loP Publishing Eur.J.Phys.38(2017)025209(12pp) ttps://do.org/10.1088/1361-6404/aa596 Understanding the power reflection and transmission coefficients of a plane wave at a planar interface Qian Ye, yikun Jiang and Haoze Lin Department of Physics, Fudan University, Shanghai 200433, People's Republic of High School Affiliated to Fudan University, Shanghai 200433, Peoples Republic of China E-mail:gyel4@fudan.edu.cn Received 2 November 2016. revised 23 December 2016 Accepted for publication 13 January 2017 Published 3 February 2017 Abstract In most textbooks, after discussing the partial transmission and reflection of a plane wave at a planar interface, the power(energy) reflection and transmis- sion coefficients are introduced by calculating the normal-to-interface com- ponents of the Poynting vectors for the incident, reflected and transmitted waves, separately. Ambiguity arises among students since, for the Poynting vector to be interpreted as the energy flux density, on the incident(reflected side, the electric and magnetic fields involved must be the total fields, namely, the sum of incident and reflected fields, instead of the partial fields which are just the incident (reflected)fields. The interpretation of the cross product of partial fields as energy flux has not been obviously justified in most textbooks Besides, the plane wave is actually an idealisation that is only ever found in textbooks then what do the reflection and transmission coefficients evaluated for a plane wave really mean for a real beam of limited extent? To provide a clearer physical picture, we exemplify a light beam of finite transverse extent by a fundamental Gaussian beam and simulate its reflection and transmission at a planar interface. Due to its finite transverse extent, we can then insert the incident fields or reflected fields as total fields into the expression of the Poynting vector to evaluate the energy flux and then power reflection and transmission coefficients. We demonstrate that the power reflection and sum of the corresponding coefficients for all constituent plane wave coas transmission coefficients of a beam of finite extent turn out to be the weight nents that form the beam. The power reflection and transmission coefficients of a single plane wave serve, in turn, as the asymptotes for the corresponding coefficients of a light beam as its width expands infinitely. 0143-0807/17/025209+12533.00 G 2017 European Physical Society Printed in the UKUnderstanding the power reflection and transmission coefficients of a plane wave at a planar interface Qian Ye1 , Yikun Jiang1 and Haoze Lin2 1 Department of Physics, Fudan University, Shanghai 200433, Peopleʼs Republic of China 2 High School Affiliated to Fudan University, Shanghai 200433, Peopleʼs Republic of China E-mail: qye14@fudan.edu.cn Received 2 November 2016, revised 23 December 2016 Accepted for publication 13 January 2017 Published 3 February 2017 Abstract In most textbooks, after discussing the partial transmission and reflection of a plane wave at a planar interface, the power (energy) reflection and transmis￾sion coefficients are introduced by calculating the normal-to-interface com￾ponents of the Poynting vectors for the incident, reflected and transmitted waves, separately. Ambiguity arises among students since, for the Poynting vector to be interpreted as the energy flux density, on the incident (reflected) side, the electric and magnetic fields involved must be the total fields, namely, the sum of incident and reflected fields, instead of the partial fields which are just the incident (reflected) fields. The interpretation of the cross product of partial fields as energy flux has not been obviously justified in most textbooks. Besides, the plane wave is actually an idealisation that is only ever found in textbooks, then what do the reflection and transmission coefficients evaluated for a plane wave really mean for a real beam of limited extent? To provide a clearer physical picture, we exemplify a light beam of finite transverse extent by a fundamental Gaussian beam and simulate its reflection and transmission at a planar interface. Due to its finite transverse extent, we can then insert the incident fields or reflected fields as total fields into the expression of the Poynting vector to evaluate the energy flux and then power reflection and transmission coefficients. We demonstrate that the power reflection and transmission coefficients of a beam of finite extent turn out to be the weighted sum of the corresponding coefficients for all constituent plane wave compo￾nents that form the beam. The power reflection and transmission coefficients of a single plane wave serve, in turn, as the asymptotes for the corresponding coefficients of a light beam as its width expands infinitely. European Journal of Physics Eur. J. Phys. 38 (2017) 025209 (12pp) https://doi.org/10.1088/1361-6404/aa5960 0143-0807/17/025209+12$33.00 © 2017 European Physical Society Printed in the UK 1