1. Introduction

Many experiments in Atomic Physics, particularly those involving laser cooling, require relatively high powers of narrow linewidth (≃1MHz) tunable laser light. Historically, researchers have made use of dye or Ti:sapphire lasers. These requirements are now often satisfied by diode lasers due to their relative low cost, reliability, and ease of use [1].

The major limitation of diode lasers in such applications is their relatively low output power. Achieving narrow linewidth light typically requires optical feedback for passive stabilization and favors the use of “single-mode” diode lasers, with an output facet sufficiently small that the diode only oscillates in a single transverse mode. However, to avoid the risk of output facet damage, the small front facet size also limits the output power of such diodes to less than 100 mW. In contrast, for the Lithium laser-cooling experiment we are constructing, approximately 200 mW of 671 nm laser power is desired. “Multi-mode” diodes with larger front facets can achieve higher powers, but at the expense of a broad, multi-mode spectrum. At present, the spectral bandwidth narrowing of a BAL using optical feedback from a grating is limited by the multi-mode transverse structure to several GHz [2].

A variety of power amplification techniques can be used to mitigate the power limitations of single-mode diode lasers. In a Master-Oscillator Power Amplifier (MOPA), a narrow linewidth “master” laser is stabilized and locked to the desired wavelength, and power from the master laser is run through amplification stages. A common practice is the use of a tapered amplifier, a gain-mediumwaveguide into which the master laser is coupled and is amplified as it propagates. While now available, 671 nm tapered amplifiers were not manufactured at the time of this work. Instead, the technique described here is based on double-pass amplification through a multi-mode “Broad Area Laser” (BAL) diode, with highly rectangular front facet dimensions of 150 µm by 1 µm.

In BAL double-pass amplification (see Fig. 1), narrow linewidth seeding light is injected into the BAL gain medium. The injected light competes with the laser’s “free-running” modes, suppressing the BAL’s normal lasing behavior, and after two passes through the BAL (reflecting once off the rear facet) it emerges as an amplified beam. The light is injected at an angle, to spatially separate the amplified output beam from the BAL’s intrinsic output in the far field.

 

Fig. 1. Schematic of double-pass amplification

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BAL amplification has been used at a variety of wavelengths, including the wavelength of interest (671 nm) [3]. Detailed descriptions of the technique are available, documenting both successful [4] and unsuccessful [5] attempts to construct amplifiers. A common thread between these previous attempts is the critical role played by the front facet reflectivity of the BAL [4]. It has been asserted that if a BAL’s front-facet reflectivity is too high, injected light cannot compete with the diode’s free-running modes, and amplification becomes impossible [5]. BAL diodes intended for use as amplifiers therefore must be given anti-reflection (AR) coatings to reduce their front facet reflectivity.

The importance of antireflection coating for the stability and control of single-mode diode lasers has been studied extensively, and has been shown to enhance the mode hop free tuning range. The development of high quality AR coatings for diode lasers has made possible the commercialization of tunable diode lasers [6, 7, 8, 9].

The upper bound on front facet reflectivity allowing amplification in a BAL is experimentally unstudied. While previous BAL amplification papers give estimates of front facet reflectivity and occasionally cite a high reflectivity as the cause of failure of the technique [5], the reflectivity values given in these papers were provided by the manufacturers, not measured. For the diodes discussed in this report, these provided reflectivity values were estimates which were found to be inconsistent with our measurements. For example, one diode was estimated by the manufacturer to have a reflectivity of 11%, while our measurements indicated 4.6±0.4%. This discrepancy may arise from uncontrolled coating process variations, or from the difference [10] between plane-wave reflectivity and the modal reflectivity measured in this report.

A technique for measuring diode front facet reflectivity based on the threshold-current vs. external feedback [10] is generalized, for the first time, to multi-mode diodes. The technique is applied to 3 differently coated BALs. The amplification ability of these BALs is also assessed [11], leading to the conclusion that a front facet reflectivity of less than 4.6% is necessary for BAL amplification.

2. Front facet reflectivity

2.1. Measurement method options

Front facet reflectivity of a laser diode cannot be measured simply by shining a light source at the laser and measuring the reflected power. It would be difficult to align the incoming beam with the active region of the laser and difficult to distinguish between reflection from the front and back facets of the diode. Furthermore, the plane-wave reflectivity of the AR coating that such a technique would measure actually differs from the reflectivity experienced by a guided mode inside the laser [10].

Thus, it is necessary to use a reflectivity measurement technique in which light is generated inside the laser diode itself. One such technique, first described in [12], is based on an examination of fine structure in the output spectrum of the laser diode when operated below threshold, to determine the diode’s Fabry-Pérot modulation depth. This modulation depth is a measure of the finesse of the laser cavity, which in turn is a measure of the facet reflectivities.

There are problems applying this method to measure BAL front-facet reflectivity. Due to its multi-transverse-mode nature, the output spectrum of a BAL varies spatially throughout its output beam due to the differing propagation constants of the different transverse modes. If a measured spectrum includes multiple transverse modes, their averaged spectra has an artificially reduced modulation depth. This results in an underestimate of the front facet reflectivity [13]. In principle it may be possible to isolate a single transverse mode to circumvent this problem. Instead, an alternate technique [10] was used here and is based on introducing additional optical feedback from a known external reflectivity to the diode.

2.2. The threshold vs. external feedback model

The reflectivity measurement method used in this work involves fitting a BAL’s threshold current vs. external reflectivity to a simple model, with front facet reflectivity as a fit parameter. The model was first presented in [10]. A short derivation is presented below.

Giving a laser feedback with an external mirror of a known reflectivity is equivalent to modifying the laser’s front facet reflectivity to some effective reflectivity (which may in principle be frequency dependent). Ignoring interference effects (following the work of [10]), the effective reflectivity for the power (or field intensity) incident on the front facet from inside the laser is given in Eq. 1, and is depicted diagrammatically in Fig. 2.

 

Fig. 2. Diagrammatic Derivation of R _eff.I represents the optical power (or field intensity) incident on the front facet

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The threshold condition for lasing in the absence of R _ext is that round trip gain and losses are equal,

where G is a gain coefficient and α is an absorption coefficient. The gain coefficient is dependent on diode current and details of the diode geometry and composition and for a quantum well laser can be modeled by: [14, 10]

Here I denotes the electric current supplied to the laser diode, and the onset of population inversion occurs for currents above the transparency current, I ₀. Combining Eq. 2 and Eq. 3 yields a relationship between threshold current and front facet reflectivity.

where we have assumed that R ₁=1. When external feedback is applied to the diode, R ₂ is replaced by the effective reflectivity R _eff from Eq. 1. If a reference threshold current I ^ref _th is measured with some applied reference external reflectivity R ^ref _ext, then a formula for threshold currents at other external reflectivities is obtained, where device-dependent coefficients other than R ₂ have been absorbed into the unitless coefficient g.

2.3. Using the model

The output optical power versus diode current is measured for each device under investigation at a range of external feedback reflectivities. The linear regions of these characteristic curves are extrapolated to the current axis, and the intercepts are taken as their threshold currents. The reference reflectivity R ^ref _ext is generally the highest R _ext used. R _ext was varied between 0.1% and 25%. A non-linear least squares fit, varying the parameters g and R ₂, is used to fit Eq. 5 to a plot of ln $\left(\frac{I_{\mathrm{th}}}{I_{\mathrm{th}}^{\mathrm{ref}}}\right)$ vs.ln $\left(\frac{R_{\mathrm{ext}}^{\mathrm{ref}}}{R_{\mathrm{ext}}}\right)$.

In the limit where R ₂≪R _ext (here R ₂≪1 so that 1-R ₂≃1), this plot is a line with slope g. In the limit where R ₂≫R _ext, the threshold current approaches the constant no-feedback value, and thus the plot is a flat line. The transition between the two regimes occurs when R ₂≈R _ext.

2.4. Limitations of the model

While convenient and simple, the model presented above has a number of limitations which must be addressed. The model assumes the diode is lasing on a single transverse mode. As a BAL supports multiple transverse modes, care must be taken to align the feedback mirror such that it only feeds back into the TEM00 mode. A procedure for this is discussed below.

Another possible limitation is that the reflectivity model neglects interference effects. In principle the external mirror and the front facet form a Fabry-Pérot cavity, with a frequency dependent reflectivity (the reflected field phase and amplitude may vary). If this reflectivity is averaged over the free spectral range of the external cavity, a reflectivity closely approximating the simple model in Eq. 1 is obtained. Such an averaging is perhaps justifiable if the coherence length of the laser is shorter than the external cavity length (1 m). We observed no evidence that the external reflectivity was sensitive (interferometrically) to the exact length of the external cavity. Moreover, previous work on single mode diodes [10], in which a piezo-electric transducer was used to change the external cavity length by small amounts, also observed no change in threshold current when the cavity length was varied, and suggests that the simplified expression is justified.

2.5. Experimental method

The reflectivities of three different BAL diodes were measured using the technique described above. Diode A (LDX-2815-680) was a double quantum well device with a step-index waveguide, producing about 870 mW of light at 682 nm (when driven with a current of 1.5 A). Diode B and Diode C were from the same wafer, and featured a single quantum well structure and a graded index waveguide (the LDX-2815-665 but with a non-standard coating). Diode B generated 580 mW of light at 664 nm, while Diode C produced only 94 mW at 662 nm (both driven with a current of 1.5 A). Each device was nominally rated for 800 mW, however, they each received different coatings from the standard coatings for these commercial lasers [15]. The output powers were all measured at a stabilized temperature near room temperature.

The reflectivity measurement set-up is depicted in Fig. 3. The BAL diodes were mounted in a custom-machined housing, driven by aWavelength Electronics MPL-2500 current controller, and temperature-stabilized using a Wavelength Electronics LFI-3751 temperature controller and a Peltier cooler. An aspheric f=4.5 mm lens collimated the BAL’s fast axis and produced a focus in the slow axis which was then collimated with a f=150 mm cylindrical lens.

A high reflectivity (R>99.9%) dielectric-coated mirror was set up normal to the optical axis in order to provide external feedback. This created an external cavity ~1 m long. A Thorlabs linear variable density filter (NDL-25C-2) was placed between the mirror and BAL housing and allowed precise control of the feedback over 4 decades. Optical power measurements were made at several points throughout the setup to determine the transmissivities of each element, using a Newport 818-SL photodetector, 883-SL attenuation plate, and the 1825-C Power Meter.

 

Fig. 3. Reflectivity measurement set-up

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Each measurement began with installing a BAL in the housing, and adjusting the collimating and cylindrical lenses until the beam’s focus was at the external mirror. The external mirror was adjusted to feed the BAL’s light back by minimizing the threshold current. To achieve the necessary sensitivity for this adjustment, the BAL was modulated through a small current range near its threshold current, while the output power was monitored on an oscilloscope. The current range was adjusted so that the BAL would only lase when there was substantial feedback.

When varying the horizontal angle of the feedback mirror, there were a number of distinct positions for which the method described above exhibited feedback induced lasing. This was due to feedback into the various transverse modes of the BAL. For the consistency in the reflectivity measurements, it was important to always feed back only into the TEM₀₀ mode of the multi-transverse-mode BAL, and thus to select the position which gives feedback into this mode. The mirror position for feedback into the TEM₀₀ was distinguished in two ways. First, it yielded a characteristic curve near threshold which exhibited a higher slope efficiency than other lasing modes selected at other mirror positions. Second, it was the central horizontal position (at which feedback induced lasing occurred) of symmetrically distributed positions which came in pairs with similar threshold currents and slope efficiencies.

Once the mirror alignment was optimized, the current range was changed to the full range used in data capture. The variable attenuator stage was moved through the working range while monitoring the shape of the characteristic curve, to ensure that steering or alignment changes during the motion did not give rise to feedback into other transverse modes. The presence of feedback into the wrong modes was indicated by deviations from a clean threshold turn-on in the characteristic curve, or by mode hop discontinuities in the curve. Each item in the beam path was aligned to eliminate accidental feedback into additional modes.

The optical output power vs. diode current was then measured at different linear stage positions. Typically around 40 data points were captured. The attenuation at each stage position was calibrated by measuring power before and after the attenuator. Using an analysis routine written in MATLAB, the threshold current was determined for each power vs. current curve. A corresponding external reflectivity for each curve was then calculated, based on the calibration data at each linear stage setting. Finally, a 2-parameter least-squares fit of Eq. 5 was performed to determine R ₂.

 

Fig. 4. Power vs. current curves, at varying external reflectivity

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2.6. Experimental limitations

External reflectivities R _ext for different variable attenuator positions were determined by taking the square of the transmissivities of each of the components in the optical path. However, other factors which influence R _ext such as alignment and aberrations, could only be determined indirectly.

The feedback alignment procedure gave consistent results (the optimal threshold current varied by less than 0.1%), and therefore we believe it is good at providing an optimal placement of the collimating lenses so that the mirror is exactly in the plane conjugate with the output facet. From the measured changes in threshold current with a given reduction in the external feedback, we infer that the coupling efficiency of the reflected beam back into the guided mode inside the BAL is not significantly limited by alignment.

Diffraction and aberrations can also limit the coupling. However, the limits imposed by the external mirror and cylindrical lens were negligible since the spot size was only weakly converging (diverging) and more than an order of magnitude smaller than the optic in each case. From measurements of the BAL’s beam divergence, we infer that the diffraction loss at the first collimating lens is less than 0.1%. Since this aspheric collimating lens is designed to provide diffraction limited imaging, we expect that aberrations also do not significantly limit the coupling.

2.7. Reflectivity results

As described above, power vs. current curves at varying external reflectivities were captured for the BAL diodes under investigation. An example data set is presented in Fig. 4. The darker blue regions indicate the linear portions of the traces used to determine threshold currents, and the red points are the extrapolated threshold currents.

Data sets for each of the tested diodes are presented along with the fits to the model in Fig. 5, Fig. 6 and Fig. 7. The vertical error bars in these plots are determined from the uncertainty in the fitted threshold current whereas the horizontal error bar in these plots originate from our uncertainty in the measured transmissivities.

 

Fig. 5. Reflectivity determination for diode A. R _ext varying from .06 to 19%. The fit resulted in g=0.096±0.007, and R ₂=12.7±1% The vertical error bars are determined from the uncertainty in the fitted threshold current whereas the horizontal error bar in these plots originate from our uncertainty in the measured transmissivities.

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Front facet reflectivity determinations for diodes A, B, and C were 12.7±1%, 4.6±0.4%, and 1.2±0.2% respectively, with g values of 0.096±0.007, 0.092±0.004, 0.106 ±0.008. A section of data was excluded from the fit to the model for diode B and is plotted as red crosses in Fig. 6. At these values of the feedback (R _ext was near the front facet reflectivity) the characteristic curves did not exhibit a clean threshold. We attribute this to unwanted feedback into different transverse modes and therefore removed these data from the analysis.

The uncertainty of the fitted parameters was estimated using a Monte Carlo simulation in which a family of data sets is generated by randomizing each data about its measured value. The random offsets are generated according to a normal distribution with standard deviation equal to the uncertainty at the data point. Each of these randomized data sets is fit to the model, and a set of parameter values is obtained whose average and standard deviation is calculated. The values reported for the reflectivity and for g were produced by the optimal fit to the progenitor data set whereas the uncertainty in these parameters is provided by the standard deviation of the Monte Carlo determined parameters.

Deviations of the data from the best fit by more than their uncertainty is observed. These deviations may be due to alignment variations as the variable attenuator was moved. In addition, there may be subtle physical effects not accounted for in the model. For the purposes of accounting for these variations in our determination of the reliability of the reflectivity fit, we uniformly increased the error bars, σ_i, of the data so that the normalized ${\chi }^2=\frac{1}{N}{{\displaystyle \sum \left(\frac{{\Delta }_i}{{\sigma }_i}\right)}}^2$ was equal to 1. Here, N is the number of data points, and Δi is the residual at point i. These scaled uncertainties were those used in the Monte Carlo simulation.

 

Fig. 6. Reflectivity determination for diode B. R _ext varying from .07 to 25%. The fit resulted in g=0.092±0.004, and R ₂=4.6±0.4%. The points in the center region (denoted by red crosses) deviate significantly from the model. At these values of the feedback (R _ext was near the front facet reflectivity) the characteristic curves did not exhibit a clean threshold and were therefore were excluded from the fit.

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Fig. 7. Reflectivity determination for diode C. R _ext varying from .06 to 6%. The fit resulted in g=0.106±0.008, and R ₂=1.2±0.2%.

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Fig. 8. Amplification Optics Layout

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3. Amplification

The method used to measure the amplification of BAL diodes (based largely on [4]) is discussed below. Greater detail is available in [11].

3.1. Amplification setup

As discussed earlier, BAL amplification is a Master-Oscillator Power Amplification scheme. A diagram of the amplification setup is provided in Fig. 8. The set-up consisted of a narrow linewidth master, an injection locked slave, a BAL for amplification, an instrumentation set-up, and associated optics.

The master laser was a Lumex 50 mW diode. It output approximately 12 mW of narrow linewidth, single-mode light at 671 nm, after being heated to 42 °C, grating-stabilized, and optically isolated. The master’s light was injected into an identical diode, which served as an intermediate injection-locked slave amplifier, boosting power available for BAL seeding to approximately 20 mW.

Shaping of the seed beam was necessary for optimal coupling into the BAL, which was accomplished using a f=400 mm plano-convex lens and a 4x expanding (horizontal) anamorphic prism pair. A f=150 mm cylindrical lens was used to both adjust the injection angle, and to horizontally collimate the BAL. Finally, an apheric f=4.5 mm collimating lens (with 3 translational degrees of freedom) was placed directly in front of the BAL to collimate its fast axis. These lenses were identical to the ones used in the reflectivity setup, and the BAL was mounted in the same custom-machined housing used for reflectivity measurements, and operated with the same current and temperature controllers as described before.

A fraction of the BAL’s output beam was directed to a CCD camera for observation. When a BAL was successfully seeded, the CCD camera revealed a marked suppression of amplified spontaneous emission in transverse modes other than the one being seeded. The amplified light was “picked off” by a small mirror after it was sufficiently spatially separated from the seed beam, and measured with a photodetector and power meter.

 

Fig. 9. Amplified BAL output power versus injected seed power at 665 nm

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3.2. Amplification results

The three BAL diodes discussed in Section 2.5 (Diodes A, B, and C) were tested as amplifiers.

BAL Diode A had a free-running wavelength of approximately 682 nm. Despite attempts to cool the diode and inject with slave light at 671 nm, no amplification could be observed. Unlike the other measured diodes, diode A did not even exhibit a shift in its threshold current when seeded.

BAL Diode B had a free-running wavelength of 664 nm. Using seeding light at 665 nm, the power in the picked-off output beam was measured as a function of seed beam power, at a variety of injection angles and BAL currents. BAL Diode B never put out more power than it was seeded with; it was not a useful amplifier.

BAL Diode C exhibited the best performance of the three. Figure 9 shows a plot of amplified output power versus seed power. At the highest current, approximately 180 mW of locked output power was obtained from 20 mW of seed power at a wavelength of 665 nm. Initially seed light at 665 nm was used, since this nearly matched the BAL’s free-running wavelength of 662 nm. Later, once favorable results had been obtained, seed light at 670.5 nm was used with similar results.

After switching to 670.5 nm seed light, and with further adjustments to the injection parameters, a gain of 10 times for BAL Diode C was ultimately obtained. With 14 mW of seed power, 140 mW of locked output power was obtained at 670.5 nm. The spectrum of the amplified output was compared to the seed beam spectrum using a Fabry-Pérot (FP) interferometer, and no difference between the two spectra was observed within the 10 MHz resolution of the FP.

The final output power from BAL Diode C was limited by how much power the slave could produce. As the BAL was not the limiting factor, this suggests that injecting with a more powerful slave could produce even greater locked output powers. Work is currently underway investigating this, however, 140 mW is sufficient to proceed with atomic trapping experiments using the BAL amplifier system. For further information on this and other BAL amplifiers, see [3, 4, 11]

4. Conclusions

A reflectivity measurement method was generalized for use on multi-mode BAL diodes. The reflectivities of three similar BAL diodes with differing front facet reflectivities were measured. The amplification abilities of these diodes were also accessed. Based on both sets of measurements, we find that a front facet reflectivity of less than 4.6% is necessary for a BAL diode to function as an amplifier.

The authors are indebted to Igor Shvarchuck for detailed discussions regarding BAL amplification. The authors would also like to thank Harold Davis and Jon Nakane for helpful guidance, Dean Micke of RPMC providing a set of differently coated BAL devices, and Jeff Morris of LDX Optronics, the maker of our BAL chips, for useful discussions. This work was supported by the Natural Sciences and Engineering Research Council of Canada and by the Canada Foundation for Innovation.