Certain exhaust after-treatment devices, at least periodically, require the addition of unburnt hydrocarbons in order to create reductant-rich exhaust conditions. The present disclosure adds unburnt hydrocarbons to exhaust from at least one combustion chamber by positioning, at least partially within a combustion chamber, a mixed-mode fuel injector operable to inject fuel into the combustion chamber in a first spray pattern with a small average angle relative to a centerline of the combustion chamber and a second spray pattern with a large average angle relative to the centerline of the combustion chamber. An amount of fuel is injected in the first spray pattern into a non-combustible environment within the at least one combustion chamber during at least one of an expansion stroke and exhaust stroke. The exhaust with the unburnt amount of fuel is moved into an exhaust passage via an exhaust valve.