Measuring the Guiding Properties of High-Index-Glass-Clad Crystal

5.3.1 Refractive Index Profiling

The optical fiber index-profiling techniques include the reflectance mapping methods [24], [69], [70], the refracted near-field methods [71], and the interferometric methods [72]–[74].

In the reflectance mapping methods, the reflectance of the fiber end face is mapped with a laser scanning microscope. The refractive index profile is then deduced from the reflectance profile with the Fresnel reflection equation. The spatial resolution is determined by the focal spot size. The flatness of the end face is critical for this technique.

A crystal fiber cannot be cleaved since the core and the cladding are made of different materials. Therefore, polishing is necessary for achieving an optically flat surface.

However, the reflectance of polished glass surfaces may change significantly due to the polishing-induced surface layer [75]–[78]. Meanwhile, in our experiences, the reflectance of the YAG crystal does not change much after polishing. Therefore, the reflectance of a polished glass-clad crystal fiber end face cannot be correctly mapped, due to different extent of the polishing-induced reflectance change in the core and the cladding region.

The refracted near-field methods and the interferometric methods all require immersing the test fiber into the fluids with the refractive index matching to that of the cladding. The n_d is 1.8328 for YAG crystal and even higher for the 4 types of high index glasses. However, the highest n_d of the non-toxic commercial index-matching fluids is only 1.81 (19160, Cargille Labs). Imperfect match of the immersion fluid index and the cladding index will result in large error for the refracted near-field methods [79] and reduced sensitivity for the interferometric methods [80].

To summarize, it is hard to obtain an accurate index profile for a YAG crystal fiber cladded with high-index glass, due to the polishing-induced reflectance change in the glass cladding and the lack of the index matching fluids.

5.3.2 Near-Field Mode Imaging

The core modes of the HIGC crystal fibers are imaged with the system illustrated in Fig. 5.5. An SMF28e patch cord was used as the input fiber of the system. The input wavelength could be changed simply by connecting the input fiber to a different fiber-pigtailed light source. Four fiber-fiber-pigtailed lasers with wavelengths of 532, 658, 780, and 1064 nm were used as the light sources. The light was collimated and focused by a pair of near-infrared objective lenses (M Plan APO NIR 5X, Mitsutoyo). These objective lenses are chromatically corrected from visible to NIR, and there is no apparent focal shift for wavelengths up to 1100 nm. The light reflected from the crystal fiber input end face was split by a broadband beam splitter for observation with naked eye. The light output from the crystal fiber was imaged on a charge-coupled device (CCD) with an aspherical lens with f = 14 mm and NA = 0.16 (5726-B-H, New Focus).

During the experiment, the coupling into the crystal fiber was optimized at the visible wavelengths. When switching to infrared wavelengths, there was no need to re-align the crystal fiber due to the good chromatic correction of the objective lenses.

However, the imaging system after the crystal fiber needs to be re-focused since the aspheric lens has strong dispersion.

EP

Fig. 5.5. Experimental setup for imaging the modes of the HIGC crystal fiber.

OBJ1 and OBJ2: objective lenses; BS: beam splitter; TL: tube lens; EP: eye piece; CF: crystal fiber; L: aspheric lens; CCD: charge-coupled device.

5.3.3 Far-Field Intensity Distribution

The setup for measuring the far-field distribution is depicted in Fig. 5.6. The light output from the crystal fiber was directly captured by the CCD without imaging with a lens.

Fig. 5.6. Experimental setup of measuring the far-field distribution of the HIGC crystal fiber.

The reason of measuring the far-field distribution is to clarify that whether the fiber was guided or not. In an unguided fiber, a ray launched into core will be split into reflected ray and transmitted ray when hitting the core-cladding interface, as depicted in Fig. 5.7.

θ1

θ2

θ2'

θ1' n1

n2

n2 > n1

Fig. 5.7. Schematic illustration of the rays propagate in and output from an unguided crystal fiber.

The transmitted light will be refracted so that the propagation angle with respect to the fiber axis becomes larger. If the transmitted rays hit the core-cladding interface again, part of the power will be transmitted back into the core. For the rays leave from the cladding region of the crystal fiber, the exit angle θ₂′ can be described as:

2 2 2

2 2 1 1

sinθ′ = n −n cos θ (5.4)

where n1 is the ray propagation angle with respect to the fiber axis inside the core, and n1 and n₂ are the refractive indices of the core the cladding, respectively. This angle has a minimum value of

2 2

2_ min 2 1

sinθ^′ = n −n (5.5)

Although some of the light was output from the core region, but the relative intensity will be small if the fiber is long enough. Therefore, the output light will exhibit as a cone with a minimum angle of θ2_ min′ . The intensity pattern captured by the CCD will be a bright ring with a relatively dark inner region.

No ring pattern will be observed if the crystal fiber is guided or if the ray is launched into the crystal fiber at the cladding region. Thus the observation of the ring pattern is a deterministic proof that the crystal fiber is unguided. The refractive index difference between the core and the cladding can also be deduced from (5.5) by measuring the angle of the inner edge of the light cone.

5.4 High-Index-Glass-Clad Pure YAG Crystal Fibers