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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 23469–23474
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Design of subwavelength-size, indium tin oxide (ITO)-clad optical disk cavities with quality-factors exceeding 104

Özlem Şenlik, Hwi Yoon Cheong, and Tomoyuki Yoshie  »View Author Affiliations


Optics Express, Vol. 19, Issue 23, pp. 23469-23474 (2011)
http://dx.doi.org/10.1364/OE.19.023469


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Abstract

Indium tin oxide is used as a top cladding electrode of optical disk resonators with subwavelength size in all dimensions. Calculated quality (Q)-factors exceed 104 in visible wavelengths (650-670nm). The disk aspect ratio is an important parameter to optimize the resonator properties. The Q-factor and threshold material gain based on finite-difference time-domain method are optimized for eight different disk resonator optical modes. Proposed cavity designs are promising for building electrically-pumped, low-threshold nano-lasers at room temperature.

© 2011 OSA

1. Introduction

Recently, many groups have considered the use of metallic cladding as a possible solution for reducing the optical resonator size below a free space resonance wavelength (λ0) in all dimensions [1

1. M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]

4

4. J. Huang, S. H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18(19), 19581–19591 (2010). [CrossRef] [PubMed]

]. Metallic materials would also satisfy the electrode requirement for current injection and electric field application in electrically-driven nano- and micro-cavity photonic devices such as current-injection nano-lasers. However, subwavelength (sub-λ) size metallic resonators suffer from low Q-factors in the order of a few hundreds since conventional metallic materials such as gold and silver are extremely lossy in the visible and near-infrared wavelengths. In order to improve the Q-factors of metal-incorporating resonators, a common design approach has been the reduction of the overlap of metallic material and the optical mode at the expense of complicated device structure and deteriorated device performance [5

5. H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004). [CrossRef] [PubMed]

]. Current-injection nano-lasers based on these resonators would suffer from (1) small thermal conductance, (2) large electric resistance due to large current path, and (3) large laser threshold current due to significant leak current induced by indirect current injection. As a different approach, compact optical resonators clad by low-loss transparent conductive oxide (TCO) electrodes are promising for room temperature (RT), continuous-wave (CW), current injection low-threshold micro-lasers due to high Q-factors and proximate placement of electrodes to a laser mode [6

6. O. Senlik, L. Tang, P. Tor-ngern, and T. Yoshie, “Optical microcavities clad by low-absorption electrode media,” IEEE Photonics J. 2(5), 794–801 (2010). [CrossRef]

].

In this letter, we show that both the radiation and absorption losses are significantly reduced in simple nano-scale disk optical resonators incorporating planar indium tin oxide (ITO) electrodes by optimizing the cavity geometry. Calculated Q-factors exceed 104 for optical cavities of the subwavelength (sub-λ) size in all dimensions.

2. Resonator structure

Analyzed ITO-containing disk resonators are composed of a high refractive index (ns = 3.4) disk of thickness h and radius r, a top ITO electrode of thickness he and a bottom AlOx layer of thickness ho; see Fig. 1
Fig. 1 (Color online) Sub-λ-scale, ITO-clad disk resonator. Schematic representation of the disk optical cavity with ITO top disk electrode, an AlOx bottom cladding layer and an AlAs current path. A substrate can be GaAs.
. The bottom AlAs cylinder with radius ra provides a current-injection path. The refractive indices of the AlOx layer and the AlAs cylinder used in the analysis are no = 1.7 and na = 2.89. We consider ITO as the electrode material as well as a cladding medium, since the optical and electrical properties are suitable for electrode-containing sub-λ scale high-Q optical resonators needed for current-injection nano-lasers. The refractive index of ITO is appropriate for electrically-pumped high-Q nanolasers, in that the real part of the refractive index is smaller than that of semiconductors (typically ~3.4) and the absorption is negligible in visible wavelength spectra. Even at infrared wavelengths, optical absorption is still small compared to gold and silver [7

7. R. A. Synowicki, “Spectroscopic ellipsometry characterization of indium tin oxide film microstructure and optical constants,” Thin Solid Films 313–314(1-2), 394–397 (1998). [CrossRef]

]. In this study, 670 nm is chosen as the resonance wavelength and we measure the corresponding refractive index of RF-sputtered ITO as ne = 1.9 + 0.01i which is used in the modeling, by spectroscopic ellipsometry. The measured refractive indices of ITO deposited under different conditions vary between 1.852 + 0.009i and 2.012 + 0.078i [8

8. Filmetrics, “Filmetrics refractive index database” (Filmetrics, 2011). http://www.filmetrics.com/refractive-index-database.

]. Thus, the refractive index value that we use for our modeling can be considered as a reasonable assumption but not the best case apparently. Moreover, ITO can form ohmic contacts on both n- and p-GaAs—required for smooth current injection and a negligible voltage drop at the semiconductor-metal contact [9

9. M. A. Matin, A. F. Jezierski, S. A. Bashar, D. E. Lacklison, T. M. Benson, T. S. Cheng, J. S. Roberts, T. E. Sale, J. W. Orton, C. T. Foxon, and A. A. Rezazadeh, “Optically transparent indium-tin-oxide (ITO) ohmic contacts in the fabrication of vertical-cavity surface-emitting lasers,” Electron. Lett. 30(4), 318–320 (1994). [CrossRef]

].

3. Optical modes and mode properties

Disk optical resonators support TEmpq-like and TMmpq-like WGMs originated from slab modes for large aspect ratio (r/h) whereas HEmpq-like and EHmpq-like hybrid cylinder modes (m≠0)—arisen from optical fiber modes—are formed as the ratio is small where indices m, p and q correspond to quantization in azimuth, radial and vertical directions. As the aspect ratio decreases from 2 to 0.5, the optical modes are evolved from slab-like modes to optical fiber-like modes, and interact with each other for the similar mode frequencies. For TE-like (TM-like) modes, Ez-field (Hz-field) component is negligible. Hybrid modes have m > 0, and contain both the Ez-field and Hz-field components; designation of these modes is based on relative contribution of these field components to a transverse field component (e.g. Er or Eϕ). When the mode is TM-dominant (Ez-field makes larger contribution), the mode is named as HEmpq-like. The mode is named as EHmpq-like when the mode is TE-dominant (Hz-field component makes larger contribution) [10

10. A. Yariv and P. Yeh, Photonics:Optical Electronics In Modern Communications (Oxford University Press, 2007), App. 2.

]. For small azimuthal mode numbers m, the optical modes suffer from the radiation loss; the Q-factors are below 50 for m < 3. Although metal enclosures of the disk reduce the radiation loss by photon recycling, optical absorption in the metal limits maximum Q-factors to a few hundred [2

2. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010). [CrossRef] [PubMed]

, 4

4. J. Huang, S. H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18(19), 19581–19591 (2010). [CrossRef] [PubMed]

]. Thus, we consider the modes HEm11-like, TEm11-like, EHm21-like, and TEm12-like (the indices are chosen based on the quantization of major field component of the corresponding mode) with m = 6 and 7 that can maintain large Q-factors and, at the same time, sub-λ-scale cavity dimensions. Figure 2
Fig. 2 Intensity z-r plane (r > 0) distributions of Ez and Hz field components of HE711, TE711, EH721 and TE712 modes respectively for various aspect ratios (r/h). Outline of the structure profile is overlaid onto image where the top rectangle is ITO cladding. The intensity is normalized by the maximum field component. Modes are stretched vertically as the aspect ratio decreases.
shows the relative intensity distributions of the Ez-field and Hz-field components of the corresponding optical modes with m = 7 for various aspect ratios. As the aspect ratio decreases, the modes are stretched vertically. For the mode labeled as TEm11-like, Ez field component becomes significant as the aspect ratio decreases below 0.9 making the mode a hybrid one. On the other hand, Ez field component of EHm11-like mode becomes negligible and radial mode number decreases to 1 about r/h = 0.7. However, we will use the same notation for consistency.

We analyzed cavity properties—mode frequencies, Q-factors, effective mode volumes (Veff), resonator sizes and confinement factors (Γ) with the disk aspect ratio (r/h) as a geometric parameter for optimization—by two-dimensional (r-z plane) finite-difference time-domain (FDTD) method, considering the azimuthal symmetry of the disk geometry. The disk height, h is chosen as the unit length and resolved by 20 mesh points. For most of the calculations, the ITO cladding thickness is equal to the disk height and resolution is 20. For specific cases, where ITO thickness is assumed as 100 nm, the resolution is 9 nm. The normalized mode frequencies with respect to h and Veff as a function of aspect ratio are presented in Figs. 3(a)
Fig. 3 Mode characteristics (a) Normalized mode frequency, (b) effective mode volume (Veff), (b) Q-factor, (d) disk diameter, (e) Purcell factor (Fp), and (f) threshold material gain (gth) as a function of disk aspect ratio (r/h). Some zigzag lines are caused by mode coupling.
and 3(b), respectively. In our analysis, we intentionally exclude the bottom AlAs current injection path, but the high-Q disk modes are typically maintained for r/ra ratios smaller than 0.82. Figure 3(c) shows that the Q-factor increases as the aspect ratio decreases from 2.0 to 0.5 where the Q-factor is the maximum for HEm11-like and EHm21-like modes. However, the Q-factors of the TEm11-like and TEm12-like modes keep increasing with the further reduction of the aspect ratio.

We obtain the Q-factor as high as 5.3x104 for EH721-like mode for an optical cavity with 0.99 λ02 footprint size, corresponding to 0.44μm2 at λ0 = 670 nm. Assuming a 100 nm thick ITO electrode and a 100 nm AlOx bottom layer, we obtain the Q-factor of HE711-like mode as high as 3x104 for the cavity with all sub-λ-size dimensions. This is much higher than the Q-factors of any other past sub-λ size, current injection, and optical cavity designs [2

2. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010). [CrossRef] [PubMed]

4

4. J. Huang, S. H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18(19), 19581–19591 (2010). [CrossRef] [PubMed]

]. The corresponding aspect ratio is 0.8 and the disk diameter (d = 2r) and the total cavity height (he + h + ho) is 0.944λ0 and 0.973 λ0, respectively. Figure 3(d) shows the normalized disk diameter with respect to the aspect ratio for the analyzed modes. For r/h < 1.2, the cavity diameter is below λ0 for the HE611-like, TE611-like, EH621-like and HE711-like modes. Our results show that absorption is the main loss mechanism for large aspect ratio disks. The fraction of the energy density stored in ITO cladding (Γ2) decreases for all the modes as the aspect ratio decreases, resulting in improvement of Q-factors. Γ2 values are given in Table1

Table 1. Fractions of the energy density stored in ITO (Γ2) for ITO-clad disk modes

table-icon
View This Table
for r/h = 2 & r/h = 0.6. For a detailed discussion about the effect of Γ2 on Q-factors of low-absorption electrode media clad microcavities, see [6

6. O. Senlik, L. Tang, P. Tor-ngern, and T. Yoshie, “Optical microcavities clad by low-absorption electrode media,” IEEE Photonics J. 2(5), 794–801 (2010). [CrossRef]

]. In addition to reduction of absorption loss, scaling down the aspect ratio also reduces the radiation loss. For HEm11-like and EHm21-like modes, reduction of absorption loss is more drastic than the reduction of the radiation loss. Hence, Q-factors of these modes for small aspect ratio disks become eventually radiation loss limited. On the contrary, for TEm11-like and TEm12-like modes radiation loss reduction is prominent, resulting in absorption loss limited Q-factor. As a result, the increase in absorption loss would significantly degrade the Q-factors of the TEm11-like and TEm12-like modes, but would have a negligible effect on the Q-factors of HEm11-like and EHm21-like modes. The zigzag behavior of the HE621-like and TE612-like data about r/h = 1.6 is attributed to interaction of these two modes.

The Purcell factor (Fp) is an indicator of the spontaneous emission enhancement that can be prominent for sub-λ-scale lasers. We calculate Fp using Fp=3Q(λ0/n)3/4π2Veff. Among all the modes, HE711-like modes exhibit the highest Fp in the analyzed parameter space, i.e., r/h (0.5,2.0). We obtain 456 as the highest Fp for the cavity design with all sub-λ dimensions; see Fig. 3(e). This is an order of magnitude higher than those of reported sub-λ-size metallic optical resonators [4

4. J. Huang, S. H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18(19), 19581–19591 (2010). [CrossRef] [PubMed]

].

In order to examine the possibility of current-injection lasing of the presented ITO-clad disk resonators, we calculate the threshold material gain (gth) as gth=ω0/[ΓQ(c/neff)] where ω0 is the angular resonance frequency, c is the speed of light, neff is the effective mode index, and Γ is the energy confinement factor. Assuming a bulk gain medium, calculated gth values are below 10 cm−1 for modes with m = 7. Figure 3(f) shows the threshold gain values with respect to the aspect ratio for all the modes. HE711-like modes require the smallest bulk threshold gain of 11 cm−1 at r/h = 0.8 among the analyzed disk resonators with sub-λ size in all dimensions. This threshold gain is significantly small compared to those of sub-λ-size metallic resonators incorporating bulk gain medium [3

3. M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010). [CrossRef]

, 11

11. A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008). [CrossRef] [PubMed]

], showing an advantage of using our designs. We also calculate the threshold gain values per well for a single quantum well (SQW) and three quantum wells (3QWs) for 7nm/10nm thick well/barrier layers placed in the middle of the disk layer. For HE711-like mode, gth per well is calculated as 364 cm−1 for SQW and 41 cm−1 for 3QWs. Even for SQW layer, gth per well is still smaller than those of metallic optical cavities with seven or nine QWs [4

4. J. Huang, S. H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18(19), 19581–19591 (2010). [CrossRef] [PubMed]

]. According to our gain analysis results, the reduction of threshold current is expected. The calculated threshold gain is achievable in compressively strained InGaP/AlGaInP QW material system at RT [12

12. G. Hunziker, W. Knop, and C. Harder, “Gain measurements on one, two, and three strained GaInP quantum well laser diodes,” IEEE J. Quantum Electron. 30(10), 2235–2238 (1994). [CrossRef]

].

4. Conclusion

In conclusion, we have optimized the disk optical resonator geometries incorporating ITO electrodes for enhanced cavity characteristics of ITO-clad, sub-λ-size disk resonators. The optimized cavities exhibit Q-factors larger than 104 and Purcell factors as high as 500. Both the demonstrated Q factors and Purcell factors are significantly higher than those of the optical metallic cavities and the designed structures still have sub-λ sizes in all dimensions. Among the analyzed modes, the HE711-like modes exhibit the highest Q-factor and Purcell factor among resonators that are sub-λ size in all dimensions. Owing to high Q-factors, small threshold gain values and the direct electrode placement above the lasing mode, the optimized optical cavity designs can be utilized to build current injection low-threshold nanolasers at room temperature. The proposed cavities would also be useful for many other electrically-driven optoelectronic devices such as modulators, switches, logic gates, photodiodes, and single photon sources.

Acknowledgment

Authors would like to acknowledge support from the National Science Foundation under the award ECCS-1102109.

References and links

1.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]

2.

K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010). [CrossRef] [PubMed]

3.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010). [CrossRef]

4.

J. Huang, S. H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18(19), 19581–19591 (2010). [CrossRef] [PubMed]

5.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004). [CrossRef] [PubMed]

6.

O. Senlik, L. Tang, P. Tor-ngern, and T. Yoshie, “Optical microcavities clad by low-absorption electrode media,” IEEE Photonics J. 2(5), 794–801 (2010). [CrossRef]

7.

R. A. Synowicki, “Spectroscopic ellipsometry characterization of indium tin oxide film microstructure and optical constants,” Thin Solid Films 313–314(1-2), 394–397 (1998). [CrossRef]

8.

Filmetrics, “Filmetrics refractive index database” (Filmetrics, 2011). http://www.filmetrics.com/refractive-index-database.

9.

M. A. Matin, A. F. Jezierski, S. A. Bashar, D. E. Lacklison, T. M. Benson, T. S. Cheng, J. S. Roberts, T. E. Sale, J. W. Orton, C. T. Foxon, and A. A. Rezazadeh, “Optically transparent indium-tin-oxide (ITO) ohmic contacts in the fabrication of vertical-cavity surface-emitting lasers,” Electron. Lett. 30(4), 318–320 (1994). [CrossRef]

10.

A. Yariv and P. Yeh, Photonics:Optical Electronics In Modern Communications (Oxford University Press, 2007), App. 2.

11.

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008). [CrossRef] [PubMed]

12.

G. Hunziker, W. Knop, and C. Harder, “Gain measurements on one, two, and three strained GaInP quantum well laser diodes,” IEEE J. Quantum Electron. 30(10), 2235–2238 (1994). [CrossRef]

OCIS Codes
(140.3410) Lasers and laser optics : Laser resonators
(140.4780) Lasers and laser optics : Optical resonators
(140.5960) Lasers and laser optics : Semiconductor lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 15, 2011
Revised Manuscript: September 10, 2011
Manuscript Accepted: October 14, 2011
Published: November 2, 2011

Citation
Özlem Şenlik, Hwi Yoon Cheong, and Tomoyuki Yoshie, "Design of subwavelength-size, indium tin oxide (ITO)-clad optical disk cavities with quality-factors exceeding 104," Opt. Express 19, 23469-23474 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23469


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References

  1. M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1(10), 589–594 (2007). [CrossRef]
  2. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express18(9), 8790–8799 (2010). [CrossRef] [PubMed]
  3. M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4(6), 395–399 (2010). [CrossRef]
  4. J. Huang, S. H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express18(19), 19581–19591 (2010). [CrossRef] [PubMed]
  5. H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science305(5689), 1444–1447 (2004). [CrossRef] [PubMed]
  6. O. Senlik, L. Tang, P. Tor-ngern, and T. Yoshie, “Optical microcavities clad by low-absorption electrode media,” IEEE Photonics J.2(5), 794–801 (2010). [CrossRef]
  7. R. A. Synowicki, “Spectroscopic ellipsometry characterization of indium tin oxide film microstructure and optical constants,” Thin Solid Films313–314(1-2), 394–397 (1998). [CrossRef]
  8. Filmetrics, “Filmetrics refractive index database” (Filmetrics, 2011). http://www.filmetrics.com/refractive-index-database .
  9. M. A. Matin, A. F. Jezierski, S. A. Bashar, D. E. Lacklison, T. M. Benson, T. S. Cheng, J. S. Roberts, T. E. Sale, J. W. Orton, C. T. Foxon, and A. A. Rezazadeh, “Optically transparent indium-tin-oxide (ITO) ohmic contacts in the fabrication of vertical-cavity surface-emitting lasers,” Electron. Lett.30(4), 318–320 (1994). [CrossRef]
  10. A. Yariv and P. Yeh, Photonics:Optical Electronics In Modern Communications (Oxford University Press, 2007), App. 2.
  11. A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett.33(11), 1261–1263 (2008). [CrossRef] [PubMed]
  12. G. Hunziker, W. Knop, and C. Harder, “Gain measurements on one, two, and three strained GaInP quantum well laser diodes,” IEEE J. Quantum Electron.30(10), 2235–2238 (1994). [CrossRef]

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