1. Introduction

Many measurement applications require single-longitudinal-mode lasers with a narrow bandwidth and long-term frequency stability. To achieve such a frequency-stable output, a good approach is to use a diode-pumped solid-state laser with a monolithic cavity, which is the subject of this paper. In addition, applications such as high resolution spectroscopy require a precise wavelength control, why tuning of the laser wavelength is also a desirable feature. Furthermore, it is very probable that the desired wavelength is not on the main peak of the gain of the laser, but rather slightly off or at a weaker sub-peak, which requires special attention in the laser design.

The simplest monolithic single-longitudinal-mode laser consists of just a flat-flat thin piece of gain material with mirrors coated onto the facets [1], where the gain profile itself in combination with a large free spectral range ensures single-longitudinal-mode lasing. However, due to spatial hole burning, the cavity cannot be too long or the pump power too high before multiple longitudinal modes appear, why the output power from such a laser is rather limited. Typically, for a 1.06 µm Nd:GdVO₄ laser the maximum thickness is 300 µm at a power level of 30 times above threshold [2, 3]. Also, this type of laser is limited to a wavelength very close to the gain peak, though some rather coarse selectivity can be achieved by the broadband coatings of the cavity mirrors. Another way to reach the desired laser specifications is to use a travelling-wave ring-cavity, such as a non-planar ring oscillator [4], though this demands the use of a non-reciprocal optical element to reinforce a single oscillation direction, increasing the complexity of the cavity. Furthermore, also in this case it is not possible to select wavelengths far away from the maximum gain peak.

In this work we propose and demonstrate a new monolithic laser design, based on a volume Bragg grating working both as a wavelength selective element and a cavity mirror in a standing wave cavity. In this way we can reach fairly high output powers in a single longitudinal mode with good wavelength stability. In addition, any wavelength in the gain spectrum can in principle be selected, which opens up for many new laser wavelengths. Previously we have demonstrated 0.85 W in a single longitudinal mode from this type of laser [2], although then consisting of two discrete components. The main focus of this work is on the wavelength stability and tunability for a monolithic cavity.

Previously, volume Bragg gratings [5] have been used to select the wavelength and narrow the bandwidth of high power diode lasers [6,7], optical parametric oscillators [8,9] and various solid state lasers, such as ErYb:glass [10], Ti:Sapphire [11], Nd:GdVO₄ [2,3] and Yb:KYW [12].

In a monolithic device, the degrees of freedom that can be used for alignment of the cavity are limited. One possibility is to have a flat-flat cavity, where the thermal lens gives stability to the cavity and very high precision is needed in the manufacturing to make sure that both end faces are parallel. Instead, we have chosen to use a hemispherical cavity where one of the cavity mirrors has a curved surface, giving a stable cavity irrespective of thermal lensing. With our design, the flat cavity mirror is easily aligned by rotation of the whole piece, while translation aligns the curved mirror. The design therefore relaxes the requirements on the polishing parallelism, which together with cheap components should yield a cheap and mass-producible laser.

To achieve tuning of the laser output, the temperature of the whole piece can be adjusted, whereby thermal expansion will move the longitudinal modes and thus the laser wavelength. Simultaneously the grating’s peak reflectivity will move with temperature, and if the tuning rate of both is the same, a large continuous tuning range can be achieved.

 

Fig. 1. Monolithic cavity consisting of a volume Bragg grating, a Nd:GdVO₄ crystal and an outcoupling mirror.

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2. Experiments

The laser cavity was formed by a single monolithic piece, which consisted of a volume Bragg grating, a Nd:GdVO₄ crystal and an outcoupler, depicted in Fig. 1. The volume Bragg grating (Optigrate, FL), which acted both as a wavelength selector and incoupling mirror, had a peak reflectivity of 99% at 1066.1 nm with a FWHM bandwidth of 0.20 nm. The physical thickness of the grating was 5 mm. The gain crystal was a 2 mm long 0.5 at.% Nd:GdVO₄, cut for propagation along the crystal a-axis. GdVO₄ was chosen among the various Nd host crystals for the reasonably good overlap between the emission in the σ-polarisation and the grating peak, see Fig. 3. The output coupler was formed by a 1.1 mm thick ordinary lens substrate in BK7 glass with a radius of curvature of 6.2 mm, with a dielectric coating to give a reflectivity of 82% at 1.06 µm.

The different components were attached together by a heat curing silicone elastomer (PDMS, polydimethylsiloxane, Sylgard 184, Dow Corning Corporation). This material has good optical quality and makes the assembly of the pieces easy, why it is suitable for a first proof of principle. Nevertheless, other methods such as diffusion bonding may be preferable in the future. Due to the different refractive indices of the gain crystal and the two surrounding glass components, as well as the intermediate PDMS, se Table 1, the roundtrip Fresnel losses of the cavity are estimated to be ~10%. Naturally, such high losses are not desirable, but can in principle be removed quite easily with appropriate antireflective thin-film coatings. In order to avoid formation of multiple coupled cavities, all surfaces inside the cavity were tilted with respect to the grating direction by a few degrees.

The laser was pumped by an 808 nm laser diode delivering a maximum pump power of 3.3 W, focussed to a spot of 40 µm radius in the laser crystal, to maximise the overlap with the laser’s lowest order transverse cavity mode. However, due to an M² for the pump of the order of 30 by 70, some volume of the crystal outside the lowest order transverse mode was pumped as well. The pump laser was linearly polarized and directed to be absorbed in the π-direction of the Nd:GdVO₄ crystal, giving an absorption of about 40%. To increase this figure, higher Nd doping concentration should be used in the future.

The optical length of the cavity was 6.4 mm, given by the outcoupler’s optical length, L_o=l_on_o, the gain medium’s optical length L_g=l_gn_g, as well as the Bragg grating’s effective length [2, 3],

$L_B=l_B\frac{\sqrt{R_{max}}}{2\mathrm{arctanh}\sqrt{R_{max}}}=0.8\mathrm{mm},$

where l_i denotes physical length, n_i refractive index and R _max is the grating peak reflectivity. The cavity length corresponds to a spacing of the longitudinal modes of 23 GHz, which as shown in [2, 3] would allow single longitudinal mode operation up to at least 30 times above threshold.

To cool off the excess heat and to be able to control the temperature of the monolithic laser, the Nd:GdVO₄ crystal was clamped in a temperature-controlled piece of copper. This also allowed for tuning of the laser wavelength. Since the frequency of the oscillating mode, for a mode number m, is ν=mc/(2L), the rate of the temperature tuning with frequency is given by the variation of the cavity length, L=L_o+L_g+L_B, through

Table 1. Material constants

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$\frac{d\nu }{dT}=-\frac{\nu }{L}\left(\frac{d{L}_o}{dT}+\frac{d{L}_g}{dT}+\frac{d{L}_B}{dT}\right).$

Ordinary thermal expansion gives

$\frac{d{L}_o}{dT}=L_o\left(\frac{1}{n_o}\frac{d{n}_o}{dT}+{\alpha }_o\right),$

where α_o is the coefficient of thermal expansion. An analogue expression is valid for L_g. The grating’s effective thermal expansion is given by

$\frac{d{L}_B}{dT}=l_B{\alpha }_B\left(1-R_{max}\right)⁄2.$

Here it is assumed that the grating strength is not altered by temperature changes around room temperature. From data presented in the literature, see Table 1, it is found that the contributions to the temperature tuning from the different parts are dL_o/dT=13 nm/K, dL_g/dT=16 nm/K, dL_B/dT=0.2 nm/K, i.e. the Bragg grating contribution is negligible. Finally, the total tuning rate of the longitudinal modes is expected to be dν/dT=-1.3 GHz/K.

In comparison, the tuning of the Bragg grating peak is given by differentiation of the Bragg condition, λ _B=2n _BΛ, yielding

$\frac{d\nu }{dT}=-\nu \left(\frac{1}{n_B}\frac{d{n}_B}{dT}+{\alpha }_B\right).$

Using the data in Table 1, we get a numerical value of dν/dT=-2.4 GHz/K, comparing well to the direct experimental value at 1 µm reported to be between 2 and 3 GHz/K [6, 8, 11]. To get a good device, it is desirable to have the same tuning rate for both the longitudinal modes and the Bragg peak. Still, from the above calculations, it seems that the tuning rate for the modes is a bit on the slow side. However, since the experimental results show that we get a wide tuning rate, the correspondance between the two rates seems to be good enough.

3. Results

The laser had a threshold of 270 mW absorbed pump power and gave a maximum laser power of about 100 mW of linearly polarised light the σ-direction of the Nd:GdVO₄, as depicted in Fig. 2. For absorbed powers below 800 mW, only the fundamental transverse mode lased, as could be seen with the scanning Fabry-Perot interferometer, see details below. However, for higher pump powers, higher order transverse modes started to oscillate too, as is also indicated by the kink in Fig. 2. This we believe is due to poor overlap between the pump and laser mode, something that should be improved in future experiments.

As expected, the laser wavelength was determined by the volume Bragg grating peak to be 1066 nm. In Fig. 3, we show the spectrum measured with a grating-based optical spectrum analyser. To investigate the spectral properties in detail, we used a scanning Fabry-Perot interferometer, consisting of one plane mirror and one 25 mm radius of curvature mirror, both highly reflecting. The distance between the mirrors was chosen to be ¾·25 mm, since this gave the best resolution, giving a degeneracy of the interferometer’s transverse modes of the third order [20]. This is the reason for the two small intermediate peaks in the trace in Fig. 4. A piezo-electric actuator was used to scan the mirror spacing. As shown by the Fabry-Perot trace in Fig. 4, measured at an absorbed pump power of 800 mW, the laser was in a single-longitudinal mode. In fact, although some higher order transverse modes showed up for higher pump powers, only a single longitudinal mode was observed. This is in good agreement with the findings in [2, 3] for the single-longitudinal-mode operating range. The finesse of the Fabry-Perot was 200, giving an upper limit to the laser linewidth of 40 MHz, shown by the inset in Fig. 4.

By adjusting the temperature of the monolithic device, it was possible to tune the laser frequency. As shown in Fig. 5, the tuning range was 80 GHz (0.3 nm) for temperatures between 16 °C and 40 °C, at an absorbed pump power of 640 mW. The upper limit for the tuning was in this case caused by an increased threshold of the laser for elevated temperatures, possibly due to reduced gain. By monitoring the spectrum with the scanning Fabry-Perot interferometer, it was possible to determine that the tuning was continuous without any mode hops. This is remarkable since the 23 GHz longitudinal mode-spacing is just a fraction of the total tuning range. As explained above, the reason is that both the Bragg grating peak and the longitudinal modes, determined by the cavity length, tune at approximately the same rate. From the data in Fig. 5, we can determine an experimental tuning rate of the longitudinal modes of -3.2 GHz/K. This is rather different from the theoretical prediction in Sec. 2 of -1.3 GHz/K, which might be an indication that the input data in Table 1 are not very accurate. Still, the important conclusion is that the two tuning rates of the longitudinal modes and the Bragg grating are close enough to get a good performance.

 

Fig. 2. Laser power

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Fig. 3. Comparison of emission cross section spectra of Nd:GdVO₄ [19] and the laser spectrum.

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Fig. 4. Fabry-Perot trace, inset shows detail of peak.

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Fig. 5. Temperature tuning of the laser frequency.

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4. Conclusions

We have demonstrated a monolithic Nd:GdVO₄ laser where the wavelength is locked by a volume Bragg grating at 1066 nm. The laser is in a single longitudinal mode with a bandwidth of less than 40 MHz. For output powers below 30 mW, only the fundamental transverse mode is lasing. Temperature tuning of the whole monolithic piece allows adjustment of the laser frequency by 80 GHz in a mode-hop free fashion, by simultaneous tuning of the longitudinal modes of the laser and the Bragg grating peak. In this way, the tuning range can be wider than both the longitudinal mode spacing and the grating bandwidth. We believe that the demonstrated concept is widely applicable for many other laser wavelengths and gain media.