Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum tunneling

Kheng Wye Chong

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Frustrated Total Internal Reflection (FTIR) has been researched since the time of Sir Issac Newton. In this paper, its application in modern optics is reviewed. A theoretical description of the phenomenon is presented beginning with Snell’s Law. The analogy between FTIR and quantum tunneling in one dimension is discussed. A quantitative and inexpensive method of demonstrating FTIR based on the attenuation of a microwave through an air gap between two wax prisms is described and a quantitative comparison of the theory with experiment is made. An extension of FTIR using microwave, as it is used in an Evanescent Wave Atomic Force Microscope (EW-AFM), is looked into and evaluated.

Related papers

Photon tunneling

Ole Keller

A paradigm of optical (photon) tunneling appears in relation to the physics of frustrated total internal reflection (FTIR); see e.g., [123, 118, 50, 224, 51]. In the FTIR process evanescent fields play an indispensable role, and the fact that the source domains of transverse and longitudinal photons generated by a current density sheet (located at z = 0) extend outside the sheet, with a current density profile given by exp(−q‖|z|), indicates that the physics in the rim zone is crucial for an understanding of the photon tunneling process. We shall reach the FTIR tunneling process starting from a broader framework. Thus, it turns out that optical near-field interaction, spatial photon localization, and photon tunneling have the same roots. The considerations to follow also lead to connections to the photon measurement problem which we shall address in Part VIII. In a broader context the problem brings us in contact with the so-called measurement theory in quantum physics, which in itself raises deep questions about the physical/philosophical structure of human observations [168, 157, 247].

CRC Press eBooks•May 13, 2014•0 citations

Universal tunneling time for all fields

G. Nimtz, A. A. Stahlhofen

Abstract Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.

Annalen der Physik•Jun 5, 2008•8 citations

Universal tunneling time for all fields

G. Nimtz, A.A. Stahlhofen

Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.

arXiv:0709.0921•Annalen der Physik•Apr 16, 2008•21 citations

Tunneling delay time in frustrated total internal reflection

Herbert G. Winful, Chao Zhang

The group delay in frustrated total internal reflection (FTIR) is shown to equal the dwell time plus a self-interference delay. The self-interference delay originates from the energy stored in the overlap between incident and reflected waves above the interface. The group delay in FTIR for finite beams is thus shown to be the lifetime of stored energy in the gap between the prisms and in the partial standing wave above the gap. As in other manifestations of tunneling the saturation of group delay with barrier length (Hartman effect) is explained by the saturation of stored energy in the region defined. No superluminal propagation is implied.

Physical Review A•Feb 23, 2009•23 citations

A visual classroom demonstration of frustrated total internal reflection as an analogue to optical tunnelling

Rabiya Salman, Shama Rashid, Muhammad Sabieh Anwar

Frustrated total internal reflection is presented as a visually attractive and convenient classroom demonstration. Optical evanescent waves penetrating through a dielectric barrier is a classical analogue to quantum mechanical tunnelling. We use the traditional double prism arrangement to demonstrate the pickup and relaunching of the evanescent wave. Total internal reflection could be completely frustrated by the insertion of an index matching fluid.

European Journal of Physics•Sep 20, 2013•8 citations

Path-integral treatment of optical and microwave tunneling

Paolo Moretti, Anedio Ranfagni, Paolo Levi Sandri

A model based on a statistical method, as deduced from a path-integral treatment of the Brownian motion proposed by Feynman and Hibbs in 1965, demonstrates to be capable of interpreting the results of delay time measurements in frustrated total internal reflection experiments at an optical and microwave scale. A plausible description of the trajectories followed by the system inside the tunneling region, the air gap between the two dielectric prisms, is given.

Physical Review E•Jun 27, 2007•3 citations
Frustrated Total Internal Reflection (FTIR) has been researched since the time of Sir Issac Newton. In this paper, its application in modern optics is reviewed. A theoretical description of the phenomenon is presented beginning with Snell’s Law. The analogy between FTIR and quantum tunneling in one dimension is discussed. A quantitative and inexpensive method of demonstrating FTIR based on the attenuation of a microwave through an air gap between two wax prisms is described and a quantitative comparison of the theory with experiment is made. An extension of FTIR using microwave, as it is used in an Evanescent Wave Atomic Force Microscope (EW-AFM), is looked into and evaluated.
A paradigm of optical (photon) tunneling appears in relation to the physics of frustrated total internal reflection (FTIR); see e.g., [123, 118, 50, 224, 51]. In the FTIR process evanescent fields play an indispensable role, and the fact that the source domains of transverse and longitudinal photons generated by a current density sheet (located at z = 0) extend outside the sheet, with a current density profile given by exp(−q‖|z|), indicates that the physics in the rim zone is crucial for an understanding of the photon tunneling process. We shall reach the FTIR tunneling process starting from a broader framework. Thus, it turns out that optical near-field interaction, spatial photon localization, and photon tunneling have the same roots. The considerations to follow also lead to connections to the photon measurement problem which we shall address in Part VIII. In a broader context the problem brings us in contact with the so-called measurement theory in quantum physics, which in itself raises deep questions about the physical/philosophical structure of human observations [168, 157, 247].
Abstract Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.
Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.
The group delay in frustrated total internal reflection (FTIR) is shown to equal the dwell time plus a self-interference delay. The self-interference delay originates from the energy stored in the overlap between incident and reflected waves above the interface. The group delay in FTIR for finite beams is thus shown to be the lifetime of stored energy in the gap between the prisms and in the partial standing wave above the gap. As in other manifestations of tunneling the saturation of group delay with barrier length (Hartman effect) is explained by the saturation of stored energy in the region defined. No superluminal propagation is implied.