Achromatic waveguide input/output coupler design

Abstract

An investigation into methods for achromatizing the coupling angle characteristics of waveguide input/output couplers is described. The basic approach involves correcting the inherent angular dispersion of conventional waveguide couplers with a diffraction grating. Two configurations are analyzed in detail: a hybrid prism/grating coupler and a double grating coupler. Expressions are derived for values of the grating parameters that produce achromatic coupling. A method is also presented to predict the achromatic wavelength range and maximize it with the available degrees of freedom. For a coupling angle tolerance of 0.005 degrees , it is found that with double grating couplers achromatic wavelength ranges of the order of 10 nm can be obtained, and that with prism/grating couplers this range can be as large as 200 nm.

Achromatic waveguide lenses

“…'IYX) = CAN(X) + (I ) dO- (13) The focal length of the doublet is, therefore, given by This approach allows us to design an achromatic waveguide lens for a system with arbitrary dispersion characteristics for the waveguide and lens regions. Note that if the condition for an achromatic modeindex lens that was given in Eq.…”

70-nm-bandwidth achromatic waveguide coupler

“…Different configurations to increase the spectral bandwidth of planar waveguide couplers have been proposed. Spaulding and Morris 11,12 suggested two different approaches to the problem: 1a2 a surfacerelief transmission grating on top of a prism coupler and 1b2 a grating coupler combined with a transmission grating tilted at a specific angle. The reported experimental full-widths at half-maximum 1FWHM's2 were 41 nm and 13 nm for prism-grating and doublegrating couplers, respectively.…”

“…In this paper we introduce a different approach to the design of achromatic couplers. Instead of working with coupling angles, [11][12][13][14] we describe the achromatization problem as an effective-index-matching process between waveguide and coupler, which is directly related to coupling efficiency. 16 The effective-index mismatch function is defined and expanded into a Taylor series in which the coefficients are defined as chromatic orders.…”

“…1, which combines two grat-ings and a prism, has simplicity and sufficient degrees of freedom. The two gratings are parallel to the waveguide, avoiding the critical alignment required in previous designs, [11][12][13][14] and can be fabricated on a single slide. As we show below, the gratings are designed with slightly different spatial frequencies to function as an equivalent long-period grating, and their linear wavelength dependence is used to correct the first chromatic order.…”

“…Our condition for canceling the first derivative of the mismatch function with respect to wavelength is equivalent to the condition given by Spaulding and Morris, 11 which imposes a zero derivative of the incident coupling angle with respect to wavelength 1du i @dl 5 02. This can be verified by taking our mismatch function as an implicit function of wavelength and coupling angle and setting it equal to zero,…”