Abstract

We report a high-contrast metastructure (HCM) mirror as a novel beam-shaping element for vertical-cavity surface-emitting lasers (VCSELs). The metastructure is monolithically integrated as a part of the VCSEL, working both as a microelectromechanical tunable mirror and output beam shaper. While providing broadband, high reflection to support lasing of the VCSEL, its angular transmission characteristics can be tailored to shape the angular profile of the output beam. Various far-field emission patterns are demonstrated for single-mode, 1550 nm VCSELs with different HCM designs. We further demonstrated two-faced VCSELs with different mode profiles from their two mirrors, for the first time, to the best of our knowledge. This bifunctional integrated metastructure opens new avenues to engineer a VCSEL’s emission properties, and shows great promise for applications that desire highly compact emitters integrated on a chip to provide versatile functionalities.

© 2018 Optical Society of America

Vertical-cavity surface-emitting lasers (VCSELs) are key light sources in optical communications, with the advantages of low power consumption, low packaging costs, and ease of fabrication into arrays for wafer-scale testing [1]. Mode-hop-free, continuous, fast, and widely tunable VCSELs enabled by microelectromechanical structures (MEMS) provide an ideal solution for the emerging swept-source optical coherence tomography (SS-OCT) as well as lidar applications [25]. The key advantage of a VCSEL is explicitly its emission from the top surface. Compared with edge emission, this not only optimizes the laser beam shape, but also greatly improves the coupling efficiency into fibers and grating couplers. It also opens up opportunities for beam shaping with integrated optical elements, such as collimators, deflectors, splitters, wave plates, planar lenses, and vortex beam generators. To date, all the demonstrated optical elements for such purposes are integrated onto a VCSEL’s top surface after the VCSEL is made, through an extra step of fabrication, often with complicated processes [615]. The complexity in the structure and fabrication process makes it challenging to achieve good coupling efficiency between a VCSEL and the optical element or a desirable beam quality. Here we demonstrate, for the first time, to our knowledge, that the beam shaping of a VCSEL can be concurrently fulfilled by its laser outcoupling mirror—a freely standalone high-contrast metastructure (HCM). The HCM is monolithically integrated with the VCSEL, enabled by straightforward fabrication processes. The HCM has a subwavelength period, and works as a broadband high-reflection mirror to support lasing of the VCSEL. Meanwhile, its angular-dependent transmission coefficient directly modulates the Fourier component of the spatial profile of the output beam, and thus its far-field profile. This dual functionality further benefits from the rich design space of the HCM, and its capability of monolithic integration. It shows promise for applications that desire VCSEL emitters with highly integrated and versatile functionalities.

The VCSEL cavity is composed of an HCM working as the top mirror, an active region with multiple quantum wells, and a stack of distributed Bragg reflectors (DBRs) as the bottom mirror. Here, we chose one-dimensional high-contrast grating (HCG) [16] as the HCM, which is suspended in air and microelectromechanically actuated, facilitating the tuning of the laser cavity length and thus the laser wavelength. A single-mode, high-speed, tunable VCSEL emitting at 1550 nm has been previously demonstrated, incorporating HCG as the top tuning mirror. The wafer-scale proton implant process generates uniform laser apertures for the devices across the wafer, reducing the complexity in the study of beam-shaping characteristics here. Details of the laser structure, fabrication process, and laser performance can be found in [17,18]. Figure 1(a) shows the scanning electron microscopy (SEM) image of a typical HCG-VCSEL device, with a zoomed-in perspective of the fully suspended HCG mirror surrounded by air. Single-mode lasing of the VCSEL at 1550 nm is realized under continuous-wave (CW) operation up to 85°C, with output power reaching 2.4 mW at 15°C. Figure 1(b) exemplifies a lasing spectrum at 15°C, with side-mode suppression ratio (SMSR) of 45 dB.

 figure: Fig. 1.

Fig. 1. InP-based HCG-VCSEL emitting at around 1550 nm. (a) SEM image of a typical TE HCG-VCSEL device, with a zoomed-in view of the fully suspended HCG surrounded by air. (b) Spectrum and LIV characteristics of a typical TE HCG-VCSEL at 15°C, showing single-mode emission with SMSR of 45 dB, and an output power of 2.4mW. (c) Schematics of the HCG platform used in this study, InP-based HCG targeting at λ1550nm with oblique incidence angle θ with respect to the z axis and ϕ with respect to the x axis. (d) Transmission of HCG at Λ=1080nm for varying airgap a versus incidence angle θ at ϕ=90°, highlighting three designs with distinct angle-dependent transmission characteristics, including (e) Design I with a=490nm, (f) Design II with a=650nm, and (g) Design III with a=700nm, showing the angular dependence of transmission (blue curve) and reflection (red curve).

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The study here involves 1550 nm HCG-VCSELs of both TE-polarized and TM-polarized modes [16,17]. The high-reflection zone covers a wide range of dimensions for HCG period (ΔΛ50nm) and airgap width (Δa200nm) under TE- and TM-polarization modes, respectively. This endues HCGs with the degrees of freedom to manipulate output properties while maintaining single-mode lasing. The typical far-field pattern of a single-mode laser is a fundamental Gaussian. The angular dependence of the HCG’s transmission coefficient provides a novel approach to shape this far-field pattern. The schematics of an HCG are shown in Fig. 1(c), illustrating an incident beam coming at an angle θ with respect to the z axis and ϕ with respect to the x axis. We simulated the HCG transmission under a varying incidence angle θ at a fixed angle ϕ=90° for TE mode, using the rigorous coupled-wave analysis (RCWA) method [19]. The transmission of the HCG at Λ=1080nm with varying airgap size (a) versus incidence angle (θ) is plotted in Fig. 1(d), showing the regions where T<1%, thus R>99%, necessary for the lasing conditions to be met in a VCSEL structure. The transmission amplitude versus θ for three different airgaps is then extracted for comparison. For Design I in Fig. 1(e) with a=490nm, the transmission decreases with incidence angle, while Design II in Fig. 1(f) with a=650nm has its transmission increasing instead. However, for Design III in Fig. 1(g) with a=700nm, the transmission increases first then decreases with incidence angle, and vice versa for reflection. It is worth noting that while the reflection amplitude remains almost the same with varying incidence angle to guarantee lasing (e.g., decreasing from 99.9% to 99.5%), the transmission amplitude can change significantly (e.g., increasing by 5 times from 0.1% to 0.5%). This fascinating characteristic empowers HCGs with dual functions. On the one hand, it provides high reflection to maintain a fundamental Gaussian lasing mode oscillating inside the cavity. On the other hand, it serves as a transmission modulation plate, which manipulates the angular components of the outcoupling lasing mode, and thus the far-field emission pattern of the VCSEL.

We build an analytical model based on Fourier optics to design and analyze the far-field pattern of a single-mode VCSEL emission. Under Fraunhofer conditions, the far field (electric field) can be approximated as the Fourier transform of the near field (electric field). When the Fourier transform is performed upon a Gaussian beam in the near-field spatial domain, in Fourier domain it is equivalent to decomposing the Gaussian beam into a series of plane waves emitting at different angles. Thus the far-field pattern is a representation of the angular components of the beam in the near field. This is the key information to understand the method in this paper. As mentioned above, these angular components can be directly manipulated by the HCG. Figure 2 illustrates how the angular dependence of HCG transmission amplitude is translated into the distribution of far-field intensities. The Gaussian beam generated by a VCSEL laser aperture propagates from the near field to the far field. As shown in Figs. 2(a) and 2(b), without encountering any optical element, the Fourier transform of the Gaussian beam g0(x,y) at near field still remains a Gaussian shape in the far field, denoted as G0(kx,ky). This can be regarded as a decomposition into plane waves at different incidence angles (θ,ϕ), which are related to (kx,ky) through the following equations:

kx=k0·sinθ·cosϕ,
ky=k0·sinθ·sinϕ,
k0=2π/λ,
where θ is the angle between the incident beam and the z axis, ϕ is the angle between the incident beam and x axis, k0 is the wave vector of the incident beam, and λ is the wavelength. G0(kx,ky) is primarily controlled by the laser aperture size and wavelength. Now that the Gaussian beam goes through an HCG before reaching the far field, if the transmission amplitude of the HCG is uniform across all incidence angles, the Gaussian beam will not be influenced. However, if the transmission amplitude of a particular HCG design has strong variance across the range of incidence angles, such an amplitude filtering factor T(kx,ky) will be superimposed upon the angular components of G0(kx,ky) to modulate the beam shape, resulting in the new far-field as
GF(kx,ky)=G0(kx,ky)·T(kx,ky).

 figure: Fig. 2.

Fig. 2. Process of far-field emission pattern manipulation with HCG design. (a) The emitted Gaussian light source in spatial domain as g0(x,y). (b) The far-field (E-field) of the Gaussian source, approximated as the Fourier transform of g0(x,y), expressed as G0(kx,ky). (c) The transmission amplitude of HCG versus angles (θ,ϕ). (d) The angular distributed HCG transmission in (c) converted into Fourier domain as T(kx,ky). (e) The resulting far-field intensity distribution denoted as |GF(kx,ky)|2. The example case here shows an HCG with transmission amplitude lower in the center than on the sides, thus yielding a double-lobe far-field pattern instead of Gaussian shape. All figures are calculated with a normalized intensity scale bar as shown in the upper right.

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Figure 2(c) exemplifies an HCG whose transmission T(θ,ϕ) varies largely with incident angles (θ,ϕ), mapping to the Fourier domain as T(kx,ky) in Fig. 2(d). For this particular HCG design, the angular-dependent transmission generates a modulated far-field distribution with intensity on the side higher than the center, resulting in a double-lobe shape. The camera captures the field intensity as |GF(kx,ky)|2, shown in Fig. 2(e). This design paradigm manipulates the far field using the angular transmission amplitude of a spatially uniform HCG, which is in contrast with the commonly used strategy where the HCG is spatially chirped to manipulate the near-field phase pattern of the transmission. The latter method can be found in the literature [20,21], where planar lenses are designed with HCGs as optical phase elements under external plane wave illumination. In our method, the reflection phase of the HCG does not vary spatially, and the relative change of the reflectivity R over incident angle is small (R>99.5%). Thus the laser dynamics inside the cavity is not perturbed and it can keep a stable lasing wavelength. It is worth noting that, in a VCSEL environment, the Gaussian-shaped light source and the finite-sized HCG make far-field pattern design more challenging [22,23].

We applied this theory to analytically calculate the far-field patterns of different HCG designs. Independently, we performed 3D finite-difference time-domain (FDTD) simulation to obtain the far-field pattern of a finite-sized HCG under Gaussian beam illumination. A wide range of HCG dimensions are fabricated for both TE- and TM-polarization modes, demonstrating a large degree of freedom for our design method. We show four different examples with far-field patterns of Gaussian, double-lobe, triple-lobe, and "bow-tie" shapes (Fig. 3). Designs A and B are TE-mode HCGs, while designs C and D are TM-mode HCGs. The experimentally measured far-field patterns [Figs. 3(i)3(l)] all match quite well with the designs [Figs. 3(a)3(d)], calculated using the analytical method in Fig. 2, and the 3D FDTD simulation [Figs. 3(e)3(h)]. Line profiles of the far-field intensity along kx (at ky=0) are extracted and compared in Fig. S1 (Supplement 1). The deviation of the experimental data from the analytical calculations and FDTD simulations are mostly due to the asymmetric size and imperfect shape of the laser aperture, which could have a large impact on the divergence angle of the laser. In the applications that desire single-mode laser beams with Gaussian profile, it is noted that for both the TE and TM VCSELs we made, Gaussian beam outputs can be designed and have been realized with large fabrication tolerance. Taking the TE mode as an example, one of the good dimension ranges that can generate Gaussian beam lies in Λ10501100nm with a450570nm. Since the HCG characteristics are different based on its material index and thickness, it is suggested that our analytical model introduced above and the open-sourced HCG solver package [24] are used together to quickly calculate whether a specific HCG design can generate a Gaussian profile. Furthermore, the angular dependence of HCG reflectivity can also facilitate laser transverse mode control to improve single-mode laser yield [4], in the cases of non-ideal aperture size and shape.

 figure: Fig. 3.

Fig. 3. Far-field patterns for four HCG designs: Design A (Λ=1080nm,a=480nm), Design B (Λ=1060nm,a=680nm), Design C (Λ=710nm,a=180nm), and Design D (Λ=730nm,a=180nm), with the corresponding (a)–(d) calculated far-field intensity distributions using the analytical method in Fig. 2, plotted in an θϕ axis system; (e)–(h) simulated far-field intensity distributions using a 3D FDTD tool, plotted in an θϕ axis system; and (i)–(l) measured far-field intensity distributions from fabricated HCG-VCSEL devices based on the designed parameters, showing good agreements with the designed and simulated patterns. All figures are calculated with normalized intensity scale bars as shown in the center.

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All the HCG-VCSELs demonstrated here lase in a single optical mode, with an excellent SMSR exceeding 40 dB. To validate the single-mode emission, we thinned down the wafer substrate and collected laser emission from the backside of the device. We experimentally demonstrated that while the top-surface emission of a HCG-VCSEL can be manipulated by a large variety of HCG designs, the bottom-surface emission always remains a Gaussian shape through the bottom DBR mirror. A “two-faced” single-mode laser is then unveiled as in Fig. 4(a), generating bidirectional dual laser beams to double the functionalities. With the transmission characteristics tailored by emission angles, the HCG can act as a transmission modulation plate while being a high-reflection mirror supporting lasing. As illustrated in Fig. 4(b), HCG-VCSEL arrays can potentially be fabricated across the same wafer with various far-field patterns, including, but not limited to, single-lobe, double-lobe, triple-lobe, “bow-tie,” “sugar cone,” and “doughnut” shapes. Furthermore, by implementing this methodology on other HCM types, such as a 2D HCG structure [25], more far-field patterns with larger design freedom can be achieved in the future. This opens new applications requiring flexible laser beam shapes from a single integrated optoelectronic chip. For example, double-lobe or multi-lobe beams can be utilized as light sources in interference-based sensor systems [26], where the beams couple into multiple fibers or gratings directly to replace a beam splitter. This also represents a new method to generate an amplitude hologram. In biological imaging, such as brain imaging, such an integrated holographic optical element can be used to replace the traditional bulky spatial light modulator to generate multiple beamlets to simultaneously image different areas or planes [27]. Multi-pattern VCSEL arrays on a single chip can also work as a compact and low-cost light source in the optoelectronic tweezer system for particle trapping and cell manipulation [28]. In all these applications, a single integrated optoelectronic VCSEL array chip has the potential to replace the conventional laser source and bulky beam-shaping optical elements, leading to a much more compact system.

 figure: Fig. 4.

Fig. 4. VCSELs with versatile functionalities. (a) The cross section of a two-faced single-mode laser, with the top-surface beam shape manipulated by HCG designs while the bottom-surface beam remains a Gaussian shape, validating the single-mode lasing of the VCSEL. (b) HCG-VCSEL arrays emitting at single-mode but with various far-field emission patterns, including single-lobe, double-lobe, triple-lobe, “bow-tie,” “sugar cone,” and “doughnut” shapes. The device image is taken with a 3D confocal optical microscope, and the far-field patterns are captured with an IR camera for each individual device.

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In summary, we reported a novel beam-shaping scheme of the far-field pattern from a single-mode VCSEL using the unique transmission characteristics of an HCG mirror. This originates from the angular dependence of HCG transmission amplitude. The design of the far-field patterns is discussed, and both the simulation and experimental results are presented, which are all in excellent agreement. The HCG is proved to be a bifunctional optical element, which can act as an integrated tunable mirror as well as an integrated beam-shaping optical element. This is the first demonstration of these two functions being integrated on a single optical element. A single-mode two-faced laser is also shown, with the top-surface beam being shaped by various HCG designs, while the bottom-surface emission remains Gaussian shaped. This work opens up possibilities to design arbitrary far-field patterns directly from a VCSEL without the addition of any secondary optical element. We believe such versatile lasers integrated on a compact chip will be promising in the fields of interference-based sensing, biological imaging, particle trapping and cell manipulation, and much more beyond.

Funding

National Science Foundation (NSF) Center for Integrated Access Networks (CIAN) (ERC EEC-08120702); Tsinghua-Berkeley Shenzhen Institute; National Natural Science Foundation of China (NSFC) (61320106001).

Acknowledgment

We thank Dr. P. Qiao for fruitful discussions.

 

See Supplement 1 for supporting content.

REFERENCES

1. R. Szweda, III-Vs Rev. 19, 34 (2006). [CrossRef]  

2. C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 6, 978 (2000). [CrossRef]  

3. P. Qiao, K. Cook, K. Li, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 23, 1700516 (2017). [CrossRef]  

4. K. Li, C. Chase, P. Qiao, and C. J. Chang-Hasnain, Opt. Express 25, 11844 (2017). [CrossRef]  

5. W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015). [CrossRef]  

6. Y. Fu, IEEE Photon. Technol. Lett. 13, 424 (2001). [CrossRef]  

7. M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003). [CrossRef]  

8. J. Justice, P. Lambkin, B. Roycroft, and B. Corbett, Proc. SPIE5824605685 (2005). [CrossRef]  

9. C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010). [CrossRef]  

10. F. Koyama and X. Gu, IEEE J. Sel. Top. Quantum Electron. 19, 1701510 (2013). [CrossRef]  

11. V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015). [CrossRef]  

12. K. Tanabe, X. Gu, A. Matsutani, and F. Koyama, in Conference on Laser and Electro-Optics, OSA Technical Digest (2015), paper SW1F.2.

13. H. Li, D. B. Phillips, X. Wang, Y. D. Ho, L. Chen, X. Zhou, J. Zhu, S. Yu, and X. Cai, Optica 2, 547 (2015). [CrossRef]  

14. S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014). [CrossRef]  

15. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, Nat. Commun. 6, 7069 (2015). [CrossRef]  

16. C. J. Chang-Hasnain and W. Yang, Adv. Opt. Photon. 4, 379 (2012). [CrossRef]  

17. Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013). [CrossRef]  

18. C. Chase, Y. Rao, W. Hofmann, and C. J. Chang-Hasnain, Opt. Express 18, 15461 (2010). [CrossRef]  

19. M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. 71, 811 (1981). [CrossRef]  

20. F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, Opt. Express 18, 12606 (2010). [CrossRef]  

21. D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausolei, Nat. Photonics 4, 466 (2010). [CrossRef]  

22. A. Liu, W. Hofmann, and D. Bimberg, Opt. Express 22, 11804 (2014). [CrossRef]  

23. A. Liu, W. Zheng, and D. Bimberg, in Asia Communications and Photonics Conference (2016), paper AF2A.52.

24. W. Yang, P. Qiao, J. Qi, V. Wang, and C. J. Chang-Hasnain, “1D/2D high contrast grating solver package,” University of California, 2014, https://light.eecs.berkeley.edu/cch/hcgsolver.html.

25. P. Qiao, K. Li, K. T. Cook, and C. J. Chang-Hasnain, Opt. Lett. 42, 823 (2017). [CrossRef]  

26. R. G. Heideman and P. V. Lambeck, Sens. Actuators B 61, 100 (1999). [CrossRef]  

27. W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016). [CrossRef]  

28. P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005). [CrossRef]  

References

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  • |

  1. R. Szweda, III-Vs Rev. 19, 34 (2006).
    [Crossref]
  2. C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 6, 978 (2000).
    [Crossref]
  3. P. Qiao, K. Cook, K. Li, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 23, 1700516 (2017).
    [Crossref]
  4. K. Li, C. Chase, P. Qiao, and C. J. Chang-Hasnain, Opt. Express 25, 11844 (2017).
    [Crossref]
  5. W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015).
    [Crossref]
  6. Y. Fu, IEEE Photon. Technol. Lett. 13, 424 (2001).
    [Crossref]
  7. M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003).
    [Crossref]
  8. J. Justice, P. Lambkin, B. Roycroft, and B. Corbett, Proc. SPIE5824605685 (2005).
    [Crossref]
  9. C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
    [Crossref]
  10. F. Koyama and X. Gu, IEEE J. Sel. Top. Quantum Electron. 19, 1701510 (2013).
    [Crossref]
  11. V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015).
    [Crossref]
  12. K. Tanabe, X. Gu, A. Matsutani, and F. Koyama, in Conference on Laser and Electro-Optics, OSA Technical Digest (2015), paper SW1F.2.
  13. H. Li, D. B. Phillips, X. Wang, Y. D. Ho, L. Chen, X. Zhou, J. Zhu, S. Yu, and X. Cai, Optica 2, 547 (2015).
    [Crossref]
  14. S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
    [Crossref]
  15. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, Nat. Commun. 6, 7069 (2015).
    [Crossref]
  16. C. J. Chang-Hasnain and W. Yang, Adv. Opt. Photon. 4, 379 (2012).
    [Crossref]
  17. Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
    [Crossref]
  18. C. Chase, Y. Rao, W. Hofmann, and C. J. Chang-Hasnain, Opt. Express 18, 15461 (2010).
    [Crossref]
  19. M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. 71, 811 (1981).
    [Crossref]
  20. F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, Opt. Express 18, 12606 (2010).
    [Crossref]
  21. D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausolei, Nat. Photonics 4, 466 (2010).
    [Crossref]
  22. A. Liu, W. Hofmann, and D. Bimberg, Opt. Express 22, 11804 (2014).
    [Crossref]
  23. A. Liu, W. Zheng, and D. Bimberg, in Asia Communications and Photonics Conference (2016), paper AF2A.52.
  24. W. Yang, P. Qiao, J. Qi, V. Wang, and C. J. Chang-Hasnain, “1D/2D high contrast grating solver package,” University of California, 2014, https://light.eecs.berkeley.edu/cch/hcgsolver.html .
  25. P. Qiao, K. Li, K. T. Cook, and C. J. Chang-Hasnain, Opt. Lett. 42, 823 (2017).
    [Crossref]
  26. R. G. Heideman and P. V. Lambeck, Sens. Actuators B 61, 100 (1999).
    [Crossref]
  27. W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016).
    [Crossref]
  28. P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
    [Crossref]

2017 (3)

2016 (1)

W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016).
[Crossref]

2015 (4)

W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015).
[Crossref]

V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015).
[Crossref]

H. Li, D. B. Phillips, X. Wang, Y. D. Ho, L. Chen, X. Zhou, J. Zhu, S. Yu, and X. Cai, Optica 2, 547 (2015).
[Crossref]

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, Nat. Commun. 6, 7069 (2015).
[Crossref]

2014 (2)

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
[Crossref]

A. Liu, W. Hofmann, and D. Bimberg, Opt. Express 22, 11804 (2014).
[Crossref]

2013 (2)

F. Koyama and X. Gu, IEEE J. Sel. Top. Quantum Electron. 19, 1701510 (2013).
[Crossref]

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

2012 (1)

2010 (4)

C. Chase, Y. Rao, W. Hofmann, and C. J. Chang-Hasnain, Opt. Express 18, 15461 (2010).
[Crossref]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, Opt. Express 18, 12606 (2010).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausolei, Nat. Photonics 4, 466 (2010).
[Crossref]

C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
[Crossref]

2006 (1)

R. Szweda, III-Vs Rev. 19, 34 (2006).
[Crossref]

2005 (1)

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[Crossref]

2003 (1)

M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003).
[Crossref]

2001 (1)

Y. Fu, IEEE Photon. Technol. Lett. 13, 424 (2001).
[Crossref]

2000 (1)

C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 6, 978 (2000).
[Crossref]

1999 (1)

R. G. Heideman and P. V. Lambeck, Sens. Actuators B 61, 100 (1999).
[Crossref]

1981 (1)

Abada, S.

V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, Nat. Commun. 6, 7069 (2015).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, Nat. Commun. 6, 7069 (2015).
[Crossref]

Ball, A. J.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, Nat. Commun. 6, 7069 (2015).
[Crossref]

Bardinal, V.

V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015).
[Crossref]

C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
[Crossref]

Beausolei, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausolei, Nat. Photonics 4, 466 (2010).
[Crossref]

Beausoleil, R. G.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
[Crossref]

Bengtsson, J.

M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003).
[Crossref]

Bimberg, D.

A. Liu, W. Hofmann, and D. Bimberg, Opt. Express 22, 11804 (2014).
[Crossref]

A. Liu, W. Zheng, and D. Bimberg, in Asia Communications and Photonics Conference (2016), paper AF2A.52.

Cai, X.

Camps, T.

V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015).
[Crossref]

C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
[Crossref]

Carrillo-Reid, L.

W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016).
[Crossref]

Chang-Hasnain, C. J.

P. Qiao, K. Li, K. T. Cook, and C. J. Chang-Hasnain, Opt. Lett. 42, 823 (2017).
[Crossref]

P. Qiao, K. Cook, K. Li, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 23, 1700516 (2017).
[Crossref]

K. Li, C. Chase, P. Qiao, and C. J. Chang-Hasnain, Opt. Express 25, 11844 (2017).
[Crossref]

W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015).
[Crossref]

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

C. J. Chang-Hasnain and W. Yang, Adv. Opt. Photon. 4, 379 (2012).
[Crossref]

C. Chase, Y. Rao, W. Hofmann, and C. J. Chang-Hasnain, Opt. Express 18, 15461 (2010).
[Crossref]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, Opt. Express 18, 12606 (2010).
[Crossref]

C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 6, 978 (2000).
[Crossref]

Chase, C.

K. Li, C. Chase, P. Qiao, and C. J. Chang-Hasnain, Opt. Express 25, 11844 (2017).
[Crossref]

W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015).
[Crossref]

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

C. Chase, Y. Rao, W. Hofmann, and C. J. Chang-Hasnain, Opt. Express 18, 15461 (2010).
[Crossref]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, Opt. Express 18, 12606 (2010).
[Crossref]

Chen, L.

Chiou, P. Y.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[Crossref]

Chitgarha, M. R.

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

Cook, K.

P. Qiao, K. Cook, K. Li, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 23, 1700516 (2017).
[Crossref]

Cook, K. T.

Corbett, B.

J. Justice, P. Lambkin, B. Roycroft, and B. Corbett, Proc. SPIE5824605685 (2005).
[Crossref]

Daran, E.

V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015).
[Crossref]

C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
[Crossref]

Doucet, J.-B.

V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015).
[Crossref]

C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
[Crossref]

Faraon, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, Nat. Commun. 6, 7069 (2015).
[Crossref]

Fattal, D.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausolei, Nat. Photonics 4, 466 (2010).
[Crossref]

Fiorentino, M.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausolei, Nat. Photonics 4, 466 (2010).
[Crossref]

Fu, Y.

Y. Fu, IEEE Photon. Technol. Lett. 13, 424 (2001).
[Crossref]

Gaylord, T. K.

Gerke, S. A.

W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015).
[Crossref]

Gu, X.

F. Koyama and X. Gu, IEEE J. Sel. Top. Quantum Electron. 19, 1701510 (2013).
[Crossref]

K. Tanabe, X. Gu, A. Matsutani, and F. Koyama, in Conference on Laser and Electro-Optics, OSA Technical Digest (2015), paper SW1F.2.

Heideman, R. G.

R. G. Heideman and P. V. Lambeck, Sens. Actuators B 61, 100 (1999).
[Crossref]

Ho, Y. D.

Hofmann, W.

Horie, Y.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, Nat. Commun. 6, 7069 (2015).
[Crossref]

Huang, M. C. Y.

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

Justice, J.

J. Justice, P. Lambkin, B. Roycroft, and B. Corbett, Proc. SPIE5824605685 (2005).
[Crossref]

Karagodsky, V.

Karlsson, M.

M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003).
[Crossref]

Khaleghi, S.

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

Koyama, F.

F. Koyama and X. Gu, IEEE J. Sel. Top. Quantum Electron. 19, 1701510 (2013).
[Crossref]

K. Tanabe, X. Gu, A. Matsutani, and F. Koyama, in Conference on Laser and Electro-Optics, OSA Technical Digest (2015), paper SW1F.2.

Lambeck, P. V.

R. G. Heideman and P. V. Lambeck, Sens. Actuators B 61, 100 (1999).
[Crossref]

Lambkin, P.

J. Justice, P. Lambkin, B. Roycroft, and B. Corbett, Proc. SPIE5824605685 (2005).
[Crossref]

Larsson, A.

M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003).
[Crossref]

Leichle, T.

C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
[Crossref]

Levallois, C.

C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
[Crossref]

Li, H.

Li, J.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausolei, Nat. Photonics 4, 466 (2010).
[Crossref]

Li, K.

Liu, A.

A. Liu, W. Hofmann, and D. Bimberg, Opt. Express 22, 11804 (2014).
[Crossref]

A. Liu, W. Zheng, and D. Bimberg, in Asia Communications and Photonics Conference (2016), paper AF2A.52.

Lu, F.

Martinsson, H.

M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003).
[Crossref]

Matsutani, A.

K. Tanabe, X. Gu, A. Matsutani, and F. Koyama, in Conference on Laser and Electro-Optics, OSA Technical Digest (2015), paper SW1F.2.

Miller, J. K.

W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016).
[Crossref]

Moharam, M. G.

Ng, K. W.

W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015).
[Crossref]

Nikolajeff, F.

M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003).
[Crossref]

Ohta, A. T.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[Crossref]

Paninski, L.

W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016).
[Crossref]

Peng, Z.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausolei, Nat. Photonics 4, 466 (2010).
[Crossref]

Phillips, D. B.

Pnevmatikakis, E.

W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016).
[Crossref]

Qiao, P.

Rao, Y.

W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015).
[Crossref]

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

C. Chase, Y. Rao, W. Hofmann, and C. J. Chang-Hasnain, Opt. Express 18, 15461 (2010).
[Crossref]

Reig, B.

V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015).
[Crossref]

Roycroft, B.

J. Justice, P. Lambkin, B. Roycroft, and B. Corbett, Proc. SPIE5824605685 (2005).
[Crossref]

Sedgwick, F. G.

Sorin, W. V.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
[Crossref]

Szweda, R.

R. Szweda, III-Vs Rev. 19, 34 (2006).
[Crossref]

Tanabe, K.

K. Tanabe, X. Gu, A. Matsutani, and F. Koyama, in Conference on Laser and Electro-Optics, OSA Technical Digest (2015), paper SW1F.2.

Tran, T.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
[Crossref]

Vergnenegre, C.

C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
[Crossref]

Vo, S.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
[Crossref]

Vukusic, J.

M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003).
[Crossref]

Wang, X.

Willner, A. E.

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

Worland, D. P.

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

Wu, M. C.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[Crossref]

Yang, W.

W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016).
[Crossref]

W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015).
[Crossref]

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

C. J. Chang-Hasnain and W. Yang, Adv. Opt. Photon. 4, 379 (2012).
[Crossref]

Yu, S.

Yuste, R.

W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016).
[Crossref]

Zheng, W.

A. Liu, W. Zheng, and D. Bimberg, in Asia Communications and Photonics Conference (2016), paper AF2A.52.

Zhou, X.

Zhu, J.

Ziyadi, M.

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

Adv. Opt. Photon. (1)

IEEE J. Sel. Top. Quantum Electron. (5)

Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
[Crossref]

F. Koyama and X. Gu, IEEE J. Sel. Top. Quantum Electron. 19, 1701510 (2013).
[Crossref]

V. Bardinal, T. Camps, B. Reig, S. Abada, E. Daran, and J.-B. Doucet, IEEE J. Sel. Top. Quantum Electron. 21, 2700308 (2015).
[Crossref]

C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 6, 978 (2000).
[Crossref]

P. Qiao, K. Cook, K. Li, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 23, 1700516 (2017).
[Crossref]

IEEE Photon. Technol. Lett. (3)

Y. Fu, IEEE Photon. Technol. Lett. 13, 424 (2001).
[Crossref]

M. Karlsson, F. Nikolajeff, J. Vukusic, H. Martinsson, J. Bengtsson, and A. Larsson, IEEE Photon. Technol. Lett. 15, 359 (2003).
[Crossref]

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, IEEE Photon. Technol. Lett. 26, 1375 (2014).
[Crossref]

III-Vs Rev. (1)

R. Szweda, III-Vs Rev. 19, 34 (2006).
[Crossref]

J. Opt. Soc. Am. (1)

Nat. Commun. (1)

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, Nat. Commun. 6, 7069 (2015).
[Crossref]

Nat. Photonics (1)

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausolei, Nat. Photonics 4, 466 (2010).
[Crossref]

Nature (1)

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[Crossref]

Neuron (1)

W. Yang, J. K. Miller, L. Carrillo-Reid, E. Pnevmatikakis, L. Paninski, and R. Yuste, Neuron 89, 269 (2016).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Optica (1)

Proc. SPIE (1)

C. Levallois, V. Bardinal, C. Vergnenegre, T. Leichle, T. Camps, E. Daran, and J.-B. Doucet, Proc. SPIE 6992, 69920W (2010).
[Crossref]

Sci. Rep. (1)

W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, Sci. Rep. 5, 13700 (2015).
[Crossref]

Sens. Actuators B (1)

R. G. Heideman and P. V. Lambeck, Sens. Actuators B 61, 100 (1999).
[Crossref]

Other (4)

A. Liu, W. Zheng, and D. Bimberg, in Asia Communications and Photonics Conference (2016), paper AF2A.52.

W. Yang, P. Qiao, J. Qi, V. Wang, and C. J. Chang-Hasnain, “1D/2D high contrast grating solver package,” University of California, 2014, https://light.eecs.berkeley.edu/cch/hcgsolver.html .

J. Justice, P. Lambkin, B. Roycroft, and B. Corbett, Proc. SPIE5824605685 (2005).
[Crossref]

K. Tanabe, X. Gu, A. Matsutani, and F. Koyama, in Conference on Laser and Electro-Optics, OSA Technical Digest (2015), paper SW1F.2.

Supplementary Material (1)

NameDescription
» Supplement 1       Supplement 1 including Fig. S1

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Figures (4)

Fig. 1.
Fig. 1. InP-based HCG-VCSEL emitting at around 1550 nm. (a) SEM image of a typical TE HCG-VCSEL device, with a zoomed-in view of the fully suspended HCG surrounded by air. (b) Spectrum and LIV characteristics of a typical TE HCG-VCSEL at 15°C, showing single-mode emission with SMSR of 45 dB, and an output power of 2.4 mW . (c) Schematics of the HCG platform used in this study, InP-based HCG targeting at λ 1550 nm with oblique incidence angle θ with respect to the z axis and ϕ with respect to the x axis. (d) Transmission of HCG at Λ = 1080 nm for varying airgap a versus incidence angle θ at ϕ = 90 ° , highlighting three designs with distinct angle-dependent transmission characteristics, including (e) Design I with a = 490 nm , (f) Design II with a = 650 nm , and (g) Design III with a = 700 nm , showing the angular dependence of transmission (blue curve) and reflection (red curve).
Fig. 2.
Fig. 2. Process of far-field emission pattern manipulation with HCG design. (a) The emitted Gaussian light source in spatial domain as g 0 ( x , y ) . (b) The far-field (E-field) of the Gaussian source, approximated as the Fourier transform of g 0 ( x , y ) , expressed as G 0 ( k x , k y ) . (c) The transmission amplitude of HCG versus angles ( θ , ϕ ) . (d) The angular distributed HCG transmission in (c) converted into Fourier domain as T ( k x , k y ) . (e) The resulting far-field intensity distribution denoted as | G F ( k x , k y ) | 2 . The example case here shows an HCG with transmission amplitude lower in the center than on the sides, thus yielding a double-lobe far-field pattern instead of Gaussian shape. All figures are calculated with a normalized intensity scale bar as shown in the upper right.
Fig. 3.
Fig. 3. Far-field patterns for four HCG designs: Design A ( Λ = 1080 nm , a = 480 nm ) , Design B ( Λ = 1060 nm , a = 680 nm ) , Design C ( Λ = 710 nm , a = 180 nm ) , and Design D ( Λ = 730 nm , a = 180 nm ) , with the corresponding (a)–(d) calculated far-field intensity distributions using the analytical method in Fig. 2, plotted in an θ ϕ axis system; (e)–(h) simulated far-field intensity distributions using a 3D FDTD tool, plotted in an θ ϕ axis system; and (i)–(l) measured far-field intensity distributions from fabricated HCG-VCSEL devices based on the designed parameters, showing good agreements with the designed and simulated patterns. All figures are calculated with normalized intensity scale bars as shown in the center.
Fig. 4.
Fig. 4. VCSELs with versatile functionalities. (a) The cross section of a two-faced single-mode laser, with the top-surface beam shape manipulated by HCG designs while the bottom-surface beam remains a Gaussian shape, validating the single-mode lasing of the VCSEL. (b) HCG-VCSEL arrays emitting at single-mode but with various far-field emission patterns, including single-lobe, double-lobe, triple-lobe, “bow-tie,” “sugar cone,” and “doughnut” shapes. The device image is taken with a 3D confocal optical microscope, and the far-field patterns are captured with an IR camera for each individual device.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

k x = k 0 · sin θ · cos ϕ ,
k y = k 0 · sin θ · sin ϕ ,
k 0 = 2 π / λ ,
G F ( k x , k y ) = G 0 ( k x , k y ) · T ( k x , k y ) .

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