Acoustic Band Gaps and Defect Modes in PeriodicallyStructured Wave Guides

1
Acoustic Band Gaps and Defect Modes in
Periodically-Structured Wave Guides

• J. N. Munday, C. Brad Bennett, and W. M.
  Robertson
• Department of Physics and Astronomy
• Middle Tennessee State University

2
Outline

• Introduction and background
• Basic theory
• Experimental configuration
• Acoustic band gaps and defect modes
• Conclusions

3
Introduction and Background

• Solid state
• Electron wave functions
• Band gaps
• Defect modes
• Optical analogy
• Electromagnetic waves
• Photonic band gaps

4
Introduction and Background

• Acoustics
• Air pressure waves
• PVC piped structure
• Band gaps
• Defect modes

5
Basic Theory

• Acoustic impedance
• Reflection/Transmission at a junction
• Periodicity
• Adapted program from optics

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Basic Theory

• Transmission Spectrum
• Periodicity and impedance similar to that of
  experiment

7
Experimental Configuration

• Pulse generation
• Data acquisition
• Add and average
• Diameter-modulated wave guide
• 17.5 cm sections (9 total)
• ¾ and 2 diameters

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Acoustic Band Gaps

• Time domain data
• Straight-through pipe
• Diameter-modulated array

9
Acoustic Band Gaps

• Frequency domain data upon Fourier Transform

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Defect Modes

• Diameter-modulated array I
• ¾ and 2 diameters
• Periodicity of 17.5 cm
• Theory
• Narrow mode with 100 transmission
• Experiment
• Greatly attenuated due to imperfections in the
  periodicity

11
Defect Modes

• Diameter-modulated array II
• ¾ and 1.25 diameters
• Periodicity of 17.5 cm
• Theory
• Slightly wider modes
• Experiment
• Wider modes are more easily detectable

12
Defect Modes

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Conclusions

• Simple yet effective model
• Band gaps
• Defect modes
• Theoretically narrow defect modes
• Experimental limitations
• Related acoustic band gap work
• Tunneling