Experimental evidence for the thermal origin of $1/f$ frequency noise in erbium-doped fiber lasers

We present experimental evidence in support of the recent theoretical proposal that intrinsic $1/f$ frequency noise in short cavity erbium-doped fiber lasers is of thermal origin. We demonstrate that the power spectral density of frequency noise in distributed-feedback fiber lasers (DFB FL) exhibits predicted $T^2$ temperature dependence across all frequencies over a temperature range of almost 200 K. This temperature dependence is observed both in direct interferometric measurements of frequency noise in a single mode DFB FL and noninterferometric measurements of polarization-beat-frequency noise in a dual frequency DFB FL. It is also shown that frequency noise of orthogonal polarization modes in the dual frequency DFB FL is substantially correlated providing a strong indication of a common origin.

Figure 1

The experimental setup used to measure frequency noise.

Figure 2

Experimental one-sided DFB FL frequency noise $\left[2S_{\nu }\left(f\right)\right]$ data measured at 369 K $\left(“\cdot ”\right)$, 293 K (“○”), 247 K (“◇”) and 195K $\left(“+”\right)$. Corresponding theoretical curves are shown as solid lines.

Figure 3

Estimated rms laser frequency deviation verses temperature (normalized to unity at 369 K): $\Delta {\nu }_5$ (“◻”) includes noise contributions up to ${10}^5\text{Hz}$; $\Delta {\nu }_4$ $\left(“+”\right)$ includes contributions up to ${10}^4\text{Hz}$; $\Delta {\nu }_3$ (“○”) includes contributions up to ${10}^3\text{Hz}$. Noise contributions below 60 Hz and between 250 and 350 Hz have been excluded.

Figure 4

(Color online) Experimental setup for measuring the polarization resolved frequency noise and temperature dependence of the polarization-beat frequency in a dual-polarization DFB fiber laser

Figure 5

Polarization resolved (one-sided) frequency noise spectra of a dual-polarization DFB fiber laser, labeled $S_{{\nu }_1}$ and $S_{{\nu }_2}$ for the respective polarization modes. Also shown is the difference between the two spectra $\left(S_{{\nu }_b}\right)$ and the polarization-beat-frequency noise measured directly (PBF).

Figure 6

One-sided power spectra density of the polarization-beat-frequency noise vs temperature.

Figure 7

(Color online) Scale factor $a^{1/2}$ obtained from a nonlinear curve fit of polarization-beat-frequency noise vs temperature.