- #1
EmilyRuck
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Hello!
Let's consider a plane wave represented by a ray, propagating in a 2D dielectric slab. It has a medium with refractive index n_1 as its core and a medium with refractive index n_2, n_2 < n_1, as its cladding. In order for this ray to represent a mode, it must satisfy two conditions:
- total internal reflection: the angle of incidence \theta_i upon the dielectric interface between the core and the cladding should be such that \sin \theta_i > n_2 / n_1;
- self-consistency: 2 k_1 d \cos (\theta_i) + 2 \varphi_r = 2 m \pi, where d is the core thickness, k_1 is the wavenumber of the plane wave inside the core and \varphi_r is the phase shift due to reflection at the dielectric interface.
More details can be found http://people.seas.harvard.edu/~jones/ap216/lectures/ls_1/ls1_u8/ls1_unit_8.html, with [VIII-36].
This gives only a certain (finite) number of allowed angles \theta_{i,m} for the ray, if the frequency f in k_1 = 2 \pi f \sqrt{\mu_0 \epsilon_1} is known.
When exciting the guide with a signal, should this signal be forced to impinge on the core/cladding interface with one of those angles? How can such a signal be usefully generated, ensuring that its k_1 vector will have the allowed angle of incidence?
Let's consider a plane wave represented by a ray, propagating in a 2D dielectric slab. It has a medium with refractive index n_1 as its core and a medium with refractive index n_2, n_2 < n_1, as its cladding. In order for this ray to represent a mode, it must satisfy two conditions:
- total internal reflection: the angle of incidence \theta_i upon the dielectric interface between the core and the cladding should be such that \sin \theta_i > n_2 / n_1;
- self-consistency: 2 k_1 d \cos (\theta_i) + 2 \varphi_r = 2 m \pi, where d is the core thickness, k_1 is the wavenumber of the plane wave inside the core and \varphi_r is the phase shift due to reflection at the dielectric interface.
More details can be found http://people.seas.harvard.edu/~jones/ap216/lectures/ls_1/ls1_u8/ls1_unit_8.html, with [VIII-36].
This gives only a certain (finite) number of allowed angles \theta_{i,m} for the ray, if the frequency f in k_1 = 2 \pi f \sqrt{\mu_0 \epsilon_1} is known.
When exciting the guide with a signal, should this signal be forced to impinge on the core/cladding interface with one of those angles? How can such a signal be usefully generated, ensuring that its k_1 vector will have the allowed angle of incidence?
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