Eur. Phys. J. Appl. Phys. (2013) 63: 10501 DOI: 10.1051/epjap/2013130196 THE EUROPEAN PHYSICAL JOURNAL APPLIED PHYSICS Regular Article Optically induced force in a curve waveguide Vladimir P. Torchigin a and Alexander V. Torchigin Institute of Informatics Problems, Russian Academy of Sciences, Nakhimovsky prospect 36/1, Moscow 119278, Russia Received: 17 April 2013 / Received in final form: 17 June 2013 / Accepted: 24 June 2013 Published online: 26 July 2013 – c  EDP Sciences 2013 Abstract. We show that optically induced force (OIF) that arises in a curve waveguide due to a change of the momentum of light wave because of a change of its direction is not a special kind of OIF. A conventional approach based on an analysis of OIF that arises in a homogeneous optical medium immersed in an alternate electrical field of light wave as well as an energetic approach can be used also. 1 Introduction At present an interest to optically induced forces (OIF) is increased because the intensity of light becomes so great in some optical devices that striction phenomena change op- tical properties of the devices. OIF can scale to remarkably high levels (greater than 104 N/m 2 ) for realistic guided power [1]. The masses and dimensions of optical devices have been miniaturized to the degree that the device tun- ing through optical actuation is possible at micro- and milliwatt power levels [2–5]. In many of these cases, OIF can scale to large values when optical fields are enhanced through high-Q resonances [6–8]. Such observations have sparked significant scientific interest in light-driven me- chanically variable systems. These mechanical functions can lead to variable directional couplers [3], parametric optical processes [2, 4, 7] in cavities, ultra-widely tunable microcavities [6]. Several different approaches to calculation of OIF are known. It is not clear in advance that the same kinds of OIF are calculated by means of various approaches. This causes debates relatively on an explanation of experimen- tal results because an experiment can give answer about a magnitude of OIF rather than about their kind. For ex- ample, the recent experiment of She et al. [8] shows that the light radiation from low-intensity laser yields an in- ward force at the end face of a vertical nanofiber. She et al. suppose that this force arises due to a change in the momentum of light on the boundary between vacuum and the end face of the fiber. They use the approach based on an analysis of a change of the momentum of light (CM approach). Brevik in his comment supposes that a kind of force known in electrostatics is responsible for a rise of this observed force [9]. He uses the electrostatic approach (ES approach). This approach is based on the fact that striction effects in electrostatics depend on the square of the strength E 2 of a static electrical field. In this case an a e-mail: v torchigin@mail.ru alternate electrical field of a light wave averaged over a pe- riod of oscillations is different from zero. In this case the surface force produced by plane waves on a plane bound- ary of optical mediums with permittivities ε 1 and ε 2 is given by f = -ε 0 (ε 2 - ε 1 )  E 2  /2, (1) where E is the strength of the electrical field, 〈...〉 de- notes average over an optical period [10–18]. The force is directed toward the optical medium which permittivity is smaller. CM approach is based on classical notions about the momentum of light wave and the force arising with a change in the momentum. This approach appears to be fruitful in some situations. For example, if it is known that a light wave penetrates completely through an arbi- trary slab, then the net OIF applied to the slab is equal to zero because a magnitude of the momentum of the light wave having penetrated through the slab is not changed. Moreover, if it is known that a part of the light wave is reflected from the slab then the slab is subject to action of OIF directed along the direction of propagation of the light wave because a magnitude of the total momentum of the light waves penetrating through the slab and reflecting from it is smaller than that of the initial momentum. A problem arises at calculation of the OIF applied to the optical medium in a form of a semi-space because there is not a generally accepted notion about a magnitude of the momentum in an optical medium. Minkowski and Abraham proposed two different approaches to this prob- lem. A great deal of controversy has centered on the rival claims of the Abraham expression for the photon momen- tum hυ/n where n is the refractive index of the medium. The Minkowski momentum is greater by n 2 times. The few available experiments seem to favor the latter, while many theories favor the former. This is not the place to review the large literature devoted to this problem. The interested reader can study the recent review by Pfiefer et al. [19]. In 2010 various arguments in favor of 10501-p1