Coherent Mid-IR Supercontinuum Generation using Tapered Chalcogenide Step-Index Optical Fiber: Experiment and modelling

Mid-infrared region of electromagnetic spectrum has increased a lot of scientific and technical interest because of its utility to figure out the molecular fingerprints. Current mid-infrared light sources including quantum cascade lasers, thermal-emitters, and synchrotron radiation are not suitable for various potential applications where we require coherent, portable and broadband light sources. During the current decade, several efforts have been put forwarded to extend the spectral range of the supercontinuum. However, the coherent mid-infrared supercontinuum spectrum in the mid-infrared region has been demonstrated rarely. Here, we demonstrate a coherent mid-infrared supercontinuum using a tapered chalcogenide fiber pumped at various wavelength ranging from 2 µm to 2.6 µm. Experimental observations show that the supercontinuum spectrum extending from ~1.6 µm to 3.7 µm can be achieved using a 3 cm long tapered chalcogenide step-index optical fiber pumped with femtosecond laser pulses at 2.6 µm. To the best of our knowledge, using short pump wavelengths at 2 µm to 2.6 µm in an all-normal dispersion engineered chalcogenide glass fiber, the coherent supercontinuum spectrum has been reported first time. Such coherent broadband light source has its key prominence for the various prospective applications in the fields of bio-medical, sensing, and multiplex coherent anti-Stokes Raman scattering microspectroscopy.


Linear characteristic of the fiber
To simulate the tapered fiber structure, we calculated the effective mode indices of the fundamental mode by employing a commercially available software called 'COMSOL Multiphysics' which is based on full vectorial finite-element-method (FEM). In the simulation, the wavelength dependent refractive indices of the AsSe2 and As2S5 chalcogenide materials were fitted using the Sellmeier equation given below [1] The numerical values of the Sellmeier coefficients are provided in the following Table-1. The group velocity dispersion contributes an important role in the broadening of supercontinuum spectrum. Group velocity dispersion determines the degree to which diverse spectral components of the ultra-short laser pulse propagate at different phase velocities in the fiber. The group velocity dispersion connected with the wavelength dependent effective mode indices of the propagating mode as the following relation [2] where, c is the speed of the light in free space, Re(neff) represents the real part of effective mode indices.
The effective-mode-area of propagating mode is calculated by the following equation where, E represents the amplitude of the electric field.

Nonlinear characteristic of the fiber
In the simulation, an initial input pulse, a hyperbolic secant pulse is considered in the simulation which is given below where A indicates an envelope of pulse, P0 represents the peak power of pulse, T0 =TFWHM/1.7627 (TFWHM represents the full-width-at-half-maxima) for a hyperbolic secant pulse, and T is the comoving frame at the group velocity of the pulse envelope.
The supercontinuum spectrum generated in the fiber was simulated using the following generalized nonlinear Schrodinger equation where ̃′ represents the envelope of an output pulse in the frequency domain which is related to the envelope of the pulse in time domain by the following equation where ℱ −1 represents the inverse Fourier transform, z shows the propagation distance, and Aeff indicates the effective-mode-area of the mode propagating in the fiber. The Eq. (5) was solved by employing the adaptive step size method with the fourth-order-Runge-Kutta algorithm [3]. ̅ ( ) indicates the frequency dependent nonlinear coefficient and given by the following equation where n2 is the nonlinear refractive index (n2 = 2.3×10 -17 m 2 /W for AsSe2 based chalcogenide glass where β represents the propagation constant, β1 is the reciprocal of group velocity of the envelope, ω0 depicts the reference frequency, and α indicates the losses in the fiber. In the numerical simulations, both the material and confinement losses of the fiber have been included.
The Raman response function is calculated using the following relation

Coherence characteristic of the generated supercontinuum spectrum
The coherence characteristic of the generated supercontinuum spectrum is affected by the existence of the quantum noise of the pulse. We used one-photon-per-mode semi-classical theory to model the noise of the input pulse [5]. The complex degree of coherence was used to consider the deficit in the coherence characteristic of the spectrum due to the spectral phase instability at each wavelength. The relation for the complex degree of coherence is as follows [6] | 12 (1) ( , 1 − 2 )| = | 〈 1 * ( , 1 ) 2 ( , 2 )〉 √〈| 1 ( , 1 )| 2 〉 √〈| 2 ( , 2 )| 2 〉 | (11) where E1 and E2 are the amplitudes of the electric field for two successive generated spectra. To focus on the wavelength dependence of the coherence, in the simulation study t1-t2=0 was taken.