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

A diode‐based external cavity diode laser (ECDL) is built in Littrow configuration and its modal behavior as well as its current and temperature‐induced wavelength shift is investigated. The ECDL is based on a laser diode (LD) in the blue spectral range with a straight ridge and low‐reflectivity front facet. A high‐resolution grating spectrometer (SPEX 1404 0.85 m double spectrometer) as well as a scanning Fabry–Pérot Interferometer (FPI, Burleigh RC‐110 with RG‐93 ramp generator) are used for spectral characterization. With the high resolution of the FPI, an upper bound of the ECDL linewidth of about 50 fm is found, which is 75 MHz in terms of frequency. The spectral shifts with temperature and with driving current are determined. The shift of 1.15 pm mA−1 of the individual mode of the external cavity is caused by a change of the group refractive index and corresponding change of the effective cavity length. The shift of 2.7 pm mA−1 of the spectral center of gravity can be explained by the faster shift of the internal modes. The single‐mode shift with temperature of 16.71 pm K−1 is consistently measured both by the spectrometer and the FPI.


Introduction
Narrow-bandwidth laser sources are important for several applications. Various types of sensors require small linewidths such as fiber optic sensors for gas monitoring [1,2] or certain light detection and ranging (LIDAR) applications. [3][4][5] Another field of application are atomic clocks, quantum optics [6][7][8] and quantum computing, as well as high resolution spectroscopy. [9] One example, which will be used in this work, is to build an external cavity diode laser, where a grating stabilizes the laser diode (LD) on one mode as described in refs. [10][11][12]. Many external cavity diode lasers (ECDLs) work in the infrared wavelength range, but there are also ECDLs in the visible wavelength range shown. [13][14][15][16] Commercially stabilized diode laser in the blue spectral region achieves linewidths below 1 MHz. [17] Besides the self-built ECDL, the intrinsic characteristics of it will be shown in this article using a grating spectrometer and a Fabry-Pérot Interferometer (FPI). The FPI allows to resolve the longitudinal modes of the external cavity and therefore to investigate single-mode operation, mode jumping, and wavelength shifts with current and temperature. The grating spectrometer allows to determine the absolute wavelength and also mode jumps larger than the free spectral range (FSR) of the FPI.

Results
Our ECDL, based on a LD in the blue spectral range fabricated in the (Al,In)GaN material system, in standard Littrow configuration, is build compact and mounted on an optical table. Details on the ECDL are provided in the experimental section at the end. The temperature of the LD is stabilized at the heat sink. The components are mounted separately and are not shielded or fixed by housing. Therefore temperature instabilities and acoustic effects may affect the ECDL. Another group also proposed to 3D print a housing for an ECDL. [18] In comparison commercial ECDLs are usually mounted in closed housings to avoid acoustic effects and operate as closed systems with temperature stabilization for the whole ECDL. Typically, commercial ECDL reach linewidths in the kilohertz range.
In the left image in Figure 1 we see a multimode behavior measured with the FPI and in comparison in orange, how the mode would look like in the grating spectrometer. Obviously, only the FPI is capable to distinguish single-and multilongitudinal mode operation of the external cavity. The full width at half maximum (FWHM) of the multimode comb is approximately equal to the resolution limit of the grating spectrometer of about 7 pm. In the right image in Figure 1 we see a clear single-mode operation.

Characterization of the ECDL
The optical power P 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 DOI: 10.1002/pssa.202200833 A diode-based external cavity diode laser (ECDL) is built in Littrow configuration and its modal behavior as well as its current and temperature-induced wavelength shift is investigated. The ECDL is based on a laser diode (LD) in the blue spectral range with a straight ridge and low-reflectivity front facet. A highresolution grating spectrometer (SPEX 1404 0.85 m double spectrometer) as well as a scanning Fabry-Pérot Interferometer (FPI, Burleigh RC-110 with RG-93 ramp generator) are used for spectral characterization. With the high resolution of the FPI, an upper bound of the ECDL linewidth of about 50 fm is found, which is 75 MHz in terms of frequency. The spectral shifts with temperature and with driving current are determined. The shift of 1.15 pm mA À1 of the individual mode of the external cavity is caused by a change of the group refractive index and corresponding change of the effective cavity length. The shift of 2.7 pm mA À1 of the spectral center of gravity can be explained by the faster shift of the internal modes. The single-mode shift with temperature of 16.71 pm K À1 is consistently measured both by the spectrometer and the FPI.
mirrors. In the P opt ðIÞ characteristic we observe a fast and a slow modulation of the curve. At the corresponding current the highresolution 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.

Linewidth
The linewidth D 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].
First, we need to calculate the FSR Δλ FSR which depends on the spacing of the two mirror plates d and the wavelength λ of our laser light This value is equal to the distance of two transmitted peaks while scanning with the FPI, which corresponds to two modes of consecutive order. The linewidth is then given as the FWHM of the peak. For further interpretation of this value it is helpful to know the achievable resolution of the FPI depending on the mirror spacing. This is given by where F is the instrumental finesse, depending on the reflectivity R of the mirrors in the FPI and the order of the mode m FP 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 ¼ 0.95 of the mirrors, corresponding to an instrumental finesse of F ¼ 61 (see Equation (3)) and incident wavelength of λ ¼ 443.5 nm, one can calculate the resolution Figure 3 gray curve). Obviously both numbers are in good agreement, so we are limited in the resolution with the mirror spacing   www.advancedsciencenews.com www.pss-a.com 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 ¼ 30 mm the measured linewidth was limited by the resolution, above this value we got a constant linewidth in the range of D FWHM ¼ 50 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 Δλ FSR =D 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][21][22][23]

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.
First, we used the grating spectrometer and changed the temperature in steps of 0.1 K starting at 19.5°C. For each step we measured a spectrum which is depicted as one line in Figure 4 in the left. With increasing temperature the bandgap energy E G decreases and the effective modal refractive index n eff of the laser wavelength increases. For a longitudinal mode with mode index m int of the LD cavity the wavelength is given by The derivative is independent of the LD cavity length, as m int scales with L int . The corresponding equations for the external cavity are and The wavelength shift with n eff and therefore with T is much smaller for the external cavity, because m ext ≫ m 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 À1 . 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 narrowcurrent 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 À1 . 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 temperatureinduced shift of 16.7 pm K À1 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 À1 . 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 ΔI ¼ 1 mA before the laser jumps between modes of the external cavity; see Figure 5, right image. In the stable range between www.advancedsciencenews.com www.pss-a.com 105.3 : : : 106.3 mA, a slope of the wavelength with current of 1.15 pm mA À1 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.

Conclusion
In this work we show the building of an ECDL from a common LD with an augmented reality (AR) coating and a holographic grating. This ECDL is characterized with the help of grating spectrometer to determine the wavelength of the emission and FPI for even higher-resolution measurements. Single-mode operation of the ECDL was achieved, for the linewidth an upper boundary of 50 fm or 75 MHz was estimated from FPI measurements. A homodyne or heterodyne technique would be appropriate to measure a linewidth in this range. Furthermore we showed the wavelength shifts induced from temperature and current changes. As expected both increasing temperature and increasing current lead to increasing wavelength. A shift of the center of gravity of the longitudinal modes with temperature was measured to be 16.7 pm K À1 , while the shift of the individual longitudinal mode with current was 1.15 pm mA À1 . Both shifts originate from the refractive index change of the LD. Stable single-line operation over a narrow current range of ΔI was demonstrated. For a stable and tunable operation, an active stabilization would be necessary.

Experimental Section
Our setup consisted of two main parts, the first part was the ECDL and the second part is the FPI. The ECDL was based on a LD, emitting in the blue spectral range and based on the (Al,In)GaN material system, with a cavity length of L int ¼ 1.2 mm. The standard Littrow configuration of the ECDL is shown in Figure 6. One facet of the diode was AR coated with a reflectivity of 0.5%, but due to the straight ridge there was still some light reflected and therefore lasing operation can be achieved. [24] The emitted light was collimated with an aspheric lens (Thorlabs AC240TM-A) and shone on an holographic grating (Thorlabs GH25-36U). There occured two reflected beams from the grating, which corresponded to the zeroth and first order of diffraction. The whole ECDL was built in the Littrow configuration and therefore the first order was used as external optical feedback and the zeroth order correspond to the outcoupled light. So our ECDL was formed by the front facet of our LD and the holographic grating. The length of the external cavity was L ext ¼ 36 mm.
The main experiment used to analyze the emitted light of the ECDL was a scanning FPI (Burleigh RC-110 with Burleigh RG-93 ramp generator). The FPI consisted of two parallel mirror plates with a high reflectivity (above 95%) and a really planar surface (roughness below λ=200), which were mounted on three big invar poles to minimize effects due to length changes in consequence of thermal instabilities. The maximum plate distance was 150 mm. One of the mirrors can be adjusted with the help of three extremely precise screws and the other one was adjusted with piezo elements. These piezo elements are also used for the scanning mechanism. The adjustment was done with the aim to get perfect interference rings for a stable separation of the two mirrors. When this was achieved the scanning led to a change of the brightness in the center of the interference pattern. This signal was measured with a photodiode.
To avoid unwanted effects in the FPI, it is necessary to provide light which is properly collimated and has a round beam shape. This was achieved with a single-mode optical fiber and the proper collimation after the outcoupling of the fiber was controlled with a shear interferometer. The coupling into the fiber was another really tricky aspect because the facet of the fiber was reflecting some light back and we therefore built another, unwanted, resonator and accordingly saw additional modes in the FPI signal. To overcome this problem we installed an optical isolator inbetween the grating and the optical fiber.
Another measurement device we used to characterize the ECDL was a grating spectrometer (SPEX 1404). This allows us to determine the www.advancedsciencenews.com www.pss-a.com wavelength of the laser, but due to the resolution of only 7 pm we cannot verify single-mode behavior of our ECDL.