# A Compact Self-Injection-Locked Narrow-Linewidth Diode Laser with Narrowband Dielectric Filter
###### Abstract
The HFFPF is inset between the aspherical lens and the mirror as a narrowband filter for the laser feedback. It is tilted slightly to optimize the longitudinal mode matching between the HFFPF and the LD cavity and to avoid unwanted feedback from the direct reflection from the HFFPF surface. Another aspherical lens is used to couple laser output into a single-mode fiber. In this laser, the distance between the LD and the partial-reflection mirror is 5 cm; hence, the FSR for this external cavity is \(\sim\)0.0062 nm. However, due to the low reflectivity, the finesse \(F\) of the cavity is only \(\sim\)1.1. So, the HFFPF is necessary for this cavity for frequency filtering to achieve a single-longitude-mode output for the self-injection locking laser. Then we characterize the output spectrum of the self-injection-locked laser. For comparison, we first measure the free-running spectrum of the LD using an optical spectrum analyzer (OSA, AQ6374, YOKOGAWA, Tokyo, Japan), and the result is shown in Figure 3a. The spectrum of the LD before the self-injection locking has several peaks between 784 nm and 786 nm, which shows a multi-longitudinal-mode output. After that, the output spectrum of the self-injection-locked laser is measured. Unlike the multi-longitudinal-mode spectrum in the free-running case, the spectrum presents a clean Lorentz-type single-longitudinal-mode spectrum peaking at 783.4 nm, as shown in Figure 3b. The side modes  
Figure 2: Setup of the self-injection-locked laser using the HFFPF. LD: laser diode; L: aspherical lens; HFFPF: High fineses Fabry–Pérot filter; M: 90 %-transmissivity partial-reflection mirror; SMF: single mode fiber. are compressed well over a large range from 770 nm to 800 nm, with a side-mode suppression ratio of over 60 dB. The wavelength difference between the first side-mode peak and the center one is 11.1 nm, which is consistent with the FSR of the HFFPF. The same spectrum is plotted in logarithmic scale in Figure 3c, and its linewidth is limited by the OSA resolution of about 0.05 nm. Then, the laser linewidth is measured more accurately using the optical heterodyne measurement [24]. Two self-injection-locked lasers are built for this measurement, with the setup shown in Figure 4a. Two pieces of HFFPF from the same batch are used for these two lasers, and the laser outputs are mixed using a 50:50 fiber coupler for the heterodyne measurement. The OSA is used for a coarse match of the laser frequencies by monitoring the spectrum of one output port. By tuning the LD temperature of one laser, we overlap the spectra of the two laser outputs within the 0.05 nm resolution limit of the OSA. Then we can see the beating signal from the photocurrent of a photodetector linking to the other output port using a real-time spectrum analyzer (RTSA, RSA306B, Tektronix). By setting the beating frequency at around 4.195 GHz, we plot the beating signal in Figure 4b, which shows a sharp RF peak. The inset is a zoom-in of the beating spectrum, and the FWHM bandwidth of the peak is fit to be about 66 kHz. Assuming the two self-injection-locked lasers have the same linewidth, the linewidth of a single laser can be estimated to be 46.7 kHz. Figure 4: (**a**) Setup for the heterodyne measurement. OSA: optical spectrum analyzer; PD: photodetector; RTSA: real-time spectrum analyzer. (**b**) Beating signal measured in optical heterodyne measurement. The black dots are measured data, and the red curve is its Lorentz fitting. In the zoom-in figure, \(t_{0}=4.197\) GHz. Figure 3: (**a**) The free-running spectrum of the laser diode. (**b**) The spectrum of the self-injection-locked laser diode. (**c**) The spectrum in the logarithmic scale. In conclusion, we develop an IAD coating method to demonstrate a high finesse Fabry-Perot filter with a bandwidth down to 0.16 nm, and a sub-100 kHz narrow-linewidth laser is built using an HFFPF. A high side-mode suppression ratio of 60 dB is measured using only a low-cost FP laser diode.