Mike P. C. Taverne, Ying-Lung D. Ho, and John G. Rarity, "Investigation of defect cavities formed in three-dimensional woodpile photonic crystals," J. Opt. Soc. Am. B 32, 639-648 (2015)
We report the optimization of optical properties of single defects in three-dimensional (3D) face-centered-cubic (FCC) woodpile photonic crystal (PC) cavities by using plane-wave expansion (PWE) and finite-difference time-domain (FDTD) methods. By optimizing the dimensions of a 3D woodpile PC, wide photonic band gaps (PBG) are created. Optical cavities with resonances in the bandgap arise when point defects are introduced in the crystal. Three types of single defects are investigated in high refractive index contrast (gallium phosphide–air) woodpile structures, and -factors and mode volumes () of the resonant cavity modes are calculated. We show that, by introducing an air buffer around a single defect, smaller mode volumes can be obtained. We demonstrate high -factors up to 700,000 and cavity volumes down to . The estimates of and are then used to quantify the enhancement of spontaneous emission and the possibility of achieving strong coupling with nitrogen-vacancy (NV) color centers in diamond.
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Summary of Achievable -factors , Modal Volumes , Purcell Factors , and Leakage Rates at the Highest- Resonant Modes () for the Defects without Air Buffer D0, D1, and D2a
Defect type
D0
D1
D2
Defect size
Air buffer size
3.3
3.3
3.3
3.3
3.3
3.3
1
1
1
0.3358
0.3358
0.3358
Dipole orientation
0.5890
0.5530
0.5255
0.5058
0.5300
0.4938
0.4922
0.5007
570.08
607.23
638.98
663.88
633.53
679.99
682.22
670.71
0.987
0.190
0.161
0.299
0.193
0.330
0.394
0.543
(GHz)
1418.48
14.79
0.62
1.66
5.66
3.27
4.13
5.56
(ns)
0.07
1.61
0.60
0.18
0.31
0.24
0.18
Diamond NV centers
Diamond nanocrystals:
637
(GHz)
1269.47
14.09
0.62
1.73
5.63
3.49
4.43
5.85
(ns)
0.07
1.60
0.58
0.18
0.29
0.23
0.17
(GHz)
()
0.025
(V/m)
(GHz)
2.57
5.85
6.37
4.67
5.81
4.45
4.07
3.46
(ns)
0.39
0.17
0.16
0.21
0.17
0.22
0.25
0.29
Simulations for the defect D0 in the direction showed no clearly distinguishable resonance modes, which is why its entries are marked n/a.
Table 2.
Summary of Achievable -factors , Modal Volumes , Purcell Factors , and Leakage Rates at the Highest- Resonant Modes () for the Defects with Air Buffer A0, A1, and A2
Defect type
A0
A1
A2
Defect size
Air buffer size
3.3
3.3
3.3
3.3
3.3
3.3
1
1
1
0.3358
0.3358
0.3358
Dipole orientation
0.5409
0.5303
0.5377
0.5513
0.5391
0.5449
0.5715
0.5440
0.5593
(nm)
620.86
633.28
624.46
609.13
622.88
616.23
587.59
617.28
600.35
0.100
0.296
0.167
0.123
0.207
0.193
0.306
0.151
0.120
(GHz)
1.32
1.90
7.82
3.32
2.85
11.45
134.14
4.13
36.91
(ns)
0.76
0.53
0.13
0.30
0.35
0.09
0.01
0.24
0.03
Diamond NV centers
Diamond nanocrystals:
637
(GHz)
1.28
1.88
7.66
3.17
2.78
11.08
123.73
4.01
34.78
(ns)
0.78
0.53
0.13
0.32
0.36
0.09
0.01
0.25
0.03
(GHz)
()
0.025
(V/m)
(GHz)
8.07
4.69
6.24
7.27
5.61
5.82
4.62
6.57
7.38
(ns)
0.12
0.21
0.16
0.14
0.18
0.17
0.22
0.15
0.14
Tables (2)
Table 1.
Summary of Achievable -factors , Modal Volumes , Purcell Factors , and Leakage Rates at the Highest- Resonant Modes () for the Defects without Air Buffer D0, D1, and D2a
Defect type
D0
D1
D2
Defect size
Air buffer size
3.3
3.3
3.3
3.3
3.3
3.3
1
1
1
0.3358
0.3358
0.3358
Dipole orientation
0.5890
0.5530
0.5255
0.5058
0.5300
0.4938
0.4922
0.5007
570.08
607.23
638.98
663.88
633.53
679.99
682.22
670.71
0.987
0.190
0.161
0.299
0.193
0.330
0.394
0.543
(GHz)
1418.48
14.79
0.62
1.66
5.66
3.27
4.13
5.56
(ns)
0.07
1.61
0.60
0.18
0.31
0.24
0.18
Diamond NV centers
Diamond nanocrystals:
637
(GHz)
1269.47
14.09
0.62
1.73
5.63
3.49
4.43
5.85
(ns)
0.07
1.60
0.58
0.18
0.29
0.23
0.17
(GHz)
()
0.025
(V/m)
(GHz)
2.57
5.85
6.37
4.67
5.81
4.45
4.07
3.46
(ns)
0.39
0.17
0.16
0.21
0.17
0.22
0.25
0.29
Simulations for the defect D0 in the direction showed no clearly distinguishable resonance modes, which is why its entries are marked n/a.
Table 2.
Summary of Achievable -factors , Modal Volumes , Purcell Factors , and Leakage Rates at the Highest- Resonant Modes () for the Defects with Air Buffer A0, A1, and A2