Guide wavelength (λg), cut off wavelength (λc) and freespace

Guide wavelength (λ_g), cut off wavelength (λ_c) and freespace wavelength (λ₀) of a waveguide are related as:

1	=	1	−	1
λ²_g	=	λ²₀	−	λ²_c

1	=	1	−	1
λ₀²	=	λ_g²	−	λ_c²

1	=	1	+	1
λ_c²	=	λ_c²	+	λ_g²

1	=	1	+	1
λ_g	=	λ₀	+	λ_c