Analysis of spatial emission structures in vertical-cavity surface-emitting lasers with feedback from a volume Bragg grating

We investigate the spatial and spectral properties of broad-area vertical-cavity surface-emitting lasers with frequency-selective feedback by a volume Bragg grating. We demonstrate wavelength locking similar to the case of edge emitters but the spatial mode selection is different from the latter. On-axis spatial solitons obtained at threshold give way to off-axis extended lasing states beyond threshold. The investigations focus on a self-imaging external cavity. We analyze how deviations from the self-imaging condition affect the pattern formation and a certain robustness of the phenomena is demonstrated.

Figure 1

Experimental setup. A, aperture; BS, beamsplitter; CCD1, CCD camera in the near-field image plane of the vertical-cavity surface-emitting laser (VCSEL); CCD2, CCD camera in the far-field image plane of the VCSEL; HWP, half-wave plate; M, mirror; OSA, optical spectrum analyzer; PD, photodiode; VBG, volume Bragg grating.

Figure 2

Near-field intensity distribution of the VCSEL showing (a) spontaneous emission at $I=200$ mA (at a temperature of $70{}^{\circ }\mathrm{C}$) without feedback (this and all other images in this article depict the intensity on a linear gray scale, with black denoting high intensity); (b) the VCSEL without feedback, $I=490\mathrm{mA}$ at $T=16{}^{\circ }\mathrm{C}$; (c) the VCSEL with feedback from a plane mirror, where $I=185\mathrm{mA}$ at $T=70{}^{\circ }\mathrm{C}$. Note that the slight nonhomogeneous behavior of the spontaneous emission (decrease in intensity from the upper left to the lower right) is due to the detection setup.

Figure 3

Near-field intensity distribution of the VCSEL with feedback from a VBG at different currents. Left column, $D_3$ at the self-imaging distance; center columns, $D_3$ too short or too large by 4 mm; right column, feedback with a plane mirror.

Figure 4

Near-field intensity distribution of the VCSEL with feedback from a VBG (a), (b), and a plane mirror (c). (a), (c), $I=450$ mA; (b) $I=550$ mA.

Figure 5

Far-field intensity distribution of the VCSEL with feedback from a VBG at different currents. Left column, $D_3$ at the self-imaging distance; center columns, $D_3$ too short or too large by 4 mm; right column, feedback with a plane mirror.

Figure 6

Solid black line: frequency shift of one mode of the VCSEL with feedback from a VBG ($M=6.25$). Solid green (light gray) line: feedback from a plane mirror. Dashed blue (gray) line: free-running laser (FRL) at $69{}^{\circ }\mathrm{C}$. Solid red (dark gray) line: fit to the FRL.

Figure 7

Mechanism for selecting the transverse wavenumber. ${\omega }_{\mathrm{g}}$, grating frequency; ${\omega }_{\mathrm{c}1}$, VCSEL frequency at low current; ${\omega }_{\mathrm{c}2}$, VCSEL frequency at higher current; ${\omega }_{\mathrm{c}3}$, VCSEL frequency at high current.

Figure 8

Effect of the magnification $M$ on the dispersion curve of the VBG. $M\approx 6$ corresponds to the short cavity, whereas $M\approx 15$ corresponds to the long cavity. $\Delta \omega$ corresponds to a frequency shift between ${\omega }_{\mathrm{g}}$ and the emission frequency.

Figure 9

Solid black line: frequency shift of the VCSEL with feedback from a VBG ($M=15.6$). Dashed blue (light gray) line: FRL at $16{}^{\circ }\mathrm{C}$. Solid red (gray) line: fit to the FRL.

Figure 10

Transverse wave number of the emission versus detuning between emission wavelength and longitudinal resonance (crosses represent data points; solid lines, fits). These plots are produced from plots of the wave number $q$ vs the current $I$ by finding the intersect $I_0$ and the scaling exponent $s$ using a fitting function, $q\left(I\right)=c{(I-I_0)}^s$. The intercept $I_0$ then corresponds to the zero detuning condition. Starting from that, the rate of 0.0035 nm/mA is applied as a coefficient to define the detuning scaling, which is used to plot the fitting (red) curve. (a) For $D_2=70.5$ mm, leading to a scaling exponent $s=0.502$; (b) for $D_2=78$ mm, leading to a scaling exponent $s=0.479$.

Figure 11

Solid (black) line: scaling exponent vs. $D_2$. Dashed (blue) line: thickness of the ring in the far field vs $D_2$.

Figure 12

Scaling exponent as function of $D_3$. The zero position indicates the self-imaging position and a negative sign means that the VBG is moved toward the telescope. Inversely, a positive sign means that the VBG is moved away from the focusing lens.