High-Resolution Investigation of a Grating-Stabilized Laser with a Fabry–Pérot Interferometer

2.1 Characterization of the ECDL

The optical power $P_{\text{opt}}$ of the ECDL as a function of the operating current I is plotted in Figure 2, with the curve of the ECDL in black and as a reference the characteristic of the used LD without external cavity as a dashed line. The lower threshold of the ECDL is due to the lower cavity losses compared to the Fabry–Pérot LD with high reflectivity and antireflectivity coating of the two mirrors. In the $P_{\text{opt}}(I)$ characteristic we observe a fast and a slow modulation of the curve. At the corresponding current the high-resolution spectra measured with the FPI reveals mode changes, which occurs due to the increasing current and therefore an increase of the temperature in the diode. These kinks are caused by interference of the longitudinal modes of the external and internal cavity, respectively.

2.2 Linewidth

The linewidth ${\mathcal{D}}_{\text{FWHM}}$ of the ECDL in stable single-mode operation was determined with the FPI as function of the mirror spacing. The following calculations are based on ref. 19.

Doing the calculations and measuring the incident light we can determine at a mirror spacing of 5 mm a linewidth of 0.33 pm of the ECDL (shown in Figure 3, black curve). With a reflectivity of $R=0.95$ of the mirrors, corresponding to an instrumental finesse of $ℱ=61$ (see Equation (3)) and incident wavelength of $\lambda =443.5 \text{nm}$, one can calculate the resolution limit for $d=5 \text{mm}$ which is about $\frac{\lambda }{\Delta \lambda }=m_{\text{FP}}\cdot ℱ=22548\cdot 61=1.38\times {10}^6$ corresponding to a $\Delta \lambda =0.32 \text{pm}$ (depicted in Figure 3 gray curve). Obviously both numbers are in good agreement, so we are limited in the resolution with the mirror spacing of 5 mm. Accordingly we increased the distance between the mirrors in steps of 5 mm up to 50 mm and redid the above calculations. Up to $d=30 \text{mm}$ the measured linewidth was limited by the resolution, above this value we got a constant linewidth in the range of ${\mathcal{D}}_{\text{FWHM}}=50 \text{fm}$ corresponding to 75 MHz in the frequency range.

In addition, the ratio of the FSR and the linewidth is depicted in blue in Figure 3. The constant value of the ratio $\Delta {\lambda }_{\text{FSR}}/{\mathcal{D}}_{\text{FWHM}}$ indicates that the measured linewidth is resolution limited for mirror spacings up to 30 mm, with a constant finesse of the FPI. For larger spacing, the ratio drops. This can be caused either by a decreasing finesse, as mirror alignment becomes difficult for large values of d or by the ECDL linewidth. Unfortunately we do not have a commercial laser with a narrow linewidth to verify, if we have measured the real linewidth of our self-built ECDL or if we have reached the resolution limit of the FPI. Therefore, the 75 MHz linewidth is an upper bound for the ECDL. For a precise measurement of the linewidth, homodyne or heterodyne methods are more appropriate.^[20-23]

2.3 Wavelength Shifts with Temperature and Current

In the following we want to analyze the temperature and current dependencies on the ECDL wavelength. The temperature is measured and regulated at the heat sink.

The wavelength shift with $n_{\text{eff}}$ and therefore with T is much smaller for the external cavity, because $m_{\text{ext}}\gg m_{\text{int}}$. Consequently, the longitudinal modes of the internal and external cavity shift to longer wavelength. The wavelength shift of the internal cavity is much faster than that of the external cavity. The observed shift to longer wavelength in Figure 4 (left) is consequently caused by the shift of the longitudinal mode of the internal LD cavity. We observe a shift of about 9 pixel of the charge-coupled device (CCD) detector over a 1 K temperature range, corresponding to a temperature-induced shift of ≈18 pm K⁻¹. During this shift the mode order of the external cavity is changing. The corresponding mode jumps cannot be observed with the limited resolution of the spectrometer. The larger jump of about 25 pm to shorter wavelengths at 20.5 K is caused by a jump of the longitudinal mode of the internal LD cavity.

Second, we measured the wavelength shift resulting from different operating currents with current in steps of 0.1 mA starting at 104.7 mA shown in Figure 4 on the right. Again, we observe a mostly continuous shift to longer wavelength caused by heating of the active region with increasing current density. In a narrow-current range, the mode switches between longitudinal modes of the Fabry–Pérot LD. With the resolution of the grating spectrometer, the spectral shift of the laser line can only be estimated to be about 1.6 pm mA⁻¹.

Therefore we measured both shifts simultaneously also with the FPI in order to resolve the shift of the longitudinal modes of the external cavity. The results are shown in Figure 5 as a function of temperature and current in the left and right image, respectively. The ECDL switches between single mode and multiple longitudinal mode operation of the external cavity. This shows the regular mode combs of 1–5 modes with a regular mode spacing of about 3 pm. From the slope, the temperature-induced shift of 16.7 pm K⁻¹ can be traced with higher accuracy. This is consistent with the spectrometer measurement and also with measurements for standard blue LDs, which typically show temperature-induced shifts of about 15 pm K⁻¹. The irregular behavior at 20.5 K is again caused by a mode jump of the short FP cavity. Because the mode spacing of about 26 pm of the short cavity is larger than the FSR of 19.8 pm of the FPI, the small shift observed in Figure 5 does not reflect the real wavelength shift of the ECDL line. The dependency on current for constant heat sink temperature shows a single mode over a current range of about $\Delta I=1 \text{mA}$ before the laser jumps between modes of the external cavity; see Figure 5, right image. In the stable range between $105.3 \dots 106.3 \text{mA}$, a slope of the wavelength with current of 1.15 pm mA⁻¹ for the individual mode was determined. This slow shift of the individual longitudinal mode of the external cavity is caused by the increasing refractive index of the LD with temperature with driving current, reduced by the optical path length according to Equation (6) and (8). The faster shift of the center of gravity of the modes over a wider range including mode jumps of the external cavity follows the faster shift of the longitudinal modes of the internal cavity. A separation of these two effects is only possible with the help of the FPI, but it is necessary to know the incident wavelength and therefore the grating spectrometer is also needed.