm {horiz}}}/w_{0,{\mathrm {vert}}} = 0.94$. The astigmatism and slight ellipticity of the beam is due to elements that break the symmetry of the cavity such as the orientation dependent thermal conductivity and natural birefringence of Nd:GdVO$_4$ or the non-zero angle of incidence of the cavity mode on the output coupler. Still the beam quality is quite good. Attaining nearly ideal beam quality is crucial for achieving good mode matching to the frequency-doubling cavity and thereby high second harmonic generation efficiency.Fig. 6. Measurement of the laser caustic for the 1342 nm laser in the (a) vertical and (b) horizontal directions. (c) Measurement of the laser caustic for the 671 nm laser beam. The inset shows a typical beam profile of the 671 nm laser beam as recorded by the CCD camera. The solid lines are fits to Eq. (8) used to determine the beam quality parameter $M^2$.
The 671 nm radiation output from the second harmonic generation cavity should be a nearly ideal gaussian beam. To verify this we also performed a measurement of the 671 nm laser caustic. In this case, we focused the laser output from the frequency-doubling cavity with a 200 mm focal length lens and measured the beam profile at a number of positions along the beam path with a charge-coupled device (CCD) camera (Thorlabs DCU223M). Figure 6(c) shows the $1/e^2$ intensity radius from gaussian fits to the laser profile as a function of position along the optical axis. The solid curves show a fit to Eq. (8) with $\lambda = 671 \, {\mathrm {nm}}$. Both the horizontal and vertical beam profiles are consistent with a value of $M^2 = 1$ within their 95% confidence interval. The fact that the caustics are fit to values of $M^2$ slightly less than one is presumably due to measurement error (e.g. small errors made in fitting the width of the gaussian profile on the CCD camera).
5.3 Wavelength tunability
The wavelength of the fundamental laser can be tuned by rotating the YAG etalon inside the laser cavity. The free spectral range of the $250 \, \mu {\mathrm {m}}$ thick etalon is 330 GHz. The finesse of the uncoated YAG etalon is $1.0$. As shown in Fig. 7(a), the wavelength of the fundamental laser can be tuned with this etalon from 1340.3 nm to 1342.1 nm, nominally over the 1.8 nm ($300 \, {\mathrm {GHz}}$) width of the gain profile. Mode hops of the thick etalon occur at either end of this nominally $300 \, {\mathrm {GHz}}$ tuning range. The power of the fundamental laser plotted in Fig. 7 is measured after the optical isolator shown in Fig. 2 which results in a moderate ($10\%$) loss of power. Each data point is the average of three or more experimental runs to better account for day to day fluctuations in performance. The error bars reflect the standard deviation in the mean of these runs. Two prominent dips in power are observed at wavelengths near 1340.5 nm and 1341.6 nm. These drops in power are associated with strong water absorption lines [37,38] as shown in Fig. 7(b).
Fig. 7. (a) Fundamental and second harmonic output power versus wavelength. The power of the fundamental laser is measured after the optical isolator in Fig. 2, just before entering the SHG cavity. (b) Spectrum of water absorption coefficient at $300^\circ \, {\mathrm {K}}$ and 50% relative humidity [37,38].
Figure 7(a) also shows the output power of the second harmonic generation cavity. At peak power, we achieve a second harmonic generation efficiency of 66% determined by the ratio of the second harmonic power to the fundamental power measured after the optical isolator. The maximum power we attain is 4 W at a wavelength of 670.6 nm which is 0.36 nm (240 GHz) to the blue of the $D_2$ line for $^7$Li and 0.38 nm (250 GHz) to the blue of the $D_2$ line for $^6$Li. All four relevant transitions for $^7$Li and $^6$Li are shown in Fig. 7(a). The $^7$Li $D_1$ and $D_2$ lines respectively occur at 670.976 nm and 670.961 nm and the $^6$Li $D_1$ and $D_2$ lines occur at 670.992 nm and 670.977 nm. The second harmonic power attained at the $D_1$ line of $^7$Li and the $D_2$ line of $^6$Li is $1.2 \, {\mathrm {W}}$.
5.4 Long term stability and residual intensity noise
The long term power stability of both the fundamental and frequency-doubled laser is ascertained by recording the power incident on a photodiode at half second intervals over a period of several hours. The time traces for both the fundamental laser and the frequency-doubled laser are shown in Fig. 8(a). For the fundamental laser, the standard deviation of the laser power is $\sigma = 0.7\%$ over a five hour period. For the second harmonic, $\sigma = 0.8\%$ over the same five hour period.
Fig. 8. (a) Fundamental and second harmonic output power over several hours. The fundamental power is measured after the optical isolator, just before entering the SHG cavity. (b) One-sided power spectral density of the residual intensity noise of the frequency-doubled laser output.
We measure the relative intensity noise of the frequency doubled laser by first recording a time series of the instantaneous power in a nominally $50 \, \mu {\mathrm {W}}$ laser beam. The power is measured using an amplified low-noise photodiode with a 50 MHz bandwidth (Thorlabs PDA8A). The time series is recorded using a modular digital oscilloscope with a 100 MHz bandwidth and a 16 Mpts memory depth (Agilent U2701A) running at 500 MS/s. The digital oscilloscope is AC coupled so that it records the fractional intensity fluctuations $\epsilon (t) = (I(t) - \left \langle I \right \rangle )/\left \langle I \right \rangle$ after the signal is normalized by the average intensity $\left \langle I \right \rangle$ (here, $\left \langle \cdots \right \rangle$ denotes a time average). The one-sided power spectral density of the residual intensity noise is then given by:
The resulting one-sided PSD is shown in Fig. 8(b). The upper most power spectral density in the plot, shown in orange, is the $S_{\mathrm {RIN}}$ measured for the 671 nm laser. The lower blue curve is the electronic noise spectrum obtained when an incoherent light source is used to produce the same photocurrent in the detector. Finally, the lowest curve shown in green is the electronic noise spectrum obtained when no light falls on the detector. The peak in the power spectral density for the 671 nm light centered at $230 \, {\mathrm {kHz}}$ is due to relaxation oscillations in the solid-state laser. The smaller peak at $50 \, {\mathrm {kHz}}$ is also associated with noise in the solid-state laser, rather than noise arising from the frequency doubling process, but its explicit origin is not well understood. Above $1 \, {\mathrm {MHz}}$ the $S_{\mathrm {RIN}}$ of the 671 nm light falls below the noise floor of the detection method. The narrow feature at $20 \, {\mathrm {MHz}}$ is due to phase modulation of the 1342 nm light used to lock the doubling cavity to the fundamental laser frequency with the Pound-Drever-Hall technique [39]. The integral of the one-sided PSD from 500 Hz to 10 MHz yields an rms noise $\epsilon _{\mathrm {rms}} = 8.7 \times 10^{-3}$. We verify that this rms noise is consistent with the directly measured rms intensity fluctuations.
6. Conclusions
We have constructed a high-power, single-longitudinal mode Nd:GdVO$_4$ ring laser by intra-band pumping at 888 nm directly to the laser emitting level. A simple model of the thermal load resulting from 888-nm pumping predicts the observed thermal lensing in the gain medium. We show that this laser is suitable, after frequency doubling, for cold atom experiments with lithium. In particular, we show that more than 1 Watt can be obtained at a wavelength of 671.0 nm which is resonant with the $D$-lines in lithium. Further, the laser system has a sufficiently narrow linewidth, long-term stability, and small residual intensity noise for it to be well suited for providing a reliable source of laser cooling and trapping light at this wavelength. What is more, we have demonstrated that 4 Watts of power can be attained at a laser frequency which is approximately 250 GHz detuned to the blue of the $D$-line transitions in lithium. Thus, this laser source can provide high-power light at a detuned wavelength which is desirable for applications that require reduced spontaneous emission such as Bragg scattering beams in lithium atom interferometers or blue-detuned optical lattices.
Higher output powers of the fundamental laser can be achieved by removing the lossy Faraday rotator and half-wave plate from the cavity and achieving uni-directional operation either by injection locking from a microchip laser or extended cavity diode laser [19] or by self-injection locking where the lossy Faraday rotator is placed in a weakly coupled external cavity [40]. Furthermore, second harmonic generation efficiency as high as 93% has been demonstrated with periodically poled potassium titanyl phosphate (ppKTP) in an external build-up cavity at a similar wavelength [20]. Such improvements to the laser operation will only increase its efficacy for potential applications, both in and outside of lithium atom experiments.
Funding
National Science Foundation (PHY-1607648); Air Force Office of Scientific Research (FA9550-15-1-0239, FA9550-15-1-0306).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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