The only active devices that's been employed in the proposed simplest 1 watt LED driver circuit are a few diodes and a mechanical switch.
The initial 6 volts from a charged battery is dropped to the required 3.5 volts limit by keeping all the diodes in series or in the path of the LED supply voltage.
Since each diode drops 0.6 volts across it, all four together allow only 3.5 volts to reach the LED, lighting it safely, yet brightly.
As the illumination of the LED drops, each diode is bypassed subsequently using the switch, to restore the brightness of the LED.
The use of the diodes for dropping the voltage level across the LEDs makes sure that the procedure does not dissipate any heat and therefore becomes very efficient in comparison to a resistor, which would have otherwise dissipated a lot of heat in the process.