Grow Lights can be adequate for indoor Herb Plant Growth.

Light intensity is the most critical of the limiting factors in photosynthesis of Growing Herbs. Because artificial light is less intense than natural sunlight, 14 to 16 hours of artificial light is required per day for most herb plants to produce adequate growth. The lower the intensity of the grow lights, the longer the herb plants need to be exposed to the light. If the herb grower is using High Intensity Discharge or HID lighting, the herbs will need less time under the lights than if fluorescent fixtures are used.
Herb plants grown in inadequate light will become what is known as "leggy". The plants will develop undersized leaves, overly long stems, and will become an anemic, yellow color rather than that of lush green, which is due to the lack of chlorophyll formation in the herb leaves.
Grow lights come in a variety of styles , types and sizes. When a grow light is used, but is sill below the optimum intensity, the stems grow closer to a normal length as the light is increased and the leaves increase in size but will still be slightly yellow from lack of chlorophyll formation. Increase the light intensity to optimum by increasing the size of the grow light, or the number of grow lights, and while the size of the herb does not change to a great extent, the leaves will begin to turn darker green because of increased production of chlorophyll.

Fluorescent Gro Light There are three basic types of grow lights available to the home herb gardener:

Fluorescent Grow Lights- Produce the lowest light intensity but with little heat, are economical to operate, inexpensive to purchase and are readily available. A quality fluorescent grow light can be home-made or purchased complete. Fluorescent grow lights should be located within inches above herb seedlings to provide adequate light intensity.

High Intensity Discharge (HID) Grow Lights are illustrated in the following examples.

High Pressure Sodium Grow Lights produce very adequate light intensity but do not produce the complete light spectrum. They produce light in the red/orange part of the color spectrum which promotes growth in the fruiting, flowering and budding stages of growth. High pressure sodium grow lights should be used for secondary or supplemental light. Like all HID lighting, High Pressure Sodium grow lights are known to produce excessive heat, are more expensive to purchase and are heavier to handle than hoppy grade fluorescent grow lights.
Metal Halide Grow lights produce light in the blue/white part of the color spectrum. They are the most full-spectrum and are the best choice when no ambient light is available. They are best for producing overall plant growth, for seedlings or leafy plants such as lettuce or herbs. Like other HID grow lights, they produce excessive heat and must be suspended farther above herb plants. Metal Halide grow lights can also be more expensive and heavy to handle.

Good quality lighting for raising top-quality herb seedlings by the home-owner can be had using readily available fluorescent lights. Simply purchase two fluorescent fixtures or shop lights, available at any home improvement store.
For an added boost to complete the color spectrum needed by your herb seedlings, simply add three 15 watt incandescent bulbs to the array.