Control of coherent backscattering by breaking optical reciprocity

Reciprocity is a universal principle that has a profound impact on many areas of physics. A fundamental phenomenon in condensed-matter physics, optical physics, and acoustics, arising from reciprocity, is the constructive interference of quantum or classical waves which propagate along time-reversed paths in disordered media, leading to, for example, weak localization and metal-insulator transition. Previous studies have shown that such coherent effects are suppressed when reciprocity is broken. Here we experimentally show that by tuning a nonreciprocal phase we can coherently control complex coherent phenomena, rather than simply suppress them. In particular, we manipulate coherent backscattering of light, also known as weak localization. By utilizing a magneto-optical effect, we control the interference between time-reversed paths inside a multimode fiber with strong mode mixing, observe the optical analog of weak antilocalization, and realize a continuous transition from weak localization to weak antilocalization. Our results may open new possibilities for coherent control of waves in complex systems.

Figure 1

Coherent backscattering of light in a multimode fiber (MMF). (a) Illustration of CBS in a random scattering sample, depicting one pair of time-reversed paths (solid and dashed arrows). The two paths accumulate the same phase inside the sample and interfere constructively in the direction opposite from the incident wave. (b) Illustration of CBS in a MMF. Due to fiber imperfections, twisting, and bending, the guided modes are strongly coupled, and the light can propagate through many different paths. Part of the light is backreflected from the output end of the fiber due to Fresnel reflection, creating time-reversed paths as illustrated. (c) Schematic of the experimental setup for observing CBS in a MMF. A laser beam $\left(\lambda =640\mathrm{nm}\right)$ is coupled to a 5-m-long step-index multimode fiber that supports ∼1500 guided modes. The incident beam is collimated, and its direction deviates from the normal of the input facet of the fiber so that the backscattering direction differs from that of the specular reflection. The backreflected light is picked up with a beam splitter (BS) and recorded by a CCD camera. An additional lens is used to image the far field of the fiber front facet to the camera. The light impinging on the fiber is circularly polarized to suppress specular reflection from the front facet of the fiber (p—linear polarizer and λ/4—quarter-wave plate). The linear polarizer is placed in front of the camera to detect light in the same polarization as the input (co-polarization channel). (d) Far field intensity distribution of the returning light, averaged over 200 fiber configurations. Enhanced intensity in the backscattering direction is observed (top arrow) and in its mirrored position is a strong specular reflection (bottom arrow). The insets show a magnified view of the CBS peak and a cross section of the averaged intensity with an enhancement factor of 1.81. The scale bar represents 0.05 rad. $\sigma =0.004\mathrm{rad}$ is the full width at half maximum of a single speckle grain.

Figure 2

Coherent backscattering in a MMF loop. (a) A collimated laser beam is split by BS1 and coupled to the two end facets of a 6-m-long step-index multimode fiber. The transmitted fields are recombined by BS1, forming a Sagnac loop. The two facets of the fiber are positioned at conjugated planes, and their combined far field images are recorded by CCD1 and CCD2. The inset shows an illustration of one pair of counterpropagating paths in the fiber. (b) Top panel: images recorded by the two cameras, averaged over 200 configurations of the fiber. On CCD1 a CBS peak is observed due to constructive interference of time-reversed paths, and on CCD2 a CBS dip is observed due to destructive interference. Since the illumination and detection channels are at different ports of BS1, the destructive interference in CCD2 does not violate the reciprocity principle. Bottom panel: intensity distribution in the vicinity of the backscattering direction (CCD1: blue solid line; CCD2: green dashed line). The CBS peak to background ratio is 1.85, and the dip to background ratio is 0.15. The scale bar represents 0.05 rad. $\sigma =0.004\mathrm{rad}$ is the full width at half maximum of a single speckle grain.

Figure 3

Control of coherent backscattering with a Faraday rotator. (a) A Faraday rotator is inserted to the fiber loop shown in Fig. 2 by splitting the multimode fiber to two segments (5-m and 1-m long) and placing the Faraday rotator in between. Two collimators are placed on both sides of the Faraday rotator to collimate the beams coming out of the fiber and refocusing them into the other fiber. (b)–(e) Magnified view of the CBS signal measured by CCD1 for four nonreciprocal phases φ induced by the Faraday rotator. (b) $\phi =0$, (c) π/4, (d) π/2, and (e) π. The scale bar represents 0.01 rad. A continuous transition is observed from a CBS peak (peak to background ratio of 1.86) to a dip (dip to background ratio of 0.15). (f) Cross sections of the images (b)–(e) ($\phi =0$ blue solid line, $\phi =\pi /4$ green dashed line, $\phi =\pi /2$ red dotted line, and $\phi =\pi$ black dashed-dotted line). $\sigma =0.004\mathrm{rad}$ is the full width at half maximum of a single speckle grain. (g)–(k): The same as (b)–(f) for the images recorded by CCD2.