Single-longitudinal mode Nd:YVO4 microchip laser with orthogonal-polarization bidirectional traveling-waves mode

Yingjun Ma; Li Wu; Hehui Wu; Weimin Chen; Yanli Wang; Shijie Gu

doi:10.1364/OE.16.018702

1. Introduction

The single-longitudinal mode (SLM) laser is essential for stable operation of intracavity frequency doubling, precision measurement, high-resolution spectroscopy, coherent lidars, coherent optical communication and laser trapping or cooling. As already known, in the common standing-wave lasers, and especially homogeneously broadened solid-state lasers, spatial hole-burning in active gain materials usually causes multimode laser operation. Various techniques have been tried to obtain SLM laser operation. SLM operations can be achieved in microchip lasers [1,2] with extraordinarily thin gain materials, owing to the large frequency interval between adjacent longitudinal modes in the relevant laser cavities. Nevertheless, these lasers are not capable of high-power output because of the thinness of the gain material and the cavity length must be selected (by temperature control) so that one of its resonant frequency fall within the laser gain region. It is well known that lasers with a thin gain-medium crystal located close to one of the mirrors can be more easily operated single mode. This is because all modes have a common node at the mirror and to a large extent share the same population of ions in the vicinity of the mirror. The effect of spatial hole burning is therefore reduced, but there will also be a reduction in the output power, since the size of the gain medium is limited. Usually a gain medium with short absorption depth, such as Nd:YVO₄, is used instead of a thin gain-medium crystal [3], these lasers are expected to operate at the single-longitudinal mode when the pump power of laser diode is less than 5 times the thresholds. Laser operation in a ring cavity [4] is another well known technique to obtain SLM output, wherein an intracavity optical diode keeps unidirectional laser propagation so that no standing-wave electric fields are formed in the cavity, leading to the elimination of spatial hole-burning in the active material. But this method cannot be used for microchip laser. Another solution to obtain SLM operation is to eliminate the spatial hole burning by employing a twisted-mode cavity (TMC) [5–7]. However, a TMC laser cannot be achieved with anisotropic laser crystals since it requires that there should be no birefringence along the resonator axis in the laser material.

The microchip laser described here is a solid-state laser whose cavity is thin and monolithic, has optical coatings directly applied to its input and output faces, and is longitudinally pumped by a strongly localized diode-laser source. The single-longitudinal mode microchip laser with high multimode threshold, high slope efficiency, high output power and wide operating temperature range is very useful for abovementioned applications and to our knowledge is not reported. In this article we report a single-longitudinal mode microchip laser consisted of Nd:YVO₄ crystal sandwiched by a pair of QWPs. Nd:YVO₄ crystal has a large birefringence and a much larger emission cross section of e-light (polarized parallel to the optical axis) than emission cross section of o-light (polarized orthogonal to the optical axis). Therefore e-light will be lasing,, and then QWP reflects and rotates the e-light by 90°, becoming o-light in opposite direction and another QWP reflects and rotates the o-light by -90°, becoming back to the e-light in original direction. In the laser cavity there are both e-light and o-light with same frequency and intensity simultaneously and form a traveling-wave in the cavity. We will call this microchip laser as “Orthogonal-polarization bidirectional Traveling-wave Mode (OTM) laser”. Bidirectional propagating traveling-waves interfere with each other and produce the standing-wave patterns of e-light and o-light in the cavity. Large birefringence brings the standing-wave patterns of e-light and o-light out of phase in the gain-medium and the spatial hole burning effects produced by the standing waves of e-light and o-light compensate with each other, which relief the spatial hole burning effects. We theoretically show and experimentally demonstrate that OTM laser is capable of suppressing the spatial hole-burning effect greater than 25 times the threshold and has high power of output (730 mw at 1.25 W pump power), high slope efficiencies (60%) and wide temperature range (30°C) of single longitudinal mode operation.

2. Theoretical analysis

Figure 1 shows the schematic drawing of the cavity of OTM laser. The cavity consists of a Nd:YVO₄ crystal as the gain medium and a pair of QWPs which sandwich Nd:YVO₄ crystal. The principle axes of QWPs are oriented with their fast axes perpendicular or parallel to each other and at θ to the optical (c-) axis of Nd:YVO₄ crystal. When θ=45° it is the case of OTM laser and θ=0° for the a conventional Nd:YVO₄ microchip laser which is not capable of suppressing the spatial hole-burning effect and will be used for a reference laser comparing with OTM laser. We evaluate the Jones eigenvectors of the polarization modes at the positions between QWP and Nd:YVO₄ crystal. The relevant matrices for the analysis are

R (θ) = [\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}]

where R is a rotation matrix, C is the transfer matrix of a birefringent plate, δ=(ne-no)kl is the phase retardation of Nd:YVO4 crystal and ζ=π/2 for QWP; p=(ne+no)kl/2 for Nd:YVO₄ crystal and q=nkd for QWP; ne and no are the refractive indices of e- and o-light in Nd:YVO4 crystal; n is an average refractive indices of QWP; k=2π/λ; l and d are thicknesses of Nd:YVO4 crystal and QWPs, respectively. A round-trip Jones matrix starting from the position between Nd:YVO₄ crystal and QWP can be expressed as

M (θ) = R (- θ) C^{2} (- ς) R (θ) C (δ) R (- θ) C^{2} (ς) R (θ) C (δ)

By evaluating the matrix elements the round-trip matrixes for OTM cavity are expressed as

M (45) = \exp (- ikL) [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

where L=(n_e+n_o)l+4nd. The condition exp(-ikL)=1 determines eigenvalues of eigenvectors of the polarization modes and gives Free-Spectra-range (FSR) for all longitudinal-mode in OTM cavity

FSR = \frac{c}{L}

where c is velocity of light in vacuum and L is optical path of round-trip in OTM cavity. Equation (4) indicates that it is a FSR for a traveling-wave in “ring-cavity” [8]. The unit matrix in Eq. (3) means that any kind of polarization mode can be eigenmode with the same FSR at this position. Particularly a pair light fields E_e and E_o with orthogonal linear polarization (parallel and perpendicular to c-axis of Nd:YVO₄, respectively) remain their polarization direction when they propagate in the Nd:YVO₄ crystal. The +z direction propagating E_e ⁺ is transferred to the −z direction propagating E_o ^- after reflected by a QWP and then the -z direction propagating E_o ^- is transferred to the +z direction propagating E_e ⁺ after reflected by another QWP. E_e ⁺ and E_o ^- with same frequency form a traveling-wave with “Clockwise (CW)” and E_e ^- and E_o ⁺ form a traveling-wave with “Counter-Clockwise (CCW)” [9]. So only in the OTM laser there exist both e-light and o-light lasing with same frequency and intensity simultaneously, which is necessary condition for suppressing the spatial hole-burning effect and important for intracavity II-type phasematch second harmonic generation (SHG). The output wave from E_e ⁺ is right-(left-) circularly polarized and the output wave from E_o ⁺ is left-(right-) circularly polarized. The polarization of combined output wave is a linear-polarization oriented at 45° to c-axis of Nd:YVO₄ crystal. In contrast only linearly-polarized E_e and/or E_o with different frequencies can be there in reference laser (θ=0). In most case only E_e modes can be excited in reference laser [10].

Fig. 1. The cavity of the OTM microchip laser

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Consider a CW standing-wave (reference) laser cavity containing a homogeneously broadened gain medium. The intensity of mode m within gain medium can be written as

I_{m} (z) = 4 I_{m} \sin^{2} (k_{m} z)

where I_m is the intensity of the beam traveling in one direction within the laser cavity and k_m=2π/λ_m. For single-longitudinal mode, the condition of oscillation for mode 1 [11] is

σ_{1} \int_{a}^{b} N (z) I_{1} (z) d z = γ_{1} I_{1}

where σ ₁ and γ ₁ are emission cross section and total round-trip loss for mode 1,

respectively;

gain medium locates between z=a and z=b. The population inversion density N(z) in (6) is

N (z) = \frac{N_{0} (z)}{1 + \frac{I_{1} (z)}{I_{sat, 1}}}

where N₀(z) is the population inversion density in the absence of saturation and is proportional to the local pump rate and the saturation intensity at lasing frequency ω is

I_{sat, 1} = \frac{ℏ \bar{ω}}{σ_{1} τ}

τ is the relaxation time for the inversion in the absence of saturation The relationship [12] between relative intensity I/I _sat and the ratio of pump power to the threshold pump power P/P_th=r (or R for OTM laser) is

\frac{I}{I_{sat}} = \frac{((4 r - 1) - {(1 + 8 r)}^{\frac{1}{2}})}{8}

In order to ensure single-mode operation, we require that the total gain is less than the round-trip loss for all other modes. For a potential second mode of weak intensity I ₂, Eq. (6) becomes

σ_{2} \int_{a}^{b} N (z) I_{2} (z) d z < γ_{2} I_{2}

where N(z) is given by Eq. (7) and is undisturbed by the present of the second mode. We find

that

the condition for single-mode operation becomes

\int_{a}^{b} N (z) [\frac{I_{2} (z)}{I_{2}} - \frac{β I_{1} (z)}{I_{1}}] d z < 0

where

β = \frac{σ_{1} γ_{2}}{σ_{2} γ_{1}}

is the discrimination factor and always greater than 1 since mode 1 must reach threshold before mode 2. Solving Eq. (11) through Eqs. (5), (7), (9) we can calculate the maximum pump power (relative to pump threshold) r for single-longitudinal-mode operation as a function of β.

In the OTM laser cavity the bidirectional propagating traveling-waves interfere with each other and produce the standing-wave patterns for e- and o- light, respectively

I_{e} (z) = 4 I \sin^{2} (k_{e} z + φ_{e}),

where k_e=2πn_e/λ; k_o=2πn_o/λ, and φ_e,φ_o are determined by the geometry of the laser cavity. Using Eq. (13), Eq. (7) becomes

N_{OTM} (z) = \frac{N_{0} (z)}{1 + \frac{I_{e} (z)}{I_{sat, e}} + \frac{I_{o} (z)}{I_{sat, o}}}

I_{sat, e} = \frac{ℏ \bar{ω}}{σ_{e} τ} and I_{sat, o} = \frac{ℏ \bar{ω}}{σ_{o} τ}

and

I (z) = 4 I [\sin^{2} (k_{e} z + φ_{e}) + (\frac{σ_{o}}{σ_{e}}) \sin^{2} (k_{o} z + φ_{o})]

σ_o/σ_e=0.25 for Nd:YVO₄ crystal [13]. With same reason all above equations can be used for OTM laser providing we use Eq. (16) for I _m(z) in the equations.

In the numerical calculations we use the parameters: n_e=2.165; n_o=1.957; n=1.55; l=0.9 mm; d=0.456 mm. Equation (4) gives FSR=46 GHz (Δλ=0.17 nm). The population inversion density N(z) (reference laser) and N_OTM(z) (OTM laser) resulting from spatial hole burning are illustrated in Fig. 2.for r=3 (a) and r=20 (b). Fig.2. shows that the population inversion density of OTM laser at some nodes of the standing-wave are reduced comparing with reference laser.

Fig. 2. The normalized population inversion density N(z) (reference laser- dot line) and N_OTM(z) (OTM laser-solid line) resulting from spatial hole burning for pump power=3 times the threshold power, r=3 (a) and =20 times the threshold, r=20 (b). For OTM laser the distribution of population inversion density is a modulated sine square wave with the period of modulation 5.1 µm.

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The reduction of population inversion density at anti-node of standing wave decreases the gain leaving for the second mode (see Eq. (10)) and it is more difficult to oscillate for the second mode. The higher the pump power is, the lower the population inversion density of OTM laser, as shown in Fig. 2. We can expect that the OTM laser will operate at single-longitudinal-mode with much higher pump power than the reference laser (conventional Nd:YVO₄ microchip laser). The N_OTM(z) is a modulated sine square wave and the period of modulation is

ρ = \frac{λ}{(n_{e} - n_{o})} = 5.1 μ m .

In order to estimate what are the maximum pump powers for the single longitudinal mode

operation of OTM and reference lasers, we solve Eq. (11) for OTM and reference lasers to get curves of R and r as a function of β. In the calculation we selected the cavity mode the nearest to the first oscillating mode λ₀ as the second mode (λ=λ₀+Δλ) and in this case λ₀=1064 nm; Δλ=0.17 nm. The integrate limits were selected a=330 µm and b=a+900µm, because the optical path length in QWP with thickness of 456µm is equal to the path length of e-light in Nd:YVO₄ crystal with thickness of 330µm. We selected several values of a in the range 250–360µm, the results are not significantly different. N₀(z) is expressed as

N_{0} (z) = e^{- α (z - a)}

where α is absorption coefficient of π-polarization, and α=72 cm^-1@808nm for 2%at.Nd:YVO₄[14]. Comparing with absorption length of 170 µm and length of gain medium of 900 µm the 5.1 µm modulation period of N_OTM(z) is so small that the calculated results are not sensitive to the selection of φ_o, φ_e values in Eq. (16). We tried some values between 0 and π, the results are almost the same.

Fig. 3. (a) The ratio of the maximum pump power of single-longitudinal-mode operation to the threshold as a function of β. for OTM laser (R—solid line), and reference laser (r—dot line). (b) R as a function of r.

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The calculated results are illustrated in Fig. 3. As Fig. 3(a) shown that the OTM laser can operate at single-longitudinal-mode with much higher pump power than the reference laser.

Fig. 3(b) shows R straightly as a function of r. From Fig. 3(b) the theory predicts that the OTM laser can operate at single longitudinal mode over 30 times the threshold pump power providing reference lasers can operate at single longitudinal mode 4–5 times the threshold pump power [15]. Our experimental results have proved the theoretical prediction.

3. Experiments and results

The structure of the OTM microchip is shown in Fig. 1. A pair of QWPs sandwich Nd:YVO₄ crystal. The principle axes of QWPs are oriented with their fast axes perpendicular with each other and at 45° to the optical (c-) axis of Nd:YVO₄ crystal. The a-cut Nd:YVO₄ crystal (Photop Technologies) is doped 2%at.Nd³⁺ and has dimension 1×1×0.9 mm³. Both end surfaces of Nd:YVO₄ crystal were antireflectance coated for 808 and 1064 nm. QWP is a piece of quarts crystal of 1×1×0.456 mm³ which is a quarter-wave plate for 1064 nm and a whole-wave plate for 808 nm. The input surface of the first QWP was coated anti-reflectance (T=98.5%) for 808 nm and high-reflectance (R=99.95%) for 1064 nm, and another surface was anti-reflectance coated for 808 and 1064 nm. The output coupling surface of second QWP was coated high-reflectance (R=95%) for 1064 nm, and another surface was anti-reflectance coated for 1064 nm. Three pieces of crystals (two QWPs and Nd:YVO₄) were optically bonded together as a microchip without adhesive [16] (see Fig. 4). The 808 nm pump source was SDL 1.2W LD (specially ordered from JDSU). The couple lens is mini lens with focusing length of 1.5 mm (Photop D-lens). All components laser diode, lens and microchip were mounted into an aluminum package with size of 12×12×20 mm³. Fig. 5 shows a 3D scenograph of the microchip laser package. In the output window there is a filter for cutting out the residual pump light (808 nm). The heat-sink can be replaced with a Thermo-Electric Cooler (TEC) to control local temperature of the microchip, if need it. We also used a bigger TEC to control the temperature of whole package during temperature test. The reference lasers have the same structures as the OTM laser except the principle axes of QWPs are parallel or perpendicular to c-axis of Nd:YVO₄.

Fig. 4. The picture of the microchip which consisted of QWP– Nd:YVO₄ –QWP optically bonded together without adhesive. Dimension- 1×1×1×1.81 mm³.

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Fig. 5. 3D scenograph of the microchip laser package. Dimension-.12×12×20 mm³

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Fig. 6. The output power and wavelength of single-longitudinal-mode operation for OTM laser as a function of pump power (a) and temperature (b).

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In the experiments the Optical Spectrum Analyzer (OSA, Ando AQ6317) with wavelength resolution of 0.01 nm was used for monitoring single-longitudinal-mode operation and measuring wavelength of the laser. The output power for lasers was measured by powermeter (Newport 1830C). All measurements were accomplished in room temperature environment (20–30°C). The output power and wavelength of single-longitudinal-mode operation for OTM laser were measured as a function of the pump power as shown in Fig. 6(a). In the calculations of the threshold and slope efficiency we used the output power of laser diode as pump power instead of power absorbed by gain medium. Fig. 6(a) shows that the threshold is below 50 mW pump power, the maximum single-mode output power was greater than 730 mW, because the maximum available output power of the laser diode was only 1250 mW. The experiment shown the OTM laser operates 25 times above the threshold before the second mode reaches threshold. Under different powers of the pump and laser the temperature in cavity was significantly changing, the difference of wavelength of the laser between the maximum and minimum output powers of the laser was almost one FSR (0.17 nm). Even under so much different environments the OTM laser still operated at single-longitudinal-mode and single transverse TEM₀₀ mode. The calculated slope efficiency is greater than 60%. The devices can be single-mode operated in a wide range of temperature. Fig. 6(b) illuminated the output power and wavelength of single longitudinal-mode operation for OTM laser as a function of temperature and shown the range of temperature is greater than 30°C under 300 mW pump power. All output beams of OTM lasers were the single transverse TEM₀₀ modes. We measured M² and it is better than 1.15. The polarizations of output beams of OTM lasers were linear polarizations oriented at 45° to c-axis of Nd:YVO₄ crystal as predicted by the theory. The extinction ratio was better than 390:1. In 200 times turn on-off test for 10 OTM lasers we didn’t observe mode-jumping and any bistable phenomenon [17]. For comparing with the theory we measured the maximum pump power of the reference lasers at single-longitudinal-mode operation. The distribution of data was diffusion and some devices can operate at single-longitudinal-mode with pump power 4–5 times above the threshold.

As an application of the OTM laser we made the intracavity doubling laser inserting a 1×1×1 mm³ KTP crystal between QWP and Nd:YVO₄ crystal. On output coupling surface of the second QWP additional antireflective film and on input surface of the first QWP additional highreflective film for 532 nm were coated, respectively. KTP crystal was cut for II-type phasematch and its fast axis was parallel to c-axis of Nd:YVO₄ crystal. In this configuration, II-type phasematch required both e- and o-fundamental waves with same intensity for optimal phasematch. Under 500mW pump power of 808nm the more than 80 mW of single-mode 532 nm laser was obtained. The light (808 nm)-to-light (532 nm) efficiency is 16% and the electro (driving power of laser diode)–to-light (532 nm) efficiency is 8%. The single-longitudinal-mode operation ensures low noise of the green laser [18]. The measured peak-peak noise and RMS noise were less than 1% and 0.1%, respectively. Fig. 7(a) shows oscilloscope traces of the laser output at 532 nm for OTM laser and very low power noise in this laser. For comparison we made a conventional green laser which consisted of Nd:YVO₄ crystal (0.5mm) and KTP crystal (2mm) and the optical axis of KTP crystal is oriented at 45° to the optical (c-) axis of Nd:YVO₄ crystal. These kind of green lasers operate at Multi-Longitudinal-Mode (MLM) and there are large-amplitude fluctuations due to longitudinal mode-coupling in the laser output. Fig. 7(b) shows the large “green noise” of MLM laser, its RMS noise is high up to 7.87% and RMS noise of OTM laser is only 0.03% (see Fig. 7(a)). Fig. 8 shows long-term stability of the laser output at 532 nm for OTM laser. .The power stability of OTM laser (532 nm) is better than 2% in longer than 10 hours and temperature of the laser was controlled in +/- 0.1°C with a TEC. In the test we used TDS 1012B oscilloscope (Tektronix, 100M) and PD15-22C photo-diode (Everlight, 400–1100 nm; 10ns).

Fig. 7. Oscilloscope trace of the laser output at 532 nm. of OTM laser (a) and MLM laser (b). RMS noise of OTM laser and MLM laser 0.03% and 7.87%, respectively.

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Fig. 8. Long-term stability of the laser output at 532 nm. of OTM laser.

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4. Conclusion

We have theoretically shown and experimentally demonstrated that the OTM microchip laser consisted of Nd:YVO₄ crystal sandwiched by a pair of QWPs, is capable of suppressing the spatial hole-burning effect and can operate under single-longitudinal-mode with pump power 25 times above the threshold. The OTM laser also present good merits: high slope efficiency (>60%); good beam quality (M²<1.12), linear polarization with ratio 390:1 and wide operation temperature range (>30°C). As one of application of OTM laser, the single longitudinal mode green lasers were made and had very low intensity noise (RMS noise is only 0.03%).

Acknowledgment

The authors thank Mr. John (Jiwu) Ling for many stimulating discussions.

References and links

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Single-longitudinal mode Nd:YVO4 microchip laser with orthogonal-polarization bidirectional traveling-waves mode

Abstract

1. Introduction

2. Theoretical analysis

3. Experiments and results

4. Conclusion

Acknowledgment

References and links

Cited By

Figures (8)

Equations (22)

Optics Express