**5.2 AR μ-PL diagram**

Pumped by the YVO4 pulse laser and the He-Cd CW laser, the measured dispersion diagrams at Г1 mode are observed as shown in Fig. 19. Around Г1 mode, the dash lines represent the simulated photonic band diagram by PWEM. The stimulated emission of the lasing phenomenon from the devices provided by the PhC in-plane resonance routes can be observed by a YVO4 pulse laser in Fig. 19(a). The PhC laser shows the vertical emission near the normal direction from the sample surface. However, the diffracted lines in this figure cannot be observed clearly because of high intensity of laser peaks. Thus, the diffracted emissions are measured by a He-Cd CW laser with a lower pumping intensity from the PCSEL devices. Therefore, the diffracted pattern can be observed more clearly in the measured dispersion diagram shown in Fig. 19(b). In this figure, the transverse upward curving lines derived from the Fabry-Perot effect provided by the device structure and modulated by the interference of the DBR layers. The electric field propagating in the PhC structure could be described as a Bloch mode: *E*(*r*) = Σ*G EG*×exp [*i*(*k//* + *G*)•*r*] to explain the observed diffraction patterns caused by a PhC nanostructure, where *E<sup>G</sup>* is the electric field component corresponding to harmonic reciprocal lattice vector *G*, and *k//* is the in-plane wave vector of the Bloch mode. The reciprocal lattice in K space is a 2-D PhC triangular lattice rotated by 30° with respect to the direct lattice in real space. The reciprocal lattice vectors can be written as: *G* = *q*1*K*1+ *q*2*K*2, where *q*1 and *q*2 are integers, and *K*1 and *K*2 are the two reciprocal lattice basis vectors. Harmonics of the Bloch mode are extracted if their inplane wave vectors are within the light cone: |*k//* + *G*| < *k*0, where *k*0 is defined as 2π/*a*.

In Fig. 19(b), there are several groups with different slopes of diffraction lines in the dispersion diagram. Different dispersion modes of the diffraction lines with different slopes can be well matched to calculated photonic band diagrams shown as dashed lines by PWEM. The parallel diffraction lines with the same slope represent different guide modes in the in-plane direction. By comparing the Fig. 19(a) with Fig. 19(b), the lasing actually occurs at the third guided mode near the Г1 band edge.

In Fig. 20, the measured AR μ-PL diagrams of another PCSEL device with different PhC structure near the K2 modes along the Γ-K direction are measured. By using YVO4 pulse laser pumping, Fig. 20(a) reveals the lasing peaks in the AR μ-PL diagram. Besides, the AR μ-PL diagram is shown in Fig. 20(b) pumped by a CW He-Cd laser. In the figure, the

Section 5.1 shows the transformation method from angular-resolved measurement data to the AR μ-PL diagrams. In Section 5.2, the AR μ-PL diagrams and the divergence angles of

After measurements by the angular-resolved measurement system, we transformed the AR μ-PL spectrums to obtain the guided modes dispersion relation (reduced frequency *u*=Λ/λ<sup>0</sup> as y-axis versus in-plane wave vector, *k*//, as x-axis) by the relation *k*//= *k*0\**sinθ*. In addition, each wavelength, *I*PL(*õ*), is normalized relatively to its integrated intensity14. The normalized AR μ-PL diagram reveals the clear dispersion relation of guided modes and detaily figures

Pumped by the YVO4 pulse laser and the He-Cd CW laser, the measured dispersion diagrams at Г1 mode are observed as shown in Fig. 19. Around Г1 mode, the dash lines represent the simulated photonic band diagram by PWEM. The stimulated emission of the lasing phenomenon from the devices provided by the PhC in-plane resonance routes can be observed by a YVO4 pulse laser in Fig. 19(a). The PhC laser shows the vertical emission near the normal direction from the sample surface. However, the diffracted lines in this figure cannot be observed clearly because of high intensity of laser peaks. Thus, the diffracted emissions are measured by a He-Cd CW laser with a lower pumping intensity from the PCSEL devices. Therefore, the diffracted pattern can be observed more clearly in the measured dispersion diagram shown in Fig. 19(b). In this figure, the transverse upward curving lines derived from the Fabry-Perot effect provided by the device structure and modulated by the interference of the DBR layers. The electric field propagating in the PhC structure could be described as a Bloch mode: *E*(*r*) = Σ*G EG*×exp [*i*(*k//* + *G*)•*r*] to explain the observed diffraction patterns caused by a PhC nanostructure, where *E<sup>G</sup>* is the electric field component corresponding to harmonic reciprocal lattice vector *G*, and *k//* is the in-plane wave vector of the Bloch mode. The reciprocal lattice in K space is a 2-D PhC triangular lattice rotated by 30° with respect to the direct lattice in real space. The reciprocal lattice vectors can be written as: *G* = *q*1*K*1+ *q*2*K*2, where *q*1 and *q*2 are integers, and *K*1 and *K*2 are the two reciprocal lattice basis vectors. Harmonics of the Bloch mode are extracted if their inplane wave vectors are within the light cone: |*k//* + *G*| < *k*0, where *k*0 is defined as 2π/*a*.

In Fig. 19(b), there are several groups with different slopes of diffraction lines in the dispersion diagram. Different dispersion modes of the diffraction lines with different slopes can be well matched to calculated photonic band diagrams shown as dashed lines by PWEM. The parallel diffraction lines with the same slope represent different guide modes in the in-plane direction. By comparing the Fig. 19(a) with Fig. 19(b), the lasing actually occurs

In Fig. 20, the measured AR μ-PL diagrams of another PCSEL device with different PhC structure near the K2 modes along the Γ-K direction are measured. By using YVO4 pulse laser pumping, Fig. 20(a) reveals the lasing peaks in the AR μ-PL diagram. Besides, the AR μ-PL diagram is shown in Fig. 20(b) pumped by a CW He-Cd laser. In the figure, the

**5. Angular-resolved optical characteristics at different band-edge modes** 

Г1, K2, and M3 modes are introduced.

out the relative excitation and out-coupling efficiency.

at the third guided mode near the Г1 band edge.

**5.1 Data normalization** 

**5.2 AR μ-PL diagram** 

Fig. 19. The measured AR μ-PL diagram near the Г1 mode ((a) pumped by YVO4 pulse laser; (b) pumped by He-Cd laser), the dash lines represent the calculated photonic band diagram.

Fig. 20. The measured AR μ-PL diagram near the K2 mode ((a) pumped by YVO4 pulse laser; (b) pumped by He-Cd laser). The dash lines represent the calculated photonic band diagrams.

diffracted lines can be observed and well matched to the calculated 2-D TE-like photonic band diagram, by using parameters of *r*/*a* = 0.285, *a* = 210 nm, *nb* = 2.560, *na* = 2.343, and *neff* = 2.498 for calculation shown as the dash lines in Fig. 20. In addition, the experiment results show the lasing beam emission angle of about 29 degree off from the normal along the Γ-K direction, which is exactly matched to the estimated value of about 30 degree derived in the previous section. Furthermore, we measured another PCSEL devices exhibited characteristics of M3 band edge mode along the Γ-M direction. The measured dispersion diagrams pumped by a YVO4 pulse laser and a He-Cd CW laser are shown in Fig. 21(a) and (b), respectively. The lasing peaks can be clearly seen in Fig. 21(a). The diffracted patterns can be observed in Fig. 21(b) and well matched by using parameters of *r*/*a* = 0.204, *a* = 230 nm, *nb* = 2.617, *na* = 1.767, and *neff* = 2.498. Shown as the dash lines in Fig. 21, the emission angle of lasing beam was about 59.5 degree off from the normal along the Γ-K direction, which was also quite matched to one of the estimated values of about 61.87

Angular-Resolved Optical Characteristics and Threshold

**6. Conclusion** 

generation.

**7. Acknowledgment** 

**8. References** 

6951.

in part, by the National Science Council in Taiwan

Gain Analysis of GaN-Based 2-D Photonics Crystal Surface Emitting Lasers 19

In the chapter, the optical pumped of GaN-based 2-D photonic crystal surface emitting lasers (PCSELs) with AlN/GaN distributed Bragg reflectors (DBR) are fabricated and measured. The laser has a 29-pair bottom DBR which plays the role of a low refractive index layer to enhance the coupling between photonic crystal (PhC) nanostructure and electrical field in the whole cavity. Therefore, the lasing action can be achieved in the optical pumping system. Each of these laser devices emits only one dominant wavelength between 395 nm and 425 nm.That normalized frequency of PhC lasing wavelength can be well matched to these three band-edge frequencies (Γ1, K2, M3) indicated that the lasing action can only occur at specific band-edges. In the angular-resolved μ-PL (AR μ-PL) system, the diffracted lines in the AR μ-PL diagrams of PCSEL devices can be further matched to the calculated 2- D TE-like photonic band diagram calculated by PWEM. These three band-edge frequencies (Γ1, K2, M3) have different emission angles in the normal direction of about 0, 29, and 59.5 and are further confirmed by the Bragg theory. The divergence angles of the (Γ1, K2, M3) modes are about 1.2, 2.5, and 2.2. Moreover, according to multiple scattering method (MSM), the resonant mode frequencies will approach to band edge frequencies compared with plane wave expansion method (PWEM). In addition, the threshold gain of four resonant modes varies with the filling factor. This result shows that the proper hole filling factor can control the PhC mode selection. Finally, all of these calculation and experiment results indicate that GaNbased PCSELs could be a highly potential optoelectronic device for lasers in the next

The authors would like to gratefully acknowledge A. E. Siegman at Stanford for his fruitful suggestion. The study was supported by the MOE ATU program, Nano Facility Center and,

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degree derived in the previous section. The reason that only one emission angle was obtained could be due to the fact that we only measured the AR μ-PL diagram along one Γ-M direction.

Fig. 21. The measured AR μ-PL diagram near the M3 mode ((a) pumped by YVO4 pulse laser; (b) pumped by He-Cd laser). The dash lines represent the calculated photonic band diagrams.

Each of PhC band-edge modes exhibited specific emission angle by different type of wave coupling mechanism in Fig. 19(a), Fig. 20(a), and Fig. 21(a). Finally, Fig. 22 shows the divergence angles of Γ1, K2, and M3 band-edge modes on the normal plane from the sample surface. The lasing emission angles are about 0, 29, and 59.5, and the divergence angles of laser beams are about 1.2, 2.5, and 2.2 for (Γ1, K2, and M3) band edge modes, respectively. Due to the alignment difficulties in the AR μ-PL system, the measured emission angles might have some offset values of about 1 to 2.

Fig. 22. The emission angles and divergence angles of Γ1, K2, and M3 band-edge modes on the normal plane from the sample surface.
