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For the correlated color temperature (CCT) of a light source to be estimated, a nonlinear optimization problem must be solved. In all previous methods available to compute CCT, the objective function has only been approximated, and their predictions have achieved limited accuracy. For example, different unacceptable CCT values have been predicted for light sources located on the same isotemperature line. In this paper, we propose to compute CCT using the Newton method, which requires the first and second derivatives of the objective function. Following the current recommendation by the International Commission on Illumination (CIE) for the computation of tristimulus values (summations at 1 nm steps from 360 nm to 830 nm), the objective function and its first and second derivatives are explicitly given and used in our computations. Comprehensive tests demonstrate that the proposed method, together with an initial estimation of CCT using Robertson's method [J. Opt. Soc. Am. 58, 1528-1535 (1968)], gives highly accurate predictions below 0.0012 K for light sources with CCTs ranging from 500 K to 10⁶ K.

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Tilted fiber Bragg grating (TFBG) presents many unique spectral characteristics for sensing. The widespread approaches to date are based on the cutoff mode resonance and surface plasmon resonance (SPR), whereas the leaky mode resonance is ignored in the literature. Herein, we theoretically demonstrate that the s-polarized (or TE/HE) leaky mode resonance (and the guided mode resonance) can be efficiently enhanced (and suppressed) by integrating graphene on the TFBG for a highly sensitive sensor. In contrast, the p-polarized (or TM/EH) mode (both leaky mode and guided counterpart) presents slight variation. The enhancement principle is discussed based on the variation in the mode characteristics induced by the graphene. The results show that the graphene enhanced leaky mode resonance presents ultra-sensitive intensity response but insensitive wavelength response to the extremely small analyte perturbation. The sensitivities are achieved up to 14108dB/RIU and 5232.6dB/RIU for the first two leaky modes in gaseous media respectively, which are 121 and 13 times higher than that of bare TFBG. This novel sensing platform provides a promising technique that can compete with the widespread SPR approach in fiber optic sensing fields, which opens up new opportunities for industrial, environmental, and biochemical sensing applications. INDEX TERMS Tilted fiber Bragg grating, graphene, leaky mode resonance, refractive index sensing.

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In this work, the tuning property and sensitivity enhancement of the long period fiber grating (LPFG) coated with the higher refractive index film are demonstrated theoretically by integrating a monolayer graphene. The general variation rule of the mode characteristics and the resonance with the chemical potential of the graphene are explored. The polarization-independent transmission and sensing characteristics are obtained even though the optical property of the graphene is polarization-dependent. The results reveal that the sensing characteristics are significantly dependent on the tunable state of the graphene, which can be used to greatly optimize the sensing performance. By this approach, an ultrahigh sensitivity up to 28 337.5 nm/RIU is achieved, which is 2.57 times higher than that of the conventional LPFG without graphene. The sensitivity can be further optimized by integrating few-layer graphene. This tunable property at a wide range makes the graphene integrated LPFG devices without destroying the fiber integrity ideal for wide applications, such as biochemical sensing and optical modulation.