Observation of Extraneous Axial Cavity Modes of a Single-Mode Solid-State Laser Using Ultrahigh-Contrast Fabry–Perot Interferometry

Abstract

Extraneous axial optical cavity modes produced by a single-mode frequency-doubled neodymium-doped yttrium orthovanadate (Nd:YVO ${}_4$ ) laser were observed in spectra obtained via ultrahigh-contrast Fabry–Perot interferometry. These modes, which are much weaker than the primary axial mode emission, are separated by $\sim 0.75$  GHz and display decreasing intensity with increasing shift from the primary laser line and with increasing laser output power. The possible presence of such modes in target sample spectra necessitates that caution be used in the interpretation of spectral peaks in laser spectroscopy studies, particularly Brillouin light scattering experiments. This work also showcases the remarkable capabilities of modern multipass Fabry–Perot interferometry in the detection of exceedingly weak optical signals shifted in frequency by only a few gigahertz from the primary laser emission line.

Graphical abstract

This is a visual representation of the abstract.

Introduction

The “single-mode” solid-state laser has become the incident light source of choice for high-resolution laser spectroscopy. Like the traditionally-used noble gas ion laser (i.e., Ar ${}^{+}$ laser) with intracavity etalon, the single-mode solid-state laser offers a narrow-bandwidth exciting line, but without the need for much of the costly maintenance and specialized infrastructure associated with the former, such as plasma tube replacement, continuous water-cooling, and a high power electric supply. Other important advantages of the single-mode solid-state laser include higher output beam power and operational lifetimes typically measured in years. It is important to note, however, that such lasers may not display single longitudinal mode performance under all operating conditions.^1–4 Furthermore, even when a measurement suggests single-mode emission, extraneous axial modes may still be present in the laser output due to the inability of the chosen spectrometer to reveal such weak signals.

In this note, we report the possible presence of incompletely suppressed axial cavity modes in the output of a single-mode solid-state laser using ultrahigh-contrast Fabry–Perot interferometry. The potential for these modes to obscure or be incorrectly assigned to phonon modes in Brillouin spectra is highlighted.

Experimental Details

The Brillouin scattering apparatus used in the present work was configured for 180 ${}^{\circ }$ backscattering. The light source was a single-mode frequency-doubled neodymium-doped yttrium orthovanadate (Nd:YVO ${}_4$ ) laser emitting at a wavelength of 532 nm. The beam was p-polarized using a half-wave plate and neutral density filters were used to adjust the power to the desired level. A 5 cm focal length camera lens was used to focus incident light onto the target sample. Scattered and diffuse reflected light was collected and collimated by the same lens and subsequently focused onto the entrance pinhole of a six-pass tandem Fabry–Perot interferometer using a 40 cm focal length converging lens. All spectra were collected at room temperature. Further details can be found elsewhere.^5,6

Results and Discussion

Figure 1 shows a spectrum containing multiple peaks collected using the Fabry–Perot interferometer set to a free spectral range of 10 GHz and with a finesse of $\sim 100$ . These peaks are very narrow ( $\sim$ 0.3 GHz, instrumentally limited) and evenly spaced, with an intensity that decreases rapidly with increasing shifts, from the center of the spectrum, as expected for axial laser cavity modes. By plotting peak frequency shift versus mode number and performing a linear least-squares fit we obtain a mode spacing of $\sim 0.75$  GHz (see Figure 1 inset). The quality of the fit is excellent ( $R^2$ is essentially unity). Extrapolation of the line of best-fit yields a vertical axis intercept of 0.02 GHz, very close to the predicted assigned shift of 0 GHz for the purposely selected operational mode, providing further support for the assignment of these peaks to incompletely suppressed axial laser cavity modes. We note that these peaks are exceedingly weak relative to the selected operational mode and are only visible because of the exceptionally high contrast ( $\sim {10}^{11}$ ) of the multipass tandem Fabry–Perot interferometer used in the present work. These peaks will therefore likely only be of concern for Brillouin spectroscopy experiments and possibly Raman scattering experiments in which the region very close to (within $<10$  GHz or, equivalently, $<0.3$  cm ${}^{-1}$ ) the primary exciting line is of interest.

Figure 1.

Spectrum containing incompletely suppressed axial optical cavity modes from the output of a single-mode solid-state Nd:YVO ${}_4$ laser obtained by spectroscopic analysis of diffuse reflected laser light from porous silicon carbide. Inset: Frequency shift versus mode number (as enumerated from the central peak at an assigned shift of 0 GHz) for several of the first few axial modes. Dashed line—best-fit to experimental data (slope = 0.75 GHz/mode, vertical axis intercept = 0.02 GHz, $R^2$  = 0.9977). Error bars are less than the size of the experimental data points.

Figure 2a shows spectra obtained from interferometric analysis of diffusely reflected and scattered laser light from aluminum and crystalline silicon. As can be seen, the peak width, the frequency interval between adjacent peaks, and the overall decrease in peak intensity with increasing shift are the same for both materials and consistent with that shown in Figure 1 for porous silicon carbide, confirming that the origin of these peaks is not the material under study.

Figure 2.

Spectra showing extraneous axial optical cavity modes produced by a single-mode frequency-doubled Nd:YVO ${}_4$ laser. Blue, aluminum; orange, crystalline silicon.

There are a variety of factors that affect the intensity of the extraneous modes in the spectrum. In fact, these modes are not observed at all for many samples that we have studied, especially transparent liquids and solids. Evidence from our experiments suggests that they are typically most intense in spectra obtained at lower incident angles from microscopically rough, highly reflective materials, for which considerable diffuse reflected laser light is captured by the collection optics and subsequently undergoes spectral analysis by the Fabry–Perot interferometer. The intensity of these peaks also depends on laser output power, increasing with decreasing laser power as shown in Figure 3. This trend further supports the peak assignment to cavity modes because it is opposite to that expected if the origin was the target sample under study. While we have not thoroughly investigated the reason for this trend, intuitively this behavior is anticipated as the power level approaches the threshold for lasing—the laser being less stable at power levels closer to a threshold. These characteristics provide simple and practical ways to eliminate or reduce the intensity of these peaks via careful a priori consideration of experimental conditions. For example, the use of high-output laser power with external attenuating filters to reduce beam power to the desired level and high angle of incidence would likely result in a much weaker signal from extraneous cavity modes in a sample spectrum than the use of low-output power and low incident angle.

Figure 3.

Spectra obtained by spectroscopic analysis of diffuse reflected and scattered light from aluminum at different laser output power levels. Sharp, evenly spaced peaks due to incompletely suppressed axial laser cavity modes are clearly seen superimposed on the Brillouin spectrum. A clear decrease in extraneous peak intensity with increasing laser output power is evident.

The presence of these incompletely suppressed axial cavity modes can have a significant impact on the assignment and observation of acoustic phonon modes in a Brillouin spectrum. This is obvious when considering spectra presented in Figure 3, where the surface acoustic phonon peak of aluminum ( $\sim 7$  GHz) is nearly indiscernible in the two lower spectra due to the dominating signal from the cavity modes. Another example is shown in Figure 4, where a portion of the blue spectrum from Figure 3 is shown along with the Rayleigh surface acoustic phonon mode from the superconductor Bi ${}_2$ Sr ${}_2$ CaCu ${}_2$ O ${}_{8+\delta }$ . In this case, the frequency shift and overall spectral line profile of the acoustic phonon and one of the cavity modes are very similar, with widths of $\sim 0.5$  GHz and $\sim 0.3$  GHz, respectively. Without knowledge of the possible presence of these axial cavity modes in a Brillouin spectrum, they could easily be incorrectly assigned to acoustic phonon modes in the target material of interest, especially when they are strongest in the frequency region where low-lying acoustic phonons are commonly observed.

Figure 4.

Collected Brillouin spectra highlighting the spectral profile similarities of a Rayleigh surface mode (from crystalline Bi ${}_2$ Sr ${}_2$ CaCu ${}_2$ O ${}_{8+\delta }$ , black)and incompletely suppressed axial laser cavity modes (from Figure 3, blue). Dashed lines indicate each respective fit.

Conclusion

We have noted the possible presence of incompletely suppressed axial optical cavity modes in the output of single-mode solid-state lasers via ultrahigh-contrast Fabry–Perot interferometry. Recognition of this fact will help prevent misinterpretation of these modes as arising from the target sample in spectra obtained in high-resolution laser spectroscopy experiments (e.g., incorrect assignment as Brillouin peaks due to sample acoustic phonon modes). In revealing and facilitating the measurement of these near-imperceptible modes, this work also highlights the remarkable capabilities of Fabry–Perot interferometry in the detection of exceedingly weak spectroscopic signals.