Intensity- and phase-noise correlations in a dual-frequency vertical-external-cavity surface-emitting laser operating at telecom wavelength

The amplitude and phase noises of a dual-frequency vertical-external-cavity surface-emitting laser (DF-VECSEL) operating at telecom wavelength are theoretically and experimentally investigated in detail. In particular, the spectral behavior of the correlation between the intensity noises of the two modes of the DF-VECSEL is measured. Moreover, the correlation between the phase noise of the radio-frequency beat note generated by optical mixing of the two laser modes with the intensity noises of the two modes is investigated. All these spectral behaviors of noise correlations are analyzed for two different values of the nonlinear coupling between the laser modes. We find that to describe the spectral behavior of noise correlations between the laser modes, it is of utmost importance to have precise knowledge about the spectral behavior of the pump noise, which is the dominant source of noise in the frequency range of interest (10 kHz to 35 MHz). Moreover, it is found that the noise correlation also depends on how the spatially separated laser modes of the DF-VECSEL intercept the noise from a multimode fiber-coupled laser diode used for pumping both the laser modes. To this aim, a specific experiment is reported which aims at measuring the correlations between different spatial regions of the pump beam. The experimental results are in excellent agreement with a theoretical model based on modified rate equations.

Figure 1

Schematic representation of the basic principle of the dual-frequency VECSEL operating at 1.5 $\mu \mathrm{m}$. The ordinary (o) and extraordinary (e) eigenpolarizations are spatially separated inside the gain medium to reduce nonlinear coupling. The pumping is done by a diode laser at 980 nm. The picture on the left represents the two partially separated modes in the pumped region of the gain medium.

Figure 2

Schematic of noise correlation measurement setup. (a) Architecture of the DF-VECSEL cavity; $d$: spatial separation between the two eigenpolarizations. (b) Noise measurement setup. $\lambda /2$: half-wave plate, BS: beam splitter, PBS: polarization beam splitter, D: detectors, RFA: rf amplifiers, ESA: electrical spectrum analyzer.

Figure 3

(a) Schematic of the pump noise correlation measurement setup. BS: beam splitter, D: detectors, RFA: rf amplifiers. (b) Pump relative intensity noise spectrum. (c) Noise correlation amplitude spectra for different values of $d$. The black thin curve (at the bottom) is the measurement floor. (d) Noise correlation phase spectra for three values of $d$. The phase measurements for $d=25\mu \mathrm{m}$ and $d=75\mu \mathrm{m}$ are not reproduced here for the sake of clarity but also give values of $\psi$ which are close to zero.

Figure 4

Results for weak coupling ($C=0.11$). Relative intensity noise spectra for two polarizations: (a) experiment and (b) theory. Correlation amplitude: (c) experiment and (d) theory. The black thin line in (c) is the measurement floor. Correlation phase: (e) experiment and (f) theory. Parameters used for theory: $r_x=1.2, r_y=1.15, {\tau }_x=9.9$ ns, ${\tau }_y=10.4$ ns, $\tau =1$ ns, $\eta =0.2, \psi =0, {\mathcal{R}}_p=-145$ dB/Hz.

Figure 5

Results for the moderately strong coupling ($C=0.74$) case. Relative intensity noise spectra for two polarizations: (a) experiment and (b) theory. Correlation amplitude: (c) experiment and (d) theory. Correlation phase: (e) experiment and (d) theory. Parameters used for theory: $r_x=1.4, r_y=1.42, {\tau }_x=16.8$ ns, ${\tau }_y=17.6$ ns, $\tau =1$ ns, $\eta =0.75, \psi =0, {\mathcal{R}}_p=-145$ dB/Hz.

Figure 6

In-phase and antiphase noise spectra. Weak coupling ($C=0.11$): (a) experiment and (b) theory. Moderately strong coupling ($C=0.74$): (c) experiment and (d) theory.

Figure 7

Results for rf phase-noise measurement. Weak coupling: (a) phase noise and (b) beat note. Moderately strong coupling: (c) phase noise and (d) beat note. RBW: resolution bandwidth, VBW: video bandwidth. Parameters used for simulation: $\alpha =10, D_T=0.372 {\mathrm{cm}}^2{\mathrm{s}}^{-1}, d\overline{n}/dt=2.0\times {10}^{-4} {\mathrm{K}}^{-1}, L_{SC}=5$ $\mu \mathrm{m}, L_{\mathrm{ext}}=4.76$ cm, $w_p=50 \mu \mathrm{m}, R_T=12 \mathrm{K}{\mathrm{W}}^{-1}, P_p=1.7$ W.

Figure 8

Correlation of rf phase noise with the intensity noises for weak coupling. Correlation amplitude: (a) experiment and (b) theory. Correlation phase: (c) experiment and (d) theory.

Figure 9

Correlation of rf phase noise with the intensity noises for moderately strong coupling. Correlation amplitude: (a) experiment and (b) theory. Correlation phase: (c) experiment and (d) theory.