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Authors
Amit Halder
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No Arabic abstract
A monochromatic linear source of light is rotated with certain angular frequency and when such light is analysed after reflection then a change of frequency or wavelength may be observed depending on the location of the observer. This change of frequency or wavelength is different from the classical Doppler effect [1] or relativistic Doppler effect [2]. The reason behind this shift in wavelength is that a certain time interval observed by an observer in the rotating frame is different from that of a stationary observer.
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We propose and substantiate experimentally the cascaded rotational Doppler effect for interactions of spinning objects with light carrying angular momentum. Based on the law of parity conservation for electromagnetic interactions, we reveal that the frequency shift can be doubled through cascading two rotational Doppler processes which are mirror-imaged to each other. This effect is further experimentally verified with a rotating half-wave plate, and the mirror-imaging process is achieved by reflecting the frequency-shifted circularly polarized wave upon a mirror with a quarter-wave plate in front of it. The mirror symmetry and thus parity conservation guarantees that this doubled frequency shift can be further multiplied with more successive mirror-imaging conjugations, with photons carrying spin and/or orbital angular momentum, which could be widely applied for detection of rotating systems ranging from molecules to celestial bodies with high precision and sensitivity.
The frequency shift of a helical light beam experiencing the rotation near the axis deferring from its own axis (conical evolution) is studied theoretically. Both the energy and the kinematic approaches lead to a paradoxical conclusion that after a whole cycle of the system rotation the beam does not return to its initial state. Another paradox is manifested in the peculiar behavior of the beam transverse pattern rotation at different geometric parameters of the evolving system. A fundamental role of the detecting system motion is substantiated. The special natural observers motion is found for which both paradoxes are eliminated. Relations of the described facts with the Hannays geometric phase concept are discussed.
Doppler cooling is a widely used technique to laser cool atoms and nanoparticles exploiting the Doppler shift involved in translational transformations. The rotational Doppler effect arising from rotational coordinate transformations should similarly enable optical manipulations of the rotational degrees of freedom in rotating nanosystems. Here, we show that rotational Doppler cooling and heating (RDC and RDH) effects embody rich and unexplored physics, such as a strong dependence on particle morphology. For geometrically confined particles, such as a nanorod that can represent diatomic molecules, RDC and RDH follow similar rules as their translational Doppler counterpart, where cooling and heating are always observed at red- or blue-detuned laser frequencies, respectively. Surprisingly, nanosystems that can be modeled as a solid particle shows a strikingly different response, where RDH appears in a frequency regime close to their resonances, while a detuned frequency produces cooling of rotation. We also predict that the RDH effect can lead to unprecedented spontaneous chiral symmetry breaking, whereby an achiral particle under linearly polarized illumination starts spontaneously rotating, rendering it nontrivial compared to the translational Doppler effect. Our results open up new exciting possibilities to control the rotational motion of molecules and nanoparticles.
The function to measure orbital angular momentum (OAM) distribution of vortex light is essential for OAM applications. Although there are lots of works to measure OAM modes, it is difficult to measure the power distribution of different OAM modes quantitatively and instantaneously, let alone measure the phase distribution among them. In this work, we demonstrate an OAM complex spectrum analyzer, which enables to measure the power and phase distribution of OAM modes simultaneously by employing rotational Doppler Effect. The original OAM mode distribution is mapped to electrical spectrum of beating signals with a photodetector. The power distribution and phase distribution of superimposed OAM beams are successfully retrieved by analyzing the electrical spectrum. We also extend the measurement to other spatial modes, such as linear polarization modes. These results represent a new landmark of spatial mode analysis and show great potentials in optical communication and OAM quantum state tomography.
We describe a time lens to expand the dynamic range of photon Doppler velocimetry (PDV) systems. The principle and preliminary design of a time-lens PDV (TL-PDV) are explained and shown to be feasible through simulations. In a PDV system, an interferometer is used for measuring frequency shifts due to the Doppler effect from the target motion. However, the sampling rate of the electronics could limit the velocity range of a PDV system. A four-wave-mixing (FWM) time lens applies a quadratic temporal phase to an optical signal within a nonlinear FWM medium (such as an integrated photonic waveguide or highly nonlinear optical fiber). By spectrally isolating the mixing product, termed the idler, and with appropriate lengths of dispersion prior and after to this FWM time lens, a temporally magnified version of the input signal is generated. Therefore, the frequency shifts of PDV can be slowed down with the magnification factor $M$ of the time lens. $M=1$ corresponds to a regular PDV without a TL. $M=10$ has been shown to be feasible for a TL-PDV. Use of this effect for PDV can expand the velocity measurement range and allow the use of lower bandwidth electronics. TL-PDV will open up new avenues for various dynamic materials experiments.
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