Directionality would be one of them. You would expect the emission output suddenly changes to a beam at the threshold.

With transition of the operation in led mode to the laser you should observe a sudden increase in beam power. Do you have any instrument to be able to see the interference fringes and laser modes?

I am only able to measure the power and spectrum so far, and I don't have any instrument to see the interference fringes and laser modes.

I think you need to measure the optical spectrum to confirm it a laser not a SLED.

To confirm you don't have an LED you should check the spectral line width and power scaling. LEDs will have broader line widths and won't show transition features.

To confirm between SLED and a Laser is a little more complicated as SLEDs are based on amplified spontaneous emission, which has many characteristics similar to lasers. One of the primary differences is the degree of coherence. If you can collimate the output into a Michelson interferometer you should be able to easily measure the coherence length of your light source. Typically SLEDs have coherence lengths on the order of 10s of microns, while Lasers tend to have coherence lengths on the order of meters.

The ouput power should increase suddently above the threshold and you also can measure the optical spectrum with an optical spectrum analyser. if you are not convinced ,you can also measure the intensity noise spectrum with an electrical spectrum analyser, in this case, you should observe a resonance peak at the relaxation oscillation frequency. Such of behavior is typical in solid state and semiconductor laser.

If I am able to get a narrow linewidth (

In addition to the narrowing of the linewidth already mentioned, if you have a video camera that works at your suspected laser wavelength you should be able to observe a speckle pattern on a surface if you really have lasing. You will probably also need a neutral density filter(s) to keep from saturating your camera. This is the Fourier transform into the spatial domain of the same physical phenomenon (long coherence length). If you don't have an interferometer handy this can sometimes be a quick, qualitative check.

You don't mention wavelength or power. Be sure to do due diligence and ensure that you have proper eye protection before directly observing any radiation that may be the result of laser action.

Unless you are in a complete vacuum, you should be able to find, beg or borrow enough mirrors to make a Michaelson. If worse comes to worse, angle-irons (like shelf supports) and beeswax are your friend. Vignette the output of the device, preferably on the axis that you suspect is lasing. Then use this as an alignment tool to ensure all mirrors are perpendicular to the beam (best proven by placing the respective spot on the vignetting card and adjusting until the spot is vertically at the same height as the original beam.)

Clean plate glass works fine as a beam splitter, but you should use cards to block secondary reflections. When you have the beam you want to diagnose passing through the beam splitter, striking the two mirrors and returning to/through the beam splitter to join on the display screen, and the beams coincide sufficiently, with the beam paths exactly the same length, fringes should form. You don't need any kind of fancy detector: a dark room and a white card work well. You _do_ need the path lengths to be identical, so if your splitter is not a beam cube, you will want to use a second piece of glass in the first-surface reflection path between the plate glass and mirror to compensate for the change in path-length taken by that arm if you want the two mirrors to be the exact same distance from where the beam strikes the first surface of the plate. (The beam from the first surface, without the compensator, only travels through the plate after reflection from the mirror, but the beam that penetrates the plate travels through it twice, to and from the mirror, before joining the first-surface beam for one final pass through the plate-glass beamsplitter, and on to the screen.)

If you can do this on an air table with kinetic-mount mirrors and a cube beam splitter, it is far better, and if one mirror can be mounted on a rail which is aligned with the beam, you can "tune" through the visible-fringe range to get an idea of coherence length. Since you say little about the device, I can give little advice on what coherence length to expect, but gas lasers (HeNe, for instance) tend to have very little, while a single-mode laser diode can show fringes over a very great coherence length. Modes in the laser output can reduce apparent coherence length, and an etalon structure or similar very-thin line-width reflector in the laser can increase this.

It is a good idea, if you have no experience with a Michaelson, to enlist someone from the optics (preferably someone skilled in Holography) department to assist you in building it and teach you to operate it. It may be that your institution has all the equipment required to make holograms squirreled away in a closet, waiting for you!

The most important things to know are that vibration is your enemy, small movements can have very large affects, and patience is always an asset. For vibration, air tables and hard kinetic mounts with micrometer adjustments are sweet, but on a budget, a heavy, flat slab (slate is good, an optical palette is better) sitting on Sorbolite(tm) balls or feet and mirrors on heavy true-square blocks will do.

Compare the fringes you get at lower power levels (clearly below transition) to higher levels (clearly above transition).

Yes. In my opinion the coherence length is the only measure:

http://en.wikipedia.org/wiki/Coherence_length

Yes, coherence of the light emited by the soure is the best way. to be sure if you have a laser or not Before, you can look to the nature of the spectrum transmited by an adequate Fabry-Perot interferometer.