How can people teleport through forcefields in Star Trek?

Occasionally, people have been able to teleport through a forcefield in Star Trek. Was there ever a consistent explanation for this?

I'd previously assumed a forcefield was like a solid wall. Or do they have gaps?

Answer

Well, if you are refering to defense screens (like the Deflector Shields on the various ships), it's a matter of frequency resonance. Think of the transporter signal like any other data transmission method; run it through a random (or pseudo random) interference pattern, and it will become meaningless noise. (Fortunately, there are inherent protections against sending in those conditions in modern transporters.. That's why you hear about getting a transporter 'lock' and such.)

BUT.. if you know the frequency that the interference will be at (assuming a basic pattern, after that), you can adjust your carrier wave to match it, and it, in effect, becomes non-existant. Much like dealing with the 60 cycle hum from sending data along a power line IRL.

From Memory Alpha (Star Trek Wiki):

Shields operated within a range of shield frequencies to allow certain specific types of energy and matter to pass through, or to increase the effectiveness of blocking them. The frequencies of shields were not usually discernible without examining the controls on board the ship deploying them, meaning that it was very difficult to tune weapons to the exact frequency of an opponent's shields to bypass them. (DS9: "The Jem'Hadar"; Star Trek Generations)

If you recall, fighting the Borg, they kept talking about shifting the shield harmonic frequency randomly, and did the same with their weapons, to attack.

Now, why the frequency can't readily be identified from the outside, I've never heard a good explanation.. it could be that this is a simplified way to explain it, and the actual mechanic is that you START at that frequency and then follow a standard pattern of small modifications over a fixed period of time. A statistical sample should still give you the base frequency.... but, who knows what other tricks they add.

Oh, btw.. It wasn't always like that:

Normally, transporters were not capable of penetrating shields. (TOS: "Arena") 23rd century Federation starships, such as the Constitution-class USS Enterprise, could not even transport through their own shields, but later starships such as the Intrepid-class and Sovereign-class vessels could transport personnel and objects freely to and from without having to lower their shields.

Also, Deflector Fields are just a specific (and better known) version of force fields, the same principles apply to true 'Force Fields' as well - Memory Alpha - Force Fields