Controlling spatial mode superposition to channel light flow in a photonic crystal

Gagandeep Kaur; Harshawardhan Wanare; Harshawardhan Wanare; Harshawardhan Wanare

doi:10.1364/JOSAB.404357

Journal of the Optical Society of America B
Vol. 37,
Issue 12,
pp. 3809-3818
(2020)
•https://doi.org/10.1364/JOSAB.404357

Controlling spatial mode superposition to channel light flow in a photonic crystal

Gagandeep Kaur and Harshawardhan Wanare

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Gagandeep Kaur and Harshawardhan Wanare, "Controlling spatial mode superposition to channel light flow in a photonic crystal," J. Opt. Soc. Am. B 37, 3809-3818 (2020)

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Abstract

We present robust control of superposition of spatial modes in a photonic crystal cavity arising from incorporating a weak localized perturbation. As expected, this perturbation breaks the symmetry of the underlying photonic crystal structure, resulting in a frequency shift of the cavity eigen modes. Engineering of the perturbation leads us to discover the comprehensive mathematical structure of the governing superposition of the spatial modes. This superposition is further designed to obtain controllable channeling of light through a cavity–waveguide system, thus demonstrating its applicabitily in realizing narrow (wide) band filters, controllable beam splitters, and wavelength multiplexers.

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Equations (18)

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Input Port	Orientation of Perturbation Axis with Respect to Propagating Signal	Reflection at Input Port	Output along Input Port Direction	Output Orthogonal to Input Port Direction		Amplitude Factors at Orthogonal Ports		Ratio of Factors
Port 1		$R_{11}$	$T_{13}$	$T_{12}$	$T_{14}$	$a_{1}^{- y}$	$a_{1}^{+ y}$	$\frac{a_{1}^{- y}}{a_{1}^{+ y}}$
(along $x$ axis)	15°	0.06	0.83	0.06	0.05	1	0.91	1.1
	30°	0.13	0.54	0.16	0.17	0.92	0.94	0.98
	45°	0.3	0.25	0.2	0.25	0.89	1	0.89
	60°	0.55	0.07	0.16	0.22	0.92	1.08	0.85
	75°	0.845	0.005	0.06	0.09	1	1.22	0.82
Port 3		$R_{33}$	$T_{31}$	$T_{32}$	$T_{34}$	$a_{1}^{- y}$	$a_{1}^{+ y}$	$\frac{a_{1}^{- y}}{a_{1}^{+ y}}$
(along – $x$ axis)	15°	0.01	0.83	0.09	0.07	1.22	1.08	1.1
	30°	0.01	0.54	0.22	0.23	1.08	1.1	0.98
	45°	0.2	0.25	0.25	0.3	1	1.1	0.91
	60°	0.53	0.07	0.17	0.23	0.94	1.1	0.85
	75°	0.875	0.005	0.05	0.07	0.91	1.08	0.84
Port 2		$R_{22}$	$T_{24}$	$T_{21}$	$T_{23}$	$a_{1}^{- x}$	$a_{1}^{+ x}$	$\frac{a_{1}^{- x}}{a_{1}^{+ x}}$
(along $y$ axis)	15°	0.06	0.83	0.06	0.05	1	0.91	1.1
	30°	0.13	0.54	0.16	0.17	0.92	0.94	0.98
	45°	0.3	0.25	0.2	0.25	0.89	1	0.89
	60°	0.55	0.07	0.16	0.22	0.92	1.08	0.85
	75°	0.845	0.005	0.06	0.09	1	1.2	0.83
Port 4		$R_{44}$	$T_{42}$	$T_{41}$	$T_{43}$	$a_{1}^{- x}$	$a_{1}^{+ x}$	$\frac{a_{1}^{- x}}{a_{1}^{+ x}}$
(along– $y$ axis)	15°	0.01	0.83	0.09	0.07	1.22	1.08	1.1
	30°	0.01	0.54	0.22	0.23	1.08	1.1	0.98
	45°	0.2	0.25	0.25	0.3	1	1.1	0.91
	60°	0.53	0.07	0.17	0.23	0.94	1.1	0.85
	75°	0.875	0.005	0.05	0.07	0.91	1.08	0.84

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Equations (18)

Journal of the Optical Society of America B