A partially and a highly antireflection coated broad area laser are operated in an external cavity Fourier-optical 4f set-up to experimentally investigate transverse mode selection. The external cavity consists of a lens and a spatial frequency filter. Running freely the lasers show non-stationary filamentation. Placing the spatial filter unit directly onto the optical axis gives cw fundamental mode operation and a transverse shift of the spatial filter in the plane of the active region allows for selective excitation of higher order modes.
© Optical Society of America
The optical output power of semiconductor lasers is limited by catastrophic optical damage (COD) of the laser facet. Therefore, laser diode arrays (LDA) or broad area lasers (BAL) having emitter widths of 50 µm or more are commonly used in high power applications. However, their performance is limited due to the strong non-linear interaction of the optical field with the active semiconductor medium. This leads to spatio-temporal instabilities [1, 2]. Both for LDAs and BALs various schemes for stabilizing and controlling the laser output have been investigated by different groups. In the case of LDAs the laser emission is stable when the single emitters are uncoupled, i.e. sufficiently far separated . For coupled devices various free space external cavity configurations were used to achieve diffraction limited single-lobed laser output [4–6].
In BALs the non-linear processes cause filamentation giving rise to a non-uniform nearfield intensity distribution leading to a double-lobed farfield. Approaches for controlling and stabilizing the emission of BALs included, for example, the modification of the laser facet by means of photolithography [7, 8]. Further, free space set-ups such as junction heating of the laser facet  and phase conjugate optical feedback  have shown their ability to stabilize the output of BALs. Only studied theoretically yet is a Fourier-optical like 4f set-up consisting of a lens and a flat mirror . It was shown that by magnifying the laser beam returning into the laser, higher order modes are discriminated and fundamental mode operation is achieved. Hess et al.  modeled an external cavity employing a convex mirror in an unstable resonator configuration where the laser output beam is fan-like reflected back into the laser. The simulations revealed that a narrow single-lobed output might be obtained. By a corresponding experimental set-up the authors of this contribution proved that this resonator configuration is indeed capable of stabilizing the emission of BALs .
The objective of this paper is to present an alternative Fourier-optical approach to transverse mode control and stabilization of filamentation in BALs. Our concept incorporates a Fourier-optical 4f free space set-up with a spatial frequency filter unit. Usually in high power applications fundamental mode operation of BALs corresponding to a single-lobed farfield is required. On the other hand, a certain emission pattern might be desired, for example, for coupling the emission of BALs into fiber arrays. The external resonator configuration investigated here allows not only for cw fundamental mode operation but also for selective excitation of higher order modes in BALs. Further, an integrated optical solution of this set-up is proposed, where the laser chip and the optical components are hybridly combined on one substrate.
2. Selective excitation of higher order modes
2.1 Fourier-optical 4f set-up
As sketched in Fig. 1, a lens L1 performs an exact Fourier-transform of the field distribution in its front focal plane into its back focal plane, the so called Fourier plane. The field distribution in this plane is identical to the farfield distribution. It consists of the spatial frequency spectrum of the initial field distribution.
High spatial frequencies, far away from the optical axis, correspond to fine structures in the initial field distribution. Placing a spatial filter into the Fourier plane the spatial frequency spectrum can easily be manipulated. When the Fourier-transform is repeated by another lens L2, i.e. an inverse transform is carried out, an inverse image of the original object is obtained in its back focal plane. This configuration is called a 4f set-up (2f1+2f2).
2.2 Experimental set-up
Two different BALs are investigated in the external cavity shown in Fig. 2 (not drawn to scale). In this configuration the output facet of the BAL is placed into the front focal plane of a lens with focal length f. A reflecting spatial filter unit is placed in its back focal plane (Fourier plane). The filter unit consists of an adjustable slit of width d perpendicular to the active layer and an adjoining mirror (R≈98%). The unit can be shifted laterally in the plane of the active layer. This configuration is a Fourier-optical 4f set-up (2f plus reflection) but folded about the Fourier-plane (filter plane) by use of the reflecting filter. The fundamental Gaussian like mode of the waveguide formed by the active region has a 1/e half width of w 0 on the output facet. After being Fourier-transformed by the lens the fundamental mode has a width in the Fourier plane of 
where λ is the laser wavelength. Further, in the sense of Fourier-optics the fundamental mode has the lowest spatial frequencies closest to the optical axis. Matching the slit width d to the width 2w and aligning the spatial filter unit onto the optical axis the emission of the BAL should be stabilized onto the fundamental mode. Higher spatial frequencies specifically corresponding to higher order modes are not coupled back into the laser. Thus, higher order modes experience higher losses and should not be excited.
Conversely, by shifting the spatial filter away from the optical axis higher order modes should be preferentially emitted.
A partially antireflection (AR) coated (R<10-5) 655 nm AlGaInP 250mW BAL  and a highly AR coated 811 nm AlGaAs 1:2WBAL are studied in the folded Fourier-optical 4f set-up. The threshold current (Ith) of the partially AR coated BAL is measured to be 400mA. The 811 nm BAL without AR coating showed a threshold current of 410mA. The onset of lasing within the external cavity depends on the excited mode order and slit width. Therefore, all pump currents (Ip) stated in the experiments with the highly AR coated BAL are normalized to the threshold current of the uncoated laser. Both BALs have an emitter size of 1 µm×100 µm and a highly reflection coated (R>95%) back facet. Antireflection coated lenses having a focal length of f=25:54mm in the case of the 655 nm BAL and f=22:30mm in the case of the 811 nm BAL are used. The nearfield and farfield intensity patterns of the BAL output are simultaneously monitored with a CCD camera.
2.3 Experimental results
Shown in Fig. 3 are scans of the nearfield (left) and farfield (right) intensity patterns of the partially AR coated 655 nm BAL for different slit positions in the Fourier-plane.
The scans are obtained from the CCD images presented in Fig. 4. The right hand side of Fig. 4 depicts the corresponding spatial filter position, where b is the distance of the middle of the spatial filter from the optical axis. The pump current is set to Ip=1.025Ith. The free running BAL shows the common filamentation (uppermost scans in Fig. 3). When the filter unit is aligned onto the optical axis with the slit width adjusted to 291 µm an almost Gaussian like nearfield and farfield distribution is obtained. This is illustrated in the 2nd scan from the top in Fig. 3 and the first image of Fig. 4. The filter unit can be shifted up to 85 µm away from the optical axis while the nearfield and farfield distributions still remain Gaussian-like. Shifting the slit further away from the optical axis higher order modes up to the 6th order mode (with seven intensity maxima) can be selectively excited when the slit is moved to the right (Fig. 3 and 4). By deliberately coupling back the appropriate spatial frequency the laser is stabilized on the matching mode. Filamentation in the sense of an unpredictable break-up of the laser field is overcome. The corresponding farfields exhibit the common broadening when higher order modes are excited. As can be seen from Figs. 3 and 4 the intensity of the filaments is not equally distributed along the laser facet. It is higher either on the left or right side of the active region depending on the direction of the slit movement. This asymmetry might indicate an only partial coupling of the excited filaments since the feedback is provided by a narrow slit on one side of the optical axis only. In Fig. 5 the number of nearfield intensity peaks is plotted against the filter position at different slit widths. As expected a V-shaped symmetric plot is found since the spatial frequencies are symmetric to the optical axis. It turns out that a variation of the slit width between 159 µm and 326 µm has only minor influence on the filtering. It is only the mode corresponding to the spatial frequency at the very center of the slit that is excited.
Due to the poor AR coating of the 655 nm BAL the influence of the external resonator diminishes at pump currents above 1.025Ith. The internal resonator provides enough feedback to cause a break-up of the laser field. Placing the highly AR coated 811 nm BAL into the 4f cavity selective excitation of higher order modes is possible up to pump currents as high as 2.1Ith. Probably due to an inhomogeneity of the laser active layer of this specific BAL sample it is impossible to excite a fundamental mode. Nevertheless, as shown in Fig. 6, higher order modes up to the 15th order mode can be selectively excited.
3. Integrated optical 4f set-up
The major drawback of a free space Fourier-optical 4f set-up is its lack of mechanical stability. Therefore, we propose a hybrid integrated optical approach. The laser chip and the optical components are to be combined on one substrate. The substrate material is glass. As depicted in Fig. 7 (not drawn to scale) the BAL is butt-coupled to a spin-on polymer waveguide, namely bencocyclobutene (BCB). BCB is chosen for its low losses and relative ease of technology. The Fourier-transform is performed by a sputtered TiO2 film lens (f typically 1 cm). A Au stripe is deposited at the waveguide edge for accomplishing both filtering and optical feedback. A metalization under the BAL chip is required for bonding and heat dissipation.
Free running BALs are subject to unpredictable filamentation. A Fourier-optical 4f (2f plus reflection) external resonator has proven its capability of controlling and stabilizing the filamentation of BALs. Fundamental mode operation is obtained when the filter unit is aligned onto the optical axis. Moreover, deliberate excitation of higher order modes is achieved when the filter unit is shifted in the plane of the active region. A very good AR coating of the BAL facet facing the external resonator is essential for selective excitation of higher order modes at high pump currents.
For the sake of mechanical stability and compactness a hybrid integrated optical solution of the Fourier-optical 4f set-up is proposed.
The authors wish to thank R. Wallenstein for providing the 811 nm BAL and Dow Chemical for samples of BCB (Cyclotene™).
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