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¹H NMR: Complex Splitting

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.

¹H NMR Signal Multiplicity: Splitting Patterns

¹H NMR Signal Multiplicity: Splitting Patterns

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...

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Updated: Jun 22, 2026

Characterization of Anisotropic Leaky Mode Modulators for Holovideo

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Published on: March 19, 2016

Variable splitting ratio 2 x 2 MMI couplers using multimode waveguide holograms.

Shuo-Yen Tseng, Canek Fuentes-Hernandez, Daniel Owens

|June 24, 2009

Summary

This summary is machine-generated.

Researchers developed variable power splitting ratio 2x2 MMI couplers using multimode waveguide holograms. This innovation allows for adjustable light distribution in photonic devices with fixed dimensions, enhancing optical performance.

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Area of Science:

Photonics and Optical Engineering
Integrated Optics
Waveguide Devices

Background:

Multimode Interference (MMI) couplers are fundamental components in integrated optics for power splitting.
Achieving variable power splitting ratios in MMI couplers often requires complex designs or active components.

Purpose of the Study:

To analyze and design 2x2 MMI couplers capable of variable power splitting ratios.
To investigate the use of multimode waveguide holograms for achieving variable splitting.
To explore fabrication tolerance for practical implementation.

Main Methods:

Theoretical analysis of multimode waveguide holograms for MMI couplers.
Design of devices with paired-imaging lengths on a silicon-on-insulator (SOI) platform.
Beam propagation simulations for performance verification and analysis.

Main Results:

Theoretical analysis confirms that surface relief holograms on fixed-dimension MMI couplers can achieve variable splitting ratios.
Device designs utilizing paired-imaging lengths were successfully simulated.
Beam propagation simulations validated the matrix theory and demonstrated device performance.

Conclusions:

Variable power splitting ratios in 2x2 MMI couplers can be realized using multimode waveguide holograms.
The proposed holographic approach offers a passive and potentially fabrication-tolerant solution for adjustable light distribution in integrated photonic circuits.