Theoretical verification of a silicon-wire flat-spectral-band wavelength filter based on multimode interference couplers with symmetric and asymmetric splitting ratios for the broadband operating range

Seok-Hwan Jeong

doi:10.1364/AO.437694

Applied Optics
Vol. 60,
Issue 30,
pp. 9411-9418
(2021)
•https://doi.org/10.1364/AO.437694

Theoretical verification of a silicon-wire flat-spectral-band wavelength filter based on multimode interference couplers with symmetric and asymmetric splitting ratios for the broadband operating range

Seok-Hwan Jeong

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Seok-Hwan Jeong, "Theoretical verification of a silicon-wire flat-spectral-band wavelength filter based on multimode interference couplers with symmetric and asymmetric splitting ratios for the broadband operating range," Appl. Opt. 60, 9411-9418 (2021)

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Abstract

A novel, to the best of our knowledge, device scheme for a silicon-nanowire flat-spectral-band wavelength optical filter is proposed and theoretically demonstrated. The proposed wavelength filter is composed of cascade-connected multiple delayed interference optical delay lines, together with several multimode interference couplers with symmetric and asymmetric splitting ratios. Theoretical calculations based on analytic and numerical simulations exhibit flatband spectra over a wavelength range of >80 nm with potentially better production yield for arbitrary channel spacing.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the author upon reasonable request.

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# Path Difference = Upper Path Length−Lower Path Length		Conventional Scheme Shown in Fig. 1(a)		Proposed Scheme Shown in Fig. 1(b)
# Path Difference = Upper Path Length−Lower Path Length		Path Difference	Phase Shift	Path Difference	Phase Shift
First-stage MDI	First	$+ 2 Δ L$	N.A.	$+ 2 Δ L$	N.A.
	Second	$- 4 Δ L$	N.A.	$+ 4 Δ L$	N.A.
	Third	$- 4 Δ L$	$- π$ [rad.]	$+ 4 Δ L$	$+ π$ [rad.]
Second-stage MDI (Upper)	First	$+ 1 Δ L$	N.A.	$+ 1 Δ L$	$+ 0.5 π$ [rad.]
Second-stage MDI (Upper)	Second	$- 2 Δ L$	N.A.	$+ 2 Δ L$	N.A.
Third-stage MDI (Lower)	First	$+ 1 Δ L$	$+ 0.5 π$ [rad.]	$+ 1 Δ L$	N.A.
Third-stage MDI (Lower)	Second	$- 2 Δ L$	$- π$ [rad.]	$+ 2 Δ L$	$+ π$ [rad.]

	DCs in Conventional	MMIs in Proposed
$W$	0.35 µm	0.35 µm
$W_{T P}$	N. A.	0.80 µm ( $L_{T P} = 6 µ m$ )
$R_{D C}$	6.2 µm	N. A.
Gap	0.2 µm	0.2 µm
Coupler Spec. (Each $κ$ means the split rate of the cross port)	$L_{D C} = 12.3 µ m$	$L_{M M I} = 18.5 µ m$
	for $κ_{D C} = 0.5$	$W_{M M I} = 2.0 µ m$
	for $κ_{D C} = 0.5$	for $κ_{M M I} = 0.5$
	$L_{D C} = 9.5 µ m$	$L_{M M I} = 11.5 µ m$
	for $κ_{D C} = 0.33$	$W_{M M I} = 2.5 µ m$
	for $κ_{D C} = 0.33$	for $κ_{M M I} = 0.72$
	$L_{D C} = 7.3 µ m$	$L_{M M I} = 9.3 µ m$
	for $κ_{D C} = 0.2$	$W_{M M I} = 2.0 µ m$
	for $κ_{D C} = 0.2$	for $κ_{M M I} = 0.85$
	$L_{D C} = 0$ , $G a p = 2.0 µ m$ for $κ_{D C} = 0.08$
	$L_{D C} = 0$ , $G a p = 2.6 µ m$ for $κ_{D C} = 0.04$

# Path Difference = Upper Path Length−Lower Path Length		Conventional Scheme Shown in Fig. 1(a)		Proposed Scheme Shown in Fig. 1(b)
# Path Difference = Upper Path Length−Lower Path Length		Path Difference	Phase Shift	Path Difference	Phase Shift
First-stage MDI	First	$+ 2 Δ L$	N.A.	$+ 2 Δ L$	N.A.
	Second	$- 4 Δ L$	N.A.	$+ 4 Δ L$	N.A.
	Third	$- 4 Δ L$	$- π$ [rad.]	$+ 4 Δ L$	$+ π$ [rad.]
Second-stage MDI (Upper)	First	$+ 1 Δ L$	N.A.	$+ 1 Δ L$	$+ 0.5 π$ [rad.]
Second-stage MDI (Upper)	Second	$- 2 Δ L$	N.A.	$+ 2 Δ L$	N.A.
Third-stage MDI (Lower)	First	$+ 1 Δ L$	$+ 0.5 π$ [rad.]	$+ 1 Δ L$	N.A.
Third-stage MDI (Lower)	Second	$- 2 Δ L$	$- π$ [rad.]	$+ 2 Δ L$	$+ π$ [rad.]

	DCs in Conventional	MMIs in Proposed
$W$	0.35 µm	0.35 µm
$W_{T P}$	N. A.	0.80 µm ( $L_{T P} = 6 µ m$ )
$R_{D C}$	6.2 µm	N. A.
Gap	0.2 µm	0.2 µm
Coupler Spec. (Each $κ$ means the split rate of the cross port)	$L_{D C} = 12.3 µ m$	$L_{M M I} = 18.5 µ m$
	for $κ_{D C} = 0.5$	$W_{M M I} = 2.0 µ m$
	for $κ_{D C} = 0.5$	for $κ_{M M I} = 0.5$
	$L_{D C} = 9.5 µ m$	$L_{M M I} = 11.5 µ m$
	for $κ_{D C} = 0.33$	$W_{M M I} = 2.5 µ m$
	for $κ_{D C} = 0.33$	for $κ_{M M I} = 0.72$
	$L_{D C} = 7.3 µ m$	$L_{M M I} = 9.3 µ m$
	for $κ_{D C} = 0.2$	$W_{M M I} = 2.0 µ m$
	for $κ_{D C} = 0.2$	for $κ_{M M I} = 0.85$
	$L_{D C} = 0$ , $G a p = 2.0 µ m$ for $κ_{D C} = 0.08$
	$L_{D C} = 0$ , $G a p = 2.6 µ m$ for $κ_{D C} = 0.04$

Abstract

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Equations (12)

Applied Optics