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Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.

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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.

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Related Experiment Video

Updated: Jun 8, 2026

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Published on: April 1, 2020

A novel scheme for 1×N optical power splitter.

Xionggui Tang¹, Jinkun Liao, Heping Li

¹School of Opto-Electronic Information, University of Electronic Science and Technology of China, Chengdu 610054, People's Republic of China. tangxg@uestc.edu.cn

|October 14, 2010

Summary

This summary is machine-generated.

A new optical power splitter using asymmetric Y-branch waveguides achieves specific power splitting. Fabricated with polymer, it shows excellent uniformity, matching simulation predictions for integrated optical systems.

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Area of Science:

Photonics and Optical Engineering
Integrated Optics

Background:

Optical power splitters are crucial components in integrated optical systems.
Achieving specific and arbitrary optical power splitting ratios remains a challenge.

Purpose of the Study:

To propose and demonstrate a novel 1 × N optical power splitter.
To achieve desired specific optical power splitting ratios using asymmetric Y-branch waveguides.

Main Methods:

Utilizing asymmetric Y-branch waveguides based on total internal reflection for power splitting.
Simulating device performance to predict splitting characteristics.
Fabricating the device using polymer materials.

Main Results:

Simulated results confirm that arbitrary expected optical power splitting can be achieved.
Experimental fabrication demonstrates good uniformity at optical power output ports.
Experimental results align with simulation predictions.

Conclusions:

The proposed novel 1 × N optical power splitter effectively realizes specific power splitting.
The polymer-based device exhibits excellent uniformity and matches simulation predictions.
This device holds significant potential for applications in integrated optical systems.