A Gaussian beam is guided through a Single mode fiber. But if we propagate a Bessel beam through a Single mode fiber, then will it guide the Bessel beam like Gaussian beam? that means will the Bessel beam show the same guiding property in the conventional single mode fiber like Gaussian beam?
A conventional single mode fibre will not support a Bessel beam.
The fundamental mode typically has a field profile which is similar to, but not precisely Gaussian. A Bessel beam has multiple annular rings with alternating phase reversals. Attempting to couple light from a Bessel beam will excite higher order modes. In a single mode fibre, these will be radiation modes, which are not supported - this is what we mean by "single mode".
Once the radiation modes have dissipated or been absorbed in the fibre coating, the output from the fibre will be approximately Gaussian. Note that the mode field diameter and the rate of divergence will depend only on the fibre properties and the wavelength, not on the input field distribution.
A conventional single mode fibre will not support a Bessel beam.
The fundamental mode typically has a field profile which is similar to, but not precisely Gaussian. A Bessel beam has multiple annular rings with alternating phase reversals. Attempting to couple light from a Bessel beam will excite higher order modes. In a single mode fibre, these will be radiation modes, which are not supported - this is what we mean by "single mode".
Once the radiation modes have dissipated or been absorbed in the fibre coating, the output from the fibre will be approximately Gaussian. Note that the mode field diameter and the rate of divergence will depend only on the fibre properties and the wavelength, not on the input field distribution.
@Zbigniew Motyka & Alan Robinson Thank you so much for your valuable comments. It helps a lot for me.
Another thing is that, When we couple a Gaussian beam into a Single mode fiber, then the spot size of the Gaussian beam (W) is a fiber dependent parameter which is expressed as:
W= a.*(0.65+1.619*V^-1.5+2.879*V^-6) ..............................(1)
Where a= radius of SMF
V=V number of SMF.
But If we couple a axicon generated Bessel-Gauss beam into a special type of hollow fiber as mentioned in your answers, then how the spot size and radial wavevector will depends on fiber parameter. That means how th.The axicon-generated Besse-Gauss beam (which is in free space) can be expressed as:
A=J0(kr*r)*exp(-r.^2/W.^2) ..................................(2)
Where kr= radial wave-vector which depends on axicon angle, W is the illuminating Gaussian beam spot size and r is the radial co-ordinate of the fiber.
After focusing and collimating this zeroth order Bessel-Gauss beam, this beam is to be coupled to a special fiber. Then, How the beam spot size of gaussian envelope of bessel-gauss beam and radial wave vector will change after coupling of Bessel-Gauss beam into the special guiding fiber. Is there any mathematical relationship like Gaussian beam spot size formula in a SMF as mentioned in equation(1)?
The hollow core fibre described by Kim et. al Optics Letters Vol. 34, Issue 19, pp. 2973-2975 (2009) does not support a Bessel beam. Instead, their paper describes a method of generating an approximation to a Bessel beam.
As far as I can tell their hollow core fibre probably supports a single guided mode in which the power is concentrated in a 3 micron wide annulus of germania-doped silica with diameter between 10 and 30 microns. A silica spacer and polymer lens are attached to the fibre to convert the annular field in the fibre to an approximately Bessel output beam. This is similar to bulk optics synthesis using an annular aperture and converging lens.
"Spot size" is not a useful measure of the field in this type of fibre. Peak intensity will be within the annular doped core. The width of the annular field depends on the effective index of the mode and the thickness and refractive index profile of the core annulus.
As Zbigniew Motyka points out, the modes of circular core step index profile multimode fibre have a Jm(kn r) field distribution within the core.
A step index fibre will propagate a truncated zero order (m=0) Bessel field distribution. For fibre core radius a.
Acore ~ J0 (kn r) (r < a)
Aclad ~ K0(zetan r) (r > a)
The field in the cladding decays rapdily from the core boundary, described by a modified Bessel function of the same order, m, as the core field.
Silica core step index fibre is widely available with either fluorine-doped glass or polymer cladding: https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6838
https://www.fiberguide.com/wp-content/uploads/2012/09/Polymer_Clad_Fiber_090712.pdf
A large core fibre will support radial modes with different radial propagation constants kn and different propagation velocities. If you excite the fibre with a Bessel-Gaussian beam, or fail to match the radial propagation constant, then you will launch multiple fibre modes with different propagation velocities.
Launching multiple modes is undesirable. Beating between modes will change the transverse field distribution along the fibre. You may also need to take account of coupling between modes of different azimuthal and radial order which can be induced by bends, diameter fluctuations and other perturbations.
Regarding your spot size formula, note that the field in a single mode fibre is not exactly Gaussian, and Marcuse's approximation (your equation (1)) applies only to step refractive index profiles.
Dear Arijit,
Bessel beam before it's first zero occurs can support single-mode propagation for single-mode fibers. Beyond that point, there are mutimode propagation that can not propagate in single-mode fiber, which all depend mostly on V-number of fiber.
@Faramarz E. Seraji thank you sir for your comments.
Is there any special kind of fiber so that a Bessel field can be guided through that fiber without changing its shape?
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