1. Introduction

Laser beam pattern shaping is an essential optical technology. This concept was already presented for structured illumination in 1960’s [1] and spread to a wide range of applications, such as super-resolution microscopy [2] and three-dimensional metrology [3]. If the target beam pattern is well-defined, the desired far-field pattern (FFP) can be projected by a combination of a laser light source and appropriately designed diffractive optical elements (DOEs). However, this requires delicate optical coupling, which can hinder the compactness and robustness of the optical system. Thereby other approaches in which patterned light is generated directly from a compact semiconductor cavity have been proposed [4,5]. In this context, “integrable spatial-phase-modulating surface-emitting lasers” (iPMSELs), which we have proposed [6,7], are promising semiconductor lasers that utilize the band edge mode of two-dimensional (2D) photonic crystals (PCs) as an in-plane resonator, while the spatial phase of the lightwaves of the band edge mode are simultaneously modulated in a holographic manner by a local positional shift of holes from their lattice points. So far, we have demonstrated that static arbitrary 2D beam patterns can be emitted from needle-tip-sized semiconductor lasers [6] and clarified the origin of the beam patterns theoretically [7].

Although iPMSELs can generate arbitrary beam patterns, the target beam patterns (1st-order beam) had accompanying subsidiary beam patterns, including a spot beam in the surface-normal direction (0th-order beam) and a symmetric beam pattern against the surface-normal direction (−1st-order beam). In previous work, we clarified the origin of these beam patterns in two types of positional shift methods, the circular (Fig. 1(b)) and the linear (Fig. 1(c)) shift methods, and demonstrated the capability to suppress the −1st-order beam [7]. Meanwhile, with respect to the 0th-order beam, it was concluded that the 0th-order beam can be eliminated when only specific positional shifts of holes are given in both positional shift methods. For example, this was achieved when the shifted radius was r = 0.38a in the circular shift method, where a is lattice constant of the virtual 2D PC, and the maximum shifted distance was $L=a/\sqrt{2}$ in the linear shift methods. However, both positional shift methods require rather large positional shifts of the holes, which causes a significant high threshold current. Thereby, an alternative approach is desired for suppressing the 0th-order beam.

 

Fig. 1 Schematic of (a) device structure and positional shift of holes in iPMSELs, Note that output plane is virtual plane where target beam patterns are designated on it. (b) circular shift method (in this work), (c) linear shift method.

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First, the 0th-order beam is the part of the band edge modes that is diffracted vertically without spatial phase modulation. In fact, this is caused by the difference of the spatial phase distribution between the ideal and actual phase shifts. Thus, a promising approach for removing the 0th-order beam is to utilize a structure where the vertical diffraction of the band edge modes is prohibited. For this purpose, we set the period of a virtual 2D PC structure from the conventional Γ₂ band edge to the M₁ band edge, where vertical diffraction is prohibited. In this case, the target beam pattern can be emitted vertically by imposing an additional spatial phase modulation that cancels the in-plane wavevector of the band edge modes at the M₁. This approach was proposed by Noda et al. in modulated photonic-crystal surface-emitting lasers, which achieved two-dimensional beam-steering [8,9]. We applied this idea to iPMSELs that project static arbitrary 2D beam patterns to remove a spot beam in the surface-normal direction.

In following sections, we begin with a discussion of the device structure. Then, the principle for removing the 0th-order beam from the output beam patterns are discussed, and experimental FFPs in which we successfully removed 0th-order beam are presented.

2. Device structure of iPMSELs

The device structure of an iPMSEL is shown in Fig. 1. The fundamental device structure is similar to that of previous work [6,7], except for the phase-modulating layer, which is described in a later section. Here, a brief description of the device structure is given. As shown in Fig. 1, an 2 μm n-AlGaAs cladding layer, 180 nm InGaAs/AlGaAs active layers, and 280 nm GaAs layer are grown by metal-organic chemical vapor epitaxy (MOCVD). The phase-modulating layer was formed on the GaAs layer using electron-beam lithography and dry etching. Then, a 2 μm p-AlGaAs cladding layer and a 150 nm p-GaAs contacting layer were grown by regrowth of MOCVD, and p and n electrodes were formed. The p-electrode made contact with the contacting layer in a 250 μm square at the center, while the n-electrode had a 500-μm square window that was coated by a SiN anti-reflection layer. Here, the lasing wavelength λ was designed to 940 nm. When injecting the electrical current, the laser light generated in the active layer was scattered by the phase-modulating layer and the target beam patterns were output through the window of the n electrode.

3. Principle of eliminating 0th-order beam in iPMSELs

In this section, we discuss the output beam of the iPMSELs and explain the principle used to remove the 0th-order beam from the output beam. The relationship between the lightwaves of the band edge mode and output beam patterns are discussed at first, and the origins of several beam orders are presented. Then, we compare the conventional iPMSELs based on the Γ₂ band edge, which accompanies 0th-order beam in the surface-normal direction, and iPMSELs based on the M₁ band edge, in which the 0th-order beam is not emitted vertically. In the case of the M₁ band edge, the additional phase shift that is required to output the target beam pattern vertically is also discussed. Finally, we explain the phase-modulating layer used in this work. For a detailed description of photonic band edge modes, information on the diffraction of a 2D PC at the band edges of Γ₂ and M₁ is given in Appendix A, which provides the basis for the operation of photonic-crystal surface-emitting lasers (PCSELs) [10,11].

3.1 Spatial phase modulation of the band edge mode in iPMSELs

It is reasonable to treat the wavevectors of the lightwaves of the band edge mode of the iPMSELs as being the same as that of an ordinary 2D PC, based on the assumption that hole shifts are negligible. On the other hand, since the target beam patterns of the iPMSELs extend into angular space two dimensionally, unlike PCSELs, the wavevectors of the band edge modes also extend in wavevector space. Moreover, the spatial phase of the lightwave of the band edge mode is modulated in a holographic manner by a positional shift of holes when the beam patterns are emitted from the cavity without any additional scattering. Therefore, the ideal spatial phase distribution of the output lightwave in a particular direction of the band edge mode of iPMSELs can be expressed in the form

 

Fig. 2 Output beam of iPMSELs from a lightwaves of the band edge mode include 0th-order beam, 1st-order beam, and −1st-order beam.

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3.2 Output beam of iPMSELs at Γ₂ band edge

In conventional iPMSELs, at the Γ₂ band edge where the lattice constant a equals a wavelength λ, the vertical diffraction of the lightwave of the band edge mode should be considered since there is no additional in-plane scattering when the beam patterns are emitted out of the plane. The in-plane component of the wavevector ${\overrightarrow{k}}_B$ is zero in this case. Then, the actual phase distribution of the lightwave of the band edge mode that contribute to the output beam patterns are simply expressed in the form

 

Fig. 3 The output beam patterns of iPMSELs in the Γ₂ band edge.

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3.3 Output beam of iPMSELs at Μ₁ band edge

In the case of the M₁ band edge where the lattice constant a is set to $\lambda /\sqrt{2}$, vertical diffraction is prohibited, unlike the Γ₂ band edge. In this case, the actual spatial phase distribution is expressed as

 

Fig. 4 (a) Schematic of the output beam patterns of iPMSELs in the Μ₁ band edge of an ordinary structure. The solid arrow indicate the target lightwave of band edge mode while the other dashed arrows indicate the other lightwaves of band edge modes. Although only one of the output beam patterns are shown for visibility, every lightwaves emit the similar beam patterns in the other directions. (b) The additional phase shift at each of the holes that cancels the wavevector of the lightwaves of the band edge mode. (c) The output beam with the additional phase shift. Bright red arrow indicate the lightwaves of band edge mode for 1st order beam, while dark red arrow indicate that of −1st order beam.

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3.4 Design of the phase-modulating layer

Here, we discuss the phase-modulating layer referred to briefly in the second section. The following procedures are based on previous work [7] except for the procedure at the M₁ band edge described in the previous section.

At first, we defined target images, as shown in Fig. 5(a), which include characters. Note that the central angle from surface-normal direction and angular width of “ABCD” in X and Y directions were approximately set to (20°, 20°) and (9°, 9°), respectively. Then, the images were converted via the inverse Fourier transform operation to a complex electromagnetic (EM) field in the device plane, which is called the near field pattern (NFP). To define the local positional shift of the holes, the argument of the EM field, which is the phase distribution ϕ(x,y), was extracted. In order to output the 1st-order beam pattern vertically, the additional shift ${\varphi }_c\left(x,y\right)=\sqrt{2}\pi /\lambda \left(x+y\right)$, which cancels in-plane wavevector of the lightwave of the band edge mode ${\overrightarrow{k}}_M=-\sqrt{2}\pi /\lambda \left(\begin{array}{ccc}1& 1& 0\end{array}\right)$, was added to the phase distribution ϕ(x,y). Thus, the positions of the holes were shifted according to the total phase distribution ϕ(x,y) + ϕ_c(x,y). The resulting phase distributions are also shown in Fig. 5(b), which clearly exhibit mosaic-like patterns, features of the M₁ band edge. In this work, circular shift methods were utilized for the positional shift method (Fig. 1(b)). The shapes of holes were octagons whose lattice constants and filling factors were 200 nm and 25%, respectively. Note that the lattice constants were shortened by a square root 2 from that of conventional iPMSELs at the Γ₂ band edge, which is typically around 280 nm. The shifted radius r was set to 0.08a. The phase-modulating layer was set in a 250 μm square under the p contact.

 

Fig. 5 (a) Target beam patterns. (b) The designated phase distribution. (Inset shows the magnified images.)

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4. Lasing characteristics and discussion

As a proof of concept, we measured the lasing characteristics of iPMSELs based on the M₁ band edge. Detail of the measurement were written in Appendix B. The devices were operated under room temperature pulsed operation.

Figure 6(a) shows the light-current characteristics of the iPMSELs. Here the threshold current I_th and slope efficiency SE were 0.31 A and 0.11 W/A, respectively. Note that we also measured the iPMSELs whose shifted radius r is 0.04a without any other structural changes under same operational condition which showed threshold current and slope efficiency of 0.25 A and 0.07 W/A, respectively. Note that output power were sum of ± 1st order beam without 0th order beam, in contrast to conventional iPMSELs based on Γ₂ band edge [6]. Here, threshold current density J_th were 0.40 kA/cm² for r = 0.04a and 0.50 kA/cm² for r = 0.08a. As shown here, threshold current increased by increasing the positional shift of holes r. This is intuitively understood by that the positional shift of holes disturb the formation of band edge mode. However, it should be notify that since typical threshold of conventional PCSEL was ~0.5 kA/cm² [11], the severe increase of threshold of iPMSEL have not observed within such small r. It should be also notified that when increasing the pattern size, namely the size of phase modulating layer (250 μm square in this work), the spatial resolution increases since the point of holes, namely point of data, increase. On the other hands, the threshold current also increases as enlarging the pattern size. Thereby, there is tradeoff between threshold current and pattern size as similar to that between threshold current and spatial resolution.

 

Fig. 6 Lasing characteristics of iPMSELs under room temperature, (a) light-current characteristics, (b) lasing spectrum at 0.5 A, (c) FFP at 0.5 A.

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The lasing spectrum was shown in Fig. 6(b). The peak wavelength and full width of half maximum (FWHM) were 930.10 nm and 0.02 nm, respectively. The peak wavelength was 10 nm shorter than the designated wavelength. This might be attributed to mismatch of lattice constant a. Meanwhile the FWHM was almost same as the resolution of the optical spectrum analyzer. Since the weak side peaks were observed around the main peak, multimode lasing might be occurred. However the main peak was dominant at the laser emission.

The experimental FFPs of the iPMSELs are shown in Fig. 6(c). The center angle from surface-normal direction and angular width of “ABCD” in X and Y directions were observed as (18.8°, 17.6°) and (9.5°, 9.5°), respectively. This results were agree with the designated values. The central spot beam in the surface-normal direction, which is observed in conventional iPMSELs based on the Γ₂ band edge, was successfully removed from the output beam patterns.

For conventional iPMSELs based on the Γ₂ band edge, it is also possible to eliminate a central spot beam by separating the optical path from the target beam patterns in the case of off-axis beam patterns that do not include the surface-normal direction. However, this enlarges and complicates the total optical system. Meanwhile, in the case of on-axis beam patterns that include the surface-normal direction, conventional iPMSELs are unable to separate the optical path of a central spot beam and target beam patterns. The technique of the iPMSELs based on the M₁ band edge addresses the issues of both of on-axis beam patterns and off-axis beam patterns.

5. Conclusion

We successfully removed a spot beam in the surface-normal direction from the 2D output beam patterns of iPMSELs. To achieve this, we utilized the M₁ band edge instead of the conventional Γ₂ band edge and introduced an additional spatial phase shift that canceled the components of the in-plane wavevectors of the lightwaves of the M₁ band edge mode. We measured the FFPs of 2D beam patterns without a 0th-order beam from the output beam patterns. The technique in this work is not only useful for making the intensity of the beam pattern including surface-normal directions uniform, but also for improving the power efficiency of the target beam patterns because the wasteful vertical diffraction of the band edge modes are not presented in Μ₁ band edge. We believe the technique used in this work will open new paths for various practical applications, such as structured illumination or 3D sensing.

Appendix A Diffraction of 2D PC structure at band edge Γ₂ and Μ₁

In the case of a square lattice 2D PC [12,13] in the Γ₂ band edge, the lattice constant a equals a wavelength λ. The 2D PC structures in real space and wavevector space are shown in Fig. 7(a), 7(b) and 7(c). Here, the wavevectors of the lightwaves of the band edge modes k_Γ1-k_Γ4, whose magnitudes are 2π/λ, are defined in terms of the wavelength as follows,

(10)$$k_{\Gamma 1}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}1& 0& 0\end{array}\right),$$

(11)$$k_{\Gamma 2}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}0& 1& 0\end{array}\right),$$

(12)$$k_{\Gamma 3}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}-1& 0& 0\end{array}\right),$$

(13)$$k_{\Gamma 4}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}0& -1& 0\end{array}\right).$$

while the reciprocal lattice vectors G_Γ1 and G_Γ2, whose magnitudes correspond to 2π/a, are expressed as

(14)$$G_{\Gamma 1}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}1& 0& 0\end{array}\right),$$

(15)$$G_{\Gamma 2}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}0& 1& 0\end{array}\right).$$

Since diffraction occurs in the directions of the vector sum between the wavevector of the incident lightwave and the reciprocal lattice vectors, these lightwaves of the band edge mode are coupled via reciprocal lattice vectors together with the conservation law of wavevectors. In addition, the wavevectors k_Γ1-k_Γ4 are diffracted in the surface-normal direction where in-plane components of the wavevectors are zero, as shown in Fig. 7(c). Note that these wavevectors are defined as follows

(16)$$k_{\Gamma 5}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}0& 0& 1\end{array}\right),$$

(17)$$k_{\Gamma 6}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}0& 0& -1\end{array}\right).$$

This is the principle of surface emission in PCSELs in the Γ₂ band edge.

 

Fig. 7 The photonic crystal structure at the band edge Γ₂ in (a) real space and (b) wavevector space. (c) Perspective view of wavevector space. Vertical diffraction also occurs. The black arrows indicate in-plane lightwaves of band edge mode, while red arrows indicate reciprocal lattice vectors. The blue arrow indicate vertical diffraction.

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For the M₁ band edge of a square lattice 2D PC, the lattice constant a along the X and Y directions decreases to $\lambda /\sqrt{2}$, which means that the length of a diagonal of the 2D PC corresponds to a wavelength λ. Figures 8(a) and 8(b) show the 2D PC structure based on the M₁ band edge in real and wavevector space, respectively. Here, the wavevector of the lightwaves of the band edge mode k_M1-k_M4 are expressed as follows,

(18)$$k_{{\rm M}1}=\frac{\sqrt{2}\pi }{\lambda }\left(\begin{array}{ccc}1& 1& 0\end{array}\right),$$

(19)$$k_{{\rm M}2}=\frac{\sqrt{2}\pi }{\lambda }\left(\begin{array}{ccc}-1& 1& 0\end{array}\right),$$

(20)$$k_{{\rm M}3}=\frac{\sqrt{2}\pi }{\lambda }\left(-\begin{array}{ccc}1& -1& 0\end{array}\right),$$

(21)$$k_{{\rm M}4}=\frac{\sqrt{2}\pi }{\lambda }\left(\begin{array}{ccc}1& -1& 0\end{array}\right),$$

while the reciprocal lattice vectors G_M1 and G_M2 are

(22)$$G_{{\rm M}1}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}\sqrt{2}& 0& 0\end{array}\right),$$

(23)$$G_{{\rm M}2}=\frac{2\pi }{\lambda }\left(\begin{array}{ccc}0& \sqrt{2}& 0\end{array}\right).$$

Since it not possible to make the in-plane components of the wavevectors of the lightwaves of the band edge mode equal zero by adding any reciprocal lattice vectors, vertical diffraction is prohibited in the M₁ band edge. Therefore, the band edge modes are diffracted in the device plane, so that the M₁ band edge is not utilized in PCSELs in the usual case.

 

Fig. 8 The photonic crystal structure at the band edge Μ₁ in (a) real space and (b) wavevector space. The black arrows indicate in-plane lightwaves of band edge mode, while red arrows indicate reciprocal lattice vectors.

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Appendix B Measurement of lasing characteristics

In this section, we described the methods of measuring the lasing characteristics include light-current characteristics, lasing spectrum, and FFP.

All of the measurements were carried out under room-temperature (25 °C) pulsed operation by using a pulsed current source (ILX Lightwave, LDP-3830) and a Peltier controller (Daitron, DPC-100) where pulse width and duty were 50 ns and 5%.

The output power was measured by using a photodiode with ND filter (Ophir, PD-300-3W), a measurement software (Ophir, Starlab) which is connected to the photodiode via a USB interconnect (Ophir, Juno). In the setting of measurement software, we set” wavelength”, “range”, and “filter” as “930 nm”, “Auto”, and “In”. The photodiode was placed approximately 1~2 mm from the emission plane of the device to capture all of the output beam patterns. The peak output power was calculated by simply divided the averaged power by the duty.

The lasing spectrum was measured by using an optical spectrum analyzer (Yokogawa, AQ6373) and single mode fiber (Optron science, SM98PKSP). The setting parameters of the optical spectrum analyzer “sens”, “average”, “span”, and “resolution” were “High3”, “2”, “4 nm”, and “0.02 nm” respectively. The lasing spectrum were acquired by the optical spectrum analyzer through the single mode fiber. The pulsed current was set at 0.5 A.

The FFP was acquired by using a CCD camera (Hamamatsu Photonics, ORCA-05G), an FFP optics (Hamamatsu Photonics, A3267-12), and beam profiler (Hamamatsu Photonics, Lepas-12). The iPMSELs were put in front of the FFP optics connected to the CCD camera. Appropriate neutral density filter (Hamamatsu Photonics, A7659-01) was inserted to prevent the saturation of the CCD camera. The exposure time was optimized and averaged eight times at the measurement. The pulsed current was set at 0.5 A.

Acknowledgments

The authors are grateful to A. Hiruma (President), T. Hara (Director), M. Yamanishi (Research Fellow), K. Takizawa, M. Niigaki, Y. Yamashita, K. Nozaki, T. Takemori, H. Toyoda, T. Hirohata, and T. Edamura of HPK for their encouragement throughout this work and A. Higuchi and M. Hitaka for their assistance with the epitaxial growth. This work was supported in part by the innovative Photonics Evolution Research Center (iPERC) in Hamamatsu, in scheme of COI STREAM of MEXT, Japan.

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