Orthogonally polarized single-longitudinal-mode operation in a dual-wavelength monolithic Nd:YAG laser at 1319&#x2009;&#x2009;nm and 1338&#x2009;&#x2009;nm

Hao Ping Cheng; Yu Cheng Liu; Tzu Lin Huang; Hsing Chih Liang; Yung Fu Chen

doi:10.1364/PRJ.6.000815

1. INTRODUCTION

Laser sources with two orthogonally polarized modes have numerous applications such as in laser interferometry, differential absorption lidar, holographic microscopy, and precision measurement [1–5]. It has been confirmed [6–14] that external mechanical forces can be used to yield a birefringence effect in a Nd:YAG crystal to achieve the emission of two orthogonally polarized modes. Furthermore, the frequency difference between two orthogonally polarized modes can be linearly tuned by varying the mechanical force. On the other hand, single-longitudinal-mode operation in two orthogonally polarized components is usually indispensable for the application of precise measurements [4,13–15]. Owyoung and Esherick [9] first reported that a mechanical force induced a tuning of a diode-pumped monolithic Nd:YAG laser in the orthogonally polarized single-longitudinal-mode operation at 1064 nm. Nowadays, monolithic miniature flat-flat laser crystals are widely used to achieve single-longitudinal-mode operation.

In addition to 1.06 μm, the ${}^{4}{F_{3 / 2}} \to {}^{4}{I_{13 / 2}}$ transition of ${Nd}^{3 +}$ -ion-doped laser crystals can emit 1.3 μm coherent lights that are often exploited in fiber communications, laser medicine, and dental surgery [16–21]. The Stark splitting levels usually lead to several transitions to emit different laser wavelengths. Two strongest emission wavelengths in the ${}^{4}{F_{3 / 2}} \to {}^{4}{I_{13 / 2}}$ transition of a Nd:YAG crystal are 1319 nm from the $R_{2} \to X_{1}$ transition and 1338 nm from the $R_{2} \to X_{3}$ transition. The comparable property of the emission cross sections at 1319 and 1338 nm in a Nd:YAG crystal has been employed to achieve dual-wavelength operation [16–21]. Dual-wavelength lasers are of great interest for many applications such as nonlinear wavelength conversion, medical instrumentation, precision spectral analysis, and terahertz (THz) frequency generation by using the difference-frequency mixing technique. The single-longitudinal-mode and single-transverse-mode operations are critically important for using a dual-wavelength laser to generate a continuous-wave (CW) THz light source. So far, there have been no explorations for the single-longitudinal-mode operation in a dual-wavelength laser at 1319 and 1338 nm. It will be practically useful to achieve the orthogonally polarized single-longitudinal-mode operation in a dual-wavelength monolithic Nd:YAG laser at 1319 and 1338 nm.

In this work, we design two types of coating specification for monolithic Nd:YAG lasers to explore the performance of the orthogonally polarized single-longitudinal-mode operation on the ${}^{4}{F_{3 / 2}} \to {}^{4}{I_{13 / 2}}$ transition. The monolithic Nd:YAG crystal with the first type of coating can emit a single-wavelength laser at 1319 nm. The crystal with the second type of coating can emit a dual-wavelength laser at 1319 and 1338 nm. The maximum output power of the orthogonally polarized single-longitudinal-mode operation in the single-wavelength 1319 nm laser can be up to 150 mW at an absorbed pump power of 880 mW. Experimental measurements reveal that the beat frequency $Δ f_{1319}$ between two orthogonally polarized modes at 1319 nm can be linearly varied from 181.3 MHz to 1.64 GHz by increasing the external mechanical force. On the other hand, at an absorbed pump power of 1.5 W, the maximum output powers for the dual-wavelength laser in the orthogonally polarized single-longitudinal-mode operation can be up to 147 and 123 mW for 1319 and 1338 nm, respectively. The beat frequencies $Δ f_{1319}$ and $Δ f_{1338}$ between two orthogonally polarized modes at 1319 and 1338 nm are found to be very close. The tuning rates of the beat frequencies subject to external mechanical force are also nearly the same. Furthermore, the frequency differences between $Δ f_{1319}$ and $Δ f_{1338}$ can also be changed from 4.5 to 19.9 MHz by increasing the external mechanical force.

2. EXPERIMENTAL SETUP

The experimental setup of the orthogonally polarized single-longitudinal-mode monolithic Nd:YAG laser is shown schematically in Fig. 1. The gain medium was a 1.1 at.% Nd:YAG crystal (Beijing Opto-Electronics Technology Co., Ltd.) with a length of 2 mm and a transverse aperture of $3 mm \times 3 mm$ . The laser crystal was wrapped with indium foil and mounted in a water-cooled copper holder at a temperature of 20°C. Both end surfaces of the laser crystal were coated to form a monolithic cavity. The front surface of the monolithic Nd:YAG crystal was high-transmittance-coated at 808 nm ( $T > 95 %$ ) and high-reflectivity-coated at 1300–1350 nm ( $R > 99.8 %$ ). To avoid emission at 1064 nm, both end surfaces of the crystal had a high-transmission coating ( $T > 50 %$ ) at 1064 nm for suppression. Figure 2(a) depicts the fluorescence spectrum between 1315 and 1350 nm at room temperature. The spectrum shows two superior peaks at 1319 and 1338 nm, which are contributed by the transitions ${}^{4}{F_{3 / 2}} (R_{2}) \to {}^{4}{I_{13 / 2}} (X_{1})$ and ${}^{4}{F_{3 / 2}} (R_{2}) \to {}^{4}{I_{13 / 2}} (X_{3})$ , respectively. It can be seen that the fluorescence intensities at 1319 and 1338 nm are nearly equal. The emission cross sections at 1319 and 1338 nm are $9.5 \times 10^{- 20}$ and $10 \times 10^{- 20} {cm}^{2}$ [22], respectively. The comparable fluorescence intensities and the emission cross sections represent the feasibility of dual-wavelength operation in the Nd:YAG laser by carefully choosing the reflectivity of the output coating. As a result, two different types of coating specification were designed for monolithic Nd:YAG lasers to investigate the performance of the orthogonally polarized single-longitudinal-mode operation on the ${}^{4}{F_{3 / 2}} \to {}^{4}{I_{13 / 2}}$ transition. Figure 2(b) reveals the reflectivity of two different output coatings for the monolithic Nd:YAG laser as a function of wavelength ranging from 1300 to 1350 nm. The reflectivities of type-A coating at 1319 and 1338 nm are designed to be 96% and 93%, respectively, to achieve single-wavelength operation at 1319 nm. The reflectivities of type-B coating at 1319 and 1338 nm are designed to be 93.5% and 93.3%, respectively, to achieve dual-wavelength operation at 1319 and 1338 nm.

Fig. 1. Configuration of an orthogonally polarized single-longitudinal-mode monolithic Nd:YAG laser at 1319 and 1338 nm.

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Fig. 2. (a) Fluorescence spectrum in the range of 1315–1350 nm at room temperature. (b) Reflectivity for two types of coating in the range of 1300–1350 nm.

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The pump source was a 3 W, 808 nm fiber-coupled laser diode (BWT Beijing Ltd.) with a 200 μm fiber core diameter and a numerical aperture of 0.16. The pump light was focused into the gain medium by using a pair of plano-convex coupling lenses each with a focal length of 50 mm and 90% coupling efficiency. The waist radius of the pump beam was approximately 100 μm. Here the absorption efficiency of the pump light was experimentally measured to be 55%. The spectral information of the laser output was analyzed with a Michelson interferometer (Advantest, Q8347) with a resolution of 0.003 nm. The autocorrelation trace was obtained with the help of a commercial autocorrelator (APE pulse check, Angewandte Physik & Elektronik GmbH). The polarization-resolved temporal behavior of the laser outputs was measured with two high-speed InGaAs photodetectors (Electro-optics Technology Inc., ET-3500—rise time of 35 ps), whose output signals were connected to a digital oscilloscope (Teledyne LeCroy, Wave Master 820Zi-A) with 20 GHz of electrical bandwidth and a sampling interval of 25 ps. The output signals of the photodetectors were also delivered to a radio frequency (RF) spectrum analyzer (Agilent, 8563EC) with a bandwidth of 9 kHz to 26.5 GHz.

3. EXPERIMENTAL RESULTS

In the beginning, we explored the single-wavelength operation at 1319 nm using the monolithic Nd:YAG crystal with coating of type A. Figure 3 depicts the experimental results for average output power as a function of absorbed pump power. The average output power reached 340 mW at an absorbed pump power of 1.5 W, corresponding to a slope efficiency of approximately 33.6%. The beam quality parameter $M^{2}$ of the output beam was measured to be approximately 1.2. The optical spectra of the single-wavelength operation at absorbed pump powers of 0.83 and 1.05 W are depicted in the insets in Fig. 3. The full widths at half-maximum (FWHMs) of the optical spectra were both measured to be 0.014 nm. Single-longitudinal-mode operation can be obtained when the absorbed pump power is lower than 0.83 W. It is confirmed that a stable single-longitudinal-mode operation can be maintained until the absorbed power $P_{abs}$ is greater than 1.78 times the lasing threshold $P_{th}$ . The structure of the multi-longitudinal-mode operation can be clearly seen at absorbed pump power over 0.94 W. We further measured the polarization-resolved oscilloscope traces to explore the polarization state of the output intensity. The lasing output intensity was found to be composed of two orthogonally polarized eigenstates with different central frequencies. The directions of the two orthogonal eigenstates were denoted as the horizontal ( $x$ ) and vertical ( $y$ ) directions with respect to the bottom wall of the holder. Figures 4(a)–4(d) show the temporal traces for the polarization-resolved output intensities $I_{θ}$ at $θ = 0 °$ , $θ = 90 °$ , $θ = 45 °$ , and $θ = 135 °$ at an absorbed pump power of 0.83 W; here $θ$ is the polarizer angle with respect to $y$ axis. It can be seen that the oscilloscope traces along the principal polarization directions, $I_{0 °}$ and $I_{90 °}$ , demonstrate CW operation with the DC signal. However, the polarization-resolved output intensities $I_{45 °}$ and $I_{135 °}$ are observed to display a phenomenon of intensity modulation with a beat frequency of 324.7 MHz, as shown in Figs. 4(c) and 4(d). The appearance of the beat frequency $Δ f$ between two principal polarization directions indicates the existence of a birefringence effect in the Nd:YAG crystal. It has been confirmed that external mechanical forces can be applied to induce a birefringence effect in an isotropic gain medium [6–12]. In our experiment, we utilized a torque wrench (Tohnichi, 6RTD) to apply an external mechanical force by fastening the screws on the copper holder. The mechanical force through the top of the holder presses the Nd:YAG crystal down against the bottom of the holder. The beat frequency was further found to be linearly dependent on the external mechanical force, as shown in Figs. 5(a), 5(c), and 5(e) for $I_{45 °}$ at applied external forces of $F = 1.6$ , 7.5, and 12.0 N, respectively. Figures 5(b), 5(d), and 5(f) reveal the RF spectra for the beat frequencies corresponding to the oscilloscope traces shown in Figs. 5(a), 5(c), and 5(e), respectively. It is experimentally measured that the beat frequency $Δ f_{1319}$ between two orthogonally polarized states at 1319 nm can be linearly adjusted from 181.3 MHz to 1.64 GHz by increasing the external mechanical force from 1.6 to 15 N, as shown in Fig. 6. The tuning rate of the beat frequency $Δ f_{1319}$ is found to be approximately 110 MHz/N. This beating phenomenon can be maintained over several hours, implying nice long-term stability.

Fig. 3. Output power versus absorbed pump power at 1319 nm. Insets: optical spectra for the single-longitudinal-mode and multi-longitudinal-mode operations at absorbed pump powers of 0.83 and 1.05 W.

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Fig. 4. Pulse trains of the polarization-resolved output intensities $I_{θ} (t)$ at a pump power of 1.5 W: (a) $θ = 0 °$ , (b) $θ = 90 °$ , (c) $θ = 45 °$ , (d) $θ = 135 °$ .

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Fig. 5. Panels (a), (c), and (e) show oscilloscope traces and panels (b), (d), and (f) show the corresponding RF spectra of the beat frequencies $Δ f_{1319}$ with three external mechanical forces of $F = 1.6$ , 7.5, and 12 N, respectively.

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Fig. 6. Experimental results and theoretical results of the beat frequency with respect to the applied external mechanical force, $F$ .

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When an external force is applied to a photoelastic material in a laser resonator, the stress-induced birefringence will lead to a laser frequency splitting phenomenon. The magnitude of the beat frequency, $Δ f$ , can be expressed as [11,12]

Δ f = \frac{ν}{L} (n_{x} - n_{y}) l_{cry} = \frac{ν}{L} C (σ_{1} - σ_{2}) L_{cry},

where

ν

is the frequency of the laser,

L

is the optical cavity length,

n_{x}

and

n_{y}

are, respectively, the refractive indices along

x

and

y

axes,

L_{cry}

is the crystal length,

C

is the relative stress-optic coefficient, and

σ_{1}

and

σ_{2}

are the orthogonal principal stresses. Extending the analysis performed by Zhang et al. [11,12] to the square-shaped crystal, the orthogonal principal stresses at the Nd:YAG crystal can be given by

σ_{1} = \frac{2 F}{2 A},

σ_{2} = \frac{- 6 F}{2 A},

where

F

is the applied mechanical force and

A

is the area of the contact surface. Substituting Eqs. (2) and (3) into Eq. (1) yields

Δ f = \frac{ν}{L} C \frac{8 F}{2 A} L_{cry} .

The values of the parameters for the Nd:YAG laser at 1319 nm are

ν = 2.274 \times 10^{14} Hz

,

L = 3.64 mm

,

C = 1.27 \times 10^{- 12} m^{2} / N

[11],

A = 6 {mm}^{2}

, and

L_{cry} = 2 mm

. Substituting these values into Eq. (4), the theoretical results can be clearly seen to be consistent with the experimental results, as shown in Fig. 6.

Next, we demonstrate dual-wavelength operation at 1319 and 1338 nm using the monolithic Nd:YAG crystal with coating of type B. The output efficiency of the dual-wavelength operation is shown in Fig. 7(a). The threshold power for the dual-wavelength operation is 0.55 W. At an absorbed pump power of 1.5 W, the total output power is approximately 270 mW. The maximum output powers for 1319 and 1338 nm were measured to be 147 and 123 mW, respectively. The slope efficiencies for the output powers at 1319 nm and 1338 nm, and for the total output power were 15.6%, 13%, and 28.6%, respectively. Here also $M^{2}$ was experimentally found to be 1.2. Figures 7(b) and 7(c) depict the lasing optical spectra of the dual-wavelength emissions at the absorbed pump power of 1.5 W. The central lasing wavelengths are located at 1319.1 and 1338.4 nm. The FWHM of the optical spectra is found to be approximately 0.013 nm. Both the emission lights are obtained to be in the single longitudinal mode when the absorbed pump power is lower than 1.5 W. The emission lights would, however, step into the multi-longitudinal-mode operation at an absorbed pump power of 1.6 W. Since the orthogonally polarized emissions are verified to exist in the single-wavelength monolithic Nd:YAG crystal at 1319 nm, we also observed the frequency splitting in the dual-wavelength monolithic Nd:YAG laser at 1319 and 1338 nm. The beat frequencies $Δ f_{1319}$ and $Δ f_{1338}$ between two orthogonally polarized states at 1319 and 1338 nm were found to be very close and were also observed to be like the results shown in Fig. 4. The tuning rates of the beat frequencies subject to the external mechanical force are nearly the same. Furthermore, the oscilloscope traces demonstrate another low-frequency beating modulation with a time span of 500 ns, as shown in Figs. 8(a), 8(c), and 8(e). It is confirmed that the low-frequency beating results from the difference in the beat frequencies between $Δ f_{1319}$ and $Δ f_{1338}$ . The frequency differences between $Δ f_{1319}$ and $Δ f_{1338}$ indicate that the induced birefringence has a tiny difference for the emission wavelengths at 1319 and 1338 nm. The frequency differences were further found to be varied for $I_{45 °}$ at stronger external mechanical forces of $F = 1.6$ , 7.5, and 15.0 N, as shown in Figs. 8(a), 8(c), and 8(e), respectively. Figures 8(b), 8(d), and 8(f) reveal the results of the RF spectra corresponding to the oscilloscope traces. The two peaks in the RF spectrum represent the beat frequencies $Δ f_{1319}$ and $Δ f_{1338}$ between orthogonally polarized states at 1319 and 1338 nm, respectively. The frequency differences between $Δ f_{1319}$ and $Δ f_{1338}$ in the RF spectra have good agreement with the temporal traces shown in Figs. 8(a), 8(c), and 8(e). Experimental measurements demonstrate that the frequency differences between $Δ f_{1319}$ and $Δ f_{1338}$ can be changed from 4.5 to 19.9 MHz by increasing the external mechanical force from 1.6 to 15.0 N, as depicted in Fig. 9. It can be seen that the theoretical analysis agrees very well with the experimental data. The strong agreement between the experimental and theoretical results not only confirms the existence of frequency differences between $Δ f_{1319}$ and $Δ f_{1338}$ , but also validates the present analysis. Finally, it is worth mentioning that the single-longitudinal-mode operation is quite significant to realize a stable CW THz light source with a dual-wavelength laser. Figure 10 reveals the autocorrelation trace of a dual-wavelength single-longitudinal-mode 1319 nm and 1338 nm laser with a delay time of 2 ps at an absorbed pump power of 1.5 W. The optical beat frequency is found to be 3.3 THz and it corresponds well with the central wavelength separation $Δ λ$ of 19.3 nm between the two emission wavelengths.

Fig. 7. (a) Output power versus absorbed pump power at 1319 and 1338 nm. Optical spectra at (b) 1319 nm and (c) 1338 nm.

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Fig. 8. Panels (a), (c), and (e) show oscilloscope traces and panels (b), (d), and (f) show the corresponding RF spectra of the frequency differences between $Δ f_{1319}$ and $Δ f_{1338}$ with three applied forces of $F = 1.6$ , 7.5, and 15 N, respectively.

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Fig. 9. Experimental results and theoretical results of the frequency difference between $Δ f_{1319}$ and $Δ f_{1338}$ with respect to the applied external mechanical force, $F$ .

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Fig. 10. Autocorrelation trace for the dual-wavelength emission with a time span of 2 ps.

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4. SUMMARY

In summary, two types of coating specification for monolithic Nd:YAG crystals were designed to realize a single-longitudinal-mode laser on the ${}^{4}{F_{3 / 2}} \to {}^{4}{I_{13 / 2}}$ transition. The monolithic Nd:YAG crystal with coating of type A can generate a single-wavelength laser at 1319 nm. On the other hand, the monolithic Nd:YAG crystal with coating of type B can generate a dual-wavelength laser at 1319 and 1338 nm. The maximum output power of the single-longitudinal-mode operation in the single-wavelength 1319 nm laser is up to 150 mW at an absorbed pump power of 0.88 W. On the other hand, the maximum output powers of the dual-wavelength laser in the single-longitudinal-mode operation can reach 147 and 123 mW for 1319 and 1338 nm, respectively, at an absorbed pump power of 1.5 W. Moreover, each longitudinal mode is found to be composed of two orthogonally polarized modes. Experimental results reveal that the frequency splitting between two orthogonal polarizations can be tuned by changing the external mechanical force applied on the Nd:YAG crystal. The beat frequency $Δ f_{1319}$ between two orthogonally polarized modes at 1319 nm can be linearly tuned from 181.3 MHz to 1.64 GHz by increasing the external mechanical force from 1.6 to 15 N. The tuning rate of the beat frequency $Δ f_{1319}$ is approximately 110 MHz/N. The beat frequencies $Δ f_{1319}$ and $Δ f_{1338}$ between two orthogonally polarized states at 1319 and 1338 nm are observed to be very close and their difference can be tuned from 4.5 to 19.9 MHz by increasing the external mechanical force from 1.6 to 15 N. The present theoretical analyses are in strong agreement with the experimental results. Finally, a CW, dual-wavelength, single-longitudinal-mode laser at 1319 and 1338 nm can generate an ultrashort beat signal with a repetition rate of 3.3 THz.

Funding

Ministry of Science and Technology, Taiwan (MOST) (106-2628-M-009-001).

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Orthogonally polarized single-longitudinal-mode operation in a dual-wavelength monolithic Nd:YAG laser at 1319 nm and 1338 nm

Abstract

1. INTRODUCTION

2. EXPERIMENTAL SETUP

3. EXPERIMENTAL RESULTS

4. SUMMARY

Funding

REFERENCES

Cited By

Figures (10)

Equations (4)

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